KR20220053029A - How to determine if a pattern is defective based on the image after development - Google Patents

Abstract

Described herein is a method for training a model that is configured to predict whether a feature associated with an imaged substrate will be defective after etching of the imaged substrate. The method comprises, via a metrology tool, (i) a post-developed image of the imaged substrate at a given location, the post-developed image comprising a plurality of features, and (ii) etching of the imaged substrate at a given location. After obtaining an image; and using the post-development image and the post-etch image to train a model configured to determine that a given one of the plurality of features in the post-development image is defective. In one embodiment, the determination of a defect is based on comparing a given feature in the post-developed image to a corresponding etched feature in the post-etch image.

Description

How to determine if a pattern is defective based on the image after development

This application is filed on EP application 19195527.7 filed on September 5, 2019 and EP application 19196323.0 filed on September 10, 2019 and EP application 19218296.2 filed on December 19, 2019 and filed on April 10, 2020 EP application 20169181.3 filed on 25 May 2020 and EP application 20176236.6 filed on May 25, 2020 and EP application 20189952.3 filed on August 6, 2020 and EP application 20192283.8 filed on August 21, 2020 It is incorporated herein by reference in its entirety.

The present disclosure relates to techniques for improving the determination of defective patterns to further improve the device manufacturing process. The techniques may be used in connection with a lithographic apparatus.

Fabricating semiconductor devices typically involves processing a substrate (eg, a semiconductor wafer) using multiple fabrication processes to form multiple layers and various features of the semiconductor device. These layers and features are typically fabricated and processed using, for example, deposition, lithography, etching, chemical-mechanical polishing, and ion implantation. Multiple devices may be fabricated at different locations on a substrate and then separated into individual devices. This device manufacturing process can be considered as a patterning process. The patterning process may include a patterning step to transfer the pattern from the patterning device to the substrate. Also, there may be one or more associated pattern processing steps, such as developing the resist by a developing apparatus, baking the substrate using a bake tool, etching the pattern on the substrate using the etching apparatus, measuring/inspecting the transferred circuit pattern, and the like. After exposure, the substrate may be subjected to other procedures such as post-exposure bake (PEB), development, hard bake, and measurement/inspection of the transferred circuit pattern. This series of procedures is used as a basis for constructing an individual layer of a device, such as an IC. Thereafter, the substrate may be subjected to various processes such as etching, ion-implantation (doping), metallization, oxidation, chemical-mechanical polishing, etc., all intended to finish individual layers of the device. If multiple layers are required in the device, the entire process or its variants are repeated for each layer. Eventually, a device will be present in each target portion on the substrate.

In one embodiment, a method is provided for training a model configured to predict whether a feature associated with an imaged substrate will be defective after etching of the imaged substrate. The method comprises, via a metrology tool, (i) a post-developed image of the imaged substrate at a given location, wherein the post-developed image includes a plurality of features, and (ii) after etching of the imaged substrate at the given location. obtaining an image, wherein the image after etching includes etched features corresponding to the plurality of features; and using the post-development image and the post-etch image to train a model configured to determine that a given one of the plurality of features in the post-development image is defective. In one embodiment, the determination of a defect is based on comparing a given feature in the post-developed image to a corresponding etched feature in the post-etch image.

Also provided is a method of determining etching conditions for an imaged substrate. The method includes obtaining a post-developed image of the imaged substrate, and initial etching conditions to be used to etch the imaged substrate; determining, via a model trained using the post-development image and initial etch conditions, a failure rate of a feature associated with the imaged substrate, the failure rate indicating that the feature is defective after etching of the imaged substrate; and modifying the initial etch conditions based on the failure rate to reduce the likelihood that the feature will be defective after etching.

Also provided is a method for determining an etch characteristic associated with an etch process. The method comprises a metrology tool that uses (i) a post-development image (ADI) of the imaged pattern at a given location on the substrate, wherein the imaged pattern includes a feature of interest and neighboring features adjacent to the feature of interest, and (ii) ) obtaining a post-etched image (AEI) of the imaged pattern at a given location on the substrate, the AEI comprising the etched feature corresponding to the feature of interest in the ADI; and determining, using the ADI and the AEI, a correlation between the etched feature and neighboring features associated with the feature of interest in the ADI, wherein the correlation characterizes an etch characteristic associated with the etch process.

Also provided is a method for determining etching conditions associated with an etching process. The method comprises: obtaining a correlation between an etched feature of interest in a post-etch image (AEI) and a neighboring feature associated with the etched feature-of-interest in a post-development image (ADI); and determining, based on the correlation, etching conditions associated with the etching process such that the correlation remains within the target range.

Further, in one embodiment, a method of developing an interpretation model configured to interpret predictions generated by the trained model is provided. The method includes obtaining a data set through execution of a trained model, the data set comprising a plurality of predictions associated with a plurality of features of a post-development image (ADI), the ADI comprising a feature of interest, and a plurality of Each prediction of the predictions is performed by the trained model; determining distances between each location of the plurality of features and the feature of interest; assigning weights to each prediction of the plurality of predictions based on the distances; and determining, based on the weighted predictions, model parameter values of the interpretation model such that a difference between the weighted predictions and an output of the interpretation model is reduced. In one embodiment, the model parameter values represent the contributions of each pixel of the ADI to the prediction related to the feature of interest.

Also, in one embodiment, a method of identifying the contributions of pixels of an image after development to a prediction generated by a trained model is provided. The method comprises the steps of: (i) a post-development image (ADI) comprising a feature of interest using a metrology tool, and (ii) obtaining an interpretive model configured to interpret a prediction associated with the feature of interest - the prediction is obtained using the trained model. created through- ; and applying the interpretive model to the ADI image to generate an interpretive map, wherein the interpretive map includes pixel values that quantify contributions of each pixel of the ADI image to the prediction of the feature of interest.

Also, in one embodiment, there is provided a computer program product comprising a non-transitory computer readable medium having instructions recorded thereon, wherein the instructions, when executed by a computer system, implement the aforementioned methods.

Also, in one embodiment, a method for developing a model for determining failure rates of features in a post-developed image is provided. The method comprises the steps of obtaining a post-developed image (ADI) of a substrate, the ADI comprising a plurality of features; generating a first portion of the model based on physical property values associated with the subset of features of the ADI; and generating a second portion of the model based on physical property values associated with the first portion of the model and all features of the plurality of features of the ADI, wherein the subset of the features of the ADI is associated with other features of the ADI. distinguished

Also, in one embodiment, a system for determining a fraction of features that will fail after etching is provided. The system includes a metrology tool that captures a post-developed image (ADI) of the substrate at a given location, the post-developed image comprising a plurality of features; and a processor configured to run the model to determine failure rates of a plurality of features of the ADI that will fail after etching. The model is based on (i) a first probability distribution function configured to estimate a distribution of physical property values for non-failing holes, and (ii) physical property values of all of the plurality of features of the ADI. a combination of a second probability distribution function configured to determine failure rates based on the second probability distribution function.

Further, in one embodiment, when executed by one or more processors, obtaining a post-developed image (ADI) of a substrate, the ADI comprising a plurality of features; generating a first portion of the model based on physical property values associated with the subset of features of the ADI; and instructions for causing tasks including generating a second portion of the model based on the first portion of the model and physical property values associated with all features of the plurality of features of the ADI. provided, a subset of the features of ADI distinguishes them from other features of ADI.

Further, in one embodiment, a method is provided for training a model configured to determine post-etch image (AEI) features based on post-development image (ADI) features, the method comprising: (i) ADI imaged on a substrate measurements of the features, and (ii) obtaining measurements of post-etched image (AEI) features on the etched substrate that correspond to the measured ADI features; allocating a first set of variables characterizing the measured ADI feature and a second set of variables characterizing the measured AEI feature; determining a correlation between the combination of the first set of variables of the measured ADI feature and the combination of the second set of variables of the measured AEI feature; and based on the correlation, training the model by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, wherein the model is used to determine an AEI feature for the input ADI feature. used- includes.

Further, in one embodiment, there is provided a beam generator configured to measure ADI features after imaging the substrate and AEI features after etching the substrate; and a metrology tool comprising a processor. The processor: obtains a correlation between the measured ADI features and the measured AEI features corresponding to the measured ADI features printed on the etched substrate - the correlation shows how the measured ADI features are converted to AEI features based on a combination of characterizing variables- ; and adjust settings of the metrology tool such that, based on the correlation, the correlation is improved, the settings are determined based on a derivative of the correlation for each setting, the derivative being the setting of the metrology It shows an improvement in the sugar correlation.

Further, in one embodiment, a method is provided for training a model configured to determine an post-etch image (AEI) based on the post-development image (ADI), the method comprising (i) the ADI of the imaged substrate, and ( ii) obtaining a post-etch image (AEI) after etching the imaged substrate; determining a correlation between the combination of the first set of variables of the ADI and the second set of variables of the AEI, the first and second sets of variables being gray scale values of the ADI and the AEI, respectively; and based on the correlation, training the model by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, wherein the model is used to determine an AEI feature for the input ADI feature. used- includes.

Also, in one embodiment, a method for determining an after-etch image (AEI) based on the post-development image (ADI) is provided. The method comprises the steps of obtaining an ADI of a substrate; and, via the trained model, determining the AEI by inputting the ADI into the trained model and outputting the ADI, wherein the trained model is a combination of a first set of variables of the measured ADI and a second set of variables of the measured AEI. is trained based on the correlations between combinations of

Further, in one embodiment, a non-transitory computer-readable medium comprising instructions that, when executed by one or more processors, cause operations to determine an post-etch image (AEI) feature based on the post-develop image (ADI) feature provided The tasks are: obtaining the ADI of the substrate; and, via the trained model, determining the AEI by inputting the ADI into the trained model and outputting the ADI, wherein the trained model is a combination of the first set of variables of the measured ADI and the first set of variables of the measured AEI. Trained based on correlations between two sets of combinations, the correlations being within a specified correlation threshold.

Further, in one embodiment, when executed by the one or more processors, the tasks include instructions that cause training a model that is configured to determine a post-etch image (AEI) feature based on the post-develop image (ADI) feature. A transitory computer readable medium is provided, the operations of which include: (i) measurements of imaged ADI features on the substrate, and (ii) post-etch image (AEI) features on a substrate that have undergone an etch process, corresponding to the measured ADI features. to obtain a measure of; assigning a first set of variables characterizing the measured ADI feature and a second set of variables characterizing the measured AEI feature; determining a correlation between the combination of the first set of variables of the measured ADI feature and the combination of the second set of variables of the measured AEI feature; and, based on the correlation, training the model by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, wherein the model is configured to determine an AEI feature for the input ADI feature. used- includes.

Further, in one embodiment, a non-transitory computer comprising instructions that, when executed by one or more processors, cause tasks to train a model configured to determine an post-etch image (AEI) based on the post-development image (ADI). A readable medium is provided, and the operations include: obtaining (i) an ADI of the imaged substrate, and (ii) a post-etch image (AEI) after etching the imaged substrate; determining a correlation between the combination of the first set of variables of the ADI and the second set of variables of the AEI, the first and second set of variables being gray scale values of the ADI and the AEI, respectively; and, based on the correlation, training the model by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, wherein the model is used to determine an AEI for the input ADI. includes

Embodiments will now be described by way of example only, with reference to the accompanying drawings:
1 is a block diagram of various subsystems of a lithographic system, according to an embodiment;
2 is an exemplary flow diagram for modeling or simulating at least a portion of a patterning process, according to one embodiment;
3 is a diagram illustrating post SEM damage of a substrate, according to one embodiment;
4A and 4B are flow diagrams of a method of training a model configured to predict whether a feature associated with an imaged substrate will be defective after etching of the imaged substrate, according to one embodiment;
5 shows an example of determination of a defective feature of a substrate based on a comparison between ADI and AEI;
FIG. 6 illustrates an example of a machine learning model with multiple layers used to train according to the method of FIG. 4A, according to one embodiment;
7A and 7B are examples of ADI and AEI showing a defective and non-defective contact hole, according to one embodiment;
7C is an exemplary critical dimension (CD) distribution associated with a defect in a feature, according to one embodiment;
8 is a flow diagram of a method for determining etch conditions for an imaged substrate based on a failure rate associated with an imaged pattern;
9 is a flow diagram of a method of determining an etch characteristic associated with an etch process, according to one embodiment;
10 illustrates an example ADI including a feature of interest and neighboring features, and an AEI image including an etched feature of interest, according to one embodiment;
11A illustrates an example correlation of ADI and AEI based on a physical characteristic (eg, CD) of a feature of interest, according to one embodiment;
11B illustrates an exemplary relationship (eg, based on CD) between neighboring features around a feature of interest in ADI and an etched feature of interest in AEI for a given dose-focus matrix, according to one embodiment;
12 is a flow diagram of a method of determining etch conditions based on a correlation (eg, determined using the method of FIG. 9 ), according to one embodiment;
13 is a diagram illustrating a decision data set (obtained using the trained model of FIG. 4A ) used to train an exemplary interpretation model, according to one embodiment;
14A is a diagram illustrating an example of a first feature of an ADI image and a first interpretation map for prediction associated with the first feature, according to an embodiment;
14B is a diagram illustrating an example of a second feature of an ADI image and a second interpretation map for prediction associated with the second feature, according to an embodiment;
14C is a diagram illustrating an example of a third feature of an ADI image and a third interpretation map for prediction associated with the third feature, according to an embodiment;
15A is a flow diagram of a method for determining an analytical model associated with a feature of interest, according to one embodiment;
15B is a flow diagram of an example approach to determining an interpretive model associated with a feature of interest, according to one embodiment;
16 is a flow diagram of a method of identifying contributions in the vicinity of a feature of interest to classifying the feature of interest as defective, according to one embodiment;
17 illustrates from ADI measurements (after etch) using a model composed of a first portion (eg, first CD distribution) and a second portion (eg, second CD distribution), according to one embodiment. a flow chart of a method for predicting the fraction of feature failures;
18A illustrates an exemplary model including a first probability distribution function and a second probability distribution function, according to an embodiment;
18B is a focus-exposure matrix (x-axis focus, y-axis dose) associated with an ADI deriving an AEI with fail and non-fail features used to print the ADI, according to one embodiment. A plot showing LCDU variation versus dose for best focus;
19 is a flow diagram of a method for determining a defect attribute of a feature in an image after development (ADI), according to one embodiment;
20 is a SEM of CD values of contact holes (eg, for 10 ⁵ contact holes) under an error prone condition (eg, less than a normal dose) in FEM, according to an embodiment. A drawing showing a plot of damage;
21 is a diagram illustrating an example of training a machine learning model according to FIG. 21 , according to an embodiment;
22 is a flow diagram of a method for determining a defect attribute of a feature in an image after development (ADI), according to one embodiment;
23A is a flow diagram of a method for training a model configured to determine a post-etch image (AEI) based on a post-development image (ADI), according to an embodiment;
23B is a flowchart of a method of determining a post-etch image (AEI) based on a post-development image (ADI) using the trained model of FIG. 22 or FIG. 23A , according to one embodiment;
23C is a flow diagram of a method of optimizing a metrology recipe (eg, SEM settings or contour extraction settings) based on a correlation between ADI and AEI measurements, according to one embodiment;
23D and 23E illustrate an example of implementing process variations through mask patterns used to obtain ADI and AEI measurements, according to one embodiment;
24A and 24B are diagrams illustrating example ADI features and an AEI feature having an example set of variables of ADI and AEI, respectively, according to one embodiment;
25A and 25B illustrate linear combinations of variables corresponding to translations of features in x and y directions, respectively, according to an embodiment;
25C illustrates a linear combination of variables corresponding to the critical dimension (CD) of AEI features affected by CDs in the ADI of a central hole and its neighbors, according to one embodiment;
25D illustrates a linear combination of variables corresponding to the triangularity of an AEI feature affected by the triangularity of the features in the ADI, according to one embodiment;
25E and 25F illustrate a linear combination of variables corresponding to the elongation of a centrally located ADI hole and the elongation of a feature determined by the size and displacement of neighboring holes, according to one embodiment;
26A is a diagram illustrating a relationship between an AEI CD and an ADI CD of a feature of interest, according to an embodiment;
26B is a diagram illustrating a relationship between CD of neighboring features of a feature of interest in ADI and an AEI CD, according to an embodiment;
27A illustrates a portion of the correlation of AEI placement described by the radius of influence of neighboring features in ADI, according to one embodiment;
27B illustrates a portion of the correlation of AEI CD described by the radius of influence of neighboring features in ADI, according to one embodiment;
28 schematically depicts one embodiment of a scanning electron microscope (SEM), according to one embodiment;
29 is a diagram schematically showing an embodiment of an electron beam inspection apparatus according to an embodiment;
30 is a block diagram of an exemplary computer system, in accordance with one embodiment;
Fig. 31 is a schematic diagram of a lithographic projection apparatus, according to an embodiment;
32 is a schematic diagram of an extreme ultraviolet (EUV) lithographic projection apparatus, according to an embodiment;
Fig. 33 is a more detailed view of the apparatus of Fig. 32, according to one embodiment; and
Fig. 34 is a more detailed view of the source collector module of the apparatus of Figs. 32 and 33, according to one embodiment.

The computing power of electronic devices has followed a pattern of increasing power and decreasing physical size over the years. This has been achieved by increasing the number of circuit components (transistors, capacitors, diodes, etc.) of each integrated circuit (IC) chip. For example, an IC chip in a smartphone could be as small as a human thumb and contain over two billion transistors, each one less than a thousandth the size of a human hair. IC manufacturing is a complex and time-consuming process with circuit components in different layers and involving hundreds of individual steps. Even errors in one step have the potential to lead to problems in the final IC. Even one “killer defect” can cause a device to fail. The goal of the manufacturing process is to improve the overall yield of the process. For example, for a 50-step process to reach 75% yield, each individual step must have a yield greater than 99.4%, and if the individual step yield is 95%, the overall process yield drops to 7%.

Corresponding difficulties, which conflict with high yields, are goals of maintaining fast production schedules (eg, known as throughput or number of wafers processed per hour). High process yield and high wafer throughput can be affected by the presence of defects, particularly when operator intervention is required to review the defects. Therefore, high throughput detection and identification of very small defects by inspection tools (such as optical or electron microscopy (SEM)) is essential to maintain high yield and low cost.

Because the microscope used to detect defects can only see a small portion of the wafer at a time, defect detection can be very time consuming, reducing overall throughput. For example, if every location on the wafer has to be inspected to look for defects, the wafer throughput can be greatly reduced because the time it takes to inspect every location of every IC on the wafer is very long. One approach to this problem is to use techniques that predict a defect location based on information obtained from a photolithography system, a system used in the manufacture of IC chips. In one example, defect inspection may be performed after imaging or post-processing, such as after etching. In one example, rather than inspecting every location on the wafer after etching to look for defects, a prediction of possible defects may be made based on the post-development process. In one example, a better model can be constructed to more accurately predict possible failures after etching based on process output prior to the etching process. For example, the model includes a first portion associated with holes that are not specifically failed, and a second portion associated with holes that are specifically failed. In one embodiment, the model is determined based on measurements of the same structure at least two times (eg, using a SEM metrology tool). The difference between the two SEM measurements can be used to develop a model or classify failures of features before the etching process. The advantages of such defect prediction are that the etch conditions can be adjusted or a significantly reduced number of locations can be inspected, allowing for a corresponding reduction in inspection time and an increase in wafer throughput. In another example, for example, a correlation between post-development and post-etch can be established so that the etch process can be controlled based on this correlation. The advantage of this correlation-based process control will be effectively used to improve the yield of the patterning process by reducing the defects after etching.

1 shows an exemplary lithographic projection apparatus 10A. The main components are a radiation source 12A (as mentioned earlier, the lithographic projection apparatus itself is need not have a radiation source); For example, illumination optics that may include optics 14A, 16Aa, and 16Ab to shape radiation from source 12A, defining partial coherence (denoted as sigma); patterning device 18A; and transmission optics 16Ac that project an image of the patterning device pattern onto the substrate plane 22A. An adjustable filter or aperture 20A in the pupil plane of the projection optics may limit the range of beam angles impinging on the substrate plane 22A, wherein the maximum possible angle is the numerical aperture of the projection optics. Define NA = n sin(Θ _max ), where n is the refractive index of the medium between the final element of the projection optics and the substrate, and Θ _max is the output from the projection optics still capable of impinging on the substrate plane 22A. is the maximum angle of the beam.

In a lithographic projection apparatus, a source provides illumination (ie, radiation) to a patterning device, and projection optics direct and shape the illumination through the patterning device onto a substrate. The projection optics may include at least some of the components 14A, 16Aa, 16Ab and 16Ac. The aerial image (AI) is the radiation intensity distribution at the substrate level. A layer of resist on the substrate is exposed and an aerial image is transferred into the layer of resist as a potential "resist image" (RI) therein. The resist image (RI) may be defined as the spatial distribution of solubility of resist in a layer of resist. A resist model can be used to compute a resist image from an aerial image, an example of which can be found in US Patent Application Publication No. US 2009-0157360, which is incorporated herein by reference in its entirety. The resist model relates only to the properties of the resist layer (eg, effects of chemical processes that occur during exposure, PEB, and development). Optical properties of the lithographic projection apparatus (eg, properties of the source, patterning device and projection optics) govern the aerial image. Since the patterning device used in a lithographic projection apparatus can change, it may be desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the source and projection optics.

In one embodiment, assist features (sub-resolution assist features and/or printable resolution assist features) may be placed in a design layout based on how the design layout is optimized in accordance with the methods of the present invention. For example, in one embodiment, the methods employ a machine learning based model to determine a patterning device pattern. A machine learning model may be a neural network, such as a convolutional neural network, that can be trained in some way (eg, as discussed in FIG. 3 ) to obtain accurate predictions at high speed, thus allowing the full- Enables chip simulation.

A neural network may be trained using a set of training data (ie, its parameters are determined). Training data may include or consist of a set of training samples. Each sample can be a pair that contains or consists of an input object (commonly a vector, called a feature vector) and a desired output value (also called a supervisory signal). A training algorithm adjusts the behavior of the neural network by analyzing the training data and adjusting parameters of the neural network (eg, weights of one or more layers) based on the training data. After training, the neural network can be used to map new samples.

In the context of determining a patterning device pattern, a feature vector may include one or more characteristics (eg, shape, arrangement, size, etc.) of a design layout constructed or formed by the patterning device, one or more characteristics of the patterning device (eg, dimensions). , one or more physical properties such as refractive index, material composition, etc.), and one or more properties (eg, wavelength) of the illumination used in the lithographic process. The monitoring signal may include one or more characteristics of the patterning device pattern (eg, a critical dimension (CD), contour, etc. of the patterning device pattern).

를 찾으며, 이때 X는 입력 공간이고 Y는 출력 공간이다. 피처 벡터는 일부 객체를 나타내는 수치적 피처(numerical feature)들의 n-차원 벡터이다. 이 벡터들과 연계된 벡터 공간은 흔히 피처 공간이라고 한다. 때로는, 최고 스코어를 제공하는 y 값을 반환하는 것으로서 g가 정의되도록 스코어링 함수(scoring function)

를 사용하여 g를 나타내는 것이 편리하다:

. F가 스코어링 함수들의 공간을 나타낸다.{(x ₁ ,y ₁ ),(x ₂ ,y ₂ ),… where x _i is the feature vector of the i-th example and y _i is its watch signal. Given a set of N training samples of the form ,(x _N ,y _N )}, the training algorithm

, where X is the input space and Y is the output space. A feature vector is an n-dimensional vector of numerical features representing some object. The vector space associated with these vectors is often referred to as the feature space. Sometimes, a scoring function such that g is defined as returning the value of y giving the highest score

It is convenient to represent g using:

. F denotes the space of scoring functions.

Neural networks can be stochastic, in which case g takes the form g(x) = P(y|x) of a conditional probabilistic model, or f takes the form of a simultaneous probabilistic model f(x,y) = P(x, y) is taken.

There are two basic approaches to choosing f or g: empirical risk minimization and structural risk minimization. Empirical risk minimization finds the best neural network for training data. Structural risk minimization includes a penalty function that controls the bias/variance tradeoff. For example, in one embodiment, the penalty function may be based on a cost function, which may be a squared error, number of defects, edge placement error (EPE), or the like. The functions (or weights within the function) can be modified such that variance is reduced or minimized.

가 정의된다. 트레이닝 샘플 (x_i,y_i)에 대해, 값

을 예측하는 손실은 L(y_i,

)이다.In both cases, it is assumed that the training set contains or consists of one or more samples of independent and equally distributed pairs (x _i ,y _i ). In one embodiment, to measure how well the function fits the training data, the loss function

is defined For the training sample (x _i ,y _i ), the value

The loss to predict is L(y _i ,

)am.

로서 추산될 수 있다.The hazard R(g) of a function g is defined as the expected loss of g. from the training data.

can be estimated as

In one embodiment, the machine learning models of the patterning process are, for example, contours for a mask pattern, patterns, CDs, and/or contours, CDs, edge placements (eg, edges in resist and/or etched images on the wafer). placement error) and the like). The purpose of training is to enable accurate prediction of, for example, contours of printed patterns on a wafer, aerial image intensity gradients, and/or CDs, etc. An intended design (eg, a wafer target layout to be printed on a wafer) is generally defined as a pre-OPC design layout, which may be provided in a standardized digital file format such as GDSII or OASIS or other file format.

An exemplary flow diagram for modeling and/or simulating portions of a patterning process is illustrated in FIG. 2 . As will be appreciated, models may represent different patterning processes and need not include all of the models described below. Source model 1200 represents optical properties (including radiation intensity distribution, bandwidth and/or phase distribution) of illumination of the patterning device. The source model 1200 may include numerical aperture settings, illumination sigma (σ) settings, and any particular illumination shape (eg, off-axis such as annular, quadrupole, dipole, etc.). axis) radiation shape], including, but not limited to, optical properties of illumination, where σ (or sigma) is the outer radius magnitude of the illuminator.

A projection optics model 1210 represents the optical properties of the projection optics, including changes to the radiation intensity distribution and/or phase distribution caused by the projection optics. The projection optics model 1210 may represent optical properties of the projection optics, including aberrations, distortions, one or more index of refraction, one or more physical dimensions, one or more physical dimensions, and the like.

The patterning device/design layout model module 1220 captures how design features are laid out within the pattern of the patterning device and provides detailed physical details of the patterning device, for example as described in US Pat. No. 7,587,704, which is incorporated by reference in its entirety. It may contain representations of properties. In one embodiment, the patterning device/design layout model module 1220 is a design layout that is formed by, or represents a configuration of features on, the patterning device (eg, a feature of an integrated circuit, memory, electronic device, etc.). the optical properties (including changes to the radiation intensity distribution and/or phase distribution caused by a given design layout) of the device design layout corresponding to Since the patterning device used in the lithographic projection apparatus can change, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the illumination and projection optics. Often the purpose of simulation is to accurately predict, for example, edge placement and CD that can be compared with subsequent device designs. The device design is typically defined as a pre-OPC patterning device layout, and will be provided in a standardized digital file format such as GDSII or OASIS.

An aerial image 1230 can be simulated from a source model 1200 , a projection optics model 1210 , and a patterning device/design layout model 1220 . The aerial image (AI) is the radiation intensity distribution at the substrate level. Optical properties of a lithographic projection apparatus (eg, properties of illumination, patterning device and projection optics) govern the aerial image.

A layer of resist on the substrate is exposed with an aerial image, which is transferred to the layer of resist as a potential “resist image” (RI) therein. The resist image (RI) can be defined as the spatial distribution of the solubility of resist in a layer of resist. A resist image 1250 may be simulated from an aerial image 1230 using the resist model 1240 . A resist model can be used to compute a resist image from an aerial image, an example of which can be found in US Patent Application Publication No. US 2009-0157360, which is incorporated herein by reference in its entirety. A resist model typically accounts for the effects of chemical processes that occur during resist exposure, post exposure bake (PEB) and development, predicting, for example, the contours of resist features formed on a substrate, and thus it typically predicts the It relates only to properties (eg, effects of chemical processes that occur during exposure, post-exposure bake and development). In one embodiment, optical properties of the resist layer, such as refractive index, film thickness, propagation and polarization effects, may be captured as part of the projection optics model 1210 .

Thus, in general, the link between the optical and resist model is the simulated aerial image intensity in the resist layer, which results from the projection of radiation onto the substrate, refraction at the resist interface, and multiple reflections in the resist film stack. The radiation intensity distribution (aerial image intensity) is transformed into a potential “resist image” by absorption of the incident energy, which is further modified by the diffusion process and various loading effects. Efficient simulation methods fast enough for full-chip applications approximate a realistic three-dimensional intensity distribution in a resist stack by means of a two-dimensional aerial (and resist) image.

In one embodiment, the resist image may be used as input to the post-pattern transfer process model module 1260 . The pattern post-transfer process model 1260 defines the performance of one or more resist post-development processes (eg, etching, developing, etc.).

Simulation of the patterning process may predict, for example, contours, CDs, edge placement (eg, edge placement errors) within resist and/or etched images. Accordingly, the purpose of the simulation is to accurately predict, for example, the edge placement of the printed pattern, and/or the aerial image intensity gradient, and/or the CD, etc. These values can be compared to designs intended for, for example, correcting the patterning process, identifying where defects are expected to occur, and the like. The intended design is generally defined as a pre-OPC design layout, which may be provided in a standardized digital file format such as GDSII or OASIS or another file format.

Thus, the model formulation accounts for most, if not all, of the known physical and chemical properties of the overall process, each of the model parameters preferably corresponding to a distinct physical or chemical effect. Thus, model formulation sets an upper bound on how well a model can be used to simulate the entire manufacturing process.

In patterning processes such as photolithography, electron beam lithography, directed self-assembly, etc., an energy-sensitive material (eg, photoresist) deposited on a substrate is typically (eg, via exposure) ) through the pattern transfer step. After the pattern transfer step, various post steps are applied, such as resist baking and subtractive processes, such as resist development, etching, and the like. These post-exposure steps or processes exert various effects on the substrate such that the patterned layer or etch has a structure having dimensions different from the target dimensions.

A computational analysis of the patterning processes employs a predictive model that, when properly calibrated, can produce an accurate prediction of dimensions output from the patterning processes. Typically, a model of post-exposure processes is calibrated based on empirical measurements. The calibration process includes running the test wafer with different process parameters, measuring the resulting critical dimensions after post-exposure processes, and calibrating the model with the measured results. Indeed, well-calibrated models that perform fast and accurate dimensional prediction serve to improve device performance or yield, improve process window, or increase design choices. In one example, the use of a deep convolutional neural network (CNN) to model post-exposure processes is similar to or more than that produced with conventional techniques that often involve modeling using physical term expressions or closed form equations. It yields excellent model accuracy. Compared with the conventional modeling techniques, the deep learning convolutional neural network alleviates the knowledge requirement of the process for model development, and increases the dependence of the engineer's personal experience on model tuning. Briefly, a deep CNN model for post-exposure processes consists of an input and output layer, and multiple hidden layers, such as convolutional layers, normalization layers, and pooling layers. The parameters of the hidden layers are optimized to give a minimum value of the loss function. In an embodiment, CNN models may be trained to model the behavior of any process, or combination of processes, associated with the patterning process.

Random stochastic failures of structures (also called features) on a substrate are considered undesirable in lithographic printing (eg, EUV lithography). Failures of structures may be identified after lithographic imaging of structures on the substrate or after etching of the imaged substrate of the substrate. The advantages of identifying and classifying post-etch failures are that it is easier to interpret images of the substrate as it provides a direct correlation to the performance (eg, yield) of the patterning process. However, identifying failures after a lithographic step is a more direct measure of lithographic performance.

A number of algorithms exist to classify failures of structures (eg, contact holes) after development in SEM pictures. For example, the Fractilia software measures what's on the substrate, not what's on the SEM image. In another example, Stochalis software analyzes CD-SEM images based on the brightness of pixels. CD-SEM refers to a critical dimension scanning electron microscope, which is a dedicated system for measuring the dimensions of micropatterns formed on a semiconductor substrate. However, the criterion for defect classification does not depend on the etching conditions used during etching, but rather is based on common sense-based interpretation of SEM images. For example, the error criterion may be the post-development SEM contrast or critical dimension (CD) of the imaged substrate.

In addition, CD can be measured using an image after development with CD-SEM (ADI) or an image after etching (AEI), and transcription of the CD can be measured. However, ADI SEM measurements damage the resist, which affects the CD after etching. Therefore, CD based on ADI and AEI is measured at different locations, and only mean CD, local CD uniformity (LCDU, standard deviation of CD) or CD distribution can be compared.

Disadvantages of current failure (or defect) classification after lithography is that defect classification does not depend on process conditions or etch conditions, whereas the final defect rate (or failure rate) associated with the substrate depends on these conditions. Defect classification is calibrated based on the capture rate of programmed defects, or by comparing defect rates before and after etching. However, programmed defects were shown to be statistically different from random defects, publication P. De Bisschop, E. Hendrickx, "Stochastic effects in EUV lithography", Proc. SPIE 10583, Extreme Ultraviolet (EUV) Lithography IX, 105831K (March 19, 2018); see doi: 10.1117/12.2300541. Therefore, a good capture rate of programmed defects does not guarantee accurate results. In addition, it has been reported that the defect rates before and after etching are generally inconsistent. For example, reference P. De Bisschop & E. Hendrickx, "Stochastic effects in EUV lithography", SPIE 2018 shows in FIG. 9 that ADI and AEI failure rates can differ by 0.1 to 1000 fold.

As previously mentioned, and also referring now to FIG. 3 , post-lithography SEM metrology damages resist layer 301/303 disposed on oxide layer 305 , for example. For example, the resist layer 301 before the SEM measurement shrinks into the layer 303 after the SEM measurement. In another case, illumination with an SEM on resist 301 may redeposit carbon. Therefore, measuring the SEM twice at the same location may affect the CD as measured by SEM after the lithography step and after the etching step.

In one embodiment, contact hole defects missing after etching are caused by a layer of resist remaining inside the contact hole. However, in the present application, it was realized that while the resist shrinks during SEM, the SEM electrons cannot completely remove the remaining resist layer in the contact hole (see FIG. 3 ). It was also realized that carbon redeposition did not fill the entire hole to be closed. Accordingly, these findings are contrary to conventional beliefs. Thus, SEM damage can affect CD but not the failure rate of structures associated with the pattern. As such, the method of this embodiment enables the determination of failure rates more accurately, wherein the determination is based on a one-to-one feature comparison between ADI and AEI rather than using an average CD-based determination of failure rate.

4A and 4B are flow diagrams of a method for training a model configured to predict whether a feature associated with an imaged substrate will be defective after etching of the imaged substrate.

Procedure P401 is performed through a metrology tool to (i) a post-developed image 401 of the imaged substrate at a given location, the post-developed image comprising a plurality of features, and (ii) the imaged substrate at the given location. It involves obtaining a post-etch image 402 of , the post-etch image comprising etched features corresponding to a plurality of features.

In one embodiment, the model is an empirical model or a machine learning model. In one embodiment, the empirical model is a function of the physical properties of the feature associated with the imaged substrate (eg, after development). An example of training based on an empirical model is illustrated in FIGS. 7A-7C , where a physical property such as CD of a feature after the development process is used as a model variable. In one embodiment, the model is trained to identify a CD threshold (eg, 16 nm) that can correctly classify 90% or more of potentially defective features based on ADI. In other words, features classified as defective in ADI will be more likely to fail post-etch than features that were not classified as defective. In another example, the gray scale values of the ADI are used to define the model. For example, train the model to identify a gray scale value threshold that can correctly classify more than 90% of potentially defective features based on ADI. In one embodiment, Figure 6 illustrates training a CNN model. Exemplary training based on CD, gray scale values and CNN model is discussed later in the present invention.

In one embodiment, obtaining the image after development includes: imaging the mask pattern on the substrate through a patterning device; obtaining a developed substrate (eg, resist development) of the imaged substrate; aligning a metrology tool (eg, SEM) to the developed substrate at a given location; and capturing an image of the developed substrate. In one embodiment, the post-developed image is a pixelated image, wherein an intensity value of a pixel indicates the presence or absence of a feature on the substrate. For example, the intensity value of a pixel is a metric for the number of secondary electrons on the substrate. The secondary electrons are: (i) the secondary electron yield of the material (eg, a higher yield for the resist than the underlying layer of the substrate), and (ii) the intensity at the hole to provide a darker and higher yield at the edge of the hole than the center. can depend on the geometry that shadows For example, a white band around the hole can be seen.

In one embodiment, the metrology tool is an optical tool or an electron beam microscope. In one embodiment, the metrology tool is SEM (eg, FIG. 28 ), and the ADI and AEI images are SEM images. In one embodiment, the alignment of the SEM with the imaged substrate or the substrate after etching is based on addressing features outside the FOV of the SEM. For example, the SEM may be configured to have a built-in option for aligning to addressing features, where addressing features are associated with locations at which scanning should be performed. In another example, since the unit cell of the pattern (eg, for a logic device) is greater than the uncertainty of the SEM positioning system, the alignment may be based on features in the image such that the pattern itself is used as a position mark. . In one embodiment, for alignment purposes, including an additional position mark inside the FOV of the SEM is undesirable as it affects the lithographic image, making the features around it non-representative. Also, it is undesirable to adjust the mask pattern within the functional area of the substrate for metrology.

In one embodiment, obtaining the post-etch image comprises: etching the imaged substrate through an etching process with specified etching conditions; aligning the metrology tool to the etched substrate at a given location; and capturing an image after etching of the etched substrate. In one embodiment, the etch conditions include etchant composition, plasma gas parameters, etch rate, electromagnetic field, plasma potential, inductive or capacitive etch type, temperature of the substrate, ion energy distribution, ion angle distribution, sputtering and redeposition rate. , or a combination thereof.

In one embodiment, the alignment is never perfect, so the correlation between the ADI and AEI images is used to confirm that the alignment is correct. However, one problem is that the addressing features used for alignment are damaged or shifted due to the etching process affecting the addressing. Thus, according to this embodiment, the AEI image is digitally shifted over a discrete number of pitches in all symmetric directions with respect to the ADI image, and it is checked for which one the correlation between ADI and AEI CD is maximum. do. In one embodiment, there is an apparent maximum due to small shifts (eg, shifts by 1 or 2 pitches).

Procedure P403 involves training, using the post-developed image 401 and the post-etched image 402 , a model configured to determine that a given one of a plurality of features in the post-developed image is defective; The determination of α is based on comparing a given feature in the post-developed image with a corresponding etched feature in the post-etch image. In one embodiment, defective includes: a binary determination of whether a defect is present or not; or the probability that a given feature is defective.

In one embodiment, the training includes: aligning the post-develop image and the post-etch image based on the plurality of features; comparing each of the features of the plurality of features in the post-development image to a corresponding feature of the etched features in the post-etch image (eg, as shown in FIG. 5 ); determining, based on the comparison, whether a given etched feature in the post-etch image satisfies a defect condition; in response to not meeting the defect condition, classifying the identified feature as defective; and adjusting the model parameter values of the model based on the presence of the identified features. In one embodiment, adjusting the model parameter value comprises adjusting values of the plurality of model parameters. In one embodiment, a defect condition refers to a desired limit associated with a physical property of a structure, and a structure is considered defective if the limit is not met.

Referring to FIG. 5 , shown is an example of a determination of a defective feature of a substrate based on a comparison between ADI and AEI. In one embodiment, the ADI and AEI are obtained via a metrology tool (eg, the SEM of FIG. 28 or the inspection tool of FIG. 29). ADI is a post-development image of a substrate obtained after imaging the substrate (eg, a pattern transfer step) through a patterning apparatus (eg, a lithographic apparatus) and further performing a post-imaging development process. An exemplary ADI includes an array of contact holes, for example holes at locations L1, L2 and L3. The AEI is the post-etch image containing the array of holes corresponding to the contact holes of the ADI. In this example, a comparison of holes in AEI and ADI indicates missing holes in AEI. For example, ADI includes holes (existing without any defects) at locations L1, L2 and L3. However, after the etching process, the AEI image shows missing holes at positions L1', L2' and L3' corresponding to positions L1 to L3, respectively, indicating failure of the contact holes. In other words, the holes L1 to L3 in the ADI are likely to be defective after etching the substrate. Accordingly, the holes of the ADI at positions L1, L2, L3 are classified as defective.

Accordingly, the present invention compares the holes at one location in the substrate after development with the holes at the same location in the substrate after etching. In contrast, the existing technique compares the holes at different locations on the substrate after the developing step and after the etching step, avoiding a one-to-one comparison of features. Thereby, the present invention produces more accurate data relating to defects associated with structures of the substrate. Thus, a model trained based on such data can more accurately predict defective features, and appropriate adjustments to the patterning process (eg, etching process) can be made to improve the yield of the patterning process. In one embodiment, the adjustments may involve changing the focus or dose of the lithographic apparatus, or adjusting the chemical composition of the resist.

In one embodiment, the model may be an empirical model trained based on a fault condition. In one embodiment, the defect condition includes: gray scale values of an enclosed contour in the image after etching; or at least one of the physical properties of a given etched feature in the image after etching. In one embodiment, the physical properties include: a critical dimension of a given etched feature; or displacement of the given etched feature relative to the given feature of the image after development.

7A-7C show examples of CD-based defect classification. In one embodiment, the empirical model is based on CD-thresholding, where the CD threshold determines whether a feature may be defective. 7C shows the CD distribution of contact holes in the ADI and corresponding contact holes in the AEI that may be defective (eg, prone to failure or not). The distribution represents CD values of contact holes in ADI, CD values of non-failing contact holes after etching, and CD values of failed holes after etching. In Fig. 7a, the comparison of ADI1 and AEI1 indicates that hole CH1 is classified as failed, which is correct as CH1' disappears in AEI1. Also, in Fig. 7b, the comparison of ADI3 and AEI3 shows that hole CH3 is classified as not failing, which is also correct as CH3' does not disappear in AEI3.

In one embodiment, the failed holes (eg, disappeared in AEI) are generally smaller in size compared to the desired size. For classification, a CD threshold may be used in ADI, where violating contact holes are classified as potential defects in AEI. For example, since the CD threshold Th1 is approximately 16 nm, holes smaller than Th1 (eg, 16 nm) may be classified as defective. In one embodiment, 91.3% of holes were classified correctly.

In one embodiment, the model is a machine learning model, such as a convolutional neural network. Then, the model parameters are weights, biases, or a combination thereof associated with one or more layers of a machine learning model (eg, CNN).

6 shows an example CNN trained using ADI and AEI data (eg, ADI and AEI images of FIG. 5 ) as input. Based on the input, the defect classification of features may be based on a comparison between ADI and AEI as discussed herein. Then, the defect classification may be the output of the CNN. In one embodiment, ADI and AEI may be feature vectors provided to CNN.

In one embodiment, the trained model (eg, CNN (eg, FIG. 5 ), CD-based threshold model (eg, discussed in FIGS. 7A-7C )) is a given pattern of the image after development. and predict a failure rate associated with , wherein the failure rate is indicative of occurrence of defects when the imaged substrate is etched using the specified etching conditions. For example, based on the defect classification of the features and the total number of features, a failure rate associated with the post-etch feature may be determined. For example, the failure rate of a feature (eg, contact holes) is a ratio of the total number of defective instances of the feature and the total number of features.

In one embodiment, further construction of the training model involves the following procedures. For example, procedure P405 involves classifying the plurality of patterns associated with the pattern of interest as defective or free of defects; Procedure P407 involves determining a total number of defective patterns associated with the pattern of interest; Procedure P409 involves calculating the failure rate of the pattern of interest as a ratio of the total number of defective patterns and the total number of patterns in the plurality of patterns.

In one embodiment, method 400 may further include adjusting the etching conditions. An example implementation involves the execution procedures of FIG. 4B . Procedure P411 involves imaging, via a patterning device, the desired pattern 411 on the substrate. The imaged substrate may be further developed (eg, developed in resist) and post-processed (eg, etched). Procedure P413 involves acquiring an image after development of the imaged pattern. Also, initial etching conditions 413 may be obtained. Procedure P415 involves running the training model 403 using the post-development image to classify whether the desired pattern will be defective after etching. Procedure P417 involves adjusting (or determining) etching conditions 417 based on the classified defective pattern so that the imaged pattern is defect-free after etching.

8 is a flow diagram of a method of determining an etch condition or plurality of etch conditions for an imaged substrate based on a failure rate associated with an imaged pattern. Procedure P901 involves obtaining a post-developed image 901 of the imaged substrate, and initial etching conditions 902 to be used to etch the imaged substrate. In one embodiment, the etch conditions include etchant composition, plasma gas parameters, etch rate, electromagnetic field, plasma potential, inductive or capacitive etch type, temperature of the substrate, ion energy distribution, ion angle distribution, sputtering and redeposition rate. , or at least one of a combination thereof.

Procedure P903 determines, via a model trained (eg, trained model 403 ) using post-development image 901 and initial etch conditions 902 , to determine the failure rate of a feature associated with the imaged substrate. step, and the failure rate indicates that the feature is defective after etching of the imaged substrate. Thus, the trained model provides a failure prediction before the actual failure that may occur after etching.

Procedure P905 involves modifying the initial etch conditions 902 based on the failure rate to reduce the likelihood that the feature will be defective after etching. The modified etch conditions 905 may be further used to etch the imaged substrate to improve the yield of the patterning process (eg, reduced failure of features/structures on the substrate).

In one embodiment, modifying the etching conditions is an iterative process. Iteration is to obtain a relationship between a given etch condition and a given failure rate associated with a given feature; determining a post-etch image associated with the imaged substrate through execution of the etch model using the post-development image and etch conditions; determining, based on the post-etch image, whether a given feature satisfies a defect condition; and in response to not satisfying the defect condition, identifying further etch conditions associated with a lower failure rate relative to the given failure rate based on the relationship.

In one embodiment, the defect condition of the feature is: missing feature; displacement range associated with the feature; or a tolerance range associated with the critical dimension of the feature.

In a lithographic process, structures printed in resist on a substrate must be etched into an underlying layer to make a functional chip. The etching process/step may be used to smooth out local variations in the CD of features such that the local CD uniformity (LCDU) is reduced after etching. One of the primary mechanisms by which the etch step reduces LCDU is due to loading effects.

The loading effect is the relationship between how much an area on the substrate is filled with structures and the etch rate. In one embodiment, the loading effect is that in a dense region of the substrate (eg, a region having a high percentage of structures within a defined region compared to other regions on the substrate), the etch rate is less dense or relatively more empty. is lower than the areas where there is (eg, less area is covered with structures). Thus, if the hole or its neighbors have large ADI holes (eg, due to local variations), eg 1 nm larger than average holes, the etch will be slow. A slower etch can cause the AEI holes to be less than 1 nm larger than the average hole AEI. The physical cause of loading effects is a lack of etchant, inhibition of etching by etching byproducts, or both.

Three exemplary parameters related to etch loading are: (i) the range of loading effects - that is, the distance at which features affect each other (eg in nm), eg a value of 40 to 100 nm, in one implementation In the example, the range is expressed by the radius "R" in the following etch rate equation - ; (ii) change in etch deflection per change in average CD of neighbors in the relevant region - The value of parameter (ii) depends on the average pattern density, the unit may be nm/nm, exemplary values according to the present invention are 0 to 0.75 nm/nm; and (iii) a correlation coefficient between the size of the neighboring holes in the ADI and the size of the etched hole in the AEI, exemplary values of the correlation coefficient may be 0 to 0.2.

In one embodiment, the etch loading is dependent on the pattern density and has various length scales from wafer-scale to sub-resolution or fractions of the wafer. In one embodiment, the pattern density is the fraction of the area occupied by structures in a given area around a structure or feature of interest. In one embodiment, the loading effect may be on a length scale of 40-100 nm (eg, 1-2 pitches). However, the present invention is not limited by this scope. In one embodiment, loading effects ranging from sub-resolution (eg, 10 nm) to OPC-range regions (eg, regions having a radius of approximately 300 nm to 1 μm) are optimized during etch optimization for a particular structure. Thus, it is possible to ensure a desired yield on the resist by tuning of the target-CD and a desired yield during pattern transfer. The traditional etch optimization process is a long and tedious procedure. For example, manual optimization involves tuning the knobs of the etching apparatus to achieve the desired yield of the die.

In one embodiment, the loading effect is a kind of saturation. The loading effect (also referred to as loading behavior) may be different for each of the etch cycles. Certain etching techniques cycle between very small differences in loading effects, for example to reduce line edge roughness (LER) or line width roughness (LWR), or to improve local CD uniformity. In addition to balancing sputter, etch and redeposition rates, the loading effect has both spatial and angular components, producing preferential etches for features of various CD/pitch/duty cycles, for example in X or Y orientation. do. The angular component depends on the electromagnetic (EM) field, the gas flow design, or both. Once the etch cycle consumes material preferential in spatial frequency and orientation based on loading effects, the cycle will effectively saturate. This saturation can be detected by a spectrometer.

In one embodiment, data from an on-board optical spectrometer that can be used to determine the composition of materials in the plasma as a means for per cycle endpoint detection is used. This could be used to trigger the next cycle. In one embodiment, data from the spectrometer may be supplemented/replaced by data from an on-board laser interferometer that may determine the thickness of the material being etched at a particular location/angle on the substrate.

FIELD OF THE INVENTION The present invention relates to the quantification of etch properties such as short-range etch loading effects or micro-loading. Currently, etch loading is characterized prior to the etch optimization process by analyzing test structures and modeling in (OPC) software suites (eg, Tachyon, Synopsis, Coventor, etc.). To this end, features with variable pitch and CD are printed and etched, and the etch rate is fitted empirically to describe an open area within a defined area (eg, a circle of a certain radius) around the point of interest. For example, the empirical model for etch rate (ER) can be defined as:

In the preceding ER model, ER is the etch rate associated with the etch process, ER _nom is the nominal etch rate associated with the etch process, τ is the sensitivity to the pattern density, and OA(R) is a circle with radius R is an open area of The parameters R, τ and ER _nom are the fit parameters of the model. In advanced models, multiple radii may additionally be used, different convolution-filters applied may be applied, or a directional dependency may be integrated.

In one embodiment, the etch rate (ER) may be used (eg, using Coventer software) to simulate an etch deflection (eg, the difference between an ADI CD and an AEI CD). In addition, the relationship between etch bias, sensitivity to pattern density, and open areas can be modeled. ADI CD and AEI CD refer to the CD of features in ADI and AEI.

In one embodiment, the pattern transfer process may include a combination of etching and (re)deposition. An exemplary etching process involves physical sputtering and chemical etching of the material. Also, the sputtered material, the added gas constituents, or a combination thereof ensures (re)deposition. In this process, a set sheath voltage affects the ion-angle of the sputtering process and the μ-wave power density of the plasma/sputtering-rate. The sputter-rate of the material depends on the angle of incidence, the ion-velocity, and the material composition allowing for the tweaking of the profiles. For example, fluorine gas pressure determines redeposition during the etching process.

In the etch optimization process, the desired etch loading and redeposition are not tuned based on expected dependencies initially simulated, but mainly by physical intuition and experimental testing of many different etch parameters affecting some of the preceding effects. is tuned

However, there are some drawbacks to existing approaches for estimating the micro-loading effect. For example, the measurements are on test structures rather than on product structures that are essential to the functioning of the chip. According to the present invention, the micro-loading effects are highly dependent on the pattern density, and thus the characterization of this loading effect on the structure of interest is more appropriate. Another exemplary disadvantage is that the short-range loading effects depend on the condition of the focus-exposure matrix (FEM). This dependence cannot yet be quantified by existing methods.

9 is a flow diagram of a method for determining an etch characteristic associated with an etch process. In one embodiment, the etch characteristics are associated with the uniformity of etching the imaged substrate. For example, the etch characteristics indicate that the substrate etches faster at the edges and slower at the center. In another example, the etch characteristics indicate that the micro-loading effect refers to an etch rate that depends on the local pattern density. In one embodiment, the etch rate refers to the etched depth per unit time, eg, 100 to 1000 angstroms per minute. The etch rate can further be used to determine the etch bias (eg, the difference between ADI CD and AEI CD) (via simulation using Coventer software). For example, etch loading refers to the difference between the etch rate associated with a given feature located in a high-density region and the same feature in a low-density (isolated) region on the same chip. This is an exemplary reason associated with the local depletion of reactants. To compensate for etch characteristics such as loading effects, pressure, diffusion rate, etchant flux, etc. can be adjusted. The method of FIG. 9 is discussed in more detail below.

In one example, measurements (eg, AEI CD) may be performed during the etching process (if there is an iterative etching procedure), or after Sequential Infiltration Synthesis (SIS), a step that may be applied prior to etching.

Note that the image after development and the image after etching are used as examples of different processes of the patterning process. However, the present invention is not limited to after development and after etching. Those skilled in the art may apply the methods of the present specification to other processes related to the patterning process. For example, a correlation may be established between a first layer (eg, a resist layer) and a subsequent layer in which a different process (eg, etching) may be performed after treatment of the first layer. The principles described herein work with any etching and combination of layers (eg, first resist, second resist layer, etc.) of the substrate being patterned.

Procedure P1001 involves (i) post-development image 1001 (ADI) of the imaged pattern at a given location on the substrate via a metrology tool, the imaged pattern including the feature of interest and neighboring features adjacent to the feature of interest; and (ii) obtaining a post-etched image 1002 (AEI) of the imaged pattern at a given location on the substrate, the AEI comprising the etched feature corresponding to the feature of interest of the ADI. For example, the imaged pattern may consist of an array of contact holes in the center of the substrate. Within the array of contact holes, the feature of interest may be a contact hole at a specific coordinate (eg, GDS coordinate).

In one embodiment, the feature of interest is a contact hole; line; line end; or at least one of critical features or portions thereof. In one embodiment, the neighboring features include a plurality of contact holes in a defined orientation with respect to the feature of interest (see, eg, FIG. 10 ); or at least one of a plurality of lines having a defined pitch. In one example, the neighbor may be a line segment of the same line that is away from the line segment of interest.

In some embodiments, multiple instances (or multiple different features) and their neighbors of a feature of interest in one image may be used to establish a correlation between a feature of interest and a corresponding etch feature of interest. In some embodiments, one feature of interest in multiple images (obtained at different locations, such as, for example, at different locations such as center, edge, or other radial distance on the substrate) may be used to establish the correlation coefficient. In another example, from the point of view of the lithographic apparatus, multiple images may be obtained that are slightly distant from each other. For example, multiple images are at least in the same die. CD may be slightly different at different wafer locations, which will dictate the correlation coefficient. An exemplary distance between the images may be 1 um.

FIG. 10 shows an exemplary ADI image including a feature of interest 1040 and neighboring features 1050a - 1050f and an AEI image including an etched feature of interest 1060 corresponding to the feature of interest 1040 , only etched. . In other words, 1040 and 1060 are both in the same contact holes at different points in the patterning process (eg, after imaging and after etching). In one embodiment, neighboring features 1050a - 1050f are adjacent to the feature of interest 1040 . Neighboring features 1050a - 1050f are located at a particular distance from the feature of interest 1040 . In one embodiment, the specific distance also affects the etch characteristics. For example, the closer the neighboring features to the feature of interest, the higher the etch loading effect.

In one embodiment, the fraction of the area occupied by neighboring features 1050a - 1050f around the feature of interest defines the pattern density. The greater the surface area covered by neighboring features, the greater the pattern density. As previously mentioned, the pattern density affects the etch characteristics of the etch process (eg, etch loading effect).

Procedure P1003 involves determining, using ADI and AEI, a correlation 1005 between an etched feature associated with a feature of interest in ADI and neighboring features, wherein the correlation determines an etch characteristic associated with the etching process. characterizes

In one embodiment, determining the correlation involves using multiple ADI images with one feature of interest. Thus, the determination of the correlation determines (i) a plurality of ADIs at a plurality of given locations on the substrate, each ADI having the same feature of interest (eg, a contact hole with a CD of about 21 nm), and (ii) may involve obtaining a plurality of AEIs at a plurality of given locations, each AEI having an etched feature of interest corresponding to the feature of interest (eg, an etched contact hole of CD 20 nm). there is. In one embodiment, the ADI CD is larger than the AEI CD of the feature of interest, for example the ADI CD may be 21 nm and the AEI CD may be 20 nm. A correlation may then be established between neighboring features of the feature of interest in each ADI and the etched feature of interest in each AEI. Although an exemplary function of correlation using CD is described below, a similar function can be established using other physical properties associated with the feature of interest (eg, quantifiable measurements).

In one embodiment, the correlation is a function of the average pattern density of neighboring features adjacent to the feature of interest. In one embodiment, the correlation between the neighboring features and the etched feature in ADI is: the feature of interest or the geometry of the neighboring features; the geometry of the bias or assist features associated with the feature of interest; distance between the feature of interest and neighboring features; distance along a line feature; a critical dimension of at least one feature; coordinates on the substrate associated with the feature of interest, neighboring features, and the etched feature of interest; assist features or lack of assist features around the feature of interest (eg, around the feature of interest refers to the end of the array of features that includes the feature of interest); or a random variation of the edge position from the predicted position associated with the feature of interest. In one embodiment, the predicted position of the edge (eg, feature outline) refers to the GDS position (eg, in the design layout) or average of similar features.

In one embodiment, the correlation is the scanner's dose and focus, etch temperature, plasma gas parameters, etchant composition, electromagnetic field, plasma potential, inductive or capacitive etching, temperature, ion energy distribution, ion angle distribution, sputtering and It can be calculated indirectly based on patterning process parameters, such as parameters associated with redeposition rate. For example, indirect determination of the correlation involves tuning or simulating the patterning process by adjusting one or more of the aforementioned patterning process parameters.

In one embodiment, the geometry of the feature may be a hole or a line. The correlation coefficient associated with the contact hole will be different from the line. For example, if the feature of interest is surrounded by a line, the loading effect may decrease along the length of the line. Also, L-shape features can have different correlations compared to lines, because L-shapes have corners and are influenced by neighboring features differently than lines. In one embodiment, the correlation also depends on the critical dimension of the neighboring features. For example, the larger the critical dimension of neighboring features, the greater the loading effect (see FIG. 11A ).

In one embodiment, the correlation is calculated using the following equation:

은 상관관계들의 벡터이며, 여기서 CDAEI는 관심 피처의 AEI CD이고; CDADI _i 는 i번째 이웃의 ADI CD이며, r는 상관 계수이고, Q _i,j = r _{CDADIi,CDADIj} 는 상관관계 매트릭스이다. 앞선 수학식은 일 예시이며, CD에 기초하여 상관관계를 제한하지 않는다. 앞서 언급된 바와 같이, 상관관계는 관심 피처 및 이웃 피처들과 연계된 다른 물리적 특성들(예를 들어, 앞서 언급된 바와 같은 기하학적 형상, 거리, 어시스트 피처들 등)에 기초하여 연산될 수 있다.In the previous formula,

is a vector of correlations, where CDAEI is the AEI CD of the feature of interest; CDADI _i is the ADI CD of the i-th neighbor, r is the correlation coefficient, and Q _i,j = r _{CDADIi,CDADIj} is the correlation matrix. The above equation is an example and does not limit the correlation based on the CD. As noted above, the correlation may be computed based on the feature of interest and other physical properties associated with neighboring features (eg, geometry, distance, assist features, etc. as mentioned above).

In an exemplary experiment, referring to FIG. 10 , a metrology tool (eg, SEM) measured 10 ⁵ contact holes exposed under 7 conditions according to a focus-exposure matrix (FEM). The contact holes are in a hexagonal grid, such that each contact hole (eg, 1040) has 6 neighbors (eg, 1050a - 1050f). An etch recipe (eg, IMEC TITAN VIA etch) was then used to etch the exposed substrate. In addition, the CD values of the contact holes before and after etching were determined using, for example, a MATLAB script configured to clean up the data for further use. Assuming a simple linear relationship between ADI and CD of the hole of AEI, a correlation between ADI and AEI can be established. For example, the portion of the variance of the AEI CD described by the ADI CD of the contact hole 1040 is simply the square of the correlation coefficient R ² given below:

의 예시적인 벡터는 다음과 같이 주어진다:For the portion of the variance of the AEI CD described by the ADI CD of the neighboring contact holes 1050a to 1050f, a vector of correlations is used. correlation

An exemplary vector of is given by:

Then, R ² _neighbors can be computed using:

및

를 나타낸다. y-축은 관심 피처 자체의 ADI CD 또는 그 이웃들의 ADI CD에 의해 설명되는 AEI CD의 변동의 분율을 나타낸다. y-축은 무차원량, 또는 100을 곱한 경우 백분율일 수 있다. 상관관계 플롯은, 단거리 에칭 로딩 효과가 가장 큰 CD에 대해 가장 강하고 상대적으로 더 작은 CD에 대해 실질적으로 더 낮다는 것을 나타낸다. 단거리는, 예를 들어 SEM의 FOV 이내일 수 있다. 따라서, 단거리 에칭 로딩은 패턴 밀도에 의존한다. 또한, 도 11b는 에칭 로딩 효과가 FEM 조건들에도 의존함을 나타내는 음의 상관관계를 나타낸다.Exemplary correlations are illustrated in FIGS. 11A and 11B . For the 7 conditions of FEM, the correlation plot (in Fig. 11a) shows the average CD of holes

and

indicates The y-axis represents the fraction of variance in the AEI CD explained by the ADI CD of the feature of interest itself or the ADI CDs of its neighbors. The y-axis can be a dimensionless quantity, or a percentage when multiplied by 100. The correlation plot shows that the short-range etch loading effect is strongest for the largest CD and substantially lower for the relatively smaller CD. The short range may be, for example, within the FOV of the SEM. Thus, the short-range etch loading is dependent on the pattern density. 11b also shows a negative correlation indicating that the etch loading effect also depends on the FEM conditions.

In the current example of FIG. 11B , the AEI CD (Y axis) is plotted against the weighted average (X axis) of the ADI CDs of neighbors for the condition with the largest average CD in FIG. 11A . The variations in CD, indicated by gray area 1103 , are due to random variations in the patterning process, and line 1105 represents the moving average of the CD of the feature of interest. Line 1105 indicates the negative correlation between the ADI CD and AEI CD of the neighbors. The negative correlation indicates that the correlation between the etched feature and neighboring features of ADI is relatively high for the indicated FEM condition printing at a relatively large average CD. For the sake of clarity, a relatively large average CD is not a randomly larger CD within the imaged pattern (e.g., if the scanner dose used is high, or the mask design is such that the CD is large), but rather its condition or pattern. CD associated with conditions or patterns with large pattern density because the average CD of is large.

In one embodiment, the method comprises determining, based on the correlation, etching conditions associated with the imaged pattern such that, at a given radial distance between a center of the substrate and an edge of the substrate, the correlation remains within a target range. is accompanied by In one embodiment, the etching conditions are: position of the substrate being etched - the position is the radial distance between the center of the substrate and the edge of the substrate (eg, the center or edge of the substrate or other distance to the region of interest on the substrate) - ; etching cycle; etching chamber; sequence of etching cycles and deposition steps; or tuning parameters associated with the etch chamber, wherein the tuning is based on the sensitivity of the correlation to changes in the tuning parameter.

In one embodiment, based on the correlation, etch conditions are determined for the imaged pattern centered on the substrate such that the correlation is within a target range. In one embodiment, the method involves determining, based on the correlation, etching conditions for the imaged pattern positioned at the edge of the substrate such that the correlation remains within a target range. In general, even if the pattern density is the same, different etching conditions may be required at different locations on the substrate due to the thickness profile of the substrate, drift associated with the etching apparatus, and the like.

In one embodiment, the etch conditions include etchant composition, plasma gas parameters, etch rate, electromagnetic field, plasma potential, inductive or capacitive etch type, temperature of the substrate, ion energy distribution, ion angle distribution, sputtering and redeposition rate. parameters associated with , an etch cycle parameter based on saturation effect, or a combination thereof. In one embodiment, the saturation effect is a loading effect that can be used to determine the composition of materials in the plasma as a means for endpoint detection per cycle. This could be used to trigger the next cycle.

In one embodiment, the etching conditions may be adjusted compared to ideal etching conditions. For example, ideal etch conditions can be changed in an existing etch apparatus (eg, adjusting parameters such as etchant composition, plasma gas parameters, etch rate, etc.) or a design tool used to determine etch conditions and , the design tool allows to adjust parameters such as electromagnetic fields, capacitive or inductive type etching, etc. so that the correlation remains within the desired target range.

In one embodiment, the method further comprises generating, based on the correlation between the AEI CD and the ADI CD, a power spectral density of the correlation (eg, a correlation established using the line as a feature). do. The power spectral density indicates the magnitude of the etch characteristic effect (eg, the loading effect) and the extent of the loading effect. In one embodiment, the power spectral density may be computed in the spatial domain (eg, along the length of a line feature). For example, the power spectral density is computed by taking the Fourier transform of the correlation in the spatial domain, where the correlation is as a continuous function of the distance between two points. Exemplary power densities of correlations for lines may indicate that correlations are relatively higher for small spacings between line segments and progressively decrease for larger spacings between line segments. Also, based on the power spectral density, appropriate etching conditions can be determined. For example, the etch recipe may be defined based on the magnitude of the loading effect along the line such that the correlation between the ADI of the line and the AEI of the line is maintained within a target range during the etch process.

In one embodiment, the correlation may be used to monitor and control the performance of the patterning process, for example by controlling the etch recipe and etch conditions (eg, tuning parameters) such that the correlation is maintained in a target range. .

For example, etch process chambers are monitored based on critical dimension uniformity across the entire substrate or CD difference between different features at different radii across the substrate.

In one example, control involves determining an effect on CD based on selectable etch knobs, eg gas-pressure, power, DC, temperature, etc. as well as correlation. Thereafter, the desired performance (eg, whether a correlation is maintained within a target range) may be monitored. The advantage is that in the final yield test, more dies on the board will be within specification. Also, an advantage of correlation-based monitoring is that it may not be necessary to check the final yield again in e-test vehicles or exhaustive inspection of, for example, millions of features.

12 is a flow diagram of a method 1200 for determining an etch condition or plurality of etch conditions associated with an etch process based on a correlation (discussed above) between an etched feature of interest and a neighboring feature of the ADI. The method 1200 is used to monitor and control the etching process based on a target range of correlation. In one embodiment, a correlation target range (eg, 0 to 0.4) may be defined, and etching conditions may be defined such that the target range is met during or after the etching process. The target range may be constant across the substrate being etched, but etching conditions may vary, for example at the center and edge of the substrate. The method 1200 is discussed in more detail below.

In one embodiment, the etch condition is determined such that a range of a plurality of parameters (eg, including a correlation) associated with loading effects is within a desired specification. For example, the impact of density variations and the fraction of variance accounted for by the ADI neighbors are also within the desired specifications. For example, the range of loading effects: less than 100 nm; Influence density range: 0.3 to 0.35 nm/nm; and an exemplary fraction of the described dispersion: 0.15 to 0.17.

Procedure P1201 involves obtaining a correlation 1201 between an etched feature of interest in the post-etch image (AEI) and a neighboring feature associated with the etched feature-of-interest in the post-development image (ADI). In one embodiment, obtaining a correlation between the etched feature and a neighboring feature includes obtaining a correlation between the etched feature and a plurality of neighboring features. In one embodiment, the step of obtaining the correlation is according to the method of FIG. 9 . For example, the step of obtaining the correlation can be performed via a metrology tool (i) a post-development image (ADI) of the imaged pattern at a given location - the imaged pattern including the feature of interest and neighboring features adjacent to the feature of interest. , and (ii) obtaining a post-etched image (AEI) of the imaged pattern at a given location, the AEI comprising the etched feature-of-interest corresponding to the feature-of-interest of the ADI; and determining, using the ADI and the AEI, a correlation between the etched feature and a neighboring feature associated with the feature of interest in the ADI.

Procedure P1203 involves determining, based on the correlation, etch conditions 1205 associated with the etch process such that the correlation remains within a target range.

In one embodiment, determining the etching conditions comprises: a location of the substrate being etched, the location being a center or edge of the substrate; the etching cycle of the etching process; an etching chamber used in the etching process; sequence of etching cycles and deposition steps; or a tuning parameter associated with the etch chamber, wherein the tuning is based on the sensitivity of the correlation to changes in the tuning parameter. In one embodiment, the tuning parameter comprises a plurality of tuning parameters.

In one embodiment, determining the etch conditions involves monitoring the CDU across the substrate or CD difference between instances of the etched feature of interest at different radii. For example, etch conditions can be determined by varying selectable etch knobs, eg gas-pressure, power, DC, temperature, etc., and evaluating the effect on CD as well as correlation. The advantage of determining etch conditions based on correlation is that more dies of the substrate will be within specification in the final yield test compared to conventional methods.

In one embodiment, an etch condition or etch recipe may be described as having a starting stage, intermediate stage(s) and a final stage. Each stage of etching may consist of one or more 'mini' etch recipes, which when taken all represent an etch recipe. In one embodiment, these 'mini' etch recipes are used to fine tune the results of the etch process (eg, characterizing the CD or yield of the etched feature of interest). Thus, different 'mini' etch recipes with slightly different behaviors such as, but not limited to, different amounts of loading can be applied to achieve the desired end result (eg CD or yield). In one embodiment, such fine tuning of etch recipes is achieved through tuning of different plasma gas parameters, power settings, gas flow settings, etc.

Although 'mini' etch recipes can be defined, etch process development is typically done based on the overall etch result rather than the pieces that can be represented as the start, middle, or end of the etch process. For example, the entire etching process may be run without interruption or interruption at the beginning, middle, or end of the etching process.

In one embodiment, when there are multiple materials on the substrate being etched, it is possible to have them etched in a combined etch process in a single chamber, wherein the etch recipe for the first material consists of multiple steps. This is followed by another etch recipe for the second material, which may consist of a different set of multiple steps (including changes to gas, etc.). For multi-material etches, a different degree of anisotropy may be required for each material, such that the profile of the etched pattern is not perfectly copied from one material to the next. These differences can lead to different correlation results. It is possible (but not universally) possible to stop the etch between layers to observe the individual profiles of the multi-profile etch. In one embodiment, the etch profile may be characterized by the geometry of the etched feature, such as height, angle, and width associated with the etched feature.

In one embodiment, determining etch conditions involves adjusting values of tuning parameters associated with a given etch chamber such that the correlation associated with the given imaged pattern remains within a target range.

Measurements according to the present invention (eg, ADI CD and AEI CD) help to understand the etching process, which can speed up the etch optimization process even if it is manual. For example, the optimization is based on the correlation obtained from the method of FIG. 3 . As measurements are performed on product structures, the resulting etch is better optimized for the most critical structures, increasing the yield of the patterning process.

Machine learning models (eg, neural networks, CNNs, DCNNs, etc.) are mainly black boxes. Even when these black box models are trained using supervised learning (e.g., via a human), process parameters (e.g., dose/focus, etch recipe) can be used to improve the patterning process. Make predictions that may not be readily interpretable to take corrective action. Therefore, when evaluating actions based on predictions or choosing whether to utilize a new model, it is desirable to understand the reasons for the predictions made by the trained model.

In an embodiment, the white box model of the patterning process may have lower accuracy than black box models of the patterning process. For example, a white box model can make predictions with 91.3% accuracy, but the predictions made by the model can be easy to explain. For example, a model that classifies features as defective or non-defective based on their CD values in an ADI image can be easily understood by looking at the CDs of features. On the other hand, a black box model (eg, CNN) can predict with higher accuracy (eg, 95.8%) than a white box model. However, the decisions of the black box model are difficult to explain. For example, the prediction of a defective feature may not be readily conceived based on the predicted results. Thus, in one embodiment, users may choose to sacrifice accuracy for interpretability.

A criterion for improving the description of the predictions of the black box model is interpretability, which provides a relationship between the input variables and the predictions of the black box model. For example, the relationship is a qualitative/quantitative relationship of predicted outcomes (eg, whether an ADI feature is defective as mentioned above) based on input variables (eg, pixel values of an ADI image). provide understanding.

In the present invention, a relationship between input variables (eg, features of ADI) may be described through an interpretation model associated with a feature of interest. In one embodiment, the analytical model helps account for the defect of a particular feature. For example, the interpretation model may identify portions of the ADI image that describe the feature's defect. In one embodiment, the interpretive model is analyzed using different approaches such as Local Interpretable Model-agnostic Explanation (LIME), principal component analysis (PCA), or discriminant analysis, such as linear discriminant analysis (LDA) or quadratic discriminant analysis (QDA). can be decided. 15A shows an exemplary flow diagram for determining an interpretation model configured to identify relevant features of an ADI that account for a defective classification of any input ADI.

Referring to FIG. 15A , the method 1530 includes procedures P1531 and P1533 discussed in detail as follows. Procedure P1531 includes the steps of obtaining via a metrology tool (i) a post-development image (ADI) of the imaged substrate at a given location, and (ii) a post-etch image (AEI) of the imaged substrate at a given location do. Procedure P1533 includes determining, based on the ADI and the AEI, an interpretation model 1510 configured to identify portions of the ADI that describe the defect of the feature in the input ADI. In one embodiment, the interpretation model is determined by employing a LIME approach that is configured to create an interpretation model that is configured to generate an interpretation map that describes the classification of the input ADI. An example of a LIME approach is described with respect to FIG. 15B below.

In one embodiment, determining the interpretation model 1510 includes determining correlation data between the ADI and the AEI; and using the correlation data, performing principal component analysis or discriminant analysis to determine eigenvectors whose eigenvalues exceed a specified threshold. In addition, the determining may include calculating a classification value by projecting the input ADI onto the eigenvectors; and in response to the classification value exceeding the specified threshold, identifying the portion of the input ADI as descriptive of a defect in the feature in the input ADI. One example of a PCA method is discussed in more detail below.

로서 표현될 수 있다. 예를 들어, ADI 이미지는 크기 51x51 픽셀들의 크롭일 수 있으므로, 길이 51²=2601의 벡터를 유도한다. 벡터

에 기초하여, 다음과 같이 모든 ADI 이미지들(예를 들어, 도 14a 내지 도 14c의 ADI10, ADI20 및 ADI30)로 상관관계 매트릭스

가 연산될 수 있다:In one embodiment, PCA (and similarly LDA or QDA) may be performed based on correlations between variables of the ADI image. In one embodiment, the correlation may be determined using pixel intensities of the ADI image. For example, PCA (and similarly LDA or QDA) may be performed as follows. In this example, grayscale values or intensities of pixels in an ADI image (eg, ADI10, ADI20, or ADI30 in FIGS. 14A-14C ) are vector

can be expressed as For example, an ADI image may be a crop of size 51x51 pixels, resulting in a vector of length 51 ² =2601. vector

Based on the correlation matrix with all ADI images (eg, ADI10, ADI20 and ADI30 in FIGS. 14A-14C ) as follows

can be computed:

In the preceding equation, <x _i > is the average values of vector x _i over all crops (eg, ADI10, ADI20, and ADI30), and σ _i σ _j is the covariance between two pixels of the image.

의 고유값들 및 고유벡터들이 연산된다. 이 고유값들은 1보다 상당히 더 크고, 대략 1이며, 1보다 훨씬 작은 약간의 고유값들일 수 있다. 더 높은 고유값들은 고도로 상관되는 대응하는 변수들의 세트를 나타낸다. 예를 들어, ADI10(도 14a)을 참조하면, 상관관계 매트릭스는 접촉홀(F10)과 관련된 픽셀들(어두운 부분)이 고도로 상관될 수 있음을 나타낼 수 있다. 따라서, 상관관계 매트릭스는 접촉홀이 존재함을 나타낼 수 있다. 반면에, ADI30(도 14b)에 대해, 상관관계 매트릭스는 실패한 접촉홀을 나타낼 수 있는 접촉홀(F30)의 픽셀들 간의 상대적으로 낮은 상관관계를 나타낼 수 있다.On correlation matrix R _ij data, PCA, LDA or QDA may be performed. In PCA, matrix

Eigenvalues and eigenvectors of are calculated. These eigenvalues can be some eigenvalues significantly greater than one, approximately equal to one, and much less than one. Higher eigenvalues indicate a set of highly correlated corresponding variables. For example, referring to ADI10 ( FIG. 14A ), the correlation matrix may indicate that pixels (dark portions) related to the contact hole F10 can be highly correlated. Accordingly, the correlation matrix may indicate that a contact hole exists. On the other hand, for the ADI30 (FIG. 14B), the correlation matrix may indicate a relatively low correlation between pixels of the contact hole F30, which may indicate a failed contact hole.

Eigenvectors corresponding to large eigenvalues (eg, greater than 1) indicate that the grayscale values of these pixels vary together, which may indicate a failed contact hole or printing hole. These eigenvectors corresponding to the large eigenvalues may be used in the interpretation model 1510 . For example, project all instances of crops onto a few eigenvectors with large eigenvalues, and check if there is strong clustering of holes that print and fail in one of these directions. Eigenvectors in which directions with strong clustering are observed are relevant features for defect classification. By converting these eigenvectors back into the form of a 51x51 crop, interpretations of relevant features in the input ADI as failure or printing can be made.

In another example, LDA/QDA also identified eigenvectors that could automatically find the projection direction that best distinguishes printing from failed holes.

In one embodiment, the interpretation model may be determined using a LIME approach, eg, the method 1500 discussed with reference to FIG. 15B . LIME is a descriptive technique that describes the predictions of any classifier in an interpretable way by learning an interpretable model around the prediction locally. An example of determining an interpretable model is described below in FIG. 13 .

13 depicts a decision data set used to train an exemplary interpretive model. The decision data set may be obtained from a trained model (eg, the CNN model of FIG. 4A ). For example, the trained model 403 predicts the presence of defects in a plurality of features after etching using an ADI image including the plurality of features. For example, predict whether an ADI feature will print defect-free or defect-free after etching using a particular etch recipe.

In FIG. 13 , the complex decision-making function of the trained machine learning model (not known to the analytical model) is represented by prediction regions R1 and R2. In one embodiment, decision making refers to predictions by the trained model 403 . Thus, the prediction regions R1 and R2 correspond to whether the features of a given ADI image will be defective or not defective after etching. In one embodiment, these prediction regions R1 and R2 are separated by a non-linear boundary that cannot be well approximated by a single linear model. Accordingly, a set of models may be defined, wherein each model may locally (eg, around a selected point) explain why a particular prediction was made.

In one embodiment, point P0 (bold cross) is the instance to be described by the analytical model. For example, point P0 represents a feature of interest in the ADI image. According to one embodiment, an interpretive model describing predictions associated with point P0 is described using fitted lines, wherein the fitting is based on data near point P0. The data near point P0 includes two types of categories represented by zones R1 and R2. For example, the first set of points P1 , P2 , P3 , P4 , P6 represents the decision of the trained machine learning model that the features will be defective after etching. On the other hand, the second set of points P10, P11, P12, P13, ..., P20 represents the decision of the trained machine learning model that the features will be defect-free after etching.

In one embodiment, a method used to determine an interpretation model includes sampling instances (eg, P1 - P20), obtaining predictions using a trained machine learning model (eg, 403); , and weighting the predictions by the proximity of the sample to the described instance P0 (eg, the feature of interest) (eg, denoted herein as the magnitude of points P1 - P20). Then, the model is fitted based on the weighted predictions by adopting a fitting method. For example, a least squares error based fitting method may be used. According to one embodiment, the fitted model is referred to as a trained analytical model.

In one embodiment, dashed line M1 represents a trained interpretation model that provides a description of point P0 locally (but not globally). For example, local refers to points in the vicinity of the instance being described. Also, the dotted line M1 may be referred to as a trained analysis model M1. In other words, the trained analytical model M1 provides a linear approximation of the non-linear boundary around the line M1 based on the non-linear boundary B1 and the data points near the point P0. In one embodiment, the interpretation model M1 may be trained such that a cost function, eg, a function of the difference between the output of the interpretation model M1 and the predictions near the point P0, is reduced (eg, minimized). The present invention is not limited to a particular fitting method. Other data fitting methods may be employed, such as least squares method, Gaussian fitting, least deviation, and the like.

The example of FIG. 13 represents binary decision making to illustrate concepts. However, the decision may be binary categorization, or may include multiple categories (eg, probability based, multiple ranges of probability corresponding to multiple categories). The scope of the present invention is not limited to binary decision making.

14A to 14C show exemplary results of applying an interpretation model (eg, M1) to ADI images including a feature of interest. In this example, the ADI images ADI10 , ADI20 , and ADI30 include features of interest F10 , F20 , and F30 , respectively. In one embodiment, a trained model (eg, 403) associated with a process (eg, an etch process) predicts whether a particular feature within the ADI will print defect-free or defect-free after etching.

14A and 14B show examples of features F10 and F20 of ADI images ADI10 and ADI20 that are predicted to be printed without defects, respectively. For example, the trained model (eg, model 403 trained according to the method of FIG. 4A ) predicts that features of images ADI10 and ADI20 will print flawlessly. 14C shows an example of a feature F30 of an ADI image ADI30 predicted to be printed with a defect. For example, the trained model (eg, model 403 trained according to the method of FIG. 4A ) predicts that features of images ADI10 and ADI20 will print flawlessly.

However, as discussed above, the trained model 403 may be a machine learning model (eg, CNN or DNN) comprising a network of neurons that are weighted, distributed over multiple layers, and connected to each other. Therefore, a rational basis for the prediction is not available.

A rational basis or explanation for these predictions can be obtained through a trained interpretive model (also called an interpretive model). For example, for each feature of interest, an interpretation model may be trained according to FIG. 13 . For example, the first interpretation model M10 is trained to account for predictions related to the feature of interest F10 of ADI10. Similarly, the second interpretive model M20 is trained to describe predictions related to the feature of interest of ADI20, and the third interpretive model M30 is trained to describe the predictions related to the feature of interest of ADI30.

In one embodiment, the interpretive models M10, M20, and M30 generate interpretive maps MAP10, MAP20, and MAP30, respectively, as shown in FIGS. 14A-14C . Interpretation maps (e.g., MAP10, MAP20, and MAP30) compare features of interest (e.g., F10, F20, and F30) and surrounding features of interest (e.g., F10, F20, and F30) to predictions (e.g., defective or non-defective) associated with the feature of interest. Shows the patches that describe the contribution of each pixel of . In one embodiment, the patches may have intensity values representing the influence of neighboring features (eg, corresponding to points P1 - P20 in FIG. 13 ) on the decision that the feature of interest is defective or not defective after etching. there is.

For example, in the interpretation map MAP10, patch E1 (eg, positive pixel values) contributes to the decision that feature F10 (of ADI10) will be defect-free after etching, while patch E2 (eg, negative The pixel values of ) contribute to the decision that feature F10 (of ADI10) will be defective after etching. Similarly, in the interpretation map MAP20, patch E3 (eg, positive pixel values) contributes to the determination that feature F20 (of ADI20) will be defect free after etching. Finally, in the interpretation map MAP30, patch E4 contributes to the decision that feature F30 (of ADI30) will be defect-free after etching, while patch E5 (eg negative pixel values) has feature F30 (of ADI30) This contributes to the decision to be defective after etching. The interpretation map or pixel values therein may be further used to take action, such as adjusting a patterning process recipe (eg, an etch recipe) to improve the yield of the patterning process.

In one embodiment, optionally, the ADI image and the corresponding interpretation map may be overlaid to create an overlaid image. For example, ADI10 and MAP10 may be overlapped to generate an overlapped image S10. Similarly, ADI20 and MAP20, and ADI30 and MAP30 may be superimposed to create superimposed images S20 and S30, respectively. In one embodiment, the superimposed image or pixel values therein may be further used to take an action, such as determining recipes for certain portions of the imaged substrate.

15B is a flow diagram of a method 1500 for determining an analytical model associated with a feature of interest. The interpretive model is configured to account for predictions related to the feature of interest. For example, if there are N features of interest, N interpretation models may be determined - one for each feature of interest. As discussed in FIGS. 13 and 14A-14C , the interpretive model can generate an interpretive map for the feature of interest, such that the interpretive map can account for the contributions of the vicinity of the feature of interest to the prediction associated with the feature of interest. there is. Further, based on the analysis map, actions related to improving the patterning process (eg, etching process) may be taken. For example, if the analysis map includes patches that have a relatively high contribution to making the prediction that the feature will be defective, the etch recipe may be adjusted for that particular patch.

In accordance with the present invention, the method 1500 may be performed after a model (eg, 403 ) associated with the patterning process is trained to predict future characteristics of any feature in the image after development, for example. Future characteristics (also called predictive) may be, for example, CD or defectivity of features. For example, the trained model 403 can predict whether features in an ADI image will print defect-free or defect-free after etching using an etch recipe. The method 1500 is not limited to a particular prediction or classification associated with a feature. In the following procedures of the method 1500 , an example of prediction is the defect of a feature. As previously discussed, the presence of defects can indicate the probability of a feature's failure after etching. In one example, to illustrate the concepts of the method, defective can be visualized in binary, for example as defective or free of defects.

Procedure P1501 includes obtaining a training data set, eg, via execution of the trained model 403 associated with a patterning process (eg, an etching process). In one embodiment, the training data set includes a plurality of predictions 1502 associated with a plurality of features near a feature of interest 1501 in a post-development image (ADI), each prediction of the plurality of predictions comprising a training is performed by the model 403 . In one embodiment, for training purposes, the vicinity of the feature of interest refers to the location of features around the feature of interest 1501 . For example, referring to FIG. 13 , points P1 to P20 are in the vicinity of a point of interest P0.

In one embodiment, obtaining the plurality of predictions 1502 includes running the trained model to predict a characteristic of each feature of the plurality of features in the vicinity of the feature of interest 1501 . In one embodiment, similar to procedure P403 discussed above, obtaining an image after development includes imaging a mask pattern on the substrate via a patterning device; obtaining a developed substrate (eg, resist development) of the imaged substrate; aligning the metrology tool (eg, the SEM of FIGS. 28 and 29 ) to the developed substrate at a given location (eg, the location of the feature of interest); and capturing an image of the developed substrate. In one embodiment, the post-development image may be obtained from a database (eg, in the computer system of FIG. 30 ) that stores metrology data (eg, SEM images) of the substrate.

In one embodiment, an ADI image comprising a plurality of features is provided as input to a trained model 403 . Then, the trained model predicts, for example, that a plurality of features are defective. In one embodiment, the prediction 1502 is that the feature in the ADI is defective, where defective indicates the probability that the feature will be defective after etching. In one embodiment, the prediction 1502 is whether the feature of interest in the ADI will print defect-free or defect-free after etching.

Procedure P1503 includes determining distances 1503 between each location of the plurality of features and the feature of interest. In one embodiment, the distance 1503 is a linear distance between two locations, in particular the location L1 of the feature of interest 1501 and the location L2 of the neighboring feature. For example, referring to FIG. 13 , the distance D1 between P0 and P1 (not shown), the distance D2 between P0 and P2, and the like.

Referring again to FIG. 15B , procedure P1505 includes assigning weights to each prediction of the plurality of predictions, based on distances 1503 . In one embodiment, assigning weights to each prediction comprises assigning a relatively higher weight to the prediction of the plurality of predictions when the associated distance is relatively small. In one embodiment, the weights may be integer values or normalized values between 0 and 1 such that the sum of the weights is 1.

For example, referring to FIG. 13 , higher weights are assigned to points P1, P2, P3, P10, P11, P12 and P13 compared to points P4, P5, P14, P15 and P16. In other words, points near the point of interest P0 are considered to contribute more to performing a specific prediction related to the point of interest P0. For example, features corresponding to points P1, P2, P3, P10, P11 and P12 are assigned a weight of 0.9, while features corresponding to points P4, P5, P15 and P16 have a weight of 0.1 can be assigned. Accordingly, higher weights are assigned to predictions associated with features in locations close to the feature of interest 1501 compared to features further away from the feature of interest 1501 . In one embodiment, the weights may be assigned according to an exponential function, eg, e ^f(D) , where f(D) is a function of distance 1503 .

Referring again to FIG. 15B , procedure P1507 is a model of the interpretation model 1510 such that, through fitting based on the weighted predictions 1505 , the difference between the output of the interpretation model 1510 and the weighted predictions 1505 is reduced. determining parameter values. In one embodiment, the model parameter values describe the contributions of each pixel of the ADI to the prediction related to the feature of interest.

In one embodiment, determining model parameter values of the interpretation model comprises: obtaining initial model parameter values and weighted predictions; running the analytical model using the initial model parameter values to produce an initial output; determining a difference between the weighted predictions and the initial output; and based on the difference, adjusting the initial model parameter values such that the difference is minimized.

In one embodiment, the interpretive model 1510 receives an ADI including the feature of interest 1501 as input and generates an interpretive map 1520 as an output. In one embodiment, the interpretive map 1520 represents contributions in the vicinity of the feature of interest 1501 to the prediction associated with the feature of interest 1501 .

In one embodiment, the interpretive model 1510 is a linear model associated with the feature of interest in the ADI. In one embodiment, a linear model is fitted to a plurality of predictions using linear regression employing least squares error. 13 shows an example of the analysis model M1.

In one embodiment, interpretation map 1520 is a pixelated image (eg, MAP10, MAP20, and MAP30 in FIGS. 14A-14C ), and model parameter values are assigned to each pixel of the pixelated image. weights or values. In one embodiment, the interpretation map is a binary map in which each pixel is assigned a value of 0 or 1. In one embodiment, the binary map is generated by assigning a value of 0 or 1 to each pixel based on the pixel value above a threshold, where 0 indicates that the feature of interest will be printed as a defect after etching, and 1 indicates that the feature of interest will be printed as a defect. indicates that it will print without defects after etching. In one embodiment, the threshold is a value above which the contribution is considered positive or favorable for prediction, and vice versa.

In one embodiment, the interpretation map 1520 is a color image to which a particular color (eg, RGB values) is assigned based on model parameter values.

After training the interpretation model 1510, it can be used to understand predictions associated with the feature of interest. For example, as shown in FIG. 14A , the ADI image ADI10 including the feature of interest F10 may be input to the analysis model 1510 . Then, the analysis model generates an analysis map, for example, MAP10. Interpretation map MAP10 includes patches E1 and E2 that visually describe which portions of the region around feature F10 contribute to the prediction that after etching feature F10 will print defect-free. For example, an interpretation may be made that the area of patch E1 is substantially larger than E2, and thus E1 has a higher contribution.

In one embodiment, the interpretation model may be optimized, for example, by modifying metrology settings and determining the portions within the ADI that best describe the quality of the defective classification. For example, two eigenvectors can be identified that improve the classification accuracy to 94% after optimization, while the initial eigenvector provides 92% classification accuracy, or 6 eigenvectors after optimization improve the classification accuracy to 99%. can be improved An exemplary optimization process for determining optimal parameters (eg, relevant eigenvectors) is discussed as follows. In one embodiment, changes may be made to metrology tool settings, multiple eigenvectors to consider, or other settings during the optimization process. Optimized parameters (eg, eigenvectors) are descriptive classifications that can be applied to any input ADI.

In one embodiment, a method of applying the analytical model 1510 is discussed with respect to FIG. 16 . 16 is a flow diagram of a method 1600 of identifying contributions in the vicinity of a feature of interest to classifying the feature of interest as defective. The method 1600 includes procedures as discussed below.

Procedure P1601 involves post-development image 1601 (eg, ADI10, ADI20, ADI30 in FIGS. 14A-14C ), including a feature of interest (eg, features F10, F20, and F30), and associates with a feature of interest. and obtaining the analyzed analysis model (eg, 1510 in FIG. 15B ). Procedure P1603 includes generating an interpretation map 1610 by applying the analysis model 1510 to the ADI 1601 . In one embodiment, the interpretation map 1610 includes pixel values that quantify the contributions of each pixel of the ADI 1601 to classifying the feature of interest as defective.

As noted herein, in one embodiment, the analytical model 1510 is a linear model associated with the feature of interest of the ADI 1601 . In one embodiment, interpretation map 1610 is a pixelated image, wherein each pixel has a weight indicating the amount of each pixel's contribution to classifying the feature of interest as defective. In one embodiment, interpretation map 1610 may be a binary map in which each pixel is assigned a value of 0 or 1.

In the preceding method, the image after development and the image after etching are used as examples for explaining the concepts of the present invention. However, the methods discussed herein are not limited to such ADI images and AEI images. A person skilled in the art can perform the preceding methods using any images obtained before and after a particular process (eg, OPC, optical process, resist process, etching, chemical mechanical polishing, etc.) or a combination of processes related to a patterning process. . The model then establishes a relationship between these images to determine the contribution of the process recipe (eg, optical process recipe, resist process recipe, etch recipe, etc.) to the probability of failure after the process is performed.

As mentioned above, there are a number of algorithms that classify failures of contact holes after development based on SEM images. Criteria for error classification may be based on common sense in interpreting SEM images. For example, the error criterion may be low SEM contrast or small critical dimension (CD). Also, an attempt has been made to estimate the failure rate from the CD distribution of the contact holes based on a predetermined criterion. For example, the criteria may include (i) contact hole failure below a certain focus-dependent critical CD, (ii) 3 standard deviations of CD from mean CD, or variations thereof, including skewness and kurtosis, also called tail CD. It can be the fraction of failures that is a function of subtraction. Prediction by tail CD can be empirical, which can depend on the process used for patterning. Also, deviations from predictions may be focus dependent.

In the present invention, AEI failure and non-failure contact holes are considered to have different properties in ADI measurements. Thus, as discussed in one example, the ADI CD distribution can be decomposed into two independent distributions that account for AEI measured failure and non-failure contact holes. The relative contribution of these ADI CD distributions determines the fraction of failed holes after etching.

In one embodiment, the ADI CD distributions of failed and non-failed holes after etching are different, but these two CD distributions may overlap. Failures may not be classified by the FEM-dependent CD threshold. However, if the CD distribution of all contact holes in a given FEM condition is obtained, it can be fitted as the sum of the two distributions, and the relative contribution of these distributions predicts the fraction of failed holes after etching.

17 is a method of predicting the fraction of post-etch feature failures from ADI measurements based on a model composed of a first portion (eg, first CD distribution) and a second portion (eg, second CD distribution). (1700) is a flowchart. Models generated using the method 1700 can be applied to improve the patterning process. For example, the model can be used to estimate the fraction of filled contact holes from ADI measurements. The estimated filled holes can be used, for example, as follows. In an exemplary application, the estimated filled holes may be used during ramp-up of a lithographic process. For example, the lithographic apparatus can be tuned to reduce the number of filled contact holes. Examples of improvements are tuning of the scanner's dose and focus or additional filtering steps to the resist. In another exemplary application, during ramp-up, the fraction of filled contact holes determines whether additional descumming or punch-through should be used prior to etching to reduce the effect of filled contact holes. can be used to evaluate In another example application, during HVM, the ADI CD distribution may be checked to see if the machine is still within specification. Note that this requires a huge amount of contact holes per wafer. However, when all data in a given time frame (eg, 1 day) are combined, such fitting may be feasible. A method 1700 for generating a model and predicting the fraction of features that may fail is discussed in detail as follows.

Procedure P1701 includes obtaining a post-developed image (ADI) 1702 of the substrate, wherein the ADI image 1702 includes a plurality of features. In one embodiment, the ADI is an image of a printed board obtained through a metrology tool or from a database that stores images of the printed board. In one embodiment, the plurality of features of the ADI image includes a plurality of holes, a plurality of pillars, a plurality of lines, or a combination thereof. Thus, in one embodiment, some of the features of the ADI image that are classified as defective after etching are: holes that are closed or disappeared after etching due to resist blocking the development of the holes; merged holes after etching; necking of one of the plurality of lines; at least one of bridging lines, or a combination thereof.

In one embodiment, the physical property may be a critical dimension (CD) of a feature in the ADI image, and the physical property threshold associated with the feature may be a CD threshold. For example, the CD of the contact hole is determined by calculating the surface area enclosed by the contour resulting from the contouring algorithm (e.g., the CD obtained from multiple metrology tool thresholds for each feature of interest), then the circle The diameter of can be determined with the same surface area. In one embodiment, the physical property is: the geometric mean of the CDs of the feature - the CDs to be measured along a first direction (eg, x-direction) or a second direction (eg, y-direction) in the ADI image. can- ; directional CD of the feature of interest in the ADI image; Dispersion of curvature of features of interest within ADI images; or CD obtained from multiple metrology tool thresholds for each feature of interest. In one embodiment, the directional CD includes: a CD measured along the x-direction; CD measured along the y-direction; or CD measured along the desired angle. The physical property values (eg, CD values) or a subset thereof may be used to create a model as discussed below. In one embodiment, the physical property may be a function of one or more of the physical properties. For example, the physical property may be the square of the CD values. The present invention is not limited to specific physical properties. One of ordinary skill in the art would appreciate that any physical property that could be used to characterize the failure of a feature could be used herein.

Procedure P1703 performs a first portion (eg, a first probability distribution) of model 1710 based on physical property values (eg, CD, EPE) associated with a subset of features SET1 of the ADI image 1702 . function (PDF1)]. Procedure P1705 includes a first portion of the model and a second portion of the model (eg, a second Probability distribution function (PDF2)]. In one embodiment, the subset of features SET1 of the ADI image is distinct from other features of the ADI image 1702 . For example, subset SET1 may be features with CD values greater than a specified threshold. In one embodiment, the subset SET1 is fitted using a truncated PDF. In one embodiment, using the truncated PDF changes the normalization of the PDF based on a threshold (eg, CD _u ) and fitting parameters.

In one embodiment, the generation of the first part of the model and the second part of the model is performed by maximizing the log-likelihood metric of the model 1710, respectively, of the first probability distribution function (PDF1) and the second probability distribution function (PDF2). Includes fittings. In one embodiment, model 1710 is a combination of a first probability distribution function (PDF1) and a second probability distribution function (PDF2). In one embodiment, the first probability distribution function PDF1 is configured to estimate the distribution of physical property values (eg CD) for non-failure features (eg non-failure holes). In one embodiment, non-failure holes may indicate having a very low probability of failure. For example, a failure rate in a given range (eg, 0 to 0.1). In an embodiment, the second probability distribution function PDF2 is configured to determine failure rates based on physical property values of all the plurality of features of the ADI image.

In one embodiment, model 1710 is a weighted sum of a first probability distribution function and a second probability distribution function. For example, the model is the total distribution computed as the weighted sum of the first function PDF1 and the second function PDF2 for failure and non-failure, respectively.

In one embodiment, the first probability distribution function includes a truncated value (eg, CD _u ) associated with a physical property, a first positional parameter describing the shift (eg, mean) of the normal distribution, and the distribution of the normal distribution ( spread), a normal distribution (or truncated normal distribution) characterized by a first scale parameter (eg, sigma). In one embodiment, as in equation (1), the square of the CD fits a normal distribution, but the CD itself may fit another (eg, GEV) distribution.

In one embodiment, the second probability distribution function includes a second position parameter (μ) that describes the shift in the GEV distribution, a second scale parameter (σ) that describes the spread of the GEV distribution, and a shape of the GEV distribution A generalized extreme value (GEV) distribution characterized by a shape parameter (ξ).

In the example of this disclosure, the model 1710 or the fitted overall distribution is the sum of the normalized distribution of squares of the ADI CDs and the generalized extreme value (GEV) distribution. For example, the overall probability distribution function (PDF) can be given as:

In the preceding equation, the variable x represents the physical properties of features of ADI, for example CD, p _GEV represents the cumulative probability of the tail of the GEV distribution, Θ _N represents the parameters of the normal distribution or the truncated normal distribution, and Θ _GEV denotes the parameters of the GEV distribution.

In one embodiment, the log-likelihood of the preceding PDF can be calculated by the following equation:

Using the previous examples of the normal distribution and the GEV distribution, the method creates a model in two steps discussed below.

In one embodiment, when an unconstrained numerical maximization of l ( p _GEV , Θ _N , Θ _rGEV ) is used, the GEV may fit the noise to a non-failure distribution rather than fitting the tail of the distribution. Therefore, p _GEV is assumed to be small. To this end, a two-step procedure (eg, including P1703 and P1705) is employed to create a model (eg, 1710) as follows.

이상의 CD ² 를 피팅한다. 예를 들어, 도 18은 절단 정규 분포(1810)의 일 예시를 나타내며, 여기서 CD _u 는 15 nm이다. 다시 말해서, 15 nm 이상의 CD 값들이 정규 분포에 피팅하는 데 사용된다.First, the truncated normal distribution truncated from the bottom and the predetermined

Fit the above CD ² . For example, FIG. 18 shows an example of a truncated normal distribution 1810 , where CD _u is 15 nm. In other words, CD values above 15 nm are used to fit a normal distribution.

및

이다. 일 실시예에서, ν _N 및 ρ _N 의 값들은 앞선 PDF(CD)의 로그-우도가 최대화될 때까지 반복적으로 해결될 수 있다. 또한, 앞선 수학식에서, PDF _N 는 정규 분포의 확률 분포 함수를 지칭하고, CDF _N 는 정규 분포 함수의 누적 분포 함수를 지칭한다. 일 실시예에서,

는 초기에 ν _N - 2ρ _N 가 되도록 선택될 수 있다. 이는 반복적으로 달성될 수 있다.In the preceding equation, ν _N and ρ _N are the relevant mean and standard deviation of the normal distribution that can be followed in the log-likelihood maximization. for example,

and

am. In an embodiment, the values of ν _N and ρ _N may be iteratively solved until the log-likelihood of the preceding PDF (CD) is maximized. In addition, in the above equation, PDF _N refers to the probability distribution function of the normal distribution, and CDF _N refers to the cumulative distribution function of the normal distribution function. In one embodiment,

can be initially chosen to be ν _N - 2ρ _N . This can be achieved iteratively.

Also, after fitting in the second step (discussed below in relation to GEV), it is to be checked whether the predicted fraction of failed holes for CD > CD _u is below a certain threshold (eg, less than 1%). can Otherwise, the procedure (eg, P1703 and P1705) may be repeated with a larger value of CD _u (eg, greater than 15 nm).

In one embodiment, the overall CD distribution is fitted with the distribution proposed in equation (1) while keeping v _N and p _N fixed to the previously obtained values. By maximizing the log-likelihood, p _GEV , ξ , σ _GEV , μ _GEV can be determined. This fitting process and the equations used therein may be implemented using any non-linear programming solver. A nonlinear programming solver can find the minimum of a given unconstrained multivariate function. In one embodiment, ξ = 0 may be chosen to improve robustness.

As discussed in connection with the preceding example, the generation of the model is based on squared (eg, CD ² ) values of a physical property of a subset of features by maximizing a first log-likelihood metric associated with a first probability distribution function. to fit a first probability distribution function (eg, a normal distribution). In one embodiment, the subset of features SET1 has physical property values above the physical property threshold. Then, the fitted first probability distribution function may be combined with the second probability distribution function. Based on the combined distribution, a second probability distribution function may be fitted based on the physical property values of all features of the plurality of features such that a second log-likelihood metric associated with the combined distribution is maximized. In one embodiment, the relative weights of the second distribution are determined in a fitting process.

18A is an example fitting of two probability distribution functions based on CD values of features in an ADI image. Dots indicate non-failure holes (eg, determined based on etch data analysis) and crosses indicate failed holes (eg, based on etch data and CD less than desired values) . A truncated normal distribution 1810 (an example of a first probability distribution function) can be fitted using CD values of non-failure holes, where holes with CD values above a CD threshold (eg, 15 nm) are They are considered non-failure holes. Also, the GEV distribution 1820 can be used for tails (eg, CD less than 15 nm), for example the overall distribution 1801 is fitted using Equation (1) above and all ADI CD values. can be In one embodiment, for an overlapping region (eg, about 15 nm), both the normal distribution and the GEV distribution may have similar weights (eg, represented by p _GEV in equation (1)). . In one example, p _GEV can be close to zero, but the value of p _GEV GEV ( x;Θ _GEV ) is ( 1 - p _GEV ) 2 CD N ( CD ² ;Θ GEV ) for small CD and best fitting parameters. _N ) is much larger than that. In one embodiment, the weight associated with the GEV distribution progressively increases as CD values progressively decrease.

In one embodiment, fitting of the first probability distribution function is an iterative process. The iterative process includes (a) determining a first log-likelihood metric using given values of parameters of the first probability distribution function; (b) determining whether the first log-likelihood metric is maximized; (c) in response to not being maximized, adjusting values of parameters of the first probability distribution function based on the slope, and performing steps (a) to (c). In one embodiment, the slope is the first derivative of the first log-likelihood metric with respect to the parameters of the first probability distribution function.

In one embodiment, the fitting of the second probability distribution function is based on the maximization of the second log-likelihood metric, without modifying the values of the parameters of the first probability distribution function, the values of the parameters of the second probability distribution function and their weight It involves the steps of determining

In one embodiment, fitting the second probability distribution function (eg, 1820 ) is an iterative process. The iterative process includes (a) obtaining a combined distribution of a fitted first probability distribution function and a second probability distribution function; (b) a second log-likelihood based on the combined distribution (eg, 1801 ) and keeping the values of the parameters of the fitted first distribution fixed, using the given values of the parameters of the second probability distribution function. determining a metric; (c) determining whether a second log-likelihood metric is maximized; (d) in response to not being maximized, adjusting values of parameters of the second probability distribution function based on the slope, and performing steps (b) to (d). In one embodiment, the slope is the first derivative of the second log-likelihood metric with respect to the parameters of the second probability distribution function. In one embodiment, the combined probability distribution function (eg, 1801 ) may be employed as the model 1710 for predicting failure rates or failure rates of ADI features.

Referring to FIG. 18B , a first focus-exposure matrix PW1 (focus in x-axis, dose in y-axis), consisting of ADI holes plotting ADI LCDU leading to non-failure features AEI, and failure after etching and It represents another focus-exposure matrix PW2 associated with ADI which may contain both non-failures. 18B also shows how the LCDU of the pattern changes with dose for fail and non-fail AEIs. There is a clear difference between LCDUs as a function of dose for all holes and for non-fail features. For example, curve 1851 shows LCDU as a function of dose for all holes and curve 1853 shows LCDU as a function of dose for non-failure holes in AEI. In one example, if there are merged holes after etching, the LCDU (curve 1851) increases at a higher dose. On the other hand, if there are non-failure holes after etching, the LCDU (curve 1853) decreases at higher doses. This relationship indicates that the fitting parameters of eg CD distribution associated with failure and non-failure features (eg contact holes) will be different. The fitted CD distribution can be used, for example, to determine a process window. In this embodiment, model 1710 captures the relationship between LCDU and dose more accurately because model 1710 is a combined distribution of the first and second distributions as discussed above. Accordingly, statistical parameters or properties of the fitted distribution 1710 may be used, for example, to more accurately determine the process window of a patterning process.

In an embodiment, the method 1700 may further include procedures P1711 and P1713 configured to determine the process window PW. In one embodiment, P1711 includes extracting statistical properties of the fitted probability distribution 1710 (eg, PDF1 of FIG. 17 ) associated with non-failure features. For example, the statistical characteristics may be mean, standard deviation, skewness, or other statistics related to contact holes printed on the substrate.

In one embodiment, in procedure P1713 , the extracted statistical properties of the fitted distribution 1710 are employed to determine a process window. For example, the process window includes a range of dose-focus values that allow features to be printed on a substrate with no defects or very few defects (eg, one defective feature in a million features). An exemplary method of determining a process window is discussed in US Patent Application No. 62/980,068, filed February 21, 2020, which is incorporated herein by reference in its entirety.

As previously discussed, the method 1700 has several applications. Accordingly, the method 1700 may be further modified to include improving the patterning process. For example, the method 1700 may include imaging a desired pattern comprising another plurality of features on another substrate via a patterning apparatus; obtaining an image after development of the imaged pattern; executing first and second probability distribution functions using the post-development image to classify some of the features in the ADI as post-etch defective; and adjusting the etching conditions based on the classified features so that the imaged pattern does not fail after etching.

In another exemplary application, the method 1700 may be further modified or used to tune a lithographic process to reduce the failure rate of ADI features after etching, wherein the tuning includes adjusting dose, focus, or both. do. In still other applications, the method 1700 can be used to determine whether an additional filtering step on the resist layer should be performed to reduce the failure rate of ADI features after etching. In another application, the method 1700 may be used to determine whether an additional disquiet or punch-through step should be performed to reduce the failure rate of ADI features after etching. In another application, the method 1700 may be used during mass manufacturing to inspect ADI features to determine whether a lithographic apparatus meets specified criteria for printing. In another application, the method 1700 may be used to rework a given substrate or lot of substrates prior to etching, based on failure rates.

In one embodiment, using a two-part model, a system may be configured to determine a fraction of features that will fail after etching based on ADI measurements. In one embodiment, the system is a metrology tool (eg, the SEM of FIGS. 28 and 29 ) that captures a post-developed image (ADI) of the substrate at a given location, the post-developed image comprising a plurality of features- ; and a processor (eg, 104 of FIG. 30 ) configured to determine failure rates based on the ADI. In one embodiment, the processor (eg, 104 ) is configured to execute a model (eg, 1710 of FIG. 17 ) for determining failure rates of a plurality of features of the ADI that will fail after etching. In an embodiment, the model is based on (i) a first probability distribution function configured to estimate a distribution of physical property values for non-failure holes, and (ii) physical property values of all of the plurality of features of the ADI. a combination of a second probability distribution function configured to determine failure rates.

In one embodiment, the system further comprises a patterning device (eg, FIG. 1 , and FIGS. 31-34 ) configured to image a desired pattern including a plurality of features on the substrate. The processor (eg, 104 ) receives the ADI of the imaged substrate via the metrology tool; run a first probability distribution (eg, fitted PDF1) and a second probability distribution (eg, fitted PDF2) to determine failure rates of features of the ADI; and tune the patterning apparatus to reduce the failure rates of the features based on the features having relatively higher failure rates. In one embodiment, the processor (eg, 104 ) may be configured to tune the dose or focus via a knob/setting of the patterning device.

In one embodiment, the processor (eg, 104 ) determines whether an additional filtering step on the resist layer should be performed to reduce the failure rate of ADI features after etching; to determine whether an additional dishing or punch-through step should be performed to reduce the failure rate of the ADI features after etching; or during mass manufacturing, the lithographic apparatus may be further configured to inspect the ADI features to determine whether it meets specified criteria for printing.

In one embodiment, the metrology tool (eg, FIGS. 28 and 29 ) includes a scanning electron microscope (SEM). SEM measures the following physical properties: average CD of multiple instances of feature of interest in ADI; directional CD of the feature of interest in ADI; Curvature variance of the feature of interest in ADI; or measure at least one of the CD obtained at multiple metrology tool thresholds for each feature of interest.

As mentioned herein, random stochastic failures (interchangeably referred to as defects) can significantly affect the performance of EUV lithographic printing. Identifying failures may be done after the lithography step or after the etching step. There are many algorithms that use SEM images to classify failures of features such as contact holes after development. The criteria for such failure classification are based on common-sense interpretation of SEM images. For example, the failure criterion may be SEM contrast or critical dimension (CD). The methods discussed above, in one embodiment, provide improved faulty classification and predictions of failures based on ADI. Additionally, methods are provided for estimating the failure rate from the CD distribution of contact holes.

As discussed above, existing methods have some limitations. For example, defect classification can be calibrated based on the capture rate of programmed defects, or by comparing defect rates before and after etching. Programmed defects were shown to be statistically different from random defects, see, for example, the aforementioned publication P. De Bisschop.

The methods discussed herein provide improved defect classification based on training data of repeated SEM measurements of ADI and AEI at the same location as described in the previous methods. The methods herein lead to successful classification of, for example, 93.5% of holes for error prone FEM conditions.

A general disadvantage of predicting failure rates across defect classifications is that little information is collected and the defect classification cannot be evaluated visually. Prediction by tail CD (ie, tail of CD distribution) is empirical and may depend on the process being performed on the substrate.

In one embodiment, the method of defect classification discussed herein shows that features that will fail after etching (eg, contact holes) differ to some extent in a static ADI image (eg, an SEM image of an ADI). uses the fact In the present invention, it has been observed that the difference in ADI images between failing and non-failing contact holes, for example after etching, is small, and in many cases may be barely visible to the naked eye. Furthermore, through an exemplary experiment, ADI SEM damage (eg, reproducibility of measurements of the same ADI or CD difference between first and second SEM “repro”) was significantly greater for failed contact holes. was observed to be large. In one embodiment, exposing the same location on the wafer two or more times to capture two different SEM measurements is referred to as an SEM “repro”. Accordingly, in one embodiment, a method is provided for using dynamic SEM information to differentiate between failed and non-failed contact holes, or to improve failure prediction with this information.

As discussed herein (eg, with respect to FIG. 3 ), performing SEM metrology after lithography damages the resist on the substrate, causing the resist to shrink or redeposit excess carbon into the resist. These damages affect the CD of features on the substrate as measured by SEM, especially when measurements are performed with SEM leaf (eg, taking two SEM images at the same location ADI). For example, in Figure 3, contact hole defects that disappeared after etching are caused by the remaining layer of resist inside the contact hole. Therefore, the geometries of the failed and non-failed holes after etching are different. Therefore, both shrinkage and carbon redeposition can be different, which yields a larger difference between SEM leaf images of failed holes after etching. In one embodiment, a method (eg, of FIG. 19 ) for determining that features are defective based on leaf measurements of the same ADI feature is provided. In one embodiment, the leaf measurements include two SEM images of the ADI from which different signatures for failure and non-failure contact holes can be determined.

19 is a flowchart of a method 1900 for determining a defect attribute of a feature in an image after development (ADI) according to one embodiment. In one embodiment, the defect attribute is whether the ADI feature is defective or non-defective, or the probability of failure associated with the ADI feature. The method 1900 determines that there is a defect based on a defect criterion, which may be, for example, CDs of the first and second images. The method 1900 includes the following procedures, discussed in detail below.

Procedure P1901 includes exposing the ADI feature to an electron beam or a charged particle beam to produce a first image of the ADI feature, wherein the ADI feature is a structure in a resist material. In one embodiment, exposing comprises exposing a plurality of ADI features to produce a first plurality of images. For example, a SEM image of multiple frames (eg, 4, 5, 6, ..., 50) may be captured corresponding to different locations of the ADI feature on the substrate.

Procedure P1903 includes re-exposing the ADI feature to an electron beam or a charged particle beam to generate a second image of the ADI feature. In one embodiment, the step of re-exposing includes a plurality of ADI features to generate a plurality of second images. For example, an SEM image of multiple frames (eg, 4, 5, 6, ..., 50) may be captured corresponding to identical locations of the ADI feature on the substrate captured at P1901.

In one embodiment, the electron beam is generated via a scanning electron microscope (SEM), and the first image and the second image are SEM images. In one embodiment, the first set of images of the ADI feature (eg, a contact hole in the resist) may be captured at different locations on the substrate. Also, a second set of images of the ADI (eg, contact hole) may be captured at the same locations on the substrate (as used for the first set of images).

In one embodiment, SEM projects high-energy electrons (also known as e-beams) onto a resist, which is a polymer, causing damage to the resist. For example, the resist may shrink, thereby increasing the ADI feature (eg, contact hole) size. In addition, SEM can deposit carbon that changes the CD of the ADI feature. SEM measurements can have different effects on ADI features with different geometries, due to different amounts of resist to which electrons can react. For example, referring to Figure 3, a certain amount of resist remaining in a contact hole will have a different geometry than another contact hole having no or relatively little resist in the contact hole. As such, for a partially filled contact hole, electrons may react with the resist at the bottom and walls of the contact hole. On the other hand, for a contact hole where there is no resist at the bottom of the hole, electrons can only react with the resist walls of the contact hole. As such, the damage to the resist of a filled contact hole will be different from an unfilled or relatively underfilled contact hole, thereby causing different geometric changes after SEM measurement. In another example, since the electron distribution in the circular contact hole and the elliptical contact hole will be different, the SEM damage caused to the resist of the circular contact hole will be different from the damage caused to the resist of the elliptical contact hole or other non-circular contact hole. can This is why a first SEM measurement performed to measure an ADI feature, followed by another SEM measurement, will give different results, for example the second SEM image may be slightly different of the same ADI feature compared to the first SEM image. It can have geometry.

Procedure P1905 includes determining a defect attribute of the ADI feature based on a physical characteristic (eg, CD) associated with the first image and the second image. For example, a first CD may be extracted from the first image, and a second CD may be extracted from the second image. In one embodiment, the physical property is a critical dimension, or pixel intensity associated with an ADI feature (eg, a contact hole).

In one embodiment, the defect attribute may be binary (eg, whether the ADI feature is defective or non-defective). In one embodiment, the defect attribute may be a probability of failure associated with an ADI feature (eg, characterized by a CD PDF fitted to failure data). In one embodiment, determining the defect attribute comprises: extracting a first feature from the first image and a second feature from the second image; determining whether a defect metric is violated based on a difference between the first characteristic and the second characteristic; and in response to the defect metric being violated, classifying the ADI feature as defective.

In one embodiment, the first image captured in the first exposure comprises a plurality of images of the ADI feature. Similarly, the second image of the re-exposure step includes a plurality of images of the same ADI feature. For example, a metrology tool such as a scanning electron microscope (SEM) scans an object (eg, an ADI feature) with a focused electron beam. To obtain reliable images with the least possible artifacts, the SEM may scan the object multiple times (eg, 8 times). The response of each scan is called a 'frame', and an averaged image can be generated by averaging over multiple 'frames'. Thus, multiple frames of an ADI feature (eg, a first set of frames) may be obtained from a first exposure step, and another multiple frames of an ADI feature (eg, a second set of frames) may be from the second exposure step. Thus, in one embodiment, the averaged image may be used as the first image from the first exposure and the second averaged image may be used as the second image from the re-exposure. In yet another case, all or a subset of the frames of the first set of frames may be considered as the first image, and all of the frames or subset of frames of the second set of frames may be considered as the second image. Accordingly, a difference (eg, CD difference, intensity difference, etc.) may be determined between all frames (or subsets) of the first set of frames and all frames (or subsets) of the second set of frames. . Those of ordinary skill in the art will understand that a frame may be represented as a pixelated image in which each pixel has a gray scale value.

In one embodiment, the determination of the difference is a physical characteristic extracted from one or more frames of a first image (eg, CD) and a physical characteristic extracted from a corresponding one or more frames of a second image (eg, CD). It involves determining the difference between For example, the first image may include four frames, and a physical characteristic (eg, CD) may be extracted from each of the four frames. For example, the extracted physical properties may be CD1, CD2, CD3 and CD4. Similarly, after the re-exposure step, the second image may include four frames, and a physical property (eg, CD) may be extracted from each of the four frames. For example, CD5, CD6, CD7 and CD8. Thus, for example, the difference between CD1 and CD5, CD2 and CD6, CD3 and CD7, and CD4 and CD8 is calculated.

In one embodiment, the defect metric is a function of a first physical characteristic of the ADI feature in the first image (eg CD1) and a second physical characteristic of the ADI feature in the second image (eg CD2) . In one embodiment, the defect metric is a bilinear function, a trained machine learning model, or a polynomial of quadratic or higher. For example, a function of two or more variables is said to be bilinear if it is linear with respect to each of those variables. The simplest example is f(x,y)=xy. In another example, the first image and the second image may include multiple frames as discussed herein. From each frame, physical properties can be extracted (eg CD1, CD2, CD3, CD4, CD5, CD6, CD7, CD8). In this case, a multivariate distribution may be adopted, wherein the multivariate distribution is a combined or combined PDF of CD1 to CD8. In the preceding example, a bivariate function is used as an example to explain concepts. However, the present invention is not limited to bivariate functions. A person skilled in the art can modify the method to include multiple frames in the first image and the second image. Further, according to the number of frames used to characterize the first image and the second image, the defect metric can be characterized by a multivariate function.

In one example, the defect metric is of the form f(CD1, CD2) < 0, where CD1 is the CD in the first SEM image of the object and CD2 is the CD of the same object in the second SEM image. One example of a defect metric is the function indicated by line 2010 in FIG. 20 .

20 is a SEM of CD values of contact holes (eg, for 10 ⁵ contact holes) under an error prone condition (eg, less than a normal dose) in FEM, according to an embodiment. It is a plot of damage. The plot shows that the SEM damage is relatively higher for CD values smaller than the nominal CD. In the present embodiment, the SEM damage is characterized by the difference in the first CD and the second CD extracted from the first SEM image and the second SEM image, respectively. As shown in Figure 20, this difference is relatively higher for CD values below 14 nm. SEM damage can be characterized in any of a variety of ways. Moving average curve 2015 of SEM damage data 2005 further indicates that SEM damage can predict failure of ADI features (eg, contact holes). For example, if the moving average of SEM damage associated with a specified range of CD values exceeds a specified damage threshold (eg, 3 nm), then the specified CD range is more likely to fail after the etch process.

In one embodiment, for example, the SEM damage information characterized by CD1 and CD2 derived from the first SEM image and the second SEM image, respectively, may be used to determine a defect classification criterion such as curve 2010. In this embodiment, the defect metric used for defect classification may be represented by curve 2010. The defect metric 2010 serves as the CD defect threshold in relation to SEM damage, which is a function of CD1 and CD2 of the same ADI feature obtained from two SEM measurements. In one embodiment, the defect metric 2010 includes defect data (eg, failed contact holes and non-failed contact holes after etching), and CD1 and CD2 extracted from the first SEM image and the second SEM image, respectively. may be established based on the values. In one embodiment, the defect metric 2010 shows that SEM damage associated with an ADI feature with a nominal CD value (characterized by CD1 and CD2 values) is greater than SEM damage associated with another ADI feature with the same nominal CD value. If high, it indicates that ADI features with higher SEM damage are relatively more likely to be defective after etching. The defect metric 2010 also represents the minimum CD threshold at which an ADI feature can be classified as defective, even if the SEM damage can be zero or close to zero. In one embodiment, the defect metric 2010 may be a bilinear function that is fitted based on measurement data. It can be understood that the bilinear function is presented as an example and does not limit the scope of the present invention. Other multivariate functions, eg 4, 8 variables, etc., may be used as the defect metric as discussed herein.

For comparison, the plot of FIG. 20 shows another defect criterion 2020. Exemplary defect criteria 2020 represent a constant CD threshold that does not depend on SEM damage. For example, this constant CD threshold 2020 may be set, for example, as discussed above with respect to FIGS. 7A and 7B . In the example of FIGS. 7A-7C , the CD threshold is set based on failure data, wherein an ADI feature having a CD value below the CD threshold can be classified as likely to fail, and having a CD value greater than or equal to the CD threshold. An ADI feature may be classified as not likely to fail. On the other hand, the defect metric 2010 based on SEM damage can more accurately classify defective features compared to the simple single-valued CD threshold 2020.

In another example, a bivariate probability density function may be employed for the defect criterion. For example, a bivariate PDF may be a combined or combined PDF of two or more variables. In one embodiment, the bivariate PDF may be determined based on the first SEM image and the second SEM image, for example as discussed with respect to FIG. 22 . The bivariate PDF may determine the probability that the first measure measures CD1 and the second measure measures CD2. In another example, the first SEM image and the second SEM may include multiple frames as discussed herein. From each frame, physical properties can be extracted (eg CD1, CD2, CD3, CD4, CD5, CD6, CD7, CD8). In this case, a multivariate distribution may be adopted, wherein the multivariate distribution is a combined or combined PDF of CD1 to CD8.

In another example, the defect metric may be a trained machine learning model (eg, CNN). The trained model comprises: (i) a plurality of image pairs, each image pair including a first image and a second image of the plurality of ADI features, and (ii) a post-etched image of the substrate corresponding to the ADI features. It can be obtained by training a machine learning model using a training data set including AEIs.

In one embodiment, training of the machine learning model comprises (a) adjusting parameters of the machine learning model such that the model determines a defect attribute of a given ADI feature based on a comparison between the first image and the second image; (b) determining whether the model determined defect attribute is within a specified range of the defect attribute of the AEI feature corresponding to the given ADI feature; and (c) in response to not being within the specified range, performing steps (a) and (b). In one embodiment, gradient descent may be employed to determine the model parameter values, which cause the model determined defect attribute to converge to the defect attribute of the AEI feature. Once trained, the trained model can be used as a defect metric or defect classification means.

21 is an example of training the machine learning model 2100 using the training data sets TD1, TD2, ..., TDn including the first images and the second images discussed above. In one embodiment, each data of the training data includes a pair of first image SEM1 and second image SEM2 and reference AEI images (not shown). In one embodiment, the reference AEI images serve as ground truth for guiding the machine learning model to correctly classify inputs as likely to fail or not likely to fail. In one embodiment, one or more ADI features (eg, contact holes, lines, etc.) may be used to generate training data. For example, the training data may be generated based on ADI features including a plurality of contact holes, a plurality of lines, and other specific structures. For each of the plurality of contact holes, and for each of the plurality of lines, a corresponding pair of SEM1 and SEM2 images may be obtained through the SEM tool. Also, for each of the plurality of contact holes and each of the plurality of lines, an AEI image may be obtained to serve as a measurement data. The output of the training of the machine learning model is the classification of the training data as likely to fail (eg, FailCH) or non-failure (eg, NotFailCH) of the ADI features, the failure being the post-etch image (AEI). ) is potentially observed. In one embodiment, the machine learning model may be a convolutional neural network or other existing neural networks that are trained using an existing training algorithm such as gradient descent. The present invention is not limited to any particular machine learning model.

22 is a flow diagram of a method 2200 for developing a model 2210 for determining failure rates of features in an image after development, according to one embodiment. In the previous example, a model was developed to predict the failure rate based on the physical properties (eg CD) of ADI features by fitting the distribution of contact holes with the following probability density function:

는 분포들의 파라미터들의 세트이며, PDF _fail 및 PDF _{no fail} 은 실패 및 실패-아닌 ADI 피처들에 대한 확률 밀도 함수들이다. 이전 실시예에서, 실패한 홀들에 대한 일반화된 극단값(GEV) 분포 및 실패-아닌 홀들에 대한

의 정규 분포가 채택되었다.In the previous equation, p _fail is the probability of failure after etching, and the vector

is the set of parameters of the distributions, PDF _fail and PDF _{no fail} are probability density functions for failed and non-failure ADI features. In the previous embodiment, the generalized extreme value (GEV) distribution for failed holes and for non-failed holes

A normal distribution of

파라미터들을 제공하지만, p _fail 은 동일하여야 한다. 이는 데이터 지점들의 수에 대해 피팅을 위한 파라미터 공간을 감소시킨다. 또한, 제 1 및 제 2 SEM 측정들은 제 1 및 제 2 분포에 대한 파라미터들

사이의 관계를 드러낼 수 있다. 관계는 피팅의 파라미터 공간을 더 감소시키는 데 사용될 수 있다.In another embodiment discussed with respect to FIG. 21 , a model was developed based on a pair of SEM images of a given ADI feature. For example, the ADI CD distribution from both the first and second SEM images is used to fit the preceding equation PDF ( CD ). In the preceding equation PDF ( CD ), the fitting of the data is ( PDF _fail and PDF _no different for the two distributions (related to _fail )

parameters, but p _fail must be the same. This reduces the parameter space for fitting over the number of data points. Also, the first and second SEM measurements are parameters for the first and second distributions.

can reveal the relationship between The relationship can be used to further reduce the parameter space of the fit.

In another example, the preceding fitting procedure of method 2200 can be modified to fit the combined distribution of CD ₁ and CD ₂ with the following probability density function:

는 피팅 프로세스를 통해 결정된 각 분포들의 파라미터들의 세트이며, p _fail 은 피팅 프로세스를 통해 결정된 실패 파라미터이다. 조합된 분포는 많은 데이터 지점들에 대해 피팅을 위한 모델 파라미터 공간을 감소시킨다. 상기 방법(2200)은 다음과 같이 더 상세히 논의된다. PDF ( CD ₁ , CD ₂ ) represents the combined distribution, vector

is a set of parameters of each distribution determined through the fitting process, and p _fail is a failure parameter determined through the fitting process. The combined distribution reduces the model parameter space for fitting over many data points. The method 2200 is discussed in more detail as follows.

Procedure P2201 is performed via a metrology tool: (i) first measurement data 2201 associated with a post-developed image (ADI) of the substrate, the ADI comprising a plurality of features, and (ii) associated with the same ADI and obtaining second measurement data 2202, the second measurement data 2202 being obtained subsequent to the first measurement. For example, the metrology tool may be an SEM, and the measurement data may be data associated with SEM images. In this example, after a first SEM image of an ADI feature is taken, a second SEM image of the same ADI feature is taken. In one embodiment, the measurement data includes physical properties of ADI features in the SEM images. In one embodiment, the measurement data may be extracted as intensity values associated with ADI features in the SEM images.

Procedure P2203 includes generating, based on the first measurement data 2201 and the second measurement data 2202 , a model 2210 for determining failure rates of features of the ADI. In one embodiment, generating the model 2210 includes adjusting values of one or more model parameters such that the metric associated with the model 2210 improves as compared to the metric associated with initial values of the model parameters. In one embodiment, as discussed herein, model 2210 determines the rate of failure of the patterning process based on failure rates of features predicted by the models for a given first measure of a given ADI and a second measure of a given ADI. It may further be used to determine the process window.

In one embodiment, generating the model 2210 includes using the first measurement data 2201 and the second measurement data 2202 to maximize the log-likelihood metric of the model, thereby increasing the failure rate parameter (eg, p _fail ) and fitting a second probability density function (PDF) associated with the complement of the failure rate parameter. In one embodiment, fitting the first probability density function comprises determining values of each model parameter of the first PDF and the second PDF by maximizing a log-likelihood metric of the model. For example, the model may be PDF ( CD ₁ , CD ₂ ) as discussed above.

)는 제 1 물리적 특성 및 제 2 물리적 특성의 조합된 분포, 및 모델 파라미터들의 제 1 세트에 의해 특징지어진다. 제 1 물리적 특성은 제 1 측정 데이터(2201)와 연계되고, 제 2 물리적 특성은 ADI의 제 2 측정 데이터(2202)와 연계된다. 제 2 PDF(예를 들어,

)는 제 1 물리적 특성 및 제 2 물리적 특성의 또 다른 조합된 분포, 및 모델 파라미터들의 제 2 세트에 의해 특징지어진다.In one embodiment, the first PDF (eg,

) is characterized by the combined distribution of the first and second physical properties, and a first set of model parameters. The first physical characteristic is associated with the first measurement data 2201 , and the second physical characteristic is associated with the second measurement data 2202 of the ADI. a second PDF (e.g.,

) is characterized by another combined distribution of the first and second physical properties, and a second set of model parameters.

In one embodiment, the first PDF comprises: a first position parameter and a second position parameter describing a shift in the bivariate distribution; and a bivariate distribution characterized by a first scale parameter and a second scale parameter describing the spread of the bivariate distribution.

In one embodiment, the second PDF includes: a third position parameter and a fourth position parameter describing a shift in the GEV distribution; a third scale parameter and a fourth scale parameter describing the spread of the GEV distribution; and a generalized extreme value (GEV) distribution characterized by a shape parameter (ξ) that describes the shape of the GEV distribution.

In an embodiment, the first measurement data 2201 is a first SEM image of the ADI, and the second measurement data 2202 is a second SEM image of the ADI. In one embodiment, the first measurement data 2201 includes first physical property values of features in a first SEM image of the ADI, and the second measurement data 2202 includes values of features in a second SEM image of the ADI. second physical property values.

In one embodiment, generating the model involves simultaneously fitting the first PDF and the second PDF to the first and second measurement data. fit the first PDF, for example, based on first physical property values of the plurality of features in the first SEM image of the ADI; Fit the second PDF based on second physical property values of the plurality of features in the second SEM image of the ADI. In one embodiment, the first PDF and the second PDF are both fitted simultaneously by maximizing the log-likelihood metric associated with the model.

In one embodiment, the fitting of the first PDF and the second PDF comprises: (a) determining a log-likelihood metric using given values of parameters of the first PDF and the second PDF; (b) determining whether the log-likelihood metric is maximized; (c) in response to not being maximized, adjust, based on the slope, values of the first set of model parameters and values of the second set of model parameters of the first PDF, and a failure rate parameter (eg, p _fail ) to do; and performing steps (a) to (c). In one embodiment, the slope is the first derivative of the log-likelihood metric for the first model parameters, the second model parameters, and the failure rate parameter.

In one embodiment, the adjusted model parameter values of the model cause the value of the failure rate parameter (eg, p _fail ) associated with the first PDF and the second PDF to be equal.

In one embodiment, the method 2200 provides a relationship between the first set of model parameters and one or more model parameters of the second set of model parameters based on the first measurement data 2201 and the second measurement data 2202 . It may further include the step of determining. The method 2200 further comprises, based on the relationship, modifying the first set of model parameters with respect to the second set of model parameters to reduce the number of the first set of model parameters or the second set of model parameters. may include The method 2200 may further include generating a model 2210 based on the modified parameters using the first measurement data 2201 and the second measurement data 2202 .

In one embodiment, the physical property is the critical dimension (CD) of the feature. In one embodiment, the physical characteristic includes: an average CD of a plurality of instances of a feature of interest in ADI; directional CD of the feature of interest in ADI; Curvature variance of the feature of interest in ADI; or CDs obtained at multiple metrology tool thresholds for each feature of interest.

In one embodiment, the directional CD includes: a CD measured along the x-direction; CD measured along the y-direction; or CD measured along the desired angle.

As discussed herein, failure rate refers to a defect condition characterized by the physical properties of an ADI feature or a corresponding AEI feature. In one embodiment, the defect condition is: omission of a feature; displacement range associated with the feature; or one or more of a tolerance range associated with the critical dimension of the feature.

As discussed herein, performing measurements with an SEM leaf can double the SEM metrology time. An alternative could be to store several subsets of frames of the SEM image, for example 2x8 or 4x4 frames. The SEM image may be a stack of 8 frames typically aligned with each other to determine an average SEM image of the ADI feature. In this embodiment, the SEM frames may be stored separately, and the first 2 to 4 frames may be analyzed from the stored SEM frames, or all 8 frames may be analyzed together, or all 8 frames may be analyzed together. can be analyzed individually. As such, 8 highly ambiguous SEM images (instead of one averaged SEM image) provide more information than an SEM averaged image of multiple frames with the same measurement. In one embodiment, a charging effect caused by an excess or shortage of electrons on the substrate being measured can affect the SEM image contrast, thereby causing differences between the SEM images. In one embodiment, compared to measuring more holes of the ADI of the substrate, it can be analyzed which of the measurement schemes provides the most added value. Accordingly, the SEM measurement data is organized and can be further used to develop a model 2210 according to the method 2200 . For example, the method 2200 can be modified to develop the model 2210 based on the various ways in which the SEM measurement data is obtained. For example, model 2210 can be developed by grouping 8 frames into 4x4 frames, where 4 frames are used to develop the model and another 4 frames are used to verify the prediction accuracy of the model. used In another example, model 2210 may be developed by grouping SEM measurement data with similar charging effects.

As discussed herein, the methods (eg, methods 1900 and 2200) have several advantages. For example, during ramp-up (eg, high-volume manufacturing (HVM)), model 2210 is based on model-predicted failure rates to reduce the number of feature failures (eg, filled contact holes). may be employed in or associated with a lithographic apparatus to tune lithographic parameters. Examples of improvements are tuning of the scanner's dose and focus, screening the resist, additional filtering steps to the resist, or other lithography related parameters. In another example, if the model 2210 predicts that the ADI feature is defective, the photoresist may be stripped or removed, the photoresist may be reapplied, and the photoresist may be re-exposed to be etched onto the substrate. Predicted defects can be prevented from occurring.

In one embodiment, accurate defect classification based on ADI may help find the root cause of AEI failures of, for example, contact holes. Also, for example, the fraction of filled contact holes can be used to evaluate whether an additional dish or punch-through should be used prior to etching to reduce the effect of filled contact holes.

In one embodiment, the methods (eg, 1700, 1900, 2200) described herein may be included as instructions in a computer-readable medium (eg, memory). For example, the non-transitory computer-readable medium, when executed by the one or more processors, may be configured to: obtain a post-developed image (ADI) of a substrate, the ADI comprising a plurality of features; generating a first portion of the model based on physical property values associated with the subset of features of the ADI; and instructions that cause tasks comprising generating a second portion of the model based on physical property values associated with the first portion of the model and all features of the plurality of features of the ADI, wherein the subset of features of the ADI includes: is distinct from other features of ADI.

In one embodiment, the non-transitory computer readable medium comprises (i) a first probability distribution function configured to estimate a distribution of physical property values for non-failure holes, and (ii) physical properties of all plurality of features of the ADI. and a model that is a combination of a second probability distribution function configured to determine failure rates based on characteristic values. In one embodiment, the model is a weighted sum of a first probability distribution function and a second probability distribution function. In one embodiment, the first probability distribution function is a normal distribution characterized by a truncated value associated with a physical property, a first position parameter describing a shift in the normal distribution, and a first scale parameter describing the spread of the normal distribution. In one embodiment, the second probability distribution function includes a second position parameter (μ) that describes the shift in the GEV distribution, a second scale parameter (σ) that describes the spread of the GEV distribution, and a shape of the GEV distribution A generalized extreme value (GEV) distribution characterized by a shape parameter (ξ).

In one embodiment, the non-transitory computer readable medium provides instructions for generating a model based on the square of values of a physical property of a subset of features by maximizing a first log-likelihood metric associated with a first probability distribution function. fitting a first probability distribution function, wherein the subset of features have physical property values greater than or equal to a physical property threshold; combining the fitted first probability distribution function and the second probability distribution function; and fitting a second probability distribution function and a relative weight associated therewith based on the physical property values of all features of the plurality of features such that, based on the combined distribution, a second log-likelihood metric associated with the combined distribution is maximized. Contains instructions that cause operations to include.

In one embodiment, a non-transitory computer readable medium includes instructions for fitting a first probability distribution function in an iterative manner. Iteration includes (a) determining a first log-likelihood metric using given values of parameters of the first probability distribution function; (b) determining whether the first log-likelihood metric is maximized; (c) in response to not being maximized, adjusting values of parameters of the first probability distribution function based on the slope, and performing steps (a) to (c). The slope is the first derivative of the first log-likelihood metric with respect to the parameters of the first probability distribution function.

In one embodiment, the non-transitory computer readable medium comprises: values of parameters of a second probability distribution function and the values of parameters of a second probability distribution function without modifying values of the parameters of the first probability distribution function based on a maximization of the second log-likelihood metric. instructions for fitting a second probability distribution function comprising determining a weight. In one embodiment, fitting of the second probability distribution function is an iterative process. The iterative process includes (a) obtaining a combined distribution of a fitted first probability distribution function and a second probability distribution function; (b) determining a second log-likelihood metric using given values of parameters of a second probability distribution function based on the combined distribution and holding values of parameters of the fitted first distribution fixed; (c) determining whether a second log-likelihood metric is maximized; (d) in response to not being maximized, adjusting values of parameters of the second probability distribution function based on the slope, and performing steps (b) to (d). The slope is the first derivative of the second log-likelihood metric with respect to the parameters of the second probability distribution function.

In one embodiment, the non-transitory computer readable medium comprises: imaging a desired pattern comprising a plurality of features on a substrate via a patterning device; obtaining an image after development of the imaged pattern; executing first and second probability distribution functions using the post-development image to classify some of the features in the ADI as post-etch defective; and, based on the classified features, adjusting etching conditions so that the imaged pattern does not fail after etching.

In one embodiment, the non-transitory computer readable medium comprises: tuning a lithographic process to reduce a failure rate of ADI features after etching, wherein tuning includes adjusting dose, focus, or both; determining whether an additional filtering step should be performed on the resist layer to reduce the failure rate of the ADI features after etching; determining whether an additional dishing or punch-through step should be performed to reduce the failure rate of the ADI features after etching; or during mass manufacturing, operations that include examining the ADI features to determine whether the lithographic apparatus meets specified criteria for printing.

In one embodiment, a computer program may be coded and implemented in a process to implement the various steps of the methods discussed herein. For example, the computer program may be configured to simulate a patterning process (eg, a lithography step, etching, resist development, etc.). Then, based on the simulation results, individual parameters are determined according to, for example, correlations between the results of different processes (eg, after resist development and after etching development) discussed in the methods described herein. It is possible to calibrate. In one embodiment, simulation-based tuning or calibration may also provide insight during manual tuning of the etch process. For example, insight relates to the effect of changes in process parameters on correlation.

As previously discussed, the present invention describes a method for quantifying the effect of short-range etch loading on the CD of features after etching. In one example, the short etch loading affects the patterns after etching. For example, the short-range loading effect characterizes the effect of neighboring features (in ADI) on the size of the feature of interest after etching. For example, the size of a centrally located contact hole is affected by the contact hole itself and its neighbors. Additionally, post-exposure processes can affect the placement of features. In one embodiment, etch loading is characterized prior to etch optimization by analyzing test structures and modeling through an OPC process. To this end, features with variable pitch and CD are printed and etched, and the etch rate is fitted empirically to describe the open area within a given circle around the point of interest.

After development of the imaged pattern on the substrate, one or more post-exposure processes are performed to transfer the pattern onto the substrate. For example, the pattern transfer process can be considered as a combination of etching and (re)deposition processes. The etching process is performed by physical sputtering and chemical etching of the material. In addition, sputtered material and/or added gas constituents ensure (re)deposition. For example, sheath voltage affects the ion-angle of the sputtering process, and u-wave power affects the density of plasma/sputter-rate. The sputter-rate of a material depends on the angle of incidence, the ion-rate, and the material composition allowing for variations in patterns. For example, fluorine gas pressure determines redeposition during post-exposure processing. In one method, the process involves first shrinking the features (“CDs”) and growing them again (with less loading) in many cycles. This allows to reduce subsequent CD fluctuations. However, comparable processes must be coordinated at every cycle to transfer the desired pattern onto the substrate. In accordance with the present invention, the methods herein are discussed in relation to an etching process. However, the present invention is not limited to the etching process, and effects associated with other post-exposure processes may be determined here.

Some existing approaches establish a relationship between ADI and AEI based on one or more parameters associated with a pattern. For example, for contact holes, relevant parameters include CD variations before and after etching and contact edge roughness (CER). CER is sensitive to SEM shot noise, for high spatial frequencies. Therefore, the size of the CER depends on the averaging of images (eg, SEM images) of the pattern employed by the contouring algorithm. Pattern transcription (eg ADI to AEI) tends to act as a convolution filter (eg smoothing), and it is not clear what relevant variations in CER will be included in the final pattern transcription. In another example, for lines, it is not clear which spatial frequency is involved in the power spectral density of the contour of the transferred pattern. Therefore, it is not clear how the averaging of the images should be applied. In some cases, the relationship between line edge roughness (LER) (a measure of variability) and average length depends on the type of resist. As such, variability metrics between different resists may not be comparable.

In an embodiment of the present invention, short-range etch loading is quantified by a measure-etch-measure experiment in which identical contact holes are imaged with SEM before and after etching. The correlation between the size of the contact hole after etching and the size of its neighbors before etching is used as a metric to quantify the intensity of the etch loading. In one embodiment, the correlation between neighbors over different distances is used as a metric for the extent to which local etch loading is relevant.

In one embodiment, ADI and AEI are SEM images of minimal features that contain a relatively large amount of noise, for example due to shot noise of the SEM image. In addition, the SEM image is a two-dimensional (2D) excitation map of a three-dimensional (3D) structure. It is not immediately clear how the 2D information in the map should be remapped to the relevant 3D information. Additionally, not all variations in a feature's ADI are relevant for predicting an AEI feature. Therefore, it is not clear to what extent the short length scale details of ADI and AEI features are relevant to quantifying the lithographic process, and which contouring methods should be used.

In one embodiment, the method described herein (discussed below) addresses effects associated with short-range loading and placement of neighboring contact holes. In one embodiment, the placement of neighboring contact holes may be described with respect to a reference grid, or a grid associated with a design layout (eg, provided in GDS format). In one embodiment, the placement is described with respect to a feature of interest. For example, moving neighboring contact holes relatively inward (eg, closer to the feature of interest) affects the CD of the central contact hole after etching. Thus, not only the size of the surrounding contact holes, but also their placement affects the patterns after etching. The present method (eg, FIG. 23A ) provides a systematic way to derive these relationships.

In one embodiment, the method of finding the ADI and AEI of relevant contour features and quantifying their transcription after etching employs canonical correlation analysis. This method can be used both to extract the relevant contour points and to quantify the transfer after etching.

In one embodiment, the ADI and AEI data used in the method may be obtained by constructing addressed SEM images of a structure on a substrate after a lithography step (eg, ADI). Next, the imaged substrate is processed using a process of interest (eg, a designated etching process). In one embodiment, after etching, SEM images at the same location are obtained based on the addressed SEM images. Also, the SEM images ADI and AEI are aligned.

In one embodiment, contours of features of interest in ADI and AEI are determined using a contour extraction algorithm. In one example, the contour extraction algorithm employs contour points or pixel intensities to describe the contour. In addition, a correlation, such as a coefficient of determination R ² between the contour points of ADI and AEI, is determined. In one embodiment, the correlation describes that the variance ratio of the linear combination of AEI contour points is described by the linear combination of the ADI contour points of the feature itself and its neighboring features. In one embodiment, the correlation determination procedure yields the optimal linear combinations of the ADI and AEI contours, and the eigen equation for determining the corresponding R ² . The method is described in more detail with reference to FIG. 23A.

23A is a flow diagram of a method 2300 for training a model configured to determine a post-etch image (AEI) based on the post-develop image (ADI). The method includes the following procedures P2301, P2303, P2305, and P2307 discussed in detail below.

Procedure P2301 includes (i) measurements of the imaged ADI features 2301 on the substrate, and (ii) obtaining measurements of post-etch image (AEI) features 2302 . The measurements of the AEI features 2302 correspond to the measured ADI features on the etched substrate. For example, the same features are measured before and after the etching process. It is understood that the method is not limited to a single ADI image or a single AEI image, and multiple ADI and AEI images may be employed.

In this disclosure, ADI feature 2301 and AEI feature 2302 are used as examples to discuss concepts. However, the present invention is not limited to ADI features or AEI features. In one embodiment, full ADI images and AEI images may be obtained without measuring specific ADI features and AEI features. Also, in one embodiment, the AEI image is not limited to a post-etch image, any other image obtained after the post-exposure step of the patterning process may be used herein and is within the scope of the present invention.

In one embodiment, the measured ADI feature 2301 and the measured AEI feature 2302 are obtained via a simulation process or metrology tool configured to generate ADI and AEI images for the input target feature. In one embodiment, the metrology tool is a scanning electron microscope (SEM) (eg, FIG. 28 ) configured to capture the ADI and AEI of the substrate. ADI includes ADI features, and AEI includes AEI features. In one embodiment, the ADI includes images obtained from first and second SEM measurements of the ADI feature prior to etching. In one embodiment, the first SEM measurement of the ADI feature is obtained by exposing the imaged substrate through an SEM tool. A second SEM measurement of the ADI feature is obtained by re-exposing the same ADI feature of the imaged substrate through the SEM tool. Similarly, the AEI includes images obtained from first and second SEM measurements of the AEI feature by exposing and re-exposing the etched substrate. The etched substrate is obtained after etching the imaged substrate.

Procedure P2303 includes assigning a first set of variables characterizing the measured ADI feature 2301 (VADI1) and a second set of variables characterizing the measured AEI feature 2302 (VAEI1). In one embodiment, the first set of variables VADI1 corresponds to a set of positions on the ADI contour of the measured ADI feature 2301 and the second set of variables VAEI1 is the AEI of the measured AEI feature 2302 Corresponds to a set of positions on the contour.

In one embodiment, the pixel intensities (eg gray scale values) of the ADI image and the pixel intensities (eg gray scale values) of the AEI image are the first set of variables VADI1 and the second set of variables Each can be used as a set VAEI1.

Procedure P2305 determines a correlation 2310 between the combination of the first set of variables of the measured ADI feature 2301 (VADI1) and the combination of the second set of variables of the measured AEI feature 2302 (VAEI1) includes In one embodiment, the combination of the first set of variables VADI1 is a linear combination, a non-linear combination, or a machine learning model. In one embodiment, the combination of the first set of variables VADI1 is a weighted sum of the first set of variables VADI1 .

In one embodiment, correlation 2310 may be determined based on canonical correlation analysis or other correlation determination methods. Combinations of these variables are considered as relevant variables to characterize, for example, ADI to AEI pattern transfer behavior. The weights may be positive values or negative values. In one embodiment, positive or negative indicates the direction of the variable, eg towards the left or right, to which the variable value should be applied. In one embodiment, positive or negative may indicate shrinkage or growth of the ADI feature. In an embodiment, the combination or one or more sub-combinations of the second set of variables VAEI1 is a linear combination, a non-linear combination, or a machine learning model. In one embodiment, the first set of variables VADI1 corresponds to a set of positions on the ADI contour of the measured ADI feature 2301 and the second set of variables VAEI1 is the AEI of the measured AEI feature 2302 Corresponds to a set of positions on the contour.

In one embodiment, the ADI features include a feature of interest and one or more neighboring features. In one embodiment, the first set of variables VADI1 comprises a first subset of variables associated with a feature of interest and a second subset of variables associated with one or more neighboring features. In one embodiment, the combination is a weighted sum of a first subset of variables associated with a feature of interest and a second subset of variables associated with one or more neighboring features. In one embodiment, the weights assigned to variables of a neighboring feature are relatively higher than variables of another neighboring feature away from the feature of interest.

24A and 24B illustrate exemplary ADI features and AEI features, respectively. In FIG. 24A , ADI includes a feature of interest ADIF1 and neighboring features ADINF1 and ADINF2 around the feature ADIF1. The first neighboring feature ADINF1 is relatively closer to the feature of interest ADIF1 than the second neighboring feature ADINF2. In one embodiment, the set of variables may be positions indicated by numbers 1 to 8 on the outline of feature ADIF1 . Similarly, another set of variables may be locations (points) on the contours of neighboring features ADINF1 and ADINF2. In one embodiment, the first set of variables VADI1 may be a set of variables of ADIF1, ADINF1 and ADINF2 (eg, contour points on the contour of the feature). In one embodiment, the second set of variables VAEI1 may be locations (points) on the contour of the AEI feature AEIF1 . In one embodiment, the AEI feature AEIF1 may be created after etching the ADI feature ADIF1 . In one embodiment, the neighboring features ADINF1 and ADINF2 may affect the shape and size of the AEI feature AEIF1. Thus, in one example, most correlated with a linear combination of variables of AEIF1 (as discussed in method 2300 herein), second most correlated, third most correlated (and so on) associated with ADIF1 A linear combination of defined variables (eg, contour points) may be determined. In another example, ADIF1 and neighboring features ADINF1 and ADINF2 most (second most, third most, etc.) correlated with a linear combination of variables of AEIF1 (as discussed in method 2300 herein) A linear combination of variables associated with can be determined.

In one embodiment, determining the correlation 2310 comprises (i) a first set of parameters associated with a combination of a first set of variables (VADI1), and (ii) a second set of variables (VAEI1). computing a correlation (2310) using the given values of the second set of parameters associated with the combination; determining whether the correlation 2310 is maximized (or is within a specified range); in response to the correlation 2310 not being maximized (or not within the specified range), adjusting the given values of the first set of parameters and the second set of parameters until the correlation 2310 is maximized. include In one embodiment, adjusting the given values of the first set of parameters and the second set of parameters is performed until the correlation 2310 is maximized (or within a specified range).

로서 표현될 수 있고,

은 변수들의 제 1 세트(VADI1)의 1 이상의 조합을 나타낸다. 일 예시에서,

은 매트릭스로서 표현될 수 있고,

은 하나보다 많은 숫자를 포함한다. 본 예시에서,

은 스칼라이고,

및

은 상관관계를 최대화하도록 최적화된다. 최적화 프로세스는 상관관계가 (국부적) 최대이고 발견된 다수 조합들에 대응하는 하나보다 많은 솔루션을 제공할 수 있다. 일 실시예에서,

은 변수들의 제 1 세트(VADI1)의 각 변수와 연계된 가중치들을 나타낸다. 일 실시예에서, AEI(예를 들어, 도 24b의 AEIF1, 또는 AEI 이미지의 픽셀 세기들)와 연계된 변수들의 제 2 세트(VAEI1)는 벡터

로서 표현될 수 있고,

은 변수들의 제 2 세트(VAEI1)의 1 이상의 조합을 나타낸다. 일 실시예에서,

은 변수들의 제 1 세트(VADI1)의 각 변수와 연계된 가중치들을 나타낸다.In one embodiment, the first set of variables VADI1 associated with the ADI (eg, the ADI feature ADIF1 , ADINF1 , or ADINF2 of FIG. 24A , or pixel intensities of the ADI image) is a vector

can be expressed as

denotes one or more combinations of the first set of variables (VADI1). In one example,

can be expressed as a matrix,

contains more than one number. In this example,

is a scalar,

and

is optimized to maximize the correlation. The optimization process may provide more than one solution for which the correlation is (locally) maximal and corresponds to the multiple combinations found. In one embodiment,

denotes the weights associated with each variable of the first set of variables VADI1. In one embodiment, the second set of variables VAEI1 associated with the AEI (eg, AEIF1 in FIG. 24B , or pixel intensities of the AEI image) is a vector

can be expressed as

denotes one or more combinations of the second set of variables (VAEI1). In one embodiment,

denotes the weights associated with each variable of the first set of variables VADI1.

및

에 대한

·

및

·

의 상호 정보의 최적화(일 실시예에서, 최대화)를 수반한다. 일 실시예에서, 상호 정보의 최적화는 분석적 접근 또는 수치적 접근에 기초하여 결정될 수 있다. 일 실시예에서, 고유 방정식들이 ADI의 변수들의 조합과 AEI의 변수들의 조합 사이의 상관관계(2310)를 최대화하기 위해 사용될 수 있다. 일 실시예에서, 상호 정보는 변수들의 조합의 공간에 걸친 확률 밀도 함수의 관점에서 결정될 수 있다. 일 실시예에서, 예를 들어 유한 데이터 세트에 대해, 확률 밀도들은 연산되지 않을 수 있고, 대신에 정규화된 히스토그램들이 사용될 수 있다. 상호 정보를 추산하기 위한 예시적인 접근법은 참고문헌 A. Kraskov, H. Stogbauer 및 P. Grassberger, "Estimating mutual information"(Phys. Rev. E 69, 2004)에서 찾아볼 수 있으며, 이는 본 명세서에서 그 전문이 인용참조된다.In one embodiment, determining the correlation 2310 includes:

and

for

·

and

·

It entails optimization (in one embodiment, maximization) of the mutual information of In one embodiment, the optimization of mutual information may be determined based on an analytical approach or a numerical approach. In one embodiment, eigen equations may be used to maximize the correlation 2310 between the combination of variables in ADI and the combination of variables in AEI. In one embodiment, the mutual information may be determined in terms of a probability density function over space of combinations of variables. In one embodiment, for example, for a finite data set, probability densities may not be computed, and normalized histograms may be used instead. An exemplary approach for estimating mutual information can be found in A. Kraskov, H. Stogbauer and P. Grassberger, "Estimating mutual information" (Phys. Rev. E 69, 2004), which is herein incorporated by reference. The full text is referenced by reference.

와

의 비선형 함수들 사이의 상관관계(예를 들어, R ² )를 최대화하는 단계를 포함한다. 이 함수들은

및

의 명백한 분석적 표현들일 수 있지만, 벡터 입력에서 스칼라를 생성하는 뉴럴 네트워크들일 수도 있다. 예를 들어, 상관관계(2310)를 결정하는 예시적인 방법은 "Andrew 2013에 의한 Deep Canonical Correlation Analysis"에 기초할 수 있으며, 이는 본 명세서에서 그 전문이 인용참조된다. 예를 들어, 최적화 프로세스는 뉴럴 네트워크의 계수들에 대한 최대화를 수반한다. 일 예시에서, 상관관계(2310)는 다음 상관관계(R ² ) 수학식을 사용하여 연산될 수 있다:In one embodiment, the combination may be a non-linear combination of variables. In the case of non-linearity, the step of determining the correlation 2310 is

Wow

maximizing the correlation (eg, R ² ) between the nonlinear functions of . these functions

and

may be explicit analytic representations of , but also neural networks that generate a scalar from a vector input. For example, an exemplary method for determining correlation 2310 may be based on “Deep Canonical Correlation Analysis by Andrew 2013”, which is incorporated herein by reference in its entirety. For example, the optimization process involves maximizing the coefficients of a neural network. In one example, correlation 2310 may be computed using the following correlation ( R ² ) equation:

을 갖는

의 미리 정의된 스칼라 함수이고, g는 파라미터들

을 갖는

의 스칼라 함수이다. f 및 g에 대한 예시들은 선형 함수(

), 이차 함수, 고차 다항식, 가중치들

및

을 갖는 기계 학습 네트워크들을 포함한다.In the preceding equation, cov and var represent the covariance and variance of the variable, and f is the parameters

having

is a predefined scalar function of , and g is the parameters

having

is a scalar function of Examples for f and g are linear functions (

), quadratic functions, higher-order polynomials, weights

and

machine learning networks with

For linear combinations, correlation 2310 is computed using the following correlation ( R ² ) equation:

은 변수들의 제 1 세트(VADI1)의 벡터 형태이고,

은 파라미터들의 제 1 세트에 대응하며,

은 변수들의 제 1 세트(VADI1)의 1 이상의 조합을 포함하고,

은 변수들의 제 2 세트(VAEI1)의 벡터 형태이며,

은 파라미터들의 제 2 세트에 대응하고,

은 변수들의 제 2 세트(VAEI1)의 1 이상의 조합을 포함하며, R ² 의 분자는

와

사이의 공분산을 나타내고, 분모는

의 분산과

의 분산의 곱을 나타낸다.In the previous formula,

is the vector form of the first set of variables (VADI1),

corresponds to the first set of parameters,

comprises one or more combinations of the first set of variables (VADI1),

is the vector form of the second set of variables (VAEI1),

corresponds to the second set of parameters,

comprises one or more combinations of the second set of variables (VAEI1), wherein the numerator of R ² is

Wow

represents the covariance between, and the denominator is

dispersion of

represents the product of the variance of .

및

에 대한 R ² 의 미분을 0으로 설정하는 단계를 포함하며, 이는 다음 표현식들을 산출한다:In one embodiment, determining the correlation 2310 includes:

and

setting the derivative of R ² with respect to 0 to 0, which yields the following expressions:

의 고유벡터를 결정하는 고유 방정식이다. 제 2 수학식(B)에서, α는 비례 연산자(proportionality operator)이다. 일 실시예에서, 상관관계(R ² )는

및

의 길이와 독립적이다. 일 실시예에 따르면, 앞선 수학식들은 가장 큰 고유값(R ² ₁ )을 갖는 벡터

및 대응하는 벡터

가 가장 잘 전사하는 선형 조합들임을 나타낸다. 가장 큰 고유값(R ² ₂ )을 갖는 벡터

및 대응하는 벡터

는 두 번째로 잘 전사하는 선형 조합들이고, 그 밖에도 마찬가지이다. 일 실시예에서,

및

는 벡터들이고

는 스칼라이며, 수학식들(A 및 B)에 대한 다수 솔루션들은 앞선 수학식의 최적화 동안(예를 들어, 상관관계를 최대화하기 위해) 결정되고, 이에 따라 상이한 변형 모드들을 얻는다.The first formula (A) is the eigenvalue of R ² and

It is an eigen equation that determines the eigenvector of . In the second equation (B), α is a proportionality operator. In one embodiment, the correlation ( R ² ) is

and

independent of the length of According to an embodiment, the above equations are the vector having the largest eigenvalue R ² ₁ .

and the corresponding vector

are the linear combinations that transcribe best. Vector with largest eigenvalue ( R ² ₂ )

and the corresponding vector

are the second best transcribed linear combinations, and so on. In one embodiment,

and

are vectors

is a scalar, and multiple solutions to equations (A and B) are determined during optimization of the preceding equation (eg, to maximize correlation), thus obtaining different transformation modes.

및

의 최소 길이이다. 이러한 0이 아닌 고유값들 중에서, 제한된 수의 고유값들만이 0보다 훨씬 큰 값들을 갖는 R ² 에 대응한다. 따라서, 제한된 수의 윤곽 속성들만이 에칭 후 전사로 간주된다. 나머지 조합들은 고려되지 않을 수 있다. 일 실시예에서, 벡터들

및

을 검사함으로써, 전달된 변수들의 물리적 의미를 찾고 이에 따라 파라미터 공간을 감소시킬 수 있다.In one embodiment, the number of non-zero eigenvalues is at most vectors

and

is the minimum length of Of these non-zero eigenvalues, only a limited number of eigenvalues correspond to R ² having values much greater than zero. Therefore, only a limited number of contour properties are considered post-etch transfer. Other combinations may not be considered. In one embodiment, vectors

and

By examining , we can find the physical meaning of the passed variables and reduce the parameter space accordingly.

In one embodiment, eigenvalue analysis may be used to determine post-etch transfer properties for a selected focus and dose condition. In one example, the first set of variables associated with ADI VADI1 may be the distances of 16 contour points to the center of mass of the contact hole for the contact hole of interest and its 6 neighbors. Thus, the first set of variables VADI1 contains 16·(1 + 6) = 112 variables. The second set of variables associated with the AEI (VAEI1) may be the distances of the 16 contour points to the center for the contact hole of the AEI of interest. Accordingly, the second set of variables VAEI1 comprises 16 variables. In one embodiment, exemplary properties of pattern transfer according to a linear combination of these variables are further illustrated in Figures 25A-25F. In one embodiment, non-zero eigenvalues and corresponding eigenvectors (eg, obtained from correlation equations A and B above) are also analyzed and described with reference to FIGS. 25A-25F .

25A-25F show optimal transcription of linear combinations of a first set of variables, as determined by eigen equations (eg, Equations A and B above). In each sub-figure in the upper right, solid lines (eg, referred to as WT_ADICH1, WT_ADICH2, WT_ADICH3, WT_ADICH4, WT_ADICH5, and WT_ADICH6) correspond to weights of the feature of interest (eg, ADICH1). In each sub-figure in the upper right, dashed lines (eg, collectively referred to as WT_NH1, WT_NH2, WT_NH3, WT_NH4, WT_NH5, and WT_NH6, respectively) indicate the neighboring features around the feature of interest (eg, ADICH1). corresponding to the weights. 25a and 25b show a linear combination of variables corresponding to the translation of features, eg, of holes in the x and y directions. 25C shows a linear combination of variables corresponding to the CD of features affected by the CD (in ADI) of the central hole and its neighbors, eg, AEI CD. 25E and 25F show a linear combination of variables corresponding to elongation of a feature determined by e.g. elongation of a centrally located ADI hole and the size and displacement of neighboring holes. 25D shows a linear combination of variables corresponding to the triangulation of features, eg, an AEI feature affected by the translation and CD of neighboring features in ADI.

Referring to FIG. 25A , the weights WT_ADICH1 of each contour point on the ADI feature ADICH1 are plotted against an angle (right graph). In addition, the weights WT_NH1 of each contour point on neighboring ADI features (eg, NCH) are plotted against angle (right graph). The graph on the left shows an exemplary arrangement of ADI contact holes in a polar representation. In the arrangement of contact holes (left graphs), the dashed contour RCH1 corresponds to a desired feature or a reference feature having contour points with a weight of zero. In this example, inward excursions to dashed contour RCH1 (eg solid contours ADICH1 ) correspond to negative weights, and outward excursions to dashed contour RCH1 (eg, Solid contours ADICH1] correspond to positive weights. Similarly, the lower graphs show weights (WT_AEICH1) of the AEI contact hole (AEICH1) and the AEI contact hole (AEICH1).

In this example, referring to FIGS. 25A-25F , linear combinations are obtained based on eigenvalue analysis. In this example, the largest eigenvalue obtained using the first set of variables (eg, 112 variables) and the second set of variables (eg, 16 variables) is R ² = 0.67 ( see Fig. 25a). The corresponding weights of the AEI variables represent the shift to the left of the contact hole (see Fig. 25a (bottom left)). In the ADI and AEI graphs (left graphs), the radius of the left edge (eg, 0° to 180°) has a positive weight, and the radius of the right edge (eg, 180° to 360°) is has a negative weight. The solid line contact hole AEICH1 in FIG. 25A (bottom left) is displaced to the left with respect to the reference contact hole RCH1 (dotted circle), and the weights WT_AEICH1 are (minus) as shown in FIG. 25A (bottom right). is the cosine. 25A (top row), the corresponding weights WT_ADICH1 and WT_NCH1 of the ADI variables are the shift of the (central) contact hole ADICH1 to the left relative to the reference hole RCH1 (dotted circle) and the neighboring holes ( NCH) showed no effect. It is observed that the variables associated with the neighboring contact holes NCH have weights WT_NCH1 of approximately zero.

Similarly, FIGS. 25B-25F illustrate weights associated with linear combinations of variables (eg, a first set of variables and a second set of variables), corresponding ADI and AEI feature transforms, and ADI transforms. A method corresponding to this AEI conversion is shown.

25A and 25B show a first eigenvalue (eg, 0.67) corresponding to combinations of a first set of variables and a second set of variables describing the translation of ADI and AEI features, respectively, according to one embodiment. and a second eigenvalue (eg, 0.64). The first and second eigenvalues correspond to translation of the contact holes ADICH1 and ADICH2 in the first direction and the second direction, respectively. In this example, the translations are the x-direction and the y-direction. 25A and 25B show that translations in both directions can be measured equally well, as the correlation R ² is approximately equal in both directions.

25C illustrates a third eigenvector corresponding to the combination of the first set of variables and the second set of variables describing the CD of ADI and AEI features, respectively, according to one embodiment. In addition, weights (WT_ADICH3, WT_NCH3, and WT_AEI3) associated with a linear combination of variables are plotted. An AEI-related eigenvector (eg, a linear combination of the second set of variables) indicates that approximately equal weights are assigned to each variable in the combination of the second set of variables. For example, the variables may be the radius (or diameters) of the contact hole measured at different orientations. Then, the radius corresponds to the CD of the AEI feature, and the average diameter length is equal to the average CD of the AEI feature. Similarly, an ADI eigenvector (eg, a linear combination of a first set of variables) corresponds to the CD of an ADI contact hole minus the average CD of neighboring holes with some weighting factor.

In one embodiment, further examination of the eigenvector (of Fig. 25c) also reveals that the placement of neighboring contact holes around contact hole ADICH3 affects the CD of AEI feature AEICH3. To understand the impact, CDs of AEI features of interest (eg, contact hole located in center of AEI) are plotted against CDs of ADI features of interest (eg, contact hole located in center of ADI) configured (see Fig. 26A). 26A shows that there is a positive correlation between the two CD parameters of ADI and AEI, however, there is significant spread in the data because the correlation ( R ² ) is 0.22. In the second plot of FIG. 26B , the CDs of the AEI feature of interest are plotted against the average CDs of the neighbors of the ADI features of interest. The plot reveals a negative correlation with a correlation ( R ² ) of 0.14. This is the local etch loading mentioned earlier. In other words, if all of the neighbors are relatively large, there will be many byproducts produced by the etching process, and there is less etchant available for the feature of interest (eg, a centrally located contact hole in an ADI). This local etch loading effect slows the etch rate and makes the AEI contact holes smaller than desired. It should be emphasized that the correlations according to this embodiment, eg the present eigen equation, correct for correlations in plotted data. For example, the corrected correlation between the hole size and the size of its neighbors is much smaller, eg R ² =0.006 and positive.

25E and 25F show a fourth and fifth corresponding combinations of a first set of variables and a second set of variables describing stretching (in both directions) of ADI and AEI features, respectively, according to one embodiment. Eigenvectors are illustrated. Also, the weights (WT_ADICH5, WT_NCH5 and WT_AEI5) associated with the linear combination of variables are plotted in FIG. 25E . The weights (WT_ADICH6, WT_NCH6 and WT_AEI6) associated with another linear combination of variables are plotted in FIG. 25F . The elongation of the contact holes AEICH5 and AEICH6 is affected by the elongation of the contact holes ADICH5 and ADICH6, respectively. Additionally, the elongation is affected by the CD and placement of neighboring holes of ADICH5 and ADICH6. In this example, since the two corresponding eigenvalues of R ² are approximately equal, stretching in any direction is equally well accounted for. However, since R ² =0.34, about 2/3 of the AEI stretch may not be accounted for by ADI measurements. Thus, the value of the correlation R ² indicates that other factors influence the height or that the ADI or AEI height measurements are prone to noise.

25D illustrates a sixth eigenvector corresponding to a combination of a first set of variables and a second set of variables describing the triangulation of ADI and AEI features, respectively, according to one embodiment. Also, the weights (WT_ADICH4, WT_NCH4 and WT_AEI4) associated with the linear combination of variables are plotted in FIG. 25D . In this example, the weights associated with ADI features are the size and displacement of neighboring holes around feature ADICH4. Since R ² =0.08, this indicates that most of the triangulation measured after etching may not be accounted for by the ADI contours.

In one embodiment, other eigenvalues below the specified correlation threshold are, for example, R ² ≤ 0.01. Correlation values below a specified threshold may indicate that ADI measurements may not account for AEI measurements and that the measured ADI's corresponding contour attributes (eg, triangulation) may not be relevant for prediction of AEI contours. .

Procedure P2307 includes training, based on correlation 2310, training model 2320 by including one or more sub-combinations of a first set of variables VADI1 having correlation values within a specified correlation threshold, , the model 2320 is used to determine the AEI features for the input ADI features.

As discussed herein, the one or more sub-combinations of the first set of variables VADI1 are linear combinations, non-linear combinations, or machine learning models. In an embodiment, the one or more sub-combinations of the first set of variables VADI1 are a weighted sum of the first set of variables VADI1 , the weights being positive or negative values. In an embodiment, the one or more sub-combinations of the second set of variables VAEI1 are linear combinations, non-linear combinations, or machine learning models. In one embodiment, a sub-combination may not be equal to a mathematical 'subset', but may be an average over all contour points.

In one embodiment, the one or more sub-combinations characterizes an amount of deformation of the ADI contour of the measured ADI feature 2301 caused by a process performed on the measured ADI feature 2301 . In one embodiment, the amount of deformation is the difference between a given position of the ADI contour and a corresponding position of the AEI contour. In one embodiment, the amount of deformation is characterized by a linear combination of the first set of variables VADI1.

In one embodiment, determining the model 2320 comprises (a) determining whether a sub-combination of the first set of variables VADI1 and the correlation 2310 of the sub-combination exceed a specified correlation threshold. to do; (b) in response to the sub-combination being exceeded, including the sub-combination in the model 2320; and (c) in response to the sub-combination not being exceeded, selecting another sub-combination of the first set of variables (VADI1); and repeating steps (a) to (c) for a specified number of iterations or until the sub-combination is exhausted. In one embodiment, the specified correlation threshold is greater than 0.01. For example, FIGS. 25A-25F show selected sub-combinations with R ² values of 0.08 or greater.

In one embodiment, the one or more sub-combinations include: translation of the measured ADI feature 2301 in a designated direction; the critical dimension of the measured ADI feature 2301; elongation in a designated direction of the measured ADI feature 2301; Triangulation of the measured ADI feature 2301; and rotation of the measured ADI feature 2301 . Examples of sub-combinations and corresponding transcription properties are discussed herein with respect to FIGS. 25A-25F .

The preceding method (eg, method 2300 ) involves image-based determination of feature transformations due to one or more processing on features, and various applications related to a lithographic process, a post-exposure process, a metrology apparatus, and It has other applications.

In one embodiment, the method 2300 may be used to quantify the placement of features and the effect of short-range etch loading. For example, a combination based on a first set of variables VADI1 associated with neighboring features of a feature of interest in ADI may be determined. Using the method 2300 , the effect of placement variations of neighboring features on CD (eg, features around a feature of interest in ADI) and placement of an AEI feature can be integrated. In one embodiment, eigenvalue analysis is used to quantify the effect of next nearest neighbors and beyond on the AEI contour. For example, the influence due to neighboring features within 180 nm of the feature of interest in ADI may be used. In one embodiment, the combinatorial parameters characterizing ADI CD, the displacement of each feature, and the elongation of the feature may be used to quantify the short-range etch loading effect.

27A illustrates a feature of interest (eg, a contact hole at the center of a pattern) and neighboring features (eg, NH1, NH2, and NH3) within the radius of the sphere of influence around the feature of interest in ADI. The fraction of variance of R ² of the AEI batch is illustrated. For example, line 2710 represents the correlation R ² associated with the x-placement of AEI as distance from a feature of interest (radius=0) increases in ADI, and dashed line 2720 represents interest in ADI. Shows the correlation ( R ² ) associated with the y-disposition with increasing distance from the feature (radius=0). Line 2710 indicates that the feature of interest (or the first set of variables associated therewith) accounts for about 62% of the x-placement variation of the AEI feature and about 60% of the y-location variation of the AEI feature.

Also, line 2710 indicates that the first neighboring feature NH1 (or a linear combination of a sub-set of the first set of variables) is 4.2% of the variance of R ² (eg, points on the y-axis and NH1 ) difference between them). Similarly, the next neighboring feature (NH2) accounts for 0.3% ^of the variance of R2 . Thus, more distant features account for fewer variations than the feature of interest itself. Similarly, line 2720 represents the fraction of variance in the y-placement variation accounted for by the feature of interest (radius=0) and more distant features (NH1, NH2 and NH3) in ADI.

27B is illustrated by a feature of interest (eg, a contact hole in the center of a pattern) and neighboring features (eg, NH1, NH2, and NH3) within the radius of the sphere of influence around the feature of interest in ADI. Describe the fraction of variance of R ² of AEI CD.

For example, line 2730 is the correlation R ² described by all variables (eg, all of the first set of variables) as the distance from the feature of interest (radius=0) increases in ADI. , and dashed line 2740 represents the correlation R ² associated with the CD related set of variables. Line 2740 represents the amount of correlation R ² that is accounted for with increasing distance from the feature of interest (radius=0) in ADI. Line 2730 indicates that all variables of the feature of interest account for about 23.5% of the CD variation of the AEI feature.

Line 2740 also indicates that the sub-set of variables associated with the CD of the feature of interest accounts for about 23.5% of the variance. Line 2730 also indicates that the first neighboring features NH1 (or a linear combination of a sub-set of the first set of variables) represent about 27% of the variance of R ² (eg, points on the y-axis and difference between NH1). In this example, neighboring features NH1 include six features equidistant from the central feature (see, eg, FIGS. 25A-25F ). Neighbor feature(s) further away from neighbor features NH1 NH2 account for about 0.5%, and neighbor feature further away from neighbor feature NH3 accounts for another 0.7%. Similarly, line 2740 represents the fraction of variance in CD variation of the AEI feature explained by the feature of interest (radius=0) and more distant features (NH1, NH2 and NH3) in ADI. In this example, the exact radius of influence that affects the AEI feature depends on the pattern density in the ADI. Also note that 11% of the AEI CD variation (the difference between line 2730 and line 2740) is due to placement variations associated with neighboring features. This batch variation is 1/5 of the fraction of the total variance accounted for.

Accordingly, FIGS. 27A and 27B show exemplary quantifications of short-range etch loading. Thus, for example, employing the present method using all parameters associated with ADI, short-range etch loading quantification can be improved (eg, by 11%). In other words, the present method will account for more variations and causes of these variations than existing methods, for example by neighboring features and transcription properties (eg placement, CD, translation, triangulation, etc.). can The identified cause can be further used, for example, to reduce CD fluctuations after development. In other words, the method can help determine the causes of CD and batch variations and post-development transfer scheme, and predict what variations will be after etching, deposition, or other post-exposure process based on ADI. .

In one embodiment, another application of the method 2300 may be monitoring process quality. For example, the method 2300 monitors process quality based on a selected combination of a first set of variables of ADI features and its sensitivity to focus and exposure conditions; and adjusting one or more process parameters to maintain process quality within a specified range. In one embodiment, monitoring comprises measuring relevant ADI contour properties (eg, a sub-combination of variables of the first set of variables) associated with the tip of the pattern; and based on the measured sensitivity and correlation, adjusting one or more process parameters to improve the transfer of tip-to-tip features from the ADI feature to the AEI feature.

For example, the behavior of etching for tip-to-tip structures depends substantially on the shape of a feature in the resist, which in turn is sensitive to focus. Additionally, when SEM is used to measure the feature shape of a resist, the resist shape changes the waveform generated by the SEM. By the method 2300, which parameters of the SEM waveform correlate with the efficiency of the tip-to-tip transfer process can be directly evaluated. These tip-to-tip features can then be closely monitored in high-volume manufacturing (HVM) of semiconductor chips. In addition, these features can be used in a (empirical) simulator of the etching process and thus can be used to optimize the process during ramp-up.

In one embodiment, SEM measurement recipes may be refined to monitor the HVM process. In one embodiment, the SEM recipe includes SEM tool settings for measuring tip-to-tip structures after development and after etching. In one embodiment, the SEM measurement recipe remains the same for both ADI and AEI measurements to inspect tip-to-tip structures. In addition, a set of variables that characterize tip-to-tip structures can be correlated to determine post-etch transfer properties. For example, whether the transcription is good (eg, within a threshold limit) and how much it fluctuates. A tip-to-tip structure may behave differently than structures such as, for example, holes or lines, which means that a tip-to-tip structure is focus-sensitive and contains a lot of 3D information (eg, over the entire height). CD variation across the Thus, setting up SEM recipes to measure tip-to-tip structures is not a trivial task.

According to an embodiment, the method 2300 of the present specification may be applied as follows. The tip-to-tip structure can be measured after development and the contour can then be extracted. In one embodiment, ADI measurements may be performed at different SEM settings, and contour information may be extracted at each SEM threshold. Next, AEI measurements may be performed to analyze the corresponding AEI contour in relation to the ADI contours. For example, correlating variations of ADI and AEI contours to determine SEM settings that best describe AEI variations based on ADI contour information. As such, the SEM setup can be quantified in terms of how good the SEM setup is for measuring tip-to-tip structures, which in turn can speed up the inspection process using the SEM tool.

In one embodiment, the procedure for determining the correlation P2305 is based on a sparsity constraint. A sparsity constraint refers to excluding one or more variables from a first set of variables or a second set of variables, or both.

In one embodiment, any contour may be used and characterized by a first set of variables. For a very detailed contour (eg, characterized by multiple contour points), most of the variance of the contour points will be determined by, for example, SEM shot noise or small resist variations. By optimizing the correlation (eg, maximizing R ² ), only relevant linear combinations of variables (eg, weighted sums of all variables) will be selected, and combinations involving eg SEM noise will not be propagated. .

Additionally, the selected combinations provide information that other shapes (eg, contour deformation at relatively higher frequencies) are not transferred after etching and thus are not relevant to quantifying the etching behavior. In one embodiment, the sparsity constraint may be introduced in a systematic manner by setting the sparsity constraint in the optimization. A sparsity constraint may be a set of equations that automatically sets the weights of irrelevant data points to zero. Sparsity constraints can be enforced by adding a regularization term to the optimization (eg including the L1-norm of the weights α and β ).

In one embodiment, the method 2300 may further include, based on the correlation, adjusting metrology tool settings to allow the correlation to improve. One example of adjusting metrology tool settings is discussed above with respect to a tip-to-tip structure. However, the present invention is not limited to a specific structure. The SEM setting may be determined for any other structures such as contact holes, lines, rectangles, or other features of interest to be printed on the substrate. In one embodiment, the metrology tool settings include at least one of: e-beam intensity, angle of incidence, voltage contrast, SEM threshold, pixel size, scan rate, or number of frames.

In one embodiment, the method 2300 may further comprise, based on the correlation, adjusting one or more parameters associated with the contour extraction algorithm to cause the correlation to improve.

In one embodiment, FIG. 23C shows a flow diagram of a method 2370 of optimizing metrology recipes based on a correlation between ADI and AEI. For example, optimization involves perturbating a metrology tool or algorithm related settings (eg, number of frames, SEM voltage, thresholds) to maximize correlation R ² . In one embodiment, the optimization is performed by perturbing only metrology-related parameters to best measure local variability. In another example, optimization of a metrology recipe involves perturbing the patterning process-related parameters as well as the metrology-related parameters to best measure the process variation. For example, the patterning process related parameters may be overlay, average CD of the pattern, focus, dose, and the like. In one embodiment, procedure P2371 includes obtaining ADI and AEI data 2372 without perturbing process parameters. In one embodiment, procedure P2371 includes acquiring ADI and AEI data 2374 by perturbing process variables (eg, overlay, CD, dose, focus). Procedure P2373 includes extracting contours (eg, via a contour extraction algorithm) from the ADI and AEI images. Procedure P2305 may be performed to determine correlation 2310 between ADI and AEI as discussed above in method 2300 . Procedure P2377 includes determining parameters of a contour extraction algorithm or a metrology recipe to allow correlation 2310 to be improved (eg, maximized).

In one embodiment, systematic optimization of SEM recipes and contour extraction algorithms may be performed as follows. For example, perform the procedures of method 2300 (eg, via the computer system of FIG. 30 ) to determine a correlation between measured ADI and AEI as discussed above. Also, perturbed the parameters of the SEM recipe or contour extraction algorithm to determine whether the perturbed parameters improve the correlation R ² between ADI and AEI. By perturbation, settings that maximize the correlation R ² can be obtained. As an example, SEM thresholds may be varied. For example, SEM thresholds such as 30%, 50% and 70% may be used for ADI and/or AEI measurements. In one example, using multiple thresholds while measuring AEI features can increase the correlation ( R ² ) for stretch and triangular transcription properties. Using multiple thresholds to measure ADI may increase the correlation ( R ² ) for translational and CD transcriptional properties.

Also, parameters of the contouring algorithm related to extracting contours from SEM images may be varied. Additionally, multiple variables of the first set of variables (eg, the radius of the contact hole measured at different orientations) may be varied such that it is determined to maximize the correlation R ² . The number of variables may be 8 or 32. Reducing the number of variables may be determined to significantly reduce the correlation R ² , so 8 spokes may be too few to describe the contour. On the other hand, increasing the number of variables to 32 can only slightly increase the correlation R ² . As such, it can be concluded that 16 variables may be sufficient to describe the contour for a given contact hole size.

In one embodiment, a range of process variations may be implemented. For example, a range of overlay values can be programmed by modifying the mask pattern. For example, as shown in FIGS. 23D and 23E , the mask patterns 2390 and 2395 include an array of contact holes. The overlay can be programmed by shifting the contact hole, or the average CD can be perturbed by increasing the size of the contact hole. For example, in the mask pattern 2390 , the contact hole 2391 is shifted to the right at a desired position (dashed line). In the mask pattern 2395, the contact hole 2396 is increased in size with respect to the desired size (dashed line). The mask pattern 2390 or 2395 may be used to fabricate a physical mask and to image a substrate. As such, for example, a shifted contact hole (corresponding to hole 2391) is imaged on the substrate. Using a metrology tool (eg, SEM), capture an ADI image of this imaged substrate. It also etches the imaged substrate and captures the AEI of the etched substrate. Overlay is measured using image AEI at nearby locations for different overlay conditions (eg, overlay in the range of -10 nm to 10 nm). Then, an average contour or unit cell may be determined for each overlay condition in both ADI and AEI. ADI and AEI data based on different overlay conditions is an example of data 2374 . Once data 2374 is obtained, further procedures of method 2370 of FIG. 23C are performed, for example, a metrology recipe that maximizes the correlation between ADI and AEI (e.g., an SEM setup or contour extraction algorithm) parameters) can be determined. As discussed herein, parameters of a metrology recipe may be, for example, e-beam intensity, angle of incidence, voltage contrast, SEM threshold, pixel size, scan rate, number of frames, or a combination thereof. In one embodiment, one or more parameters associated with contour extraction algorithms may be modified.

In one embodiment, as discussed herein, repeated SEM measurements to capture the ADI and AEI are performed at the SEM location. In another embodiment where test boards are used to obtain data 2374 , ADI and AEI may not be performed in the same location. Thus, in the present invention, metrology recipe optimization is not only applicable to measure local variability, but also refers to process related variations such as overlay.

In one embodiment, the method 2300 includes adjusting parameters associated with a resist process or etching process such that the patterning process yield is greater than a specified yield threshold through simulation of the patterning process and the etch process using correlation. include more

In one embodiment, the method 2300 further comprises adjusting parameters related to the lithographic process such that, through simulation of the patterning process using correlation, a performance metric of the lithographic apparatus is within a specified performance threshold. In an embodiment, the parameters of the patterning process include dose or focus conditions set via the lithographic apparatus.

In one embodiment, the method 2300 may be modified to train a model configured to determine a post-etch image (AEI) based on the post-development image (ADI). For example, the correlation is determined based on gray scale values of pixels of ADI and AEI. In one embodiment, the method comprises: obtaining (i) an ADI of the imaged substrate, and (ii) a post-etch image (AEI) after etching the imaged substrate; determining a correlation between the combination of the first set of variables of the ADI and the second set of variables of the AEI, the first and second sets of variables being gray scale values of the ADI and the AEI, respectively; and based on the correlation, training the model by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, wherein the model is used to determine an AEI for the input ADI. includes Accordingly, procedures P2305 and P2307 may be modified to regard the first set of variables as gray scale values of pixels in the full ADI and the second set of variables as gray scale values of pixels in the full AEI.

In one embodiment, a metrology tool (eg, FIG. 28 ) is provided that is configured to adjust metrology tool settings based on a correlation between ADI and AEI. In one embodiment, the metrology tool comprises: a beam generator configured to measure ADI features after imaging the substrate and AEI features after etching the substrate; and a processor (eg, processor 100 ) configured to determine a setting based on a correlation between the ADI and the AEI measured via the e-beam.

In one embodiment, the processor obtains a correlation between the measured ADI feature and the measured AEI feature corresponding to the measured ADI feature printed on the etched substrate - the correlation is that the measured ADI feature is an AEI feature based on a combination of variables that characterize the way it is transformed into - ; Based on the correlation, it may be configured to adjust settings of the metrology tool such that the correlation is improved. The settings may be determined based on a derivative of the correlation for each setting, wherein the derivative represents an improvement in the correlation per setting of the metrology tool.

In one embodiment, the metrology tool is a scanning electron microscope (SEM). In an embodiment, the settings of the metrology tool include values of at least one of: e-beam intensity, angle of incidence, voltage contrast, SEM threshold, pixel size, scan rate, or number of frames. In one embodiment, the beam generator is an electron beam generator.

23B is a flow diagram of a method 2350 of determining a post-etch image (AEI) based on a post-development image (ADI) using a trained machine learning model 2210 ( FIG. 22 ) or 2320 ( FIG. 23A ). The method includes the following procedures P2352 and P2354 discussed in detail below.

Procedure P2352 includes obtaining the ADI of the substrate. For example, ADI may be obtained through a metrology tool such as SEM as discussed herein. Procedure P2354 includes, via the trained model 2210 or 2320, determining the AEI by inputting the ADI to the trained model and outputting the ADI. In one embodiment, for example, as discussed in FIGS. 22 and 23A , the trained model provides a correlation between a combination of a first set of variables of a measured ADI and a combination of a second set of variables of a measured AEI. It is obtained by training based on The correlation is within the specified correlation threshold.

In one embodiment, as discussed above, the correlation is (i) a first set of parameters associated with a combination of a first set of variables, and (ii) a second set of parameters associated with a combination of a second set of variables. compute a correlation using the two sets of given values; determine whether the correlation is maximized; In response to the correlation not being maximized, the determination is made by adjusting the given values of the first set of parameters and the second set of parameters until the correlation is maximized.

In one embodiment, the trained model: (a) determines whether a correlation of sub-combinations and sub-combinations of first and second sets of variables exceeds a specified correlation threshold; (b) in response to the sub-combinations being exceeded, including the sub-combination in the model; (c) in response to the sub-combinations not being exceeded, select another sub-combination of the first set of variables; obtained by repeating steps (a) to (c) for a specified number of iterations or until the sub-combination is exhausted.

In one embodiment, as discussed above, the combination or one or more sub-combinations of the first set of variables is a linear combination, a non-linear combination, or a machine learning model. In one embodiment, the combination of the first set of variables is a weighted sum of the first set of variables, wherein the weights are positive or negative values. In one embodiment, the combination of the second set of variables is a linear combination, a non-linear combination, or a machine learning model. In one embodiment, the ADI comprises an ADI feature, the AEI comprises an AEI feature corresponding to the ADI feature, and the AEI feature is determined via a trained model.

In one embodiment, the trained model includes: translation of features in ADI in a designated direction; critical dimensions of features in ADI; elongation of a feature in the ADI in a specified direction; Triangulation of features in ADI; or determine one or more of the rotations of the features in the ADI.

In one embodiment, the processor may further comprise instructions stored in the processor configured to adjust, based on the correlation, one or more parameters associated with the contour extraction algorithm to cause the correlation to be improved. For example, as discussed above, 16 variables may be sufficient to obtain an improved correlation associated with a given contact hole as discussed above.

In one embodiment, one or more combinations of variables include: translation of the measured ADI feature in a designated direction; the critical dimension of the measured ADI feature; elongation in a specified direction of the measured ADI feature; Triangulation of measured ADI features; and rotation of the measured ADI feature.

In one embodiment, a non-transitory computer readable medium is provided comprising instructions that, when executed by one or more processors, cause tasks including the procedures of methods 2200, 2300, or 2400 discussed above. In one embodiment, the non-transitory computer readable medium may be embodied in a metrology tool, computer hardware system, lithographic apparatus, or other systems associated with a patterning process. Such a non-transitory computer readable medium improves the patterning process, metrology results and overall yield of the patterning process.

In one embodiment, the methods discussed above (eg, method 400 , 900 , 1700 , 2200 or 2300 ) may be implemented via a processor (eg, 104 of computer system 100 ). In one embodiment, a computer program product comprises a non-transitory computer readable medium having instructions recorded thereon, which when executed by a computer implement the procedures of the methods discussed herein.

In some embodiments, the inspection apparatus may be a scanning electron microscope (SEM) that yields an image of a structure (eg, some or all of the structure of a device) that is exposed or transferred onto a substrate. 28 shows one embodiment of an SEM tool. After the primary electron beam EBP emitted from the electron source ESO is converged by the condensing lens CL, it passes through the beam deflector EBD1, the E x B deflector EBD2, and the objective lens OL to focus to irradiate the substrate PSub on the substrate table ST.

When the substrate PSub is irradiated with the electron beam EBP, secondary electrons are generated from the substrate PSub. The secondary electrons are deflected by the E x B deflector (EBD2) and detected by the secondary electron detector (SED). For example, with continuous movement of the substrate PSub by the substrate table ST in the other of the X or Y directions, the electron beam EBP by the beam deflector EBD1 in the X or Y direction A two-dimensional electron beam image can be obtained by detecting electrons generated from the sample in synchronization with repeated scanning or two-dimensional scanning of the electron beam by the beam deflector EBD1.

A signal detected by a secondary electron detector (SED) is converted into a digital signal by an analog-to-digital (A/D) converter (ADC), and the digital signal is transmitted to an image processing system (IPU). In one embodiment, the image processing system (IPU) may have a memory (MEM) that stores all or part of the digital images for processing by the processing unit (PU). A processing unit (PU) (eg, specially designed hardware or a combination of hardware and software) is configured to transform or process the digital images into datasets representing the digital images. Additionally, the image processing system IPU may have a storage medium STOR configured to store digital images and corresponding datasets in a reference database. A display device DIS may be connected with an image processing system IPU, allowing an operator to perform necessary operations of the equipment with the aid of a graphical user interface.

As noted above, SEM images can be processed to extract contours that describe edges of objects representing device structures in the image. Then, these contours are quantified via a CD-like metric. Thus, images of device structures are typically compared and quantified via a simple metric such as edge-to-edge distance (CD) or simple pixel differences between images. Conventional contour models that detect edges of objects in an image to measure CD use image gradients. Indeed, these models rely on strong image gradients. In practice, however, images are typically noisy and have discrete boundaries. Techniques such as smoothing, adaptive thresholding, edge-detection, erosion and dilation can be used to process the results of image gradient contour models to resolve noisy and discontinuous images, but , which will ultimately lead to low-resolution quantification of high-resolution images. Thus, in most cases, mathematical manipulation of images of device structures that reduce noise and automate edge detection leads to loss of resolution of the image, leading to loss of information. Consequently, the result is a low-resolution quantification that corresponds to a simple representation of a complex high-resolution construct.

Thus, for example, whether the structures are in a latent resist image, in a developed resist image, or transferred to a layer on a substrate, for example by etching, a patterning process that can preserve resolution and account for the general shape of the structures is thus developed. It is desirable to have a mathematical representation of the structures created using or expected to be created using (eg, circuit features, alignment marks or metrology target portions (eg, grating features), etc.). In the context of lithography or other patterning processes, a structure may be a device or part thereof being fabricated, and the images may be SEM images of the structure. In some cases, the structure may be a feature of a semiconductor device, eg, an integrated circuit. In this case, the structure may be referred to as a pattern comprising a plurality of features of a semiconductor device or a desired pattern. In some cases, the structure is an alignment mark or portion thereof (eg, alignment) used in an alignment measurement process to determine alignment of an object (eg, a substrate) with another object (eg, a patterning device). lattice of marks), or a metrology target or part thereof (eg, a lattice of a metrology target) used to measure parameters of the patterning process (eg overlay, focus, dose, etc.) . In one embodiment, the metrology target is, for example, a diffraction grating used to measure overlay.

29 schematically shows another embodiment of the inspection device. The system is used to inspect a sample 90 (such as a substrate) on a sample stage 88 , including a charged particle beam generator 81 , a condenser lens module 82 , a probe forming objective lens module 83 , charged particles a beam deflection module 84 , a secondary charged particle detector module 85 , and an image forming module 86 .

A charged particle beam generator 81 generates a primary charged particle beam 91 . The condensing lens module 82 condenses the generated primary charged particle beam 91 . The probe forming objective lens module 83 focuses the focused primary charged particle beam to the charged particle beam probe 92 . The charged particle beam deflection module 84 scans the formed charged particle beam probe 92 across the surface of the region of interest on the sample 90 fixed to the sample stage 88 . In one embodiment, the charged particle beam generator 81 , the collecting lens module 82 and the probe forming objective lens module 83 , or their equivalent designs, alternatives or any combination thereof, are combined to scan charged particles together. A charged particle beam probe generator that generates a beam probe 92 is formed.

The secondary charged particle detector module 85 is configured to emit secondary charged particles 93 from the sample surface (possibly along with other reflected or scattered charged particles from the sample surface) when bombarded by the charged particle beam probe 92 . ) to generate a secondary charged particle detection signal 94 . The image forming module 86 (eg, computing device) is coupled with the secondary charged particle detector module 85 to receive a secondary charged particle detection signal 94 from the secondary charged particle detector module 85 , thereby to form at least one scanned image. In one embodiment, secondary charged particle detector module 85 and image forming module 86, or equivalent designs, alternatives or any combination thereof, together are bombarded by charged particle beam probe 92 An image forming apparatus is formed that forms a scan image from the detected secondary charged particles emitted from the receiving sample 90 .

In one embodiment, the monitoring module 87 is coupled to the image forming module 86 of the image forming apparatus to monitor the patterning process using the scanned image of the sample 90 received from the image forming module 86; control, etc., and/or derive parameters for patterning process design, control, monitoring, and the like. Accordingly, in one embodiment, the monitoring module 87 is configured or programmed to cause execution of the methods described herein. In one embodiment, the monitoring module 87 comprises a computing device. In one embodiment, the monitoring module 87 provides the functionality of the present disclosure and includes a computer program encoded in a computer readable medium that forms or is disposed within the monitoring module 87 .

In one embodiment, as with the electron beam inspection tool of FIG. 28 that uses a probe to inspect the substrate, the current in the system of FIG. 29 is significantly greater compared to a CD SEM as shown in FIG. 28, for example. , the probe spot may be large enough to speed up the inspection. However, the resolution may not be as high as compared to CD SEM due to the large probe spot. In one embodiment, the inspection apparatus discussed above may be a single beam or multi-beam apparatus without limiting the scope of the present invention.

For example, SEM images from the system of FIG. 28 or 29 can be processed to extract contours that describe edges of objects representing device structures in the image. These contours are then quantified via CD-like metrics in user-defined cut-lines. Thus, images of device structures are typically compared and quantified via metrics such as edge-to-edge distance (CD) measured in extracted contours or simple pixel differences between images.

30 is a block diagram illustrating a computer system 100 that may be helpful in implementing the methods and flows disclosed herein. Computer system 100 includes a bus 102 or other communication mechanism for conveying information, and a processor 104 (or multiple processors 104 and 105) coupled with bus 102 for processing information. . Computer system 100 also includes main memory 106 coupled to bus 102 , such as random access memory (RAM) or other dynamic storage device that stores information and instructions to be executed by processor 104 . do. Main memory 106 may also be used to store temporary variables or other intermediate information in the execution of instructions to be executed by processor 104 . Computer system 100 further includes a read only memory (ROM) 108 or other static storage device coupled to bus 102 that stores static information and instructions for processor 104 . A storage device 110 , such as a magnetic or optical disk, is provided and coupled to the bus 102 to store information and instructions.

Computer system 100 may be coupled, via bus 102 , to a display 112 , such as a cathode ray tube (CRT) or flat panel or touch panel display that presents information to a computer user. An input device 114 comprising alphanumeric and other keys is coupled to the bus 102 to communicate information and command selections to the processor 104 . Another type of user input device communicates directional information and command selections to processor 104 , and cursor control, such as a mouse, trackball, or cursor direction keys, for controlling cursor movement on display 112 . : 116). This input device has two degrees of freedom in a first axis (eg x) and a second axis (eg y), which are typically two axes that allow the device to specify positions in a plane. Also, a touch panel (screen) display may be used as the input device.

Portions of a process may be performed by the computer system 100 in response to the processor 104 executing one or more sequences of one or more instructions contained in the main memory 106 , according to one embodiment. These instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110 . Execution of the sequences of instructions contained within main memory 106 causes processor 104 to perform the process steps described herein. Also, more than one processor in a multi-processing arrangement may be employed to execute sequences of instructions contained within main memory 106 . In an alternative embodiment, hard-wired circuitry may be used in combination with or instead of software instructions. Accordingly, the disclosure herein is not limited to any particular combination of hardware circuitry and software.

The term “computer-readable medium” as used herein refers to any medium that participates in providing instructions to the processor 104 for execution. Such media can take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks such as storage device 110 . Volatile media includes dynamic memory, such as main memory 106 . Transmission media include coaxial cable, copper wire, and optical fiber, including wires including bus 102 . In addition, the transmission medium may take the form of an acoustic wave or a light wave, such as wavelengths generated during radio frequency (RF) and infrared (IR) data communication. Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, a hard disk, magnetic tape, any other magnetic medium, CD-ROM, DVD, any other optical medium, Punch card, paper tape, any other physical medium having a pattern of holes, RAM, PROM, and EPROM, FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or a computer including any other medium readable by the

Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may initially be stored on a magnetic disk of a remote computer (bear). The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 may receive the data on the telephone line and convert the data to an infrared signal using an infrared transmitter. An infrared detector coupled to the bus 102 may receive data carried in an infrared signal and place the data on the bus 102 . Bus 102 passes the data to main memory 106 where processor 104 retrieves and executes instructions. Instructions received by main memory 106 may optionally be stored in storage device 110 before or after execution by processor 104 .

Computer system 100 also preferably includes a communication interface 118 coupled to bus 102 . A communication interface 118 couples to a network link 120 that is coupled to a local network 122 to provide two-way data communication. For example, communication interface 118 may be an integrated services digital network (ISDN) card or a modem that provides a data communication connection to a corresponding type of telephone line. As another example, communication interface 118 may be a local area network (LAN) card that provides a data communication connection to a compatible LAN. A wireless link may also be implemented. In any such implementation, communication interface 118 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

Typically, network link 120 provides data communication to other data devices over one or more networks. For example, network link 120 may provide a connection through local network 122 to data equipment operated by a host computer 124 or an Internet Service Provider (ISP) 126 . In turn, the ISP 126 provides data communication services over a worldwide packet data communication network, now commonly referred to as the “Internet” 128 . Local network 122 and Internet 128 both use electrical, electromagnetic or optical signals to carry digital data streams. Signals over various networks, and signals on network link 120 via communication interface 118 that carry digital data to and from computer system 100 are exemplary forms of carrier waves that carry information.

Computer system 100 may send messages and receive data, including program code, over network(s), network link 120 and communication interface 118 . In the Internet example, server 130 may transmit the requested code for an application program over Internet 128 , ISP 126 , local network 122 , and communication interface 118 . One such downloaded application may provide, for example, the lighting optimization of this embodiment. The received code may be executed by the processor 104 when received and/or stored in the storage device 110 or other non-volatile storage for later execution. In this way, the computer system 100 may obtain the application code in the form of a carrier wave.

31 schematically depicts an exemplary lithographic projection apparatus that may be used with the techniques described herein. The device is:

- an illumination system IL, which conditions the radiation beam B, which in this particular case also comprises a radiation source SO;

- a first object table (for example) provided with a patterning device holder for holding the patterning device MA (for example a reticle) and connected to a first positioner for accurately positioning the patterning device with respect to the item PS , patterning device table) (MT);

- a second object table (substrate) provided with a substrate holder holding a substrate W (eg a resist-coated silicon wafer) and connected to a second positioner for accurately positioning the substrate with respect to the item PS table) (WT); and

- a projection system (“lens”) PS (eg, a projection system) for imaging the irradiated portion of the patterning device MA onto a target portion C (eg comprising one or more dies) of the substrate W for example, refractive, catoptric or catadioptric optical systems].

As shown herein, the apparatus is configured to be transmissive (ie, has a transmissive patterning device). However, in general it may be of a reflective type (with a reflective patterning device), for example. The apparatus can employ different kinds of patterning devices with typical masks; Examples include a programmable mirror array or LCD matrix.

A source SO (eg, a mercury lamp or excimer laser, LPP (laser generated plasma) EUV source) generates a beam of radiation. For example, this beam is fed to the illumination system (illuminator) IL, either directly or after crossing a conditioning means such as a beam expander (Ex). The illuminator IL may comprise adjustment means AD for setting the outer and/or inner radial magnitudes (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution within the beam. It will also typically include various other components such as an integrator IN and a capacitor CO. In this way, the beam B incident on the patterning device MA has the desired uniformity and intensity distribution in its cross-section.

31 , the source SO may be within the housing of the lithographic projection apparatus (as is often the case where the source SO is, for example, a mercury lamp), although it may be remote from the lithographic projection apparatus, It should be noted that the radiation beam it generates may enter the device interior (eg, with the aid of suitable directing mirrors); This latter scenario is often where the source SO is an excimer laser (eg, based on KrF, ArF or F ₂ lasing).

The beam B then intercepts the patterning device MA which is held on the patterning device table MT. Having traversed the patterning device MA, the beam B passes through the lens PS, which focuses the beam B on the target portion C of the substrate W. With the aid of the second positioning means (and the interferometric means IF), the substrate table WT can be moved precisely, for example to position a different target part C in the path of the beam B. . Similarly, the first positioning means can be arranged relative to the path of the beam B, for example after mechanical retrieval of the patterning device MA from a patterning device library or during scanning. MA) can be used to accurately position the In general, the movement of the object tables MT, WT can be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning). , which is not clearly shown in FIG. 31 . However, in the case of a stepper (as opposed to a step-and-scan tool), the patterning device table MT can only be connected or fixed to a short-stroke actuator.

The tool shown can be used in two different modes:

- In step mode, the patterning device table MT remains essentially stationary, and the entire patterning device image is projected onto the target portion C at one time (ie with a single “flash”). Then, the substrate table WT is shifted in the x and/or y direction so that different target portions C can be irradiated by the beam B;

- In scan mode, basically the same scenario applies except that a given target part C is not exposed with a single "flash". Instead, the patterning device table MT is movable in a given direction (the so-called “scan direction”, for example the y direction) at a speed of v, such that the projection beam B is directed to scan over the patterning device image. ; Concurrently, the substrate table WT is moved simultaneously in the same or opposite direction at a speed V = Mv, where M is the magnification of the lens PS (typically, M = 1/4 or 1/5). In this way, a relatively wide target portion C can be exposed without degrading the resolution.

32 schematically shows another exemplary lithographic projection apparatus 1000 , which includes:

- a source collector module (SO) providing radiation;

- an illumination system (illuminator) IL configured to condition the radiation beam B (eg EUV radiation) from the source collector module SO;

- a support structure (eg mask table) configured to support a patterning device (eg mask or reticle) MA and connected to a first positioner PM configured to precisely position the patterning device (MT);

- a substrate table (eg wafer table) configured to hold a substrate (eg resist coated wafer) W and connected to a second positioner PW configured to precisely position the substrate (eg wafer table) ( WT); and

- a projection system (eg comprising one or more dies) configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (eg comprising one or more dies) of the substrate W For example, a reflective projection system (PS).

As shown herein, the apparatus 1000 is of a reflective type (eg employing a reflective mask). It should be noted that, since most materials are absorptive within the EUV wavelength range, the patterning device may have multilayer reflectors comprising, for example, a multi-stack of molybdenum and silicon. In one example, the multi-stack reflector has 40 layers of molybdenum and silicon pairs, with each layer being a quarter wavelength thick. Even smaller wavelengths can be created with X-ray lithography. Because most materials are absorptive at EUV and x-ray wavelengths, flakes of patterned absorptive material on the patterning device topography (eg, TaN absorber on top of the multilayer reflector) may or may not be printed (positive resist) or not printed (negative). resist) defines the location of the features.

Referring to FIG. 32 , the illuminator IL receives the extreme ultraviolet radiation beam from the source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, converting a material having at least one element having at least one emission line within the EUV range, such as xenon, lithium or tin, into a plasma state. In one such method, commonly referred to as laser-generated plasma (“LPP”), the plasma can be created by irradiating a fuel, such as droplets, streams, or clusters of material, with a pre-emitting element with a laser beam. The source collector module SO may be part of an EUV radiation system including a laser (not shown in FIG. 32 ) that provides a laser beam to excite the fuel. The resulting plasma emits output radiation, for example EUV radiation, which is collected using a radiation collector disposed in the source collector module. For example, if a CO2 laser is used to provide a laser beam for fuel excitation, the laser and source collector module may be separate entities.

In this case, the laser is not considered to form part of the lithographic apparatus and the radiation beam is passed from the laser to the source collector module, for example with the aid of a beam delivery system comprising suitable directing mirrors and/or a beam expander. . In other cases, the radiation source may be an integral part of the source collector module, for example if the radiation source is a discharge generating plasma EUV generator, commonly referred to as a DPP radiation source.

The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. In general, at least the outer and/or inner radial magnitudes (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the illuminator can be adjusted. The illuminator IL may also include various other components, such as facetted field and pupil mirror devices. The illuminator may be used to condition the radiation beam to have a desired uniformity and intensity distribution in the cross-section of the radiation beam.

The radiation beam B is incident on a patterning device (eg mask) MA held on a support structure (eg mask table) MT and is patterned by the patterning device. After being reflected from the patterning device (eg mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. . With the aid of the second positioner PW and the position sensor PS2 (for example an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT is, for example, in the path of the radiation beam B It can be precisely moved to position the different target portions (C). Similarly, the first positioner PM and another position sensor PS1 can be used to accurately position the patterning device (eg mask) MA with respect to the path of the radiation beam B. . Patterning device (eg, mask) MA and substrate W may be aligned using patterning device alignment marks M1 , M2 and substrate alignment marks P1 , P2 .

The illustrated apparatus 1000 may be used in at least one of the following modes:

1. In step mode, the support structure (eg mask table) MT and substrate table WT remain essentially stationary, while the entire pattern imparted to the radiation beam is applied to the target portion C at one time. ) onto the image (ie, a single static exposure). Thereafter, the substrate table WT is shifted in the X and/or Y direction so that different target portions C can be exposed.

2. In the scan mode, the support structure (eg mask table) MT and the substrate table WT are scanned synchronously while the pattern imparted to the radiation beam is projected onto the target portion C [i.e. , single dynamic exposure]. The speed and direction of the substrate table WT relative to the support structure (eg, mask table) MT may be determined by the magnification (reduction) and image reversal characteristics of the projection system PS.

3. In another mode, the support structure (eg mask table) MT holds the programmable patterning device so that it remains essentially stationary, wherein the pattern imparted to the radiation beam is applied onto the target portion C. The substrate table WT is moved or scanned while being projected onto the . In this mode, generally a pulsed radiation source is employed, and the programmable patterning device is updated as needed after every movement of the substrate table WT, or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography using a programmable patterning device, such as a programmable mirror array of a type as mentioned above.

33 shows the apparatus 1000 in greater detail including a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained within an enclosing structure 220 of the source collector module SO. EUV radiation emitting plasma 210 may be formed by a discharge generating plasma radiation source. EUV radiation may be produced by a gas or vapor, such as Xe gas, Li vapor or Sn vapor, in which a very hot plasma 210 is created to emit radiation within the EUV range of the electromagnetic spectrum. The ultra-hot plasma 210 is generated, for example, by an electrical discharge that causes an at least partially ionized plasma. For efficient generation of radiation, a partial pressure of Xe, Li, Sn vapor or any other suitable gas or vapor, for example 10 Pa, may be required. In one embodiment, a plasma of excited tin (Sn) is provided to produce EUV radiation.

The radiation emitted by the ultra-high temperature plasma 210 is transmitted through an optional gas barrier or contaminant trap 230 (in some cases, a contaminant barrier or foil) located within or behind an opening of a source chamber 211 . through a trap) from the source chamber 211 into a collector chamber 212 . The contaminant trap 230 may include a channel structure. Further, the contaminant trap 230 may include a gas barrier, or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further shown herein comprises at least a channel structure as known in the art.

The collector chamber 212 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252 . Radiation traversing the collector CO may be reflected from a grating spectral filter 240 and focused on a virtual source point IF along the optical axis indicated by dashed line 'O'. The virtual source point IF is commonly referred to as an intermediate focus, and the source collector module is positioned such that the intermediate focus IF is located at or near the opening 221 in the enclosure structure 220 . The virtual source point IF is an image of the radiation emitting plasma 210 .

Subsequently, the radiation traverses the illumination system IL, so as to provide the desired angular distribution of the radiation beam 21 in the patterning device MA as well as the desired uniformity of the radiation intensity in the patterning device MA. disposed facet field mirror device 22 and facet pupil mirror device 24 . Upon reflection of the radiation beam 21 at the patterning device MA, which is held by the support structure MT, a patterned beam 26 is formed, which is transmitted by means of the projection system PS. The reflective elements 28 , 30 are imaged onto the substrate W held by the substrate table WT.

In general, more elements than shown may be present in the illumination optics unit IL and the projection system PS. The grating spectral filter 240 may optionally be present depending on the type of lithographic apparatus. Also, there may be more mirrors than shown in the figures, for example 1 to 6 additional reflective elements than shown in FIG. 33 may be present in the projection system PS.

The collector optic CO as illustrated in FIG. 33 is shown as a nested collector with grazing incidence reflectors 253 , 254 and 255 , merely as one example of a collector (or collector mirror). The grazing incidence reflectors 253 , 254 and 255 are arranged axisymmetrically around the optical axis O, and a collector optic CO of this type is preferably used in combination with a discharge generating plasma radiation source.

Alternatively, the source collector module SO may be part of an LPP radiation system as shown in FIG. 34 . A laser (LAS) is arranged to deposit laser energy in a fuel such as xenon (Xe), tin (Sn) or lithium (Li), and a highly ionized plasma (highly ionized plasma) having an electron temperature of several tens of eV: 210 ) is created. The energetic radiation generated during the de-excitation and recombination of these ions is emitted from the plasma and collected by a near normal incidence collector optic (CO), enveloping structure. Focus is on the opening 221 of 220 .

These embodiments can be further described using the following items:

1. A method of training a model configured to predict whether a feature associated with an imaged substrate will be defective after etching of the imaged substrate, comprising:

Via the metrology tool, (i) a post-developed image of the imaged substrate at a given location, wherein the post-developed image includes a plurality of features, and (ii) a post-etched image of the imaged substrate at a given location— obtaining the post-etched image including etched features corresponding to the plurality of features; and

using the post-development image and the post-etch image to train a model configured to determine that a given one of a plurality of features in the post-development image is defective;

A method wherein the determination of a defect is based on comparing a given feature in the post-developed image to a corresponding etched feature in the post-etched image.

2. The method of clause 1, wherein the model is an empirical model or a machine learning model, wherein the empirical model is a function of a physical property of a feature associated with the imaged substrate.

3. The method of 1 or 2, wherein the step of obtaining an image after development comprises:

imaging the mask pattern on the substrate through the patterning device;

obtaining a developed substrate of the imaged substrate;

aligning the metrology tool to the developed substrate at a given location; and

A method comprising capturing an image of the developed substrate.

4. The method according to any one of items 1 to 3, wherein obtaining the image after etching comprises:

etching the imaged substrate through an etching process with specified etching conditions;

aligning the metrology tool to the etched substrate at a given location; and

and capturing an image after etching of the etched substrate.

5. The etching conditions according to clause 4, wherein the etchant composition, plasma gas parameters, etch rate, electromagnetic field, plasma potential, inductive or capacitive etching type, temperature of the substrate, ion energy distribution, ion angle distribution, sputtering and ash A method comprising a deposition rate, or a combination thereof.

6. The step of any of 1-5, wherein the training comprises:

aligning the post-develop image and the post-etch image based on the plurality of features;

comparing each of the features of the plurality of features in the post-developed image to a corresponding feature of the etched features in the post-etched image;

determining, based on the comparison, whether a given etched feature in the post-etch image satisfies a defect condition;

in response to not meeting the defect condition, classifying the identified feature as defective; and

and adjusting the model parameter values of the model based on the presence of the identified feature.

7. The method of clause 6, wherein adjusting the model parameter value comprises adjusting values of the plurality of model parameters.

8. The method of clause 6, wherein the defect condition is a physical property of a given etched feature in the post-etch image.

9. The method of 8, wherein the physical properties are:

the critical dimension of a given etched feature; or

at least one of a displacement of a given etched feature relative to a given feature of the image after development.

10. The method according to any one of items 1 to 9, wherein the defect comprises:

Binary determination of whether a defect is present or not; or

A method characterized by at least one of the probabilities that a given feature is defective.

11. The method according to any of clauses 2 to 10, wherein the machine learning model is a convolutional neural network.

12. The method of clause 11, wherein the model parameters are weights or biases associated with one or more layers of the machine learning model.

13. The method of clause 11, wherein the model parameters that are weights or biases include model parameters that are weights and biases.

14. The method according to any one of items 1 to 13, wherein the metrology tool is an optical microscope or an electron beam microscope.

15. The method according to any one of clauses 1 to 13, wherein the metrology tool is a scanning electron microscope (SEM) and the measured values are obtained from SEM images.

16. The method of any one of clauses 1-15, wherein the trained model is further configured to predict a failure rate associated with a given pattern of the post-development image, the failure rate being that of when the imaged substrate is etched using the specified etching conditions. How to indicate the occurrence of a defect.

17. The method according to any one of clauses 1 to 16, wherein the further configuration of the training model comprises:

classifying the plurality of patterns associated with the pattern of interest as defective or non-defective;

determining a total number of defective patterns associated with the pattern of interest; and

and calculating a failure rate of the pattern of interest as a ratio of the total number of defective patterns and the total number of patterns in the plurality of patterns.

18. according to any one of items 1 to 17,

imaging the desired pattern on the substrate, via the patterning device;

obtaining an image after development of the imaged pattern;

running a training model using the post-development image to classify whether the desired pattern will be defective after etching; and

based on the classified defective pattern, adjusting etching conditions such that the imaged pattern is defect-free after etching.

19. A method of determining etching conditions for an imaged substrate, comprising:

obtaining an image after development of the imaged substrate, and initial etching conditions to be used to etch the imaged substrate;

determining, via the model trained using the post-development image and initial etch conditions, a failure rate of a feature associated with the imaged substrate, the failure rate indicating that the feature is defective after etching of the imaged substrate; and

based on the failure rate, modifying the initial etching conditions to reduce the likelihood that the feature is defective after etching.

20. The step of clause 19, wherein modifying the etch conditions is an iterative process, the iteration comprising:

obtaining a relationship between a given etch condition and a given failure rate associated with a given feature;

determining a post-etch image associated with the imaged substrate through execution of the etch model using the post-development image and etch conditions;

determining, based on the post-etch image, whether a given feature satisfies a defect condition; and

and in response to not satisfying the defect condition, identifying further etch conditions associated with a lower failure rate compared to a given failure rate based on the relationship.

21. The conditions of clauses 19 or 20, wherein the defect condition of the feature is:

missing features;

displacement range associated with the feature; or

at least one of a tolerance range associated with a critical dimension of a feature.

22. A method of determining an etch characteristic associated with an etch process, comprising:

Via the metrology tool, (i) a post-development image (ADI) of the imaged pattern at a given location on the substrate, the imaged pattern including the feature of interest and neighboring features adjacent to the feature of interest, and (ii) the substrate obtaining a post-etched image (AEI) of the imaged pattern at a given location of AEI, wherein the AEI contains the etched feature corresponding to the feature of interest in the ADI; and

A method comprising determining, using the ADI and the AEI, a correlation between the etched feature and neighboring features associated with the feature of interest in the ADI, the correlation characterizing an etching characteristic associated with an etching process.

23. The method of clause 22, wherein the feature of interest comprises a plurality of features of interest.

24. The method of clauses 22 or 23, wherein the correlation is a function of the density of neighboring features adjacent to the feature of interest.

25. The correlation of any of clauses 22-24 between the neighboring features and the etched feature in ADI is:

the geometry of the feature of interest or neighboring features;

the geometry of the bias or assist features associated with the feature of interest;

distance between the feature of interest and neighboring features;

distance along a line feature;

critical dimension of the feature;

coordinates on the substrate associated with the feature of interest, neighboring features, and the etched feature of interest;

assist features or lack of assist features around the feature of interest; or

A method dependent on at least one of a deviation of an edge position from an expected position associated with a feature of interest.

26. The correlation according to any one of clauses 22 to 25, wherein the correlation based on the critical dimension of the feature is computed using the following equation:

은 상관관계들의 벡터이며, 여기서 CDAEI는 관심 피처의 AEI CD이고; CDADI _i 는 i번째 이웃의 ADI CD이며, r는 상관 계수이고, Q _i,j = r _{CDADIi,CDADIj} 는 상관관계 매트릭스인 방법.

is a vector of correlations, where CDAEI is the AEI CD of the feature of interest; How CDADI _i is the ADI CD of the i-th neighbor, r is the correlation coefficient, and Q _i,j = r _{CDADIi,CDADIj} is the correlation matrix.

27. The feature of any of clauses 22-26, wherein the feature of interest is:

contact hole;

line; or

at least one of the line ends.

28. Any of clauses 22-27, wherein the neighboring features are:

a plurality of contact holes in a defined orientation with respect to the feature of interest; or

at least one of the plurality of lines having a defined pitch.

29. The method of any of clauses 22-28, further comprising generating a correlated power spectral density in the spatial domain, wherein the power spectral density represents the magnitude of the etch characteristic effect and the extent of the loading effect.

30. Etch associated with the imaged pattern according to any one of clauses 22-29 such that, based on the correlation, and at a given radial distance between the center of the substrate and the edge of the substrate, the correlation remains within the target range. The method further comprising determining conditions.

31. The method of any of clauses 22-30, further comprising determining, based on the correlation, etching conditions for the imaged pattern centered on the substrate such that the correlation is within a target range.

32. The method of any of clauses 22-31, further comprising determining, based on the correlation, etching conditions for the imaged pattern positioned at the edge of the substrate such that the correlation remains within the target range.

33. The etch conditions according to paragraphs 31 or 32, wherein the etchant composition, plasma gas parameters, etch rate, electromagnetic field, plasma potential, inductive or capacitive etching type, temperature of the substrate, ion energy distribution, ion angle distribution, A method comprising parameters associated with sputtering and redeposition rates, etch cycle parameters based on saturation effects, or a combination thereof.

34. The etching conditions according to any of clauses 30 to 33, wherein:

the position of the substrate being etched, the position being the radial distance between the center of the substrate and the edge of the substrate;

etching cycle;

etching chamber;

sequence of etching cycles and deposition steps; or

A method that depends on at least one of tuning parameters associated with the etch chamber, wherein the tuning is based on a sensitivity of the correlation to changes in the tuning parameter.

35. The method of any of clauses 30-34, wherein determining the correlation comprises:

(i) a plurality of ADIs at a plurality of given locations of the substrate, each ADI having the same feature of interest, and (ii) a plurality of AEIs at a plurality of given locations, each AEI corresponding to a feature of interest. having an etched feature of interest that

and establishing a correlation between neighboring features of the feature of interest at each ADI and the etched feature of interest at each AEI.

36. A method of determining etching conditions associated with an etching process, comprising:

obtaining a correlation between the etched feature of interest in the post-etch image (AEI) and neighboring features associated with the etched feature-of-interest in the post-develop image (ADI); and

based on the correlation, determining etching conditions associated with the etching process such that the correlation remains within a target range.

37. The method of clause 36, wherein obtaining a correlation between the etched feature and a neighboring feature comprises obtaining a correlation between the etched feature and a plurality of neighboring features.

38. The step of clause 36, wherein determining etching conditions comprises:

the position of the substrate being etched, the position being the radial distance between the center of the substrate and the edge of the substrate;

the etching cycle of the etching process;

an etching chamber used in the etching process;

sequence of etching cycles and deposition steps; or

A method that depends on at least one of a tuning parameter associated with an etch chamber tuning parameter associated with the etch chamber, wherein the tuning is based on a sensitivity of the correlation to a change in the tuning parameter.

39. The method of clause 38, wherein the tuning parameter comprises a plurality of tuning parameters.

40. The step of any of clauses 36-39, wherein determining the etching conditions comprises:

A method comprising adjusting values of a tuning parameter associated with a given etch chamber such that a correlation associated with a given imaged pattern is maintained within a target range.

41. The step of any of paragraphs 36-40, wherein obtaining the correlation comprises:

Via the metrology tool, (i) a post-development image (ADI) of the imaged pattern at a given location, wherein the imaged pattern includes the feature of interest and neighboring features adjacent to the feature of interest, and (ii) at the given location obtaining a post-etched image (AEI) of the imaged pattern of the AEI comprising the etched feature-of-interest corresponding to the feature-of-interest of the ADI; and

A method comprising determining, using the ADI and the AEI, a correlation between the etched feature and a neighboring feature associated with the feature of interest in the ADI.

42. A method of developing an interpretation model configured to interpret predictions generated by the trained model, the method comprising:

obtaining, through execution of the trained model, a data set, the data set comprising a plurality of predictions associated with a plurality of features of the post-development image (ADI), the ADI comprising a feature of interest, and Each prediction is performed by a trained model- ;

determining distances between each location of the plurality of features and the feature of interest;

assigning weights to each prediction of the plurality of predictions based on the distances; and

based on the weighted predictions, determining model parameter values of the interpretation model such that a difference between the weighted predictions and an output of the interpretation model is reduced.

43. The method of 42, wherein obtaining the plurality of predictions comprises:

A method, comprising: running a trained model to predict a characteristic of each feature of a plurality of features in ADI, wherein the characteristic is indicative of a defect in the plurality of features.

44. The method of clause 43, wherein the defectiveness of a given feature in the ADI indicates the probability that the given feature will be defective after etching.

45. The method of any of clauses 42-44, wherein the prediction is whether the feature of interest in the ADI will print defect-free or defect-free after etching.

46. The method of any of clauses 42-45, wherein assigning weights to each prediction comprises: assigning a relatively higher weight to the prediction of the plurality of predictions when the associated distance is relatively small. Way.

47. The method according to any one of clauses 42 to 46, wherein determining model parameter values of the analytical model comprises:

obtaining initial model parameter values and weighted predictions;

running the analytical model using the initial model parameter values to produce an initial output;

determining a difference between the weighted predictions and the initial output; and

A method, which is a fitting process comprising, based on the difference, adjusting initial model parameter values such that the difference is minimized.

48. The interpretive model of any of clauses 42-47, wherein the interpretive model receives an ADI comprising the feature of interest as an input and generates an interpretive map as an output, the interpretive map comprising the vicinity of the feature of interest for prediction associated with the feature of interest. How to represent contributions.

49. The method according to any one of clauses 42 to 48, wherein the interpretation map is a pixelated image and the model parameter values are weights assigned to each pixel of the pixelated image.

50. A method according to any of clauses 42 to 49, wherein the interpretation map is a binary map in which each pixel is assigned a value of 0 or 1.

51. The binary map of any of clauses 42-50, wherein the binary map is created by assigning a value of 0 or 1 to each pixel based on a pixel value exceeding a threshold, where 0 is the feature of interest printed as a post-etch defect. method, where 1 indicates that the feature of interest will be printed without defects after etching.

52. The method according to any of clauses 42 to 51, wherein the interpretation map is a color image to which a particular color is assigned based on model parameter values.

53. The method of any of clauses 42-52, wherein the analytical model is a linear model associated with the feature of interest in the ADI.

54. The method according to any of clauses 42 to 53, wherein the linear model is fitted to the plurality of predictions using linear regression employing least squares error.

55. A method of identifying the contributions of pixels of an image after development to a prediction generated by a trained model, comprising:

(i) using a metrology tool to obtain a post-development image (ADI) comprising the feature of interest, and (ii) an interpretive model configured to interpret the prediction associated with the feature of interest, the prediction being generated via the trained model. ; and

A method comprising: applying an interpretive model to the ADI image to generate an interpretive map, the interpretive map comprising pixel values that quantify contributions of each pixel of the ADI image to a prediction of a feature of interest.

56. The method of 55, wherein the analytical model is a linear model associated with the feature of interest of the ADI.

57. A method according to clauses 55 or 56, wherein the interpretation map is a binary map in which each pixel is assigned a value of 0 or 1.

58. The method according to any one of clauses 55 to 57, wherein the prediction is defective of the feature of interest, and wherein the prediction is performed via a trained model.

59. A method according to any of clauses 55 to 58, wherein the interpretation map is a binary map in which each pixel is assigned a value of 0 or 1.

60. A method for developing a model for determining failure rates of features in a post-development image, comprising:

obtaining a post-developed image (ADI) of the substrate, the ADI comprising a plurality of features;

generating a first portion of the model based on physical property values associated with the subset of features of the ADI; and

generating a second portion of the model based on the first portion of the model and physical property values associated with all features of the plurality of features of the ADI, wherein the subset of the features of the ADI is distinct from other features of the ADI how to be

61. The method of 60, wherein generating the first portion of the model and the second portion of the model comprises fitting the first probability distribution function and the second probability distribution function, respectively, by maximizing a log-likelihood metric of the model.

62. The clause of clause 61, wherein the model is (i) a first probability distribution function configured to estimate a distribution of physical property values (eg, CD) for non-failure holes, and (ii) all plurality of ADI's A method, wherein the method is a combination of a second probability distribution function configured to determine failure rates based on physical property values of the features.

63. The method of clause 61, wherein the model is a weighted sum of the first probability distribution function and the second probability distribution function.

64. The method of 61, wherein the generation of the model comprises:

fitting a first probability distribution function based on squares of physical property values of a subset of features by maximizing a first log-likelihood metric associated with the first probability distribution function, wherein the subset of features has a physical property threshold above a physical property threshold. have property values- ;

combining the fitted first probability distribution function and the second probability distribution function; and

fitting, based on the combined distribution, a second probability distribution function and a relative weight associated therewith, based on the physical property values of all features of the plurality of features, such that a second log-likelihood metric associated with the combined distribution is maximized; How to include.

65. The fitting of the first probability distribution function of clause 61 is:

(a) determining a first log-likelihood metric using given values of parameters of the first probability distribution function;

(b) determining whether the first log-likelihood metric is maximized; and

(c) in response to not being maximized, adjusting values of parameters of the first probability distribution function based on the slope, and performing steps (a) to (c),

wherein the slope is the first derivative of the first log-likelihood metric with respect to the parameters of the first probability distribution function.

66. The fitting of the second probability distribution function of clause 61 is:

and determining, based on the maximization of the second log-likelihood metric, values of parameters of a second probability distribution function and a weight thereof without modifying values of parameters of the first probability distribution function.

67. The fitting of the second probability distribution function of clause 61 is:

(a) obtaining a combined distribution of a fitted first probability distribution function and a second probability distribution function;

(b) determining a second log-likelihood metric using given values of parameters of a second probability distribution function based on the combined distribution and holding values of parameters of the fitted first distribution fixed;

(c) determining whether a second log-likelihood metric is maximized; and

(d) in response to not being maximized, adjusting values of parameters of the second probability distribution function based on the slope, and performing steps (b) to (d),

wherein the slope is the first derivative of the second log-likelihood metric with respect to the parameters of the second probability distribution function.

68. The method of any one of clauses 61-67, wherein the first probability distribution function comprises a truncated value associated with the physical property, a first position parameter describing the shift of the normal distribution, and a first scale parameter describing the dispersion of the normal distribution. A method that is characterized by a normal distribution.

69. The second probability distribution function according to any one of clauses 61 to 68, wherein the second probability distribution function comprises a second position parameter (μ) describing a shift in the GEV distribution, a second scale parameter (σ) describing the spread of the GEV distribution; and a generalized extreme value (GEV) distribution characterized by a shape parameter (ξ) that describes the shape of the GEV distribution.

70. The method according to any one of items 61 to 69,

imaging, via the patterning device, a desired pattern comprising another plurality of features on another substrate;

obtaining an image after development of the imaged pattern;

executing first and second probability distribution functions using the post-development image to classify some of the features in the ADI as post-etch defective; and

based on the classified features, adjusting etching conditions so that the imaged pattern does not fail after etching.

71. The method of any of clauses 61-70, wherein the plurality of features comprises a plurality of holes, a plurality of lines, a plurality of pillars, or a combination thereof.

72. A portion of the features of the ADI classified as defective after etching of 70 or 71 are:

a hole closed after etching due to a resist blocking the development of the hole;

merged holes after etching;

A method comprising at least one of necking of one of the plurality of lines.

73. The method according to any one of 60 to 72,

tuning the lithography process to reduce the failure rate of ADI features after etching, wherein the tuning includes adjusting dose, focus, or both;

determining whether an additional filtering step should be performed on the resist layer to reduce the failure rate of the ADI features after etching;

determining whether an additional dishing or punch-through step should be performed to reduce the failure rate of the ADI features after etching;

during mass manufacturing, inspecting the ADI features to determine whether the lithographic apparatus meets specified criteria for printing; or

based on the failure rate, reworking the predetermined substrate or lot of substrates prior to etching.

74. The method of any one of 60-73, wherein the ADI is an image of the printed substrate obtained through a metrology tool or from a database storing images of the printed substrate.

75. The method of any of clauses 60-74, wherein the physical property is a critical dimension (CD) of the feature and the physical property threshold is a CD threshold.

76. The physical property of any one of items 60-74, wherein:

geometric mean of the CDs of the feature, the CDs being measured along the first direction or the second direction in the ADI;

directional CD of the feature of interest within the ADI;

variance of curvature of features of interest within ADI; or

at least one of a CD obtained from multiple metrology tool thresholds for each feature of interest.

77. The method of 76, wherein the directional CD is:

CD measured along the x-direction;

CD measured along the y-direction; or

at least one of the CDs measured along the desired angle.

78. The method according to any one of items 60 to 77,

extracting, from the model, statistical properties associated with non-failure holes; and

The method further comprising determining a process window of the patterning process based on the statistical characteristics.

79. A system for determining a fraction of features that will fail after etching, comprising:

a metrology tool that captures a post-developed image (ADI) of the substrate at a given location, the post-developed image comprising a plurality of features; and

a processor configured to run a model for determining failure rates of a plurality of features of the ADI that will fail after etching;

The model is configured to determine failure rates based on (i) a first probability distribution function configured to estimate a distribution of physical property values for non-failure holes, and (ii) physical property values of all of the plurality of features of the ADI. A system that is a combination of a second probability distribution function that is

80. The apparatus of clause 79, further comprising a patterning device configured to image a desired pattern comprising a plurality of features on the substrate;

The processor is:

receive, via the metrology tool, the ADI of the imaged substrate;

performing the first probability distribution and the second probability distribution to determine failure rates of features of the ADI;

A system configured to tune the patterning apparatus to reduce failure rates of features based on features having relatively higher failure rates.

81. The system of 80, wherein the processor is configured to tune the dose or focus via a knob/setting of the patterning device.

82. The processor of clause 81, further comprising:

determine whether an additional filtering step should be performed on the resist layer to reduce the failure rate of the ADI features after etching;

to determine whether an additional dishing or punch-through step should be performed to reduce the failure rate of the ADI features after etching; or

A system further configured to inspect the ADI features during mass manufacturing to determine whether the lithographic apparatus meets specified criteria for printing.

83. The method of any one of clauses 79-82, wherein the metrology tool comprises a scanning electron microscope (SEM), the SEM having the following physical properties:

an average CD of a plurality of instances of a feature of interest in ADI;

directional CD of the feature of interest in ADI;

Curvature variance of the feature of interest in ADI; or

A system configured to measure at least one of the CD obtained at multiple metrology tool thresholds for each feature of interest.

84. A non-transitory computer readable medium comprising:

When executed by more than one processor,

obtaining an image (ADI) after development of the substrate, the ADI comprising a plurality of features;

generating a first portion of the model based on physical property values associated with the subset of features of the ADI; and

instructions that cause tasks including generating a second portion of the model based on physical property values associated with the first portion of the model and all features of the plurality of features of the ADI;

A subset of the features of ADI is a non-transitory computer-readable medium that is distinct from other features of the ADI.

85. The method of clause 84, wherein the model is based on (i) a first probability distribution function configured to estimate a distribution of physical property values for non-failure holes, and (ii) physical property values of all of the plurality of features of the ADI. A non-transitory computer-readable medium that is a combination of a second probability distribution function configured to determine failure rates based on the second probability distribution function.

86. The non-transitory computer-readable medium of clause 85, wherein the model is a weighted sum of a first probability distribution function and a second probability distribution function.

87. The method of 85, wherein the generation of the model comprises:

fitting a first probability distribution function based on squares of physical property values of a subset of features by maximizing a first log-likelihood metric associated with the first probability distribution function, wherein the subset of features has a physical property threshold above a physical property threshold. have property values- ;

combining the fitted first probability distribution function and the second probability distribution function; and

fitting, based on the combined distribution, a second probability distribution function and a relative weight associated therewith, based on the physical property values of all features of the plurality of features, such that a second log-likelihood metric associated with the combined distribution is maximized; A non-transitory computer readable medium comprising

88. The fitting of the first probability distribution function according to clause 85, wherein:

(a) determining a first log-likelihood metric using given values of parameters of the first probability distribution function;

(b) determining whether the first log-likelihood metric is maximized; and

(c) in response to not being maximized, adjusting, based on the slope, values of parameters of the first probability distribution function, and performing steps (a) to (c);

wherein the slope is the first derivative of a first log-likelihood metric with respect to the parameters of a first probability distribution function.

89. The fitting of the second probability distribution function according to clause 85, wherein:

determining, based on the maximization of the second log-likelihood metric, values of parameters of a second probability distribution function and their weights without modifying values of parameters of the first probability distribution function; media.

90. The fitting of the second probability distribution function of clause 85 is:

(a) obtaining a combined distribution of a fitted first probability distribution function and a second probability distribution function;

(b) determining a second log-likelihood metric using given values of parameters of a second probability distribution function based on the combined distribution and holding values of parameters of the fitted first distribution fixed;

(c) determining whether a second log-likelihood metric is maximized; and

(d) in response to not being maximized, adjusting values of parameters of the second probability distribution function based on the slope, and performing steps (b) to (d),

wherein the slope is the first derivative of a second log-likelihood metric with respect to the parameters of a second probability distribution function.

91. The method of any one of 85-90, wherein the first probability distribution function comprises a truncated value associated with the physical property, a first position parameter describing the shift of the normal distribution, and a first scale parameter describing the dispersion of the normal distribution. A non-transitory computer readable medium characterized by a normal distribution.

92. The method according to any one of clauses 85 to 91, wherein the second probability distribution function comprises a second position parameter (μ) describing the shift in the GEV distribution, a second scale parameter (σ) describing the spread of the GEV distribution; and a generalized extreme value (GEV) distribution characterized by a shape parameter (ξ) that describes the shape of the GEV distribution.

93. The method according to any one of 85 to 92,

imaging, via the patterning apparatus, a desired pattern comprising a plurality of features on a substrate;

obtaining an image after development of the imaged pattern;

executing first and second probability distribution functions using the post-development image to classify some of the features in the ADI as post-etch defective; and

Based on the classified features, the non-transitory computer-readable medium further causing tasks comprising adjusting etching conditions such that the imaged pattern does not fail after etching.

94. The method according to any one of items 84 to 93,

tuning the lithography process to reduce the failure rate of ADI features after etching, where tuning includes adjusting dose, focus, or both;

determining whether an additional filtering step should be performed on the resist layer to reduce the failure rate of the ADI features after etching;

determining whether an additional dishing or punch-through step should be performed to reduce the failure rate of the ADI features after etching; or

A non-transitory computer readable medium that further causes operations including, during mass manufacturing, examining ADI features to determine whether a lithographic apparatus meets specified criteria for printing.

95. The non-transitory computer-readable medium of any one of clauses 83-93, wherein the physical property is a critical dimension (CD) of the feature, and wherein the physical property threshold is a CD threshold.

96. A method for determining a defect attribute of a feature in an image after development (ADI), comprising:

exposing the ADI feature to a beam of charged particles to produce a first image of the ADI feature, wherein the ADI feature is a structure in a resist material;

re-exposing the ADI feature to the charged particle beam to produce a second image of the ADI feature; and

A method comprising determining, based on data derived from the first image and the second image, a defect attribute of the ADI feature.

97. The step of clause 96, wherein determining the defect attribute comprises:

extracting a first feature from the first image and a second feature from the second image;

determining whether a defect metric is violated based on a difference between the first characteristic and the second characteristic; and

in response to the defect metric being violated, classifying the ADI feature as defective.

98. The method of 97, wherein the derived data is a physical property comprising a critical dimension or pixel intensity.

99. The method of clause 98, wherein the defect metric is a function of a first physical characteristic of the ADI feature in the first image and a second physical characteristic of the ADI feature in the second image.

100. The method of any of clauses 97-99, wherein the defect metric is a multivariate function, a bilinear function, a trained machine learning model, or a polynomial at least quadratic.

101. The machine learning model of 100, wherein the trained machine learning model comprises:

(i) a plurality of image pairs, each image pair including a first image and a second image of the plurality of ADI features, and (ii) post-etch images (AEI) of the substrate corresponding to the ADI features. A method obtained by training a machine learning model using a training data set comprising

102. The step of clause 101, wherein the training step comprises:

(a) adjusting parameters of the machine learning model such that the model determines a defect attribute of a given ADI feature based on a comparison between the first image and the second image;

(b) determining whether the model determined defect attribute is within a specified range of the defect attribute of the AEI feature corresponding to the given ADI feature; and

(c) in response to not being within the specified range, performing steps (a) and (b).

103. The method of any of clauses 96-102, wherein the electron beam is generated via a scanning electron microscope (SEM), and wherein the first image and the second image are SEM images.

104. The method of any of clauses 96-103, wherein the defect attribute is whether the ADI feature is defective or not defective, or a probability of failure associated with the ADI feature.

105. The method of any of clauses 96-104, wherein the first image comprises a plurality of frames obtained from a first exposure and the second image comprises a plurality of frames obtained from a re-exposure of the ADI feature.

106. The method of 105, wherein determining comprises:

A method comprising determining a difference between one or more frames of the first image and a physical property associated with the corresponding one or more frames of second images.

107. A method according to any one of clauses 96 to 106, wherein the charged particle beam is an electron beam.

108. A method for developing a model for determining failure rates of features in a post-developed image, comprising:

Via the metrology tool, (i) first measurement data associated with a post-developed image (ADI) of the substrate, the ADI comprising a plurality of features, and (ii) second measurement data associated with the same ADI; second measurement data is obtained subsequent to the first measurement; and

based on the first measurement data and the second measurement data, generating a model for determining failure rates of features of the ADI, the generating comprising:

A method comprising adjusting values of one or more model parameters such that the metric associated with the model improves as compared to the metric associated with initial values of the model parameters.

109. The method of clause 108, further comprising, based on the model, determining a process window of the patterning process based on failure rates of features predicted by the models for a given first measurement of a given ADI and a second measurement of a given ADI. How to include more.

110. The method of 108, wherein generating the model comprises:

A first probability density function (PDF) associated with the failure rate parameter by maximizing the log-likelihood metric of the model using the first and second measurement data, and a second probability density function associated with the freeness of the failure rate parameter ( PDF).

111. The step of clause 110, wherein fitting the first probability density function comprises:

and determining values of each model parameter associated with the first PDF and the second PDF by maximizing a log-likelihood metric of the model.

112. The method of clause 111, wherein the model is:

a first PDF characterized by a combined distribution of the first and second physical properties, and a first set of model parameters - a first physical property associated with the first measurement data, and wherein the second physical property is of the ADI associated with the second measurement data-; and

A method comprising: another combined distribution of the first physical property and the second physical property; and a second PDF characterized by a second set of model parameters.

113. The method of 110, wherein the first PDF is:

a first positional parameter and a second positional parameter describing the shift of the multivariate distribution; and

A method which is a multivariate distribution characterized by a first scale parameter and a second scale parameter that describe the spread of the multivariate distribution.

114. The method of 110, wherein the second PDF is:

a third position parameter and a fourth position parameter describing the shift in the GEV distribution;

a third scale parameter and a fourth scale parameter describing the spread of the GEV distribution; and

A method that is a generalized extreme value (GEV) distribution characterized by a shape parameter (ξ) that describes the shape of the GEV distribution.

115. The method of any of clauses 108-114, wherein the metrology tool is a scanning electron microscope (SEM).

116. The method of clause 115, wherein the first measurement data is a first SEM image of the ADI and the second measurement data is a second SEM image of the ADI.

117. The method of clause 116, wherein the first measurement data comprises first physical property values of features in the first SEM image of the ADI, and the second measurement data comprises second physical property values of the features in the second SEM image of the ADI. How to include values.

118. The method of clause 117, wherein generating the model comprises:

fitting a first PDF based on first physical property values of a plurality of features in a first SEM image of the ADI; and

fitting a second PDF based on second physical property values of the plurality of features in a second SEM image of the ADI;

A method wherein the first PDF and the second PDF are both fitted simultaneously by maximizing a log-likelihood metric associated with the model.

119. The fitting of clause 118, of the first PDF and the second PDF:

(a) determining a log-likelihood metric using given values of parameters of the first PDF and the second PDF;

(b) determining whether the log-likelihood metric is maximized;

(c) in response to not being maximized, adjusting, based on the slope, the values of the first set of model parameters and the values of the second set of model parameters of the first PDF, and the failure rate parameter, and steps (a) ) to (c) is an iterative process comprising the steps of:

wherein the slope is the first derivative of the log-likelihood metric for the first model parameters, the second model parameters, and the failure rate parameter.

120. The fitting of clause 118, wherein the fit of the model is:

wherein the values of the failure rate parameter associated with the first PDF and the second PDF are the same.

121. The method according to any one of items 111 to 120,

determining a relationship between the first set of model parameters and one or more model parameters of the second set of model parameters based on the first measurement data and the second measurement data;

modifying the first set of model parameters with respect to the second set of model parameters to reduce a number of the first set of model parameters or the second set of model parameters based on the relationship; and

using the first measurement data and the second measurement data to generate a model based on the modified parameters.

122. The method of any of clauses 112-121, wherein the physical property is the critical dimension (CD) of the feature.

123. The physical property of any one of clauses 112 to 122, wherein the physical property is:

an average CD of a plurality of instances of a feature of interest in ADI;

directional CD of the feature of interest in ADI;

Curvature variance of the feature of interest in ADI; or

at least one of a CD obtained from multiple metrology tool thresholds for each feature of interest.

124. The method of 123, wherein the directional CD is:

CD measured along the x-direction;

CD measured along the y-direction; or

at least one of the CDs measured along the desired angle.

125. The method of any one of clauses 108-124, wherein the failure rate represents a fault condition characterized by a physical property of the ADI feature or the corresponding AEI feature, wherein the fault condition is:

missing features;

displacement range associated with the feature; or

A method comprising at least one of a tolerance range associated with a critical dimension of a feature.

126. A non-transitory computer readable medium comprising:

When executed by more than one processor,

exposing the ADI feature to a beam of charged particles to produce a first image of the ADI feature, wherein the ADI feature is a structure in a resist material;

re-exposing the ADI feature to the charged particle beam to produce a second image of the ADI feature; and

A non-transitory computer-readable medium having stored thereon instructions for causing tasks including determining a defect attribute of an ADI feature based on a physical characteristic associated with the first image and the second image.

127. The method of clause 126, wherein determining the defect attribute comprises:

extracting a first feature from the first image and a second feature from the second image;

determining whether a defect metric is violated based on the difference between the first characteristic and the second characteristic; and

and in response to a defect metric being violated, classifying the ADI feature as defective.

128. The non-transitory computer-readable medium of clause 127, wherein the physical property is a critical dimension or pixel intensity.

129. The non-transitory computer-readable medium of clause 127, wherein the defect metric is a function of a first physical characteristic of the ADI feature in the first image and a second physical characteristic of the ADI feature in the second image.

130. The non-transitory computer-readable medium of any of clauses 127-129, wherein the defect metric is a multivariate function, a bilinear function, a trained machine learning model, or a polynomial at least quadratic.

131. The machine learning model of 130, wherein the trained machine learning model comprises:

(i) a plurality of image pairs, each image pair including a first image and a second image of the plurality of ADI features, and (ii) post-etch images (AEI) of the substrate corresponding to the ADI features; A non-transitory computer-readable medium obtained by training a machine learning model using a training data set comprising:

132. The step of clause 131, wherein the training step comprises:

(a) adjusting parameters of the machine learning model such that the model determines a defect attribute of a given ADI feature based on a comparison between the first image and the second image;

(b) determining whether the model determined defect attribute is within a specified range of the defect attribute of the AEI feature corresponding to the given ADI feature; and

(c) in response to not being within the specified range, performing steps (a) and (b).

133. The non-transitory computer readable medium of any of clauses 126-132, wherein the electron beam is generated via a scanning electron microscope (SEM), and wherein the first image and the second image are SEM images.

134. The non-transitory computer-readable medium of any one of clauses 126-133, wherein the fault attribute is whether the ADI feature is defective or non-defective, or a probability of failure associated with the ADI feature.

135. The non-transitory of any of clauses 126-134, wherein the first image comprises a plurality of frames obtained from a first exposure and the second image comprises a plurality of frames obtained from a re-exposure of the ADI feature. computer readable medium.

136. The method of 135, wherein determining comprises:

A non-transitory computer-readable medium comprising determining a difference between one or more frames of a first image and a physical property associated with the corresponding one or more frames of second images.

137. The non-transitory computer readable medium of any of clauses 128-135, wherein the charged particle beam is an electron beam.

138. A non-transitory computer readable medium comprising:

When executed by more than one processor,

Via the metrology tool, (i) first measurement data associated with a post-developed image (ADI) of the substrate, the ADI comprising a plurality of features, and (ii) second measurement data associated with the same ADI; the second measurement data is obtained subsequent to the first measurement; and

Stored are instructions that cause tasks including generating a model for determining failure rates of features of the ADI based on the first measurement data and the second measurement data, the generating comprising:

A non-transitory computer-readable medium comprising adjusting values of one or more model parameters such that the metric associated with the model improves compared to the metric associated with initial values of the model parameters.

139. The method of clause 138, further comprising, based on the model, determining the process window of the patterning process based on failure rates of features predicted by the models for a given first measurement of a given ADI and a second measurement of a given ADI. further comprising a non-transitory computer readable medium.

140. The method of 138, wherein generating the model comprises:

Using the first and second measured data, a first probability density function (PDF) associated with the failure rate parameter by maximizing the log-likelihood metric of the model, and a second probability density function associated with the freeness of the failure rate parameter ( PDF), which is a non-transitory computer readable medium.

141. The method of 140, wherein the fitting of the first probability density function is:

A non-transitory computer-readable medium comprising determining values of each model parameter associated with a first PDF and a second PDF by maximizing a log-likelihood metric of the model.

142. The method of 141, wherein the model is:

a first PDF characterized by the combined distribution of the first physical property and the second physical property, and a first set of model parameters - a first physical property associated with the first measurement data, and the second physical property being an ADI's associated with the second measurement data-; and

A non-transitory computer-readable medium comprising a second PDF characterized by another combined distribution of a first physical property and a second physical property, and a second set of model parameters.

143. The method of 142, wherein the first PDF is:

a first positional parameter and a second positional parameter describing the shift of the multivariate distribution; and

A non-transitory computer-readable medium that is a multivariate distribution characterized by a first scale parameter and a second scale parameter that describe the spread of the multivariate distribution.

144. The second PDF of 143, wherein:

a third position parameter and a fourth position parameter describing the shift in the GEV distribution;

a third scale parameter and a fourth scale parameter describing the spread of the GEV distribution; and

A non-transitory computer readable medium that is a generalized extreme value (GEV) distribution characterized by a shape parameter (ξ) that describes the shape of the GEV distribution.

145. The non-transitory computer readable medium of any one of clauses 137-144, wherein the metrology tool is a scanning electron microscope (SEM).

146. The non-transitory computer readable medium of clause 145, wherein the first measurement data is a first SEM image of the ADI and the second measurement data is a second SEM image of the ADI.

147. The first measurement data of clause 146, wherein the first measurement data comprises first physical property values of features in the first SEM image of the ADI, and the second measurement data includes second physical property values of the features in the second SEM image of the ADI. A non-transitory computer-readable medium containing values.

148. The method of 147, wherein generating the model comprises:

fitting the first PDF based on first physical property values of the plurality of features in the first SEM image of the ADI; and

fitting a second PDF based on second physical property values of the plurality of features in a second SEM image of the ADI;

The first PDF and the second PDF are both fitted simultaneously by maximizing a log-likelihood metric associated with the model.

149. The fitting of clause 148, of the first PDF and the second PDF is:

(a) determining a log-likelihood metric using given values of parameters of the first PDF and the second PDF;

(b) determining whether the log-likelihood metric is maximized;

(c) in response to not being maximized, adjusting, based on the slope, the values of the first set of model parameters and the values of the second set of model parameters of the first PDF, and the failure rate parameter, and steps (a) ) to (c) is an iterative process comprising the steps of:

wherein the slope is the first derivative of the log-likelihood metric for the first model parameters, the second model parameters, and the failure rate parameter.

150. The fitting of clause 149 of the model is:

A non-transitory computer-readable medium, wherein a value of a failure rate parameter associated with the first PDF and the second PDF is the same.

151. The method according to any one of items 141 to 150,

determining a relationship between the first set of model parameters and one or more model parameters of the second set of model parameters based on the first measurement data and the second measurement data;

modifying the first set of model parameters with respect to the second set of model parameters to reduce a number of the first set of model parameters or the second set of model parameters based on the relationship; and

The non-transitory computer-readable medium further comprising using the first measurement data and the second measurement data to generate a model based on the modified parameters.

152. The non-transitory computer readable medium of any of clauses 142-151, wherein the physical property is a critical dimension (CD) of the feature.

153. The physical property of any one of clauses 142 to 152, wherein the physical property is:

an average CD of a plurality of instances of a feature of interest in ADI;

directional CD of the feature of interest in ADI;

Curvature variance of the feature of interest in ADI; or

A non-transitory computer readable medium that is at least one of a CD obtained at multiple metrology tool thresholds for each feature of interest.

154. The directional CD of 153, wherein:

CD measured along the x-direction;

CD measured along the y-direction; or

A non-transitory computer readable medium that is at least one of a CD measured along a desired angle.

155. The method of any one of clauses 138-154, wherein the failure rate represents a fault condition characterized by a physical property of the ADI feature or the corresponding AEI feature, wherein the fault condition is:

missing features;

displacement range associated with the feature; or

A non-transitory computer-readable medium comprising one or more of a tolerance range associated with a critical dimension of a feature.

156. A method of training a model configured to determine post-etch image (AEI) features based on post-develop image (ADI) features, the method comprising:

(i) measurements of the imaged ADI features on the substrate, and (ii) obtaining measurements of post-etched image (AEI) features on the etched substrate that correspond to the measured ADI features;

allocating a first set of variables characterizing the measured ADI feature and a second set of variables characterizing the measured AEI feature;

determining a correlation between the combination of the first set of variables of the measured ADI feature and the combination of the second set of variables of the measured AEI feature; and

based on the correlation, training the model by including one or more sub-combinations of a first set of variables having correlation values within a specified correlation threshold, the model being used to determine an AEI feature for the input ADI feature. - How to include.

157. The method of 156, wherein determining the correlation comprises:

calculating a correlation using given values of (i) a first set of parameters associated with a first set of combinations of variables, and (ii) a second set of parameters associated with a second set of combinations of variables. ;

determining whether the correlation is maximized; and

in response to the correlation not being maximized, adjusting the given values of the first set of parameters and the second set of parameters until the correlation is maximized.

158. The method of 157, wherein adjusting the given values of the first set of parameters and the second set of parameters is performed until the correlation is within a specified range.

159. The method according to any one of clauses 156 to 158, wherein training the model comprises:

(a) determining whether a correlation of sub-combinations and sub-combinations of the first and second sets of variables exceeds a specified correlation threshold;

(b) in response to the sub-combinations being exceeded, including the sub-combination in the model; and

(c) in response to the sub-combinations not being exceeded, selecting another sub-combination of the first set of variables, and for a specified number of iterations or until the sub-combination is exhausted, steps (a) to ( c) repeating.

160. The method of 159, wherein the designated correlation threshold is greater than 0.01.

161. The method of any of clauses 156-160, wherein the combination or one or more sub-combinations of the first set of variables is a linear combination, a non-linear combination, or a machine learning model.

162. The method of 161, wherein the combination or one or more sub-combinations of the first set of variables is a weighted sum of the first set of variables, wherein the weights are positive values or negative values.

163. The method of any of clauses 156-162, wherein the combination or one or more sub-combinations of the second set of variables is a linear combination, a non-linear combination, or a machine learning model.

164. The clause of clause 163, wherein the correlation is calculated using the following equation:

은 변수들의 제 1 세트의 벡터 형태이고,

은 파라미터들의 제 1 세트에 대응하며,

은 변수들의 제 1 세트의 1 이상의 조합을 포함하고,

은 변수들의 제 2 세트의 벡터 형태이며,

은 파라미터들의 제 2 세트에 대응하고,

은 변수들의 제 2 세트의 1 이상의 조합을 포함하며, R ² 의 분자는

와

사이의 공분산을 나타내고, 분모는

의 분산과

의 분산의 곱을 나타내는 방법.

is the vector form of the first set of variables,

corresponds to the first set of parameters,

comprises one or more combinations of the first set of variables,

is the vector form of the second set of variables,

corresponds to the second set of parameters,

comprises one or more combinations of the second set of variables, wherein the numerator of R ² is

Wow

represents the covariance between, and the denominator is

dispersion of

A method of representing the product of variance of .

165. The first set of variables of any of clauses 156-164, wherein the first set of variables corresponds to a set of positions on the ADI contour of the measured ADI feature, and the second set of variables is a set of positions on the AEI contour of the measured ADI feature. How to respond to a set.

166. The method of any of clauses 156-165, wherein the one or more sub-combinations characterizes the amount of deformation of the ADI contour of the measured ADI feature caused by a process performed on the measured ADI feature.

167. The method of 166, wherein the amount of deformation is a difference between a given position of the ADI contour and a corresponding position of the AEI contour.

168. The method of 167, wherein the amount of deformation is characterized by a linear combination of the first set of variables.

169. The method of any one of items 156-168, wherein the one or more sub-combinations are:

translation of the measured ADI feature in a specified direction;

the critical dimension of the measured ADI feature;

elongation in a specified direction of the measured ADI feature;

Triangulation of measured ADI features; and

A method of characterizing one or more of the rotations of a measured ADI feature.

170. The method of any one of clauses 156-169, wherein determining the correlation is based on a sparsity constraint excluding the at least one variable from the first set of variables or the second set of variables, wherein the at least one variable is greater than 0.01. How to associate with small correlation values.

171. The method of any of clauses 156-170, wherein the measured ADI and the measured AEI are obtained via a simulation process or metrology tool configured to generate an ADI feature and an AEI feature for an input target feature.

172. The method of 171, wherein the metrology tool is a scanning electron microscope (SEM) configured to capture the ADI and AEI of the substrate, the ADI comprising an ADI feature, and the AEI comprising an AEI feature.

173. The method of 171, wherein the ADI comprises images obtained from the first and second SEM measurements of the ADI feature, and the AEI comprises images obtained from the first and second SEM measurements of the AEI feature.

174. The method of any of clauses 156-173, wherein the ADI feature comprises a feature of interest and one or more neighboring features.

175. The method of 174, wherein the first set of variables comprises a first subset of variables associated with a feature of interest and a second subset of variables associated with one or more neighboring features.

176. The combination or one or more sub-combinations of clause 175, wherein the combination or one or more sub-combinations is a weighted sum of the first subset of variables associated with the feature of interest and the second subset of the variables associated with the one or more neighboring features, the variables of the neighboring feature The weights assigned to the method are relatively higher than the variables of other neighboring features away from the feature of interest.

177. The method according to any one of items 156 to 176,

based on the correlation, adjusting the metrology tool settings to cause the correlation to improve.

178. The method of 177, wherein the metrology tool settings include at least one of: e-beam intensity, angle of incidence, voltage contrast, SEM threshold, pixel size, scan rate, or number of frames.

179. The method according to any one of items 156 to 178,

based on the correlation, adjusting one or more parameters associated with the contour extraction algorithm such that the correlation is improved.

180. The method according to any one of items 156 to 179,

and adjusting parameters associated with the resist process or the etch process such that, through simulation of the patterning process and the etch process using correlation, a yield of the patterning process is greater than a specified yield threshold.

181. The method according to any one of items 156 to 180,

The method further comprising adjusting parameters associated with the lithographic process such that, through simulation of the patterning process using correlation, a performance metric of the lithographic apparatus is within a specified performance threshold.

182. The method of clause 181, wherein the parameters of the patterning process include: dose or focus conditions associated with the lithographic apparatus.

183. The method according to any one of items 156 to 182,

monitoring process quality based on the selected combination of the first set of variables of the ADI features and its sensitivity to focus and exposure conditions; and

The method further comprising adjusting one or more process parameters to maintain process quality within a specified range.

184. The method of 183, wherein the monitoring comprises:

measuring relevant ADI contour properties of the tip-to-tip pattern; and

based on the measured sensitivity and correlation, adjusting one or more process parameters to improve tip-to-tip conversion of the ADI feature to the AEI feature.

185. A metrology tool comprising:

a beam generator configured to measure the ADI features after imaging the substrate and the AEI features after etching the substrate; and

A processor, comprising:

Obtain a correlation between the measured ADI features and the measured AEI features corresponding to the measured ADI features printed on the etched substrate - the correlation is a variable that characterizes how the measured ADI features are converted into AEI features based on a combination of - ;

and adjust settings of the metrology tool such that, based on the correlation, the correlation is improved, the settings are determined based on a derivative of the correlation for each setting, wherein the derivative is per setting of the metrology tool A metrology tool that shows improvement in correlation.

186. The metrology tool of clause 185, wherein the metrology tool is a scanning electron microscope (SEM).

187. The metrology tool of clause 186, wherein the settings of the metrology tool include values of at least one of: e-beam intensity, angle of incidence, voltage contrast, SEM threshold, pixel size, scan rate, or number of frames.

188. The metrology tool of 186, wherein the beam generator is an electron beam generator.

189. The processor of any of clauses 185-188, further comprising:

The metrology tool further configured to adjust, based on the correlation, one or more parameters associated with the contour extraction algorithm to improve the correlation.

190. The method of any one of items 185-188, wherein the one or more sub-combinations are:

translation of the measured ADI feature in a specified direction;

critical dimension of the measured ADI feature;

elongation in a specified direction of the measured ADI feature;

Triangulation of measured ADI features; or

A metrology tool that characterizes one or more of the rotations of a measured ADI feature.

191. The method of 185, wherein the processor comprises:

varying one or more process parameters associated with the patterning process;

A metrology tool further configured to obtain ADI and AEI images of the patterned substrate using the varied process parameters.

192. The parameters of 191, wherein the changed parameters are:

overlay through shifting of features in the mask pattern used to pattern the substrate;

average CD through resizing of features in the mask pattern used to pattern the substrate;

focus of the patterning device; or

A metrology tool comprising at least one of a dose of a patterning device.

193. A method of training a model configured to determine a post-etch image (AEI) based on the post-develop image (ADI), the method comprising:

(i) obtaining an ADI of the imaged substrate, and (ii) a post-etch image (AEI) after etching the imaged substrate;

determining a correlation between the combination of the first set of variables of the ADI and the second set of variables of the AEI, the first and second sets of variables being gray scale values of the ADI and the AEI, respectively; and

based on the correlation, training the model by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, the model being used to determine the AEI for the input ADI. How to include.

194. The method of 193, wherein determining the correlation comprises:

calculating a correlation using given values of (i) a first set of parameters associated with a first set of combinations of variables, and (ii) a second set of parameters associated with a second set of combinations of variables. ;

determining whether the correlation is maximized; and

in response to the correlation being not within the specified range, adjusting the given values of the first set of parameters and the second set of parameters until the correlation is maximized.

195. The method of 193 or 194, wherein training the model comprises:

(a) determining whether a sub-combination of a first set of variables and a correlation of the sub-combination exceed a specified correlation threshold;

(b) in response to the sub-combination being exceeded, including the sub-combination in the model; and

(c) in response to the sub-combination not being exceeded, selecting another sub-combination of the first set of variables, and for a specified number of iterations or until the sub-combination is exhausted, steps (a) to ( c) repeating.

196. A non-transitory computer readable medium comprising:

instructions that, when executed by the one or more processors, cause the operations to train a model configured to determine a post-etch image (AEI) feature based on the post-develop image (ADI) feature, the operations comprising:

(i) measurements of the imaged ADI features on the substrate, and (ii) obtaining measurements of post-etched image (AEI) features on the substrate that have been subjected to the etching process, corresponding to the measured ADI features;

assigning a first set of variables characterizing the measured ADI feature and a second set of variables characterizing the measured AEI feature;

determining a correlation between the combination of the first set of variables of the measured ADI feature and the combination of the second set of variables of the measured AEI feature; and

training the model, based on the correlation, by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, the model being used to determine an AEI feature for the input ADI feature A non-transitory computer readable medium comprising - configured to be

197. The method of 196, wherein determining the correlation comprises:

calculating a correlation using given values of (i) a first set of parameters associated with a first set of combinations of variables, and (ii) a second set of parameters associated with a second set of combinations of variables. ;

determining whether the correlation is maximized; and

in response to the correlation not being maximized, adjusting the given values of the first set of parameters and the second set of parameters until the correlation is maximized.

198. The non-transitory computer-readable medium of clause 197, wherein adjusting the given values of the first set of parameters and the second set of parameters is performed until the correlation is within a specified range.

199. The method of any one of clauses 196-198, wherein training the model comprises:

(a) determining whether a correlation of sub-combinations and sub-combinations of the first and second sets of variables exceeds a specified correlation threshold;

(b) in response to the sub-combinations being exceeded, including the sub-combination in the model; and

(c) in response to the sub-combinations not being exceeded, selecting another sub-combination of the first set of variables, and steps (a)-( A non-transitory computer readable medium comprising repeating c).

200. The non-transitory computer readable medium of clause 199, wherein the designated correlation threshold is greater than 0.01.

201. The non-transitory computer-readable medium of any of clauses 196-200, wherein the combination or one or more sub-combinations of the first set of variables is a linear combination, a non-linear combination, or a machine learning model.

202. The non-transitory computer-readable medium of clause 201, wherein the combination or one or more sub-combinations of the first set of variables is a weighted sum of the first set of variables, the weights being positive values or negative values.

203. The non-transitory computer-readable medium of any of clauses 196-202, wherein the combination or one or more sub-combinations of the second set of variables is a linear combination, a non-linear combination, or a machine learning model.

204. The clause of clause 203, wherein the correlation is computed using the following equation:

은 변수들의 제 1 세트의 벡터 형태이고,

은 파라미터들의 제 1 세트에 대응하며,

은 변수들의 제 1 세트의 1 이상의 조합을 포함하고,

은 변수들의 제 2 세트의 벡터 형태이며,

은 파라미터들의 제 2 세트에 대응하고,

은 변수들의 제 2 세트의 1 이상의 조합을 포함하며, R ² 의 분자는

와

사이의 공분산을 나타내고, 분모는

의 분산과

의 분산의 곱을 나타내는 비-일시적 컴퓨터 판독가능한 매체.

is the vector form of the first set of variables,

corresponds to the first set of parameters,

comprises one or more combinations of the first set of variables,

is the vector form of the second set of variables,

corresponds to the second set of parameters,

comprises one or more combinations of the second set of variables, wherein the numerator of R ² is

Wow

represents the covariance between, and the denominator is

dispersion of

A non-transitory computer readable medium representing the product of the variances of .

205. The first set of variables of any of clauses 196-204, wherein the first set of variables corresponds to a set of positions on the ADI contour of the measured ADI feature, and the second set of variables is a set of positions on the AEI contour of the measured AEI feature. A non-transitory computer-readable medium corresponding to a set.

206. The non-transitory computer readable according to any one of clauses 196-205, wherein the one or more sub-combinations characterizes an amount of deformation of the ADI contour of the measured ADI feature caused by a process performed on the measured ADI feature. media.

207. The non-transitory computer-readable medium of clause 206, wherein the amount of deformation is a difference between a given position of the ADI contour and a corresponding position of the AEI contour.

208. The non-transitory computer-readable medium of clause 207, wherein the amount of deformation is characterized by a linear combination of the first set of variables.

209. The method of any one of clauses 196-208, wherein the one or more sub-combinations comprise: translation of the measured ADI feature in a designated direction; critical dimension of the measured ADI feature; elongation in a specified direction of the measured ADI feature; Triangulation of measured ADI features; or a non-transitory computer readable medium characterizing one or more of the measured rotation of the ADI feature.

210. The method of any one of clauses 196-209, wherein determining the correlation is based on a sparsity constraint excluding the at least one variable from the first set of variables or the second set of variables, wherein the at least one variable is less than 0.01. A non-transitory computer readable medium associated with a correlation value.

211. The non-transitory computer of any of clauses 196-210, wherein the measured ADI and the measured AEI are obtained via a simulation process or metrology tool configured to generate the ADI feature and the AEI feature for the input target feature. readable medium.

212. The non-transitory computer read of clause 211, wherein the metrology tool is a scanning electron microscope (SEM) configured to capture the ADI and AEI of the substrate, the ADI comprising the ADI feature, and the AEI comprising the AEI feature. possible medium.

213. The non-transitory computer read of clause 212, wherein the ADI comprises images obtained from the first and second SEM measurements of the ADI feature and the AEI comprises images obtained from the first and second SEM measurements of the AEI feature. possible medium.

214. The non-transitory computer-readable medium of any of clauses 196-213, wherein the ADI features include a feature of interest and one or more neighboring features.

215. The non-transitory computer-readable medium of clause 214, wherein the first set of variables comprises a first subset of variables associated with a feature of interest and a second subset of variables associated with one or more neighboring features.

216. The combination or one or more sub-combinations of clause 215, wherein the combination or one or more sub-combinations is a weighted sum of the first subset of variables associated with the feature of interest and the second subset of the variables associated with the one or more neighboring features, the variables of the neighboring feature The weights assigned to the non-transitory computer-readable medium are relatively higher than variables of another neighboring feature away from the feature of interest.

217. The method of any one of paragraphs 196-216,

based on the correlation, adjusting metrology tool settings to cause the correlation to be improved.

218. The non-transitory computer-readable medium of clause 217, wherein the metrology tool settings include at least one of: e-beam intensity, angle of incidence, voltage contrast, SEM threshold, pixel size, scan rate, or number of frames.

219. The method of any one of 196-218,

based on the correlation, adjusting one or more parameters associated with the contour extraction algorithm to cause the correlation to be improved.

220. The method of any one of items 196 to 219,

and adjusting parameters associated with the resist process or the etch process such that, through simulation of the patterning process and the etch process using correlation, a yield of the patterning process is greater than a specified yield threshold.

221. The method according to any one of 196-220,

The non-transitory computer readable medium further comprising adjusting parameters related to the lithographic process such that, through simulation of the patterning process using correlation, a performance metric of the lithographic apparatus is within a specified performance threshold.

222. The non-transitory computer readable medium of clause 221, wherein the parameters of the patterning process include: dose or focus conditions associated with a lithographic apparatus.

223. The method according to any one of 196 to 222,

monitoring process quality based on the selected combination of the first set of variables of the ADI features and its sensitivity to focus and exposure conditions; and

The non-transitory computer readable medium further comprising adjusting one or more process parameters to maintain process quality within a specified range.

224. The method of 223, wherein the monitoring comprises:

measuring relevant ADI contour properties of the tip-to-tip pattern; and

A non-transitory computer readable medium comprising adjusting one or more process parameters to improve tip-to-tip conversion of an ADI feature to an AEI feature based on the measured sensitivity and correlation.

225. A non-transitory computer readable medium comprising:

instructions that, when executed by the one or more processors, cause the operations to train a model configured to determine a post-etch image (AEI) based on the post-development image (ADI), the operations comprising:

obtaining (i) an ADI of the imaged substrate, and (ii) a post-etch image (AEI) after etching the imaged substrate;

determining a correlation between the combination of the first set of variables of the ADI and the second set of variables of the AEI, the first and second set of variables being gray scale values of the ADI and the AEI, respectively; and

training the model, based on the correlation, by including one or more sub-combinations of the first set of variables having correlation values within a specified correlation threshold, wherein the model is configured to be used to determine an AEI for an input ADI. - A non-transitory computer readable medium comprising a.

226. The method of 225, wherein determining the correlation comprises:

calculating a correlation using given values of (i) a first set of parameters associated with a first set of combinations of variables, and (ii) a second set of parameters associated with a second set of combinations of variables. ;

determining whether the correlation is maximized; and

responsive to the correlation being not within the specified range, adjusting the given values of the first set of parameters and the second set of parameters until the correlation is maximized.

227. The method of 225 or 226, wherein training the model comprises:

(a) determining whether a sub-combination of a first set of variables and a correlation of the sub-combination exceed a specified correlation threshold;

(b) in response to the sub-combination being exceeded, including the sub-combination in the model; and

(c) in response to the sub-combination not being exceeded, selecting another sub-combination of the first set of variables, and for a specified number of iterations or until the sub-combination is exhausted, steps (a) to ( A non-transitory computer readable medium comprising repeating c).

228. A method of determining an image after etching (AEI) based on the image after development (ADI), the method comprising:

obtaining the ADI of the substrate; and

through the trained model, determining the AEI by inputting the ADI into the trained model and outputting the ADI - the trained model is a combination of the first set of variables of the measured ADI and the second set of variables of the measured AEI trained based on correlations between combinations, wherein the correlations are within a specified correlation threshold.

229. The clause of 228, wherein the correlation is:

calculating a correlation using given values of (i) a first set of parameters associated with a first set of combinations of variables, and (ii) a second set of parameters associated with a second set of combinations of variables. ;

determining whether the correlation is maximized; and

in response to the correlation not being maximized, adjusting the given values of the first set of parameters and the second set of parameters until the correlation is maximized.

230. The model of 228 or 229, wherein the trained model comprises:

(a) determining whether a correlation of sub-combinations and sub-combinations of the first and second sets of variables exceeds a specified correlation threshold;

(b) in response to the sub-combinations being exceeded, including the sub-combination in the model; and

(c) in response to the sub-combinations not being exceeded, selecting another sub-combination of the first set of variables, and for a specified number of iterations or until the sub-combination is exhausted, steps (a) to ( c) repeating step.

231. The method of any of 228-230, wherein the combination or one or more sub-combinations of the first set of variables is a linear combination, a non-linear combination, or a machine learning model.

232. The method of 231, wherein the combination of the first set of variables is a weighted sum of the first set of variables, wherein the weights are positive values or negative values.

233. The method of any of clauses 228-232, wherein the combination of the second set of variables is a linear combination, a non-linear combination, or a machine learning model.

234. The method of any of clauses 228-233, wherein the ADI comprises an ADI feature and the AEI comprises an AEI feature corresponding to the ADI feature, wherein the AEI feature is determined via a trained model.

235. The model according to any one of clauses 228 to 233, wherein the trained model comprises:

translation of features in ADI in a specified direction;

critical dimensions of features in ADI;

elongation of a feature in the ADI in a specified direction;

Triangulation of features in ADI; or

How to determine one or more of the rotations of a feature in ADI.

236. A non-transitory computer readable medium comprising:

instructions that, when executed by the one or more processors, cause the operations to determine a post-etch image (AEI) feature based on the post-develop image (ADI) feature, the operations comprising:

obtaining the ADI of the substrate; and

determining, via the trained model, the AEI by inputting the ADI to the trained model and outputting the ADI, wherein the trained model is a combination of a first set of variables of the measured ADI and a second set of variables of the measured AEI; A non-transitory computer-readable medium trained based on correlations between combinations of sets, wherein the correlations are within a specified correlation threshold.

237. The correlation of 236, wherein the correlation is:

calculating a correlation using given values of (i) a first set of parameters associated with a first set of combinations of variables, and (ii) a second set of parameters associated with a second set of combinations of variables. ;

determining whether the correlation is maximized; and

in response to the correlation not being maximized, adjusting the given values of the first set of parameters and the second set of parameters until the correlation is maximized.

238. The model of 236 or 237, wherein the trained model comprises:

(a) determining whether a correlation of sub-combinations and sub-combinations of the first and second sets of variables exceeds a specified correlation threshold;

(b) in response to the sub-combinations being exceeded, including the sub-combination in the model; and

(c) in response to the sub-combinations not being exceeded, selecting another sub-combination of the first set of variables, and for a specified number of iterations or until the sub-combination is exhausted, steps (a) to ( A non-transitory computer readable medium obtained by repeating c).

239. The non-transitory computer-readable medium of any one of clauses 236-238, wherein the combination or one or more sub-combinations of the first set of variables is a linear combination, a non-linear combination, or a machine learning model.

240. The non-transitory computer-readable medium of clause 237, wherein the combination of the first set of variables is a weighted sum of the first set of variables, the weights being positive values or negative values.

241. The non-transitory computer-readable medium of any of clauses 236-240, wherein the combination of the second set of variables is a linear combination, a non-linear combination, or a machine learning model.

242. The non-transitory computer-readable according to any one of clauses 236 to 241, wherein the ADI comprises an ADI feature, the AEI comprises an AEI feature corresponding to the ADI feature, and wherein the AEI feature is determined via a trained model. media.

243. The model of any one of clauses 236 to 242, wherein the trained model comprises:

translation of features in ADI in a specified direction;

critical dimensions of features in ADI;

elongation of a feature in the ADI in a specified direction;

Triangulation of features in ADI; or

A non-transitory computer readable medium that determines one or more of rotations of features of the ADI.

244. A method for determining an interpretation model associated with a defect in an image after development, comprising:

Obtaining, via a metrology tool, (i) a post-development image (ADI) of the imaged substrate at a given location, and (ii) a post-etch image (AEI) of the imaged substrate at a given location; and

A method comprising determining, based on the ADI and the AEI, an interpretation model configured to identify portions of the ADI that describe a defect in the feature in the ADI.

245. The method of 244, wherein determining an interpretation model comprises:

A method, comprising: applying a local interpretable model-agnostic explanation (LIME) approach to determine an interpretation model, wherein the interpretation model uses the ADI as an input to generate an interpretation map describing the defect of a feature of the ADI.

246. The method of 244, wherein determining an interpretation model comprises:

determining correlation data between the ADI and the AEI; and

using the correlation data, performing principal component analysis or discriminant analysis to determine eigenvectors whose eigenvalues exceed a specified threshold.

247. The method of 246,

calculating a classification value by projecting the ADI onto the eigenvectors; and

responsive to the classification value exceeding the specified threshold, identifying the portion of the input ADI as delineating that a feature in the input ADI is defective.

248. A non-transitory computer readable medium for determining portions of an image after development associated with a defect in a feature, comprising:

When executed by more than one processor,

receiving a post-development image (ADI) of the patterned substrate;

inputting the ADI into the analytical model, the analytical model being trained to determine the portions of the ADI that account for the defect in the features of the ADI; and

A non-transitory computer-readable medium comprising instructions that cause tasks including generating, via an interpretation model, data associated with one or more portions of the ADI that describes a defect in a feature of the ADI.

249. A system for determining portions of an image after development that account for a defect in a feature, comprising:

a storage circuit configured to store the analytical model, the analytical model being trained to determine portions that describe defects in a feature based on a set of training data comprising an after-development image (ADI) and a post-etch image (AEI) of the pattern. become- ;

Control circuit - which is:

receive ADI of the patterned substrate;

input the ADI into the analysis model;

configured to generate, through the interpretive model, data associated with one or more portions of the ADI that describes a defect in a feature of the ADI; and

A system comprising input/output circuitry configured to display the generated data on a display device.

The concepts disclosed herein may simulate or mathematically model any general imaging system imaging sub-wavelength features, and may be particularly useful with emerging imaging technologies capable of producing increasingly shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet) lithography, which can use ArF lasers to generate wavelengths of 193 nm, and even 157 nm using fluorine lasers. Also, EUV lithography can generate wavelengths in the 20-5 nm range by hitting a material (solid or plasma) with high-energy electrons to generate photons within this range, or by using a synchrotron.

While the concepts disclosed herein may be used for imaging on a substrate, such as a silicon wafer, the disclosed concepts are applicable to any type of lithographic imaging systems, for example those used for imaging on substrates other than silicon wafers. It should be understood that it can also be used as

Although reference is made herein to specific uses of the embodiments in IC fabrication, it should be understood that the embodiments herein may have many other possible applications. For example, it may be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, micromechanical systems (MEMS), and the like. One of ordinary skill in the art, in the context of these alternative applications, will refer to any use of the terms "reticle", "wafer" or "die" herein in the context of the more generic term "patterning device", "substrate" or "target portion", respectively. It will be understood that the terms may be considered synonymous or interchangeable. The substrates referred to herein may be processed before or after exposure, for example in a track (a tool that typically applies a layer of resist to a substrate and develops the exposed resist) or a metrology or inspection tool. Where applicable, the teachings herein may be applied to these and other substrate processing tools. Also, as the substrate may be processed more than once, for example to create a multilayer IC, the term substrate as used herein may also refer to a substrate comprising layers that have already been processed multiple times.

As used herein, the terms “radiation” and “beam” refer to particle beams such as ion beams or electron beams (eg, about 365, about 248, about 193, about 157, or about 126 nm). It encompasses all forms of electromagnetic radiation, including ultraviolet radiation (having a wavelength of

The terms “optimizing” and “optimizing” as used herein refer to a patterning apparatus such that results and/or processes have more desirable properties, such as higher projection accuracy of a design pattern on a substrate, a larger process window, etc. (eg, a lithographic apparatus) refers to or means to adjust a patterning process, etc. Thus, as used herein, the terms “optimizing” and “optimizing” refer to one or more that provide an improvement, e.g., a local optimum, in at least one relevant metric, compared to an initial set of one or more values for one or more parameters. Refers to or means the process of identifying one or more values for a parameter. "Optimal" and other related terms should be interpreted accordingly. In one embodiment, optimization steps may be applied iteratively to provide further improvements in one or more metrics.

Aspects of the invention may be embodied in any convenient form. For example, an embodiment may be transmitted by one or more suitable computer programs, which may be delivered on a suitable transmission medium, which may be a tangible transmission medium (eg, a disk) or an intangible transmission medium (eg, a communication signal). can be implemented. Embodiments of the present invention may be implemented using any suitable apparatus, which may take the form of a programmable computer running a computer program specifically arranged to implement the method described herein. Accordingly, embodiments of the present invention may be implemented in hardware, firmware, software, or any combination thereof. Further, embodiments of the invention may be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (eg, a computing device). For example, machine-readable media may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory device; electrical, optical, acoustic, or other forms of propagated signals (eg, carrier waves, infrared signals, digital signals, etc.), and the like. Also, firmware, software, routines, and instructions may be described herein as performing certain operations. It should be understood, however, that these descriptions are for convenience only, and that such operations may in fact occur from a computing device, processor, controller, or other device executing firmware, software, routines, instructions, or the like.

In the block diagrams, illustrated components are shown as individual functional blocks, but embodiments are not limited to systems in which the functionality described herein is configured as illustrated. The functionality provided by each of the components may be provided by software or hardware modules that are configured differently than presently shown, for example, such software or hardware (eg, within a data center or geographically ) may be mixed, combined, replicated, separated, distributed, or otherwise configured differently. The functions described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine-readable medium. In some cases, third-party content delivery networks may host some or all of the information passed over the network, in which case, to the extent that the information (eg, content) is supplied or otherwise said to be made available, the information may be transmitted through the content delivery network. may be provided by sending instructions to retrieve the information from the network.

Unless specifically indicated otherwise, as is clear from the discussion, descriptions using terms such as "processing", "operation", "compute", "determining", etc. throughout this specification refer to special purpose computers or similar special purpose electronic devices. It is understood to refer to the operation or process of a particular apparatus, such as a processing/computing device.

It should be understood that this application describes several inventions. Rather than isolating these inventions into a number of separate patent applications, these inventions have been grouped into a single document because their related subject matter is suitable for savings in the filing process. However, the separate advantages and aspects of these inventions should not be combined. In some instances, while embodiments solve all of the deficiencies specified herein, the present inventions are useful independently, and some embodiments solve only a subset of these problems or other, not mentioned, which will be apparent to one of ordinary skill in the art upon reviewing this disclosure. It should be understood that it provides advantages. Due to cost constraints, some inventions disclosed herein may not be claimed now and may be claimed in future applications as amended claims or as continuation applications. Similarly, due to space constraints, neither the Abstract nor the Summary portions of this document should be considered an exhaustive list of all such inventions or an inclusive of all embodiments of such inventions.

It is understood that the description and drawings are not intended to limit the invention to the specific form disclosed, but, on the contrary, to cover all modifications, equivalents and alternatives falling within the spirit and scope of the invention as defined by the appended claims. should understand

Modifications and alternative embodiments of various embodiments of the invention will be apparent to those skilled in the art in view of this description. Accordingly, this description and drawings are to be construed as illustrative only, and are intended to teach those skilled in the art the general manner of carrying out the invention. It is to be understood that the forms of the invention shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those shown and described herein, parts and processes may be reversed or omitted, certain features may be used independently, and features of the embodiments or embodiments. These may be combined, all of which will be apparent to those skilled in the art after having the benefit of this description. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as set forth in the following claims. The headings used herein are for organizational purposes only and should not be used to limit the scope of the description.

While the concepts disclosed herein may be used for imaging on a substrate, such as a silicon wafer, the disclosed concepts are applicable to any type of lithographic imaging systems, for example those used for imaging on substrates other than silicon wafers. It should be understood that it can also be used as

As used herein, unless specifically stated otherwise, the term "or" encompasses all possible combinations except where impractical. For example, where it is stated that a database may include A or B, the database may include A, or B, or A and B, unless specifically stated otherwise or impracticable. As a second example, where it is stated that a database may comprise A, B, or C, the database is A, or B, or C, or A and B, or It may include A and C, or B and C, or A and B and C.

The above description is for the purpose of illustration and not limitation. Accordingly, it will be understood by those skilled in the art that modifications may be made as set forth without departing from the scope of the claims set forth below.

In the preceding description, any processes, descriptions, or blocks in a flowchart represent modules, segments, or portions of code comprising one or more executable instructions for implementing particular logical functions or steps in a process. It should be understood that, and as will be understood by those skilled in the art, alternative implementations of the present invention may exist in which the functions may be performed outside the order shown or discussed, including being performed substantially concurrently or in reverse order depending on the functions involved, as will be understood by those skilled in the art. Included within the scope of examples.

To the extent that any U.S. patent, U.S. patent application, or other material (eg, article) is cited by reference, the text of such U.S. patent, U.S. patent application, and other material is in conflict between such material and the disclosure and drawings set forth herein. It is cited only to the extent that it is not. In case of such conflict, any such conflicting text in such referenced US patents, US patent applications and other materials is not specifically incorporated by reference herein.

While certain embodiments have been described, these embodiments have been presented by way of example only and are not intended to limit the scope of the invention. Indeed, the novel methods, apparatuses, and systems described herein may be embodied in various other forms; In addition, various omissions, substitutions, and changes in the form of the methods, apparatuses, and systems described herein may be made without departing from the spirit of the present invention. The appended claims and their equivalents are intended to cover such forms or modifications as fall within the spirit and scope of the present invention.

Claims (15)

A method of training a model configured to predict whether a feature associated with an imaged substrate will be defective after etching of the imaged substrate, comprising:
Via a metrology tool, (i) a post-developed image of the imaged substrate at a given location, the post-developed image comprising a plurality of features, and (ii) an image of the imaged substrate at the given location. obtaining a post-etch image, wherein the post-etch image includes etched features corresponding to the plurality of features; and
training a model configured to determine a defectiveness of a given one of the plurality of features in the post-developed image using the post-developed image and the post-etched image;
including,
wherein the determination of the defect is based on comparing a given feature in the post-developed image to a corresponding etched feature in the post-etch image. The method of claim 1,
wherein the model is an empirical model or a machine learning model, wherein the empirical model is a function of a physical property of a feature associated with the imaged substrate. The method of claim 1,
The steps of obtaining an image after the development are:
imaging the mask pattern on the substrate through the patterning device;
obtaining a developed substrate of the imaged substrate;
aligning the metrology tool to the developed substrate at the given position; and
and capturing an image of the developed substrate. The method of claim 1,
The steps of obtaining an image after the etching include:
etching the imaged substrate through an etching process with specified etching conditions;
aligning the metrology tool to the etched substrate at the given location; and
and capturing an image after etching of the etched substrate. 5. The method of claim 4,
The etch conditions may include etchant composition, plasma gas parameters, etch rate, electromagnetic field, plasma potential, inductive or capacitive etching type, temperature of the substrate, ion energy distribution, ion angle distribution, sputtering and redeposition rates, or these A method comprising a combination of The method of claim 1,
The training steps include:
aligning the post-developed image and the post-etched image based on the plurality of features;
comparing each of the features of the plurality of features in the post-developed image to a corresponding feature of the etched features in the post-etched image;
determining, based on the comparison, whether a given etched feature in the post-etched image satisfies a defect condition;
in response to not meeting the defect condition, classifying the identified feature as defective; and
and adjusting model parameter values of the model based on the presence of the identified feature. 7. The method of claim 6,
wherein adjusting the model parameter value comprises adjusting values of a plurality of model parameters. 7. The method of claim 6,
wherein the defect condition is a physical property of a given etched feature in the post-etched image. 9. The method of claim 8,
The physical properties are:
the critical dimension of the etched feature given above; or
at least one of the displacement of the given etched feature relative to the given feature of the image after developing. The method of claim 1,
The above defects are:
Binary determination of whether a defect is present or not; or
characterized by at least one of a probability that the given feature is defective. 3. The method of claim 2,
wherein the machine learning model is a convolutional neural network. 12. The method of claim 11,
wherein model parameters are weights or biases associated with one or more layers of the machine learning model. 12. The method of claim 11,
wherein the model parameters that are weights or biases include model parameters that are weights and biases. The method of claim 1,
wherein the metrology tool is an optical microscope or an electron beam microscope. A system for determining a fraction of features that will fail after etching, comprising:
a metrology tool that captures a post-developed image (ADI) of the substrate at a given location, the post-developed image comprising a plurality of features; and
a processor configured to run a model for determining failure rates of a plurality of features of the ADI that will fail after etching
including,
The model includes (i) a first probability distribution function configured to estimate a distribution of physical property values for non-failing holes, and (ii) a physical property of all of the plurality of features of the ADI. a combination of a second probability distribution function configured to determine failure rates based on the values.

Images