CN118348748A

CN118348748A - Diffraction field simulation and error measurement sensitivity analysis method and equipment for overlay mark

Info

Publication number: CN118348748A
Application number: CN202410540973.8A
Authority: CN
Inventors: 江浩; 陈侃; 刘佳敏; 崔雪; 李磊; 王威
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Filing date: 2024-04-30
Publication date: 2024-07-16

Abstract

The application belongs to the field of photoetching analysis, and particularly discloses a diffraction field simulation and error measurement sensitivity analysis method and equipment for overlay marks, wherein the diffraction field simulation method comprises the following steps: determining the position of an emergent point of the incident light after the incident light passes through the overlay mark by combining the parameter of the overlay mark and the measurement parameter number, wherein the emergent light comprises at least one of zero-order diffraction light and high-order diffraction light; acquiring a Jones matrix of each emergent point according to the position of each emergent point and combining the measurement parameters; determining emergent light electric field vectors at all emergent points by combining the Jones matrix of all the emergent points; and acquiring the light intensity of each emergent point according to the emergent light electric field vector. According to the application, the sensitivity of the overlay information is analyzed through the different areas of the overlay mark objective lens back focal plane diffraction optical frequency domain image, the measurement conditions, the overlay mark morphology parameters and other configuration parameters, so that a detection area with higher overlay error perception sensitivity can be obtained, and the configuration combination of the measurement conditions can be optimized.

Description

Diffraction field simulation and error measurement sensitivity analysis method and equipment for overlay mark

Technical Field

The application belongs to the field of photoetching analysis, and particularly relates to a diffraction field simulation and error measurement sensitivity analysis method and equipment for overlay marks.

Background

With the continuous progress of integrated circuit fabrication processes, integrated circuit fabrication processes have entered the nanometer scale, making the circuit more compact, lower power consumption and more powerful. Photolithography is used as a core process in the integrated circuit manufacturing process, and the main processes comprise deposition, gluing, soft baking, exposure, hard baking, development, photoresist pattern detection, etching, ion implantation and photoresist removal. The area of the exposed area on the wafer is at a premium and for the integration of more complex circuits in limited exposed areas, multiple photolithography is often performed on the wafer to increase chip integration. In order to ensure that the stacked circuit of multiple photolithography processes can work normally, the pattern (current layer) left on the photoresist after exposure and development is registered with the existing pattern (previous layer) on the wafer substrate. The overlay error means the overlay error between the current layer and the reference layer along the x and y directions, and is one of three performance indexes of the lithography machine.

Typical Overlay error measurement methods are mainly classified into an Image-Based Overlay error (IBO) detection method and a Diffraction-Based Overlay error Detection (DBO) method. As the process node descends, the overlay error gradually exceeds the limits of the IBO measurement method and gradually loses dominance. The DBO method mainly includes an empirical DBO method (eDBO) and a model-based mDBO (model-based DBO). The mDBO method solves the complex partial differential equation in real time by calling the forward optical model for extracting parameters and comparing the measured diffraction signals, and is difficult to meet the time requirement of online in-situ measurement. The eDBO method utilizes the alignment error to be in a certain range, and a linear relation exists between the zero-order light reflectivity R ₀ of the periodic alignment mark and the alignment error OV:

R₀＝K·OV+b (1)

Wherein K represents the sensitivity of R ₀ to the overlay error OV, and b represents the intercept; by using the empirical linear relation, the dependence on a forward optical model can be eliminated, so that the rapid extraction of the overlay error is realized. In subsequent researches, it is found that when the overlay error is within a certain range, the difference between the reflectivity of the higher-order diffracted light of the periodic overlay mark and the overlay error also has a linear relationship, and when the overlay error is zero, the difference between the reflectivity is zero, that is, the intercept b in the formula (1.1) is equal to 0, as shown in fig. 1, so that measurement of one direction overlay error can be realized by using two overlay marks, and the occupied area of the overlay mark on the mask plate is greatly reduced, as shown in fig. 2, so that the method is also the overlay error extraction method mainstream in the industry at present.

The special overlay mark of the DBO technology is a periodic nano grating structure which is specially designed, so in the eDBO method, optical characteristic modeling is generally needed to be carried out on the nano structure to be detected firstly, namely, the relation between the geometric parameter, the material optical constant, the measurement condition and the like of the nano structure to be detected and the optical diffraction amount of the reflectivity and the like is established. Strictly coupled wave analysis (Rigorous Coupled WAVE ANALYSIS, RCWA) is a numerical method for analyzing the propagation and diffraction of light waves in periodic structures that can provide high accuracy diffraction efficiency and field distribution information. RCWA is widely used in modeling of nanostructure optical properties due to its relatively simple numerical solution process.

Although the eDBO method relies on the linear relation between the optical diffraction amount and the overlay error when extracting the overlay error, and does not need to call a forward optical model of the overlay mark, the sensitivity of the overlay mark to the overlay information of different areas of the overlay mark objective lens back focal plane diffraction optical frequency domain image, measurement conditions, overlay mark morphology parameters and other configuration parameters is different. Meanwhile, in order to realize rapid and robust extraction of the overlay error by the eDBO method, the sensitivity of the optical diffraction quantity on the overlay error needs to be higher, so that the influence of measurement noise on the overlay error measurement result is resisted, and the measurement result with higher precision is obtained. Therefore, ideal forward simulation modeling and sensitivity analysis are required, and basis and optimal configuration are provided for overlay error measurement.

Disclosure of Invention

Aiming at the defects of the prior art, the application aims to provide a diffraction field simulation and error measurement sensitivity analysis method and equipment for overlay marks, and aims to solve the problems that the prior art cannot simulate the frequency domain light field distribution of a multi-level diffraction field, cannot obtain a detection area with higher overlay error perception sensitivity and optimizes measurement condition configuration combination.

In order to achieve the above object, in a first aspect, the present application provides a diffraction field simulation method for overlay error, including:

Determining the position of an emergent point of the incident light after the incident light passes through the overlay mark by combining the parameter of the overlay mark and the measurement parameter number, wherein the emergent light comprises at least one of zero-order diffraction light and high-order diffraction light;

Acquiring a Jones matrix of each emergent point according to the position of each emergent point and combining the measurement parameters;

Determining emergent light electric field vectors at all emergent points by combining the Jones matrix of all the emergent points;

and acquiring the light intensity of each emergent point according to the emergent light electric field vector.

It will be appreciated that the present application is capable of simulating the light field of single-or multi-order diffracted light, i.e., the frequency domain image of multi-order diffracted light. The sensitivity of the sets of measurement parameters at the exit areas can also be analyzed based on the simulated light field, see in particular the relevant description of the second aspect.

In an alternative implementation, the incident light passes through the objective lens and then enters the overlay mark; the parameters of the overlay mark comprise the period parameters of the mark; the measurement parameters comprise the wavelength of incident light and the numerical aperture of an objective lens in the measurement device;

The position of the exit point is determined by:

Determining the position of an emergent point of zero-order diffraction light according to the incident coordinate and the incident angle of the incident light;

and determining the position of an emergent point of the higher-order diffraction light according to the incident coordinate of the incident light, the incident angle of the incident light, the period parameter of the overlay mark, the wavelength of the incident light and the numerical aperture of the objective lens.

In an alternative implementation manner, when the overlay mark is a periodic nano grating structure, the exit point position is specifically:

the zero-order diffraction light emergent point coordinates are opposite to the incident coordinates, the emergent angle is the same as the incident angle of the incident light, and the azimuth angle is 180 degrees different; and

The exit point coordinates (x _m,y_m) of the higher order diffracted light are:

(x_m,y_m)＝(-x_in+Δ,-y_in)

Wherein the subscript m represents different diffraction orders, (x _in,y_in) represents the coordinates of an incident point, delta represents the offset of the corresponding emergent point of the diffracted light of the adjacent order, Lambda is the wavelength of the incident light and lambda is the period of the grating.

In an alternative implementation, when the overlay mark is a periodic nano grating structure, a jones matrix of each point in the exit surface is calculated according to the position of each exit point, including:

determining an incident angle, an emergent angle and an azimuth angle corresponding to any point on a back focal plane of the objective according to the numerical aperture of the objective;

determining electromagnetic fields of an incident area and a transmission area based on the incident angle, the exit angle and the azimuth angle by combining maxwell's equations;

performing Fourier series expansion on the dielectric constant and the electromagnetic field in the periodic nano grating area to obtain a corresponding coupled wave differential equation;

and applying electromagnetic field boundary conditions on the upper and lower boundaries of the periodic nano grating region, and solving the amplitude of each diffraction order by combining the coupled wave differential equation so as to determine the Jones matrix of each point.

It should be noted that, the calculation process of the specific jones matrix may refer to the description of the related art, and the present application is not limited to this, and those skilled in the art may calculate the corresponding jones matrix according to the related art according to actual needs.

In an alternative implementation, the emergent light electric field vector at each emergent point is determined by combining the jones matrix of each emergent point, specifically:

Where E _output represents the outgoing light electric field vector, E _input represents the electric field vector of the incoming light, Represents azimuth angle, θ represents incident angle, R () represents rotation matrix,Indicating the rotation azimuth angle of the exit point coordinate system relative to the incident planeP1 represents a polarizer and P2 represents a polarizing beam splitter, the polarizer being used to modulate the polarization state of incident light; the polarization beam splitter is used for dividing the pupil plane frequency domain image of the diffraction light into a Co-pol Co-polarization pupil plane frequency domain image and a Cross-pol Cross-polarization pupil plane frequency domain image; The jones matrix representing the exit point, J _M, J _P1, the jones matrix of the polarizer, and J _P2 the jones matrix of the polarizing beam splitter.

It can be appreciated that the polarizing beam splitter is configured to divide the pupil plane frequency domain image of the diffracted light into a Co-pol Co-polarized pupil plane frequency domain image and a Cross-pol Cross-polarized pupil plane frequency domain image, so as to obtain a frequency domain image of the multi-order diffracted light, and implement light field analysis of the multi-order diffracted light.

In an alternative implementation, the light intensity of each exit point is obtained by multiplying the electric field vector of the exiting light at the exit point with its conjugate and then modulo the result.

In a second aspect, the present application provides a measurement sensitivity analysis method for overlay error, including:

Determining the light intensity of each exit point at different overlay errors for a set of measurement parameters using the method described in the first aspect or any of the alternative implementations of the first aspect;

And determining the sensitivity of the set of measurement parameters to the overlay error at each exit point according to the change of the light intensity of the exit point under the set of measurement parameters relative to the change of the overlay error.

Optionally, the overlay error can be a known parameter, and the overlay error measurement sensitivity of different emergent areas under different measurement parameters of a single-stage or multi-stage diffraction field can be determined by analyzing the optical field of the single-stage or multi-stage diffraction field and the detection sensitivity of the overlay error. Through the sensitivity analysis, the corresponding diffraction field, the corresponding measurement parameters and the corresponding emergent region are selected to measure the overlay error, so that high-precision overlay error measurement is realized.

It can be understood that it is obvious that the sensitivity of the overlay error needs to be higher, the more favorable the resistance to the influence of the measurement noise on the overlay error measurement result, and the measurement result with higher precision is obtained.

In an alternative implementation, the light intensity difference at the exit points before and after the overlay error changes is divided by the overlay error change value, and then the sensitivity of the set of measurement parameters at each exit point is obtained by multiplying the difference by a preset coefficient.

In a third aspect, the present application provides an electronic device comprising: at least one memory for storing a program; at least one processor for executing a memory-stored program, the memory-stored program, when executed, operable to perform the method of the first aspect or any of the alternative implementations of the first aspect.

In a fourth aspect, the present application provides a computer readable storage medium storing a computer program which, when run on a processor, causes the processor to perform the method described in the first aspect or any of the alternative implementations of the first aspect.

In a fifth aspect, the application provides a computer program product which, when run on a processor, causes the processor to perform the method described in the first aspect or any of the alternative implementations of the first aspect.

It will be appreciated that the advantages of the second to fifth aspects may be found in the relevant description of the first aspect, and are not described here again.

In general, the above technical solutions conceived by the present application have the following beneficial effects compared with the prior art:

The application provides a diffraction field simulation and error measurement sensitivity analysis method and equipment for overlay marks, which can fully utilize incident angle and azimuth angle information in a pupil plane range to obtain frequency domain vector images of zero-order light and high-order diffraction light through a numerical modeling method. The sensitivity analysis is carried out on the overlay error by utilizing the frequency domain vector image, the detection area with higher perceived sensitivity on the overlay error can be obtained by the different areas of the overlay mark objective lens back focal plane diffraction optical frequency domain image and the sensitivity of configuration parameters such as measurement conditions, overlay mark morphology parameters and the like, the configuration combination of the measurement conditions can be optimized, meanwhile, theoretical basis can be provided for the design and improvement of the overlay mark morphology parameters, the influence of measurement noise on the overlay error measurement result can be resisted, the measurement result with higher precision can be obtained, and theoretical basis can be provided for the establishment of subsequent instruments and actual measurement.

Drawings

FIG. 1 is a typical eDBO optical characterization graph;

FIG. 2 is a schematic diagram of an exemplary eDBO overlay mark;

FIG. 3 is a flow chart of a diffraction field simulation method for overlay marks provided by an embodiment of the present application;

FIG. 4 is a flowchart of an overlay error measurement sensitivity analysis method provided by an embodiment of the present application;

FIG. 5 (a) is a front view of an objective lens simplified geometric model beam converging and collecting through the objective lens provided by an embodiment of the present application;

FIG. 5 (b) is a schematic diagram of a Cartesian coordinate system of a simplified model back focal plane of an objective lens according to an embodiment of the present application;

FIG. 6 is a schematic diagram of an amplitude-division type polarization analyzer-based scatterometer according to an embodiment of the present application;

FIG. 7 is a schematic diagram of overlay mark nanostructure morphology parameters and materials provided by an embodiment of the present application;

FIG. 8 is a graph of total intensity image of back focal plane vector frequency domain of an overlay mark objective provided by an embodiment of the present application;

FIG. 9 is a simulation of the back focal plane sensitivity of selected overlay marks at 532nm wavelength under different sets of measurement parameters provided by an embodiment of the present application; (a) TM, na=0.85; (b) TE, na=0.85; (c) TM, na=0.90; (d) TE, na=0.90;

Fig. 10 is a schematic diagram of an electronic device according to an embodiment of the present application.

Detailed Description

The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.

The term "and/or" herein is an association relationship describing an associated object, and means that there may be three relationships, for example, a and/or B may mean: a exists alone, A and B exist together, and B exists alone. The symbol "/" herein indicates that the associated object is or is a relationship, e.g., A/B indicates A or B.

In embodiments of the application, words such as "exemplary" or "such as" are used to mean serving as an example, instance, or illustration. Any embodiment or design described herein as "exemplary" or "e.g." in an embodiment should not be taken as preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "such as" is intended to present related concepts in a concrete fashion.

First, technical terms involved in the embodiments of the present application will be described.

(1) Overlay mark

Overlay mark points are an important element in the printing process, especially in the die cutting process. These mark points are designed to ensure accuracy and smooth processing. Specifically, the overlay left and right marking points need to be kept horizontal, and they serve as datum points to ensure the accuracy of the die cut pattern during the die cutting process. If the two marking points are not on the same horizontal line, the two marking points are offset to one side, so that the precision of the die cutting processing is reduced, and even the problem of incomplete die cutting can occur.

(2) Overlay error

Overlay error, also known as Overlay error, refers to the relative positional relationship between a current layer and a reference layer on a wafer during integrated circuit fabrication; the current layer, e.g., photoresist pattern, and the reference layer, e.g., in-substrate pattern. Ideally, the patterns of the current layer and the reference layer should be perfectly aligned, i.e. the overlay error is zero. However, due to various systematic errors and occasional errors, the positions of the two patterns may deviate, resulting in overlay errors. Overlay error is a key indicator for monitoring the quality of a lithographic process and describes the deviation of a current pattern from a reference pattern in the X and Y directions and its distribution over the wafer surface. In order to ensure that the upper and lower layers of the design can be reliably connected, the alignment deviation between a certain point in the current layer and the corresponding point in the reference layer must be less than 1/3 of the minimum pitch of the pattern. As technology nodes advance, the critical lithography layer allowed alignment deviations (i.e., overlay errors) will shrink at a scale of about 80%. For example, in the 20nm node, the overlay error requirement for the critical layer is 8.0nm. Measurement and reduction of overlay errors is critical to ensure the accuracy and reliability of integrated circuits.

Next, the technical scheme provided in the embodiment of the present application is described.

FIG. 3 is a flow chart of a diffraction field simulation method for overlay marks provided by an embodiment of the present application; as shown in fig. 3, the method comprises the following steps:

Step S11, determining the position of an emergent point of incident light after the incident light passes through the overlay mark by combining the parameter of the overlay mark and the number of measured parameters, wherein the emergent light comprises at least one of zero-order diffraction light and high-order diffraction light;

Step S12, acquiring a Jones matrix of each exit point according to the position of each exit point and combining the measurement parameters;

Step S13, determining emergent light electric field vectors at all emergent points by combining the Jones matrix of all the emergent points;

And S14, acquiring the light intensity of each emergent point according to the emergent light electric field vector.

It should be noted that, the scheme provided by the application can simulate the light field distribution condition of the diffracted light after the incident measuring device is incident on the overlay mark by combining the parameter of the overlay mark and the measurement parameter.

FIG. 4 is a flowchart of an overlay error measurement sensitivity analysis method according to an embodiment of the present application; as shown in fig. 4, the method comprises the following steps:

Step S21, determining the light intensity of each emergent point under a group of measurement parameters in different overlay errors by adopting the diffraction field simulation method provided by FIG. 3;

Step S22, determining the sensitivity of the set of measurement parameters to the overlay error at each of the exit points according to the change of the light intensity of the exit points under the set of measurement parameters relative to the overlay error.

It should be noted that, the method provided by the application can simulate the overlay mark frequency domain image with overlay error, and does not pay attention to the measurement of the overlay error, and the value of the overlay error can be preset.

It can be understood that the application establishes the frequency domain vector imaging model of the overlay mark to calculate and solve the emergent light intensity by the electric field vector in the form of Jones matrix of zero-order light and higher-order diffraction light, simulates the post-focal plane vector frequency domain image of the objective lens designed by us based on the amplitude-division type polarization-analysis angle resolution scatterometer, and analyzes the sensitivity of the overlay error by means of the simulation image, thereby providing a theoretical basis for the measurement condition selection and configuration optimization analysis of the overlay error.

In a more specific embodiment. The application provides a frequency domain imaging vector modeling and sensitivity measurement configuration optimization method of overlay marks, which comprises the following steps:

Step 101, determining the nanostructure morphology parameters and the material optical constants of the overlay mark.

Preferably, the nanostructure morphology parameters of the overlay mark in step 101 include a line width CD ₁ of the top layer grating, a line width CD ₂ of the bottom layer grating, a period Pitch of the top layer grating and the bottom layer grating, a wall height H ₁ of the top layer grating, a wall height H ₃ of the bottom layer grating, a middle thin film layer thickness H ₂, an overlay offset OV, a right side wall angle (RIGHT SIDE WALL ANGLE, RSWA) of left side wall angles (LEFT SIDE WALL ANGLE, LSWA) of the top layer grating and the bottom layer grating, and a slice number slice_num (the trapezoid grating can be differentially sliced into multiple layers of gratings with different line widths); the optical constant of the material refers to the complex refractive index of the material.

Step 102, configuring corresponding measurement conditions (for simulation) according to the nanostructure morphology parameters and the material optical constants of the overlay mark determined in step 101, and calculating the zero-order light emergent point of the incident light and the emergent position of the higher-order diffraction light through the established objective lens back focal plane model.

Preferably, the configuration measurement conditions described in step 102 include wavelength of incident light, numerical aperture NA of objective lens, number nu of simulation points, and polarization angle p_angle; as shown in fig. 5 (a) and 5 (b), the objective lens back focal plane model shows that, under the condition of a large incident angle, the paraxial approximation condition of the principal plane is not established, so that the objective lens is simplified to a principal spherical surface with the front focal point of the objective lens as the center of sphere, and the radius is the front focal length f of the objective lens, as shown in fig. 5 (a). The distance d _i between the coordinate (x _i,y_i) of any point on the back focal plane of the objective lens and the optical axis and the incident angle θ _i corresponding to the point have the following relationships:

d_i＝f·sinθ_i (2)

the numerical aperture NA of the objective lens and its limit acceptance angle are defined as follows:

NA＝n·sinθ_max (3)

Where n is the refractive index of the working medium of the objective lens, n is 1 and θ _max is the limit acceptance angle of the objective lens since the objective lens works in air. As shown in fig. 5 (b), the cartesian coordinate system of the entire back focal plane is normalized by the coordinates of the entire back focal plane of the objective lens, and the normalized reference length r has the following relationship:

r＝f·sinθ_max (4)

According to equations (2) to (4), the incident angle or exit angle information corresponding to any point (x _i,y_i) on the back focal plane of the objective lens can be obtained:

azimuth corresponding to any point Information:

the overlay mark is a periodic nano structure, and the 0-order diffraction light emergent point is opposite to the incident coordinate, the incident angle is the same, and the azimuth angle is 180 degrees different. The higher order diffracted light coordinate points may be according to the grating diffraction formula:

mλ＝Λ·(sinθ_in±sinθ_m) (7)

m represents different diffraction orders: 0, ±1, ±2 …, θ _in represents an incident angle, θ _m represents a diffraction angle, λ is an incident light wavelength, and Λ is a grating period. The offset delta of the corresponding emergent point of the adjacent-order diffraction light is as follows:

the exit point coordinates (x _m,y_m) of the higher order diffracted light are:

(x_m,y_m)＝(-x_in+Δ,-y_in) (9)

(x _in,y_in) represents the coordinates of the incident point.

Step 103, calculating corresponding incidence angle, emergence angle and azimuth angle according to the incidence point, emergence point and higher-order diffraction light emergence position information stored in step 102, and calculating Jones matrix of each point by using RCWA.

Preferably, the principles of calculating the incident angle, the exit angle and the azimuth angle in step 103 are already embodied in the objective lens back focal plane model. The modeling method RCWA mainly comprises three steps: (1) Deducing electromagnetic field expressions of the incident field area and the transmission field area by using a Maxwell equation set and performing Fourier expansion; ; (2) In the grating area, carrying out Fourier expansion on the dielectric constant and an electromagnetic field parallel to the boundary surface, and establishing an equation between Fourier expansion coefficients of the electromagnetic field by using a Maxwell rotation equation; (3) Electromagnetic field boundary conditions are applied to the upper and lower boundaries of the grating region to obtain diffraction order amplitudes, and optical diffraction amounts such as Jones matrix are further calculated.

Step 104, substituting the Jones matrix calculated in step 103 into the established system model of the whole instrument, multiplying the system model by the optical devices through which the light sequentially passes, and calculating electric field vectors E _output of the zero-order light and the high-order diffracted light respectively.

Preferably, as shown in fig. 6, the apparatus in step 104 is configured such that light emitted by the light source is collimated and then focused on the surface of the sample by the high NA objective lens, and diffracted light of different orders containing the morphological information of the sample after being diffracted by the sample is collected by the objective lens and imaged onto the main detection light path CCD by the relay lens, and an auxiliary light path is added in combination with the measurement requirement to determine the alignment mark position. The polarizing beam splitter PBS divides the pupil plane frequency domain image into a Co-pol Co-polarized pupil plane frequency domain image and a Cross-pol Cross-polarized pupil plane frequency domain image, where the Co-pol Co-polarized pupil plane frequency domain image contains stronger signals, its symmetrical information contains the morphological structure information of the sample, including height, critical dimension CD, material properties, etc., while the Cross-pol Cross-polarized pupil plane frequency domain image contains weaker signal intensity, and its asymmetrical information generally includes overlay information.

Considering each device as an ideal device, the devices for changing the light beam property only comprise a polaroid, a sample to be tested and a polarization beam splitter, if the incident light beam is described by an electric field intensity vector, a system model is described by a Jones matrix according to the sequence of the light beam passing through each device:

Where E _input denotes the electric field vector of the incident light, E _output denotes the electric field vector of the outgoing light, Represents azimuth angle, θ represents incident angle, R () represents rotation matrix,Indicating the rotation azimuth angle of the coordinate system relative to the incident surfaceP1 represents a polarizer, P2 represents a polarizing beam splitter, J _s represents a jones matrix of an overlay mark, J _P1 represents a jones matrix of a polarizer, and J _P2 represents a jones matrix of a polarizing beam splitter. The light is reflected on the overlay mark, the direction of the electric field intensity vector is reversed with the direction of the Cartesian coordinate system, and the reflection transformation matrix J _M is introduced. The concrete form of each jones matrix is as follows:

Step 105, calculating the light intensity I through the electric field vector E _output, sequentially outputting the light intensity I of the zero-order light and the light intensity I of each high-order diffraction light, obtaining the vector frequency domain image of the back focal plane of the objective lens of the zero-order light and each high-order diffraction light, and meanwhile, performing scalar superposition according to the position information of the emergent point to obtain the total light intensity image of the vector frequency domain of the back focal plane of the objective lens.

In particular, the light source can be considered as an ideal light source, then the incident light field vectorThe system matrix can calculate the zero-order light and each higher-order diffraction light to obtain an emergent light electric field vector E _output respectively, and calculate the light intensity I, wherein the light intensity I can be expressed as:

representing the conjugate vector of E _output.

And 106, selecting a plurality of groups of measurement configurations, and repeating the steps to obtain the vector frequency domain image and the total light intensity image of the back focal plane of the objective lens of the zero-order light and each higher-order diffraction light again. Images reflecting the sensitivity of different areas (different areas correspond to different incidence angles and azimuth angles) and the changed measurement configuration conditions to the overlay error values can be obtained through calculation, theoretical basis is provided for measurement condition selection and configuration optimization analysis, and an optimal scheme is selected for measurement experiments.

Preferably, step 106 further comprises the expression for overlay error sensitivity:

s _i is a sensitivity coefficient of the Overlay error Overlay under the I-th group measurement configuration, deltax represents a variable quantity of the Overlay error Overlay, which can be a known quantity, I' represents an Overlay simulation image after the change, I represents an Overlay simulation image before the change, and a is an amplification coefficient which is an adjustable numerical value; the specific numerical value of the amplification factor can be designed according to actual needs by a person skilled in the art, and can be adjusted at any time, and the specific numerical value of the parameter is not limited in the application.

The application provides a frequency domain imaging vector modeling and sensitivity measurement configuration optimization method of an overlay mark, which establishes a frequency domain vector imaging model of the overlay mark, solves the light intensity of emergent light by calculating electric field vectors in a Jones matrix form of zero-order light and higher-order diffraction light, simulates an objective lens back focal plane vector frequency domain image which is designed by us and is based on an amplitude-division type polarization-analysis angle resolution scatterometer, and performs sensitivity analysis on overlay errors by means of simulation images, thereby providing theoretical basis for overlay error measurement condition selection and configuration optimization analysis.

In a specific embodiment, the implementation process of the method for modeling the frequency domain imaging vector and optimizing the sensitivity measurement configuration of the overlay mark provided in the embodiment is as follows:

1. Determining the shape parameters and the material optical constants of the nanostructure of the overlay mark, wherein as shown in fig. 7, the linewidth of the top layer grating and the linewidth of the bottom layer grating are both 300 nanometers, the period Pitch of the top layer grating and the bottom layer grating is 600 nanometers, the wall height H ₁ of the top layer grating is 150 nanometers, the wall height H ₃ of the bottom layer grating is 150 nanometers, the thickness H ₂ of the middle film layer is 30 nanometers, the overlay offset value OV is 10 nanometers, the left side wall angle LSWA and the right side wall angle RSWA of the top layer grating and the bottom layer grating are both 90 degrees, and the slice numbers slice_num of the top layer grating and the bottom layer grating are both 1 because of the rectangular gratings; the top layer grating is made of photoresist, the grating ridge refractive index n _rd is 3, and the grating groove refractive index n _gr is 1.0; the intermediate layer is made of silicon dioxide, and the refractive index is 1.551; the bottom layer grating is made of silicon, the grating ridge refractive index n _rd is 1.48, and the grating groove refractive index n _gr is 1.0. And loading a corresponding material model file, and calculating the complex refractive index of each layer of material.

2. According to the nanostructure morphology parameters and material information of the overlay mark, corresponding measurement conditions are configured, the wavelength of detected light is set to 532 nanometers, the number of simulation points nu is set to 101 x 101, the preset overlay error OV is 10 nanometers, the numerical aperture NA of the objective lens is set to 0.85, the polarizing angle P_angle is set to 0 degrees, the diffraction order range is set to-2 to +2 orders (the diffracted light of the higher order exceeds the range of the pupil plane of the frequency domain). In this embodiment, the wavelength of the detected light, the grating period pitch, the numerical aperture NA, and the material complex refractive index are all set as simulated global variables. The modeling method further comprises setting the shape of a diaphragm, setting no diaphragm in the embodiment, inputting the number nu of simulation points, the range of diffraction orders, the polarizing angle P_angle and the numerical aperture into a back focal plane model (calcu _stop) of the objective lens, calculating the emergent point of zero-order light of incident light and the emergent position of high-order diffraction light, and storing the calculated emergent point and emergent position in coordinate variables.

3. According to the stored incident point, emergent point and information of the emergent position of the higher diffraction light, corresponding incident angle, emergent angle and azimuth angle are calculated and stored in the stop1 variable. The calculated angle information and the calculated position information are input into an RCWA_for_ ellips calculation file, and a Jones matrix of each point is calculated by using a strict coupled wave analysis (RCWA) modeling method and is correspondingly stored according to the position information of each point.

4. The Jones matrix information obtained in the above steps is brought into a model matrix of the whole system, an emergent electric field vector E _output is calculated for diffraction light of-2 level, -1 level, 0 level, +1 level and +2 level respectively, the light intensity value of each point is calculated by using a formula (15), the light intensities I of zero level light and each high level diffraction light are sequentially output, an objective lens back focal plane vector frequency domain image of the zero level light and each high level diffraction light can be obtained, and meanwhile scalar superposition is carried out according to the position information of the emergent point, and an objective lens back focal plane vector frequency domain total light intensity image can be obtained, as shown in figure 8.

5. Changing the measurement condition configuration, repeating the steps, and obtaining the back focal plane vector frequency domain image and the frequency domain total light intensity image of the objective lens of the zero-order light and the diffraction light of each higher order again. Images reflecting the sensitivity of different areas (different areas correspond to different incidence angles and azimuth angles) and the changed measurement configuration conditions to the overlay error values can be obtained through calculation, theoretical basis is provided for measurement condition selection and configuration optimization analysis, and an optimal scheme is selected for measurement experiments. The present embodiment only shows the difference in polarization angle, i.e. the effect of the combination of the configuration of the polarization state of the incident light and the change in numerical aperture NA of the objective lens on the overlay error sensitivity, as shown in fig. 9, for the same mark, there are different measurement sensitivities for different polarization states (TE, TM) and different objective lens NA and different areas on the back focal plane. Referring to fig. 9, the sensitivity value of the middle small area in fig. 9 (b) is the largest (the brightness is the largest), and the measurement parameters of the group (b) and the data of the image area with the largest brightness in fig. 9 can be selected to measure the overlay error, so as to realize high-precision error measurement. The selection of the measurement parameters and the selection of the diffraction light orders can also be adjusted to determine the sensitivity under each group of parameters, so as to select proper measurement parameters and diffraction light and realize overlay error measurement meeting the measurement requirements.

Further, in an alternative embodiment, the present application also provides a diffraction field simulation system of overlay error, which may include:

The system comprises an emergent point position simulation unit, a control unit and a control unit, wherein the emergent point position simulation unit is used for determining the emergent point position of incident light after the incident light passes through the overlay mark by combining the parameter of the overlay mark and the number of measurement parameters, and the emergent light comprises at least one of zero-order diffraction light and high-order diffraction light;

the Jones matrix acquisition unit is used for acquiring the Jones matrix of each emergent point according to the position of each emergent point and combining the measurement parameters;

An outgoing light electric field determining unit for determining an outgoing light electric field vector at each outgoing point in combination with the jones matrix of each outgoing point;

And the emergent point light intensity acquisition unit is used for acquiring the light intensity of each emergent point according to the emergent light electric field vector.

Illustratively, the incident light passes through the objective lens and then enters the overlay mark; the parameters of the overlay mark comprise the period parameters of the mark; the measurement parameters comprise the wavelength of incident light and the numerical aperture of an objective lens in the measurement device;

The exit point position simulation unit determines the exit point position of zero-order diffraction light according to the incident coordinate and the incident angle of incident light; and determining the position of an emergent point of the higher-order diffraction light according to the incident coordinate of the incident light, the incident angle of the incident light, the period parameter of the overlay mark, the wavelength of the incident light and the numerical aperture of the objective lens.

Further, in another alternative embodiment, the present application further provides a method for analyzing measurement sensitivity of overlay error, including:

The light intensity determining unit is used for determining the light intensity of each emergent point under a group of measurement parameters in different overlay errors by adopting the method provided by the embodiment in fig. 3 and the embodiment above;

and the sensitivity analysis unit is used for determining the sensitivity of the set of measurement parameters for measuring the overlay error at each exit point according to the condition that the light intensity of the exit point changes relative to the overlay error under the set of measurement parameters.

The sensitivity analysis unit divides the light intensity difference at the exit points before and after the overlay error changes by the overlay error change value, and then multiplies the light intensity difference by a preset coefficient to obtain the sensitivity of the set of measurement parameters at each exit point.

It should be understood that, the two systems are used to execute the method in the foregoing embodiment, and corresponding program modules in the systems implement principles and technical effects similar to those described in the foregoing method, and the working process of the system may refer to the corresponding process in the foregoing method, which is not repeated herein.

Based on the method in the foregoing embodiment, an embodiment of the present application provides an electronic device, as shown in fig. 10, where the electronic device may include: processor 1010, communication interface 1020, memory 1030, and communication bus 1040, wherein processor 1010, communication interface 1020, and memory 1030 communicate with each other via communication bus 1040. Processor 1010 may invoke logic instructions in memory 1030 to perform the methods of the embodiments described above.

Further, the logic instructions in the memory 1030 described above may be implemented in the form of software functional units and stored in a computer readable storage medium when sold or used as a stand alone product. Based on this understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present application.

Based on the method in the above embodiment, the embodiment of the present application provides a computer-readable storage medium storing a computer program, which when executed on a processor, causes the processor to perform the method in the above embodiment.

Based on the method in the above embodiments, an embodiment of the present application provides a computer program product, which when run on a processor causes the processor to perform the method in the above embodiments.

It is to be appreciated that the processor in embodiments of the present application may be a central processing unit (centralprocessing unit, CPU), other general purpose processor, digital signal processor (digital signalprocessor, DSP), application Specific Integrated Circuit (ASIC), field programmable gate array (field programmable GATE ARRAY, FPGA) or other programmable logic device, transistor logic device, hardware components, or any combination thereof. The general purpose processor may be a microprocessor, but in the alternative, it may be any conventional processor.

The steps of the method in the embodiment of the present application may be implemented by hardware, or may be implemented by executing software instructions by a processor. The software instructions may be comprised of corresponding software modules that may be stored in random access memory (random access memory, RAM), flash memory, read-only memory (ROM), programmable ROM (PROM), erasable programmable ROM (erasable PROM, EPROM), electrically Erasable Programmable ROM (EEPROM), registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC.

In the above embodiments, it may be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, produces a flow or function in accordance with embodiments of the present application, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a computer network, or other programmable apparatus. The computer instructions may be stored in or transmitted across a computer-readable storage medium. The computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by a wired (e.g., coaxial cable, fiber optic, digital Subscriber Line (DSL)), or wireless (e.g., infrared, wireless, microwave, etc.). The computer readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that contains an integration of one or more available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid State Drive (SSD)), etc.

It will be appreciated that the various numerical numbers referred to in the embodiments of the present application are merely for ease of description and are not intended to limit the scope of the embodiments of the present application.

It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the application and is not intended to limit the application, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the application are intended to be included within the scope of the application.

Claims

1. A diffraction field simulation method for overlay error, comprising:

2. The method of claim 1, wherein the incident light passes through the objective lens before entering the overlay mark; the parameters of the overlay mark comprise the period parameters of the mark; the measurement parameters comprise the wavelength of incident light and the numerical aperture of an objective lens in the measurement device;

The position of the exit point is determined by:

3. The method according to claim 2, wherein when the overlay mark is a periodic nanograting structure, the exit point location is specifically:

The exit point coordinates (x _m,y_m) of the higher order diffracted light are:

(x_m,y_m)＝(-x_in+Δ,-y_in)

4. The method of claim 1, wherein when the overlay mark is a periodic nanograting structure, calculating a jones matrix for each point in the exit face based on the location of each point, comprising:

5. The method according to claim 1, characterized in that the outgoing light electric field vector at each outgoing point is determined in combination with the jones matrix of each outgoing point, in particular:

Where E _output represents the outgoing light electric field vector, E _input represents the electric field vector of the incoming light, Represents azimuth angle, θ represents incident angle, R () represents rotation matrix,Indicating the rotation azimuth angle of the exit point coordinate system relative to the incident planeP1 represents a polarizer and P2 represents a polarizing beam splitter, the polarizer being used to modulate the polarization state of incident light; the polarization beam splitter is used for dividing the pupil plane frequency domain image of the diffraction light into a Co-pol Co-polarization pupil plane frequency domain image and a Cross-pol Cross-polarization pupil plane frequency domain image; ) The jones matrix representing the exit point, J _M, J _P1, the jones matrix of the polarizer, and J _P2 the jones matrix of the polarizing beam splitter.

6. A method according to any one of claims 1 to 5, wherein the intensity of the light at each exit point is obtained by multiplying the electric field vector of the exiting light at the exit point by its conjugate and then modulo.

7. A measurement sensitivity analysis method of overlay error, comprising:

determining the light intensity of each exit point at different overlay errors for a set of measured parameters using the method of any one of claims 1 to 6;

8. The method of claim 7, wherein the sensitivity of the set of measurement parameters at each exit point is obtained by dividing the difference in light intensity at the exit point before and after the overlay error is changed by the overlay error change value and then multiplying the divided difference by a predetermined coefficient.

9. An electronic device, comprising:

At least one memory for storing a computer program;

At least one processor for executing the memory-stored program, which processor is adapted to perform the method according to any of claims 1-6 when the memory-stored program is executed.

10. A computer readable storage medium storing a computer program, characterized in that the computer program, when run on a processor, causes the processor to perform the method according to any one of claims 1-6.