TWI812086B - Method for generating optical proximity correction model - Google Patents

Abstract

A method for generating an optical proximity correction model is provided. The method includes: receiving optical proximity correction data; adding adjustment terms including a weight operation and a penalty operation into a cost function to generate an adjusted cost function; performing a regression operation on the optical proximity correction data to generate an optical proximity correction model according to the adjusted cost function.

Description

Method for generating optical proximity correction model

The present invention relates to a photolithography correction method, and in particular to a method for generating an optical proximity correction model of a neural network.

Traditionally, optical proximity correction (OPC) uses lithography enhancement technique to compensate for image errors that may be caused by proximity effects such as diffraction, interference, and other process effects. ) caused by critical dimension deviation.

However, in order to improve the accuracy of the OPC model using Artificial Neural Network (ANN), it is usually necessary to collect more Scanning Electron Microscope (SEM) data and use it in the neural network-like OPC model. More empirical terms lead to longer data collection time and OPC model generation time. Moreover, when performing regression calculations through cost functions, the empirical terms easily cause the wafer data to differ from the OPC model. Fitted (over-fitted), thereby reducing the stability of the OPC model.

The present invention provides a method for generating an optical proximity correction model, which is used to adjust the cost function using weight operations and penalty operations, thereby generating an OPC model.

Embodiments of the present invention provide a method for generating an optical proximity correction model. The generation method of the optical proximity correction model includes: receiving optical proximity correction data; adding adjustment terms including weight operation and penalty operation to the cost function to generate an adjusted cost function; performing a regression operation on the optical proximity correction data according to the adjusted cost function to generate Optical proximity correction model.

Based on the above, in some embodiments of the present invention, by adding adjustment terms with weight operations and penalty operations to the cost function to generate the OPC model, the accuracy of the OPC model can be increased and the generation speed of the OPC model can be increased, and the process can be further reduced. fitting effect.

In order to make the above-mentioned features and advantages of the present invention more obvious and easy to understand, embodiments are given below and described in detail with reference to the accompanying drawings.

10:OPC model generation system

110:Computing device

120: Measuring device

130: Test mask

S210, S220, S230, S240, S250, S260, S270, S280, S285, S290, S295, S310, S320, S330, S340, S350, S360, S370, S410, S420, S430: Steps

FIG. 1 is a block diagram of an OPC model generation system according to an embodiment of the present invention.

FIG. 2 is a schematic diagram of an OPC model generation method according to an embodiment of the present invention.

FIG. 3 is a flowchart of machine learning operations according to an embodiment of the present invention.

FIG. 4 is a flow chart of an OPC model generation method according to an embodiment of the present invention.

The term "coupling (or connection)" used throughout the specification of this case (including the scope of the patent application) can refer to any direct or indirect connection means. For example, if a first device is coupled (or connected) to a second device, it should be understood that the first device can be directly connected to the second device, or the first device can be connected through other devices or other devices. A connection means is indirectly connected to the second device. In addition, wherever possible, elements/components/steps with the same reference numbers are used in the drawings and embodiments to represent the same or similar parts. Elements/components/steps using the same numbers or using the same terms in different embodiments can refer to the relevant descriptions of each other.

FIG. 1 is a block diagram of an OPC model generation system according to an embodiment of the present invention. Referring to FIG. 1 , the OPC model generation system 10 includes but is not limited to a computing device 110 , a measuring device 120 and a test mask 130 . The measurement device 120 is used to measure a plurality of test points of a test mask pattern (Test Pattern, not shown) in the test mask 130 to generate a plurality of measurement data and output them to the computing device 110 . The test mask pattern is used to project the circuit pattern onto the wafer during the lithography process, and the present invention does not limit the type and size of the test mask pattern. The computing device 110 can use machine learning operations to sample a plurality of preset data preset during design of the test mask pattern to generate a plurality of sampling data, and calculate the optical proximity correction based on the plurality of sampling data and the plurality of measurement data. (OPC) data. Computing device 110 may add adjustments to The cost function performs regression operations on the OPC data to generate the OPC model. Details will be given later.

In this embodiment, the computing device 110 is, for example, a desktop computer (Desktop Computer), a personal computer (Personal Computer, PC), a portable terminal product (Portable Terminal Product), or a personal digital assistant (Personal Digital Assistant, PDA). , Tablet PC or server, etc. The computing device 110 can be installed with electronic design automation (Electronic Design Automation, EDA) related auxiliary tools to perform data sampling and calculation of the OPC model. The measuring device 120 is, for example, a critical dimension scanning electron microscope (Critical Dimension Scanning Electron Microscope, CD-SEM) or other scanning electron microscope (Scanning Electron Microscope, SEM).

FIG. 2 is a schematic diagram of an OPC model generation method according to an embodiment of the present invention. Referring to FIG. 2 , in step S210 , the computing device 110 receives a plurality of preset data of a plurality of test points in the test mask pattern. Specifically, each test mask pattern, such as a strip pattern, can have multiple test points, and each test point has corresponding preset data (layout design data) when designing the test mask pattern. The default data is, for example, It is to test the size, distance, etc. of the mask pattern.

Next, in step S220, the computing device 110 uses machine learning operations to sample a plurality of preset data to generate a plurality of sampled data. In this embodiment, the machine learning operation can group the data to reduce the number of samples, thereby reducing the sampling time. Details of the machine learning operation will be described in detail in Figure 3 .

In step S230, the measuring device 120 is, for example, a CD-SEM. The CD-SEM Measure multiple test points in the test mask pattern to generate multiple measurement data. The measurement data is, for example, related parameters such as the size and distance of the test mask pattern. Next, in step S240, the computing device 110 calculates differences between a plurality of sampling data and measurement data to generate OPC data. Specifically, the sampling data is equivalent to the design values of the test mask pattern with respect to size and distance, while the measurement data is equivalent to the actual values of the test mask pattern with respect to size and distance. Therefore, the computing device 110 calculates a plurality of differences between a plurality of sampling data and a plurality of measurement data to generate OPC data. The OPC data is used to compensate for image errors caused by proximity effects.

Please refer to step S250, step S260 and step S270 at the same time. In step S250, the computing device 110 performs a regression operation on the OPC data to generate an OPC model. In this embodiment, the regression operation is related to the neural network, usually by establishing a cost function of the OPC data and calculating the minimum cost function of the OPC data in an iterative manner to train the OPC data. ). The cost function is, for example, root mean square (RMS).

In step S260, the computing device 110 may add the cost weight term and the specification penalty term to the cost function. In step S270, the computing device 110 adds the normalized penalty term to the cost function. In one embodiment, the computing device 110 can add an adjustment term to the cost function to improve the accuracy of the OPC model and reduce overfitting. Specifically, the computing device 110 may add an adjustment term including a weight operation and a penalty operation to the cost function. The adjustment term may include a cost weight term _Wi , a specification penalty term αμ(f) and a normalization penalty term λΩ ( Wi ). . The weight operation includes the cost weight term _Wi , and the penalty operation includes the specification penalty term αμ(f) and the regularization penalty term λΩ ( Wi ).

其中i為光罩圖樣類型，Si為每種光罩圖樣類型的校正規格，Qi為每種光罩圖樣類型的資料數量，m為光罩圖樣類型的數量。 Regarding the cost weight item _Wi , the computing device 110 can provide corresponding weights according to the quantity and correction specifications of different test mask pattern types, so that each test mask pattern type has different cost weights according to the quantity and correction specifications. (cost weighting). Different types of test mask patterns include strip type, L type, triangle type, etc. For example, the computing device 110 can increase the cost weight of data points with a smaller specification tolerance, and reduce the cost weight of data points with a larger specification tolerance, so as to improve the accuracy and convergence speed of the regression operation. Specifically as shown in formula (1):

Where i is the mask pattern type, Si is the calibration specification of each mask pattern type, Qi is the number of data for each mask pattern type, and m is the number of mask pattern types.

其中α為懲罰係數，m為光罩類型的數量，n為超出預設規格的測試點的數量，i為光罩圖樣類型，j為每種光罩圖樣類型中超出預設規格的測試點，fi,j為超出預設規格的測試點的擬合誤差(fiterror)，Si為每種光罩圖樣類型的校正規格。 Regarding the specification penalty term αμ(f), the computing device 110 may add the specification penalty term αμ(f) for test points exceeding the preset specification to the cost function. Specifically, the difference between the test point data exceeding the preset specification in the regression operation and the preset specification is squared as the specification penalty term αμ(f), so that each test point data is corrected into the preset specification. Within specifications, thereby improving the accuracy and convergence speed of regression operations. Specifically as shown in formula (2):

where α is the penalty coefficient, m is the number of mask types, n is the number of test points that exceed the preset specifications, i is the mask pattern type, and j is the test points that exceed the preset specifications in each mask pattern type. fi,j is the fitting error (fiterror) of test points that exceed the preset specifications, and Si is the correction specification for each mask pattern type.

其中λ為正規化係數，i為光罩圖樣類型，m為光罩圖樣類型的數量，Wi為權重。 Regarding the regularization penalty term λ Ω ( Wi ), in this embodiment, the regularization penalty term λ Ω ( Wi ) is related to L2 regularization (L2 Regulation) in machine learning. Specifically, the computing device 110 may assign lower weights to features with lower values to limit the influence of useless features in the process of minimizing the cost function, thereby reducing the overfitting effect. Specifically, it is shown in formula (3):

Where λ is the normalization coefficient, i is the mask pattern type, m is the number of mask pattern types, and Wi is the weight.

Next, in step S280, the computing device 110 determines whether the OPC model generated by the regression operation meets the preset specifications. Specifically, please refer to FIG. 3 at the same time. The computing device 110 can input the multiple training data divided in step S310 into the OPC model generated by the regression operation to generate multiple correction results, and determine whether the multiple correction results are correct. Find out whether the OPC model meets the preset specifications within the preset specifications. The preset specifications can be a set of preset numerical ranges, which are determined based on actual design requirements, but are not limited to this. If the OPC model meets the preset specifications, step S290 is entered. If the OPC model does not meet the preset specifications, step S285 is entered. In step S285, when the OPC model does not meet the preset specifications, the computing device 110 may adjust the OPC model. In an embodiment, the computing device 110 may adjust the aforementioned adjustment items and return to step S250. Specifically, the computing device 110 may adjust the parameters in the cost weight term _Wi , the specification penalty term αμ(f), and the normalization penalty term λΩ ( Wi ), and re-perform the regression operation. Next, in step S290, the computing device 110 may output the OPC model. In step S295, the test data divided in step S310 in Figure 3 can be used to verify the OPC model.

Figure 3 is a flowchart of machine learning operations according to an embodiment of the present invention. Process map. Specifically, FIG. 3 relates to the specific flow of the machine learning operation in step S220 of FIG. 2 . Referring to FIG. 3 , in step S310 , the computing device 110 divides a plurality of preset data corresponding to a plurality of test points in the test mask pattern into a plurality of training data and a plurality of test data. For example, the computing device 110 can divide 100 preset data into 80 training data and 20 test data. The 80 training data are used to perform the subsequent process of the machine learning operation, and the 20 test data are used in FIG. 2 In step S295, the OPC model is verified.

Next, in step S320, the computing device 110 performs optical operations on the plurality of training data according to the exposure conditions to generate a plurality of optical parameters. Exposure conditions may include but are not limited to light intensity, numerical aperture (NA) of the projection lens, etc. For example, the computing device 110 may use the Vector Hopkins model to calculate 80 training data based on exposure conditions such as light intensity and the numerical aperture (NA) of the projection lens to generate multiple optical parameters such as the maximum light intensity Imax, the minimum light intensity Imax, and the minimum light intensity Imax. Light intensity Imin, light intensity logarithmic slope NILS, mask error enhancement factor MEEF.

In step S330, the computing device 110 pre-processes a plurality of optical parameters to generate a plurality of first transient parameters. In an embodiment, the computing device 110 may perform at least one of a feature scaling operation and an outlier detection operation on the plurality of optical parameters to generate a plurality of first transient parameters. In a preferred embodiment, the computing device 110 may first perform a feature scaling operation on the plurality of optical parameters, and then perform an outlier detection operation to generate a plurality of first transient parameters. Specifically, the feature scaling operation is, for example, taking the logarithm (log) of multiple optical data, and the outlier detection is, for example, the quartile method (Quartile), the box-and-whisker method (Bot Plot), etc., to reduce variation. value and increase data representativeness.

In step S340, the computing device 110 may perform feature transformation on multiple optical parameters to generate multiple feature parameters. In one embodiment, the computing device 110 may perform principal component analysis (PCA) on the plurality of first transient parameters generated in step S330 to generate a plurality of characteristic parameters. For example, the computing device 110 can use PCA to reduce the dimensionality of the four-dimensional optical parameters (such as Imax, Imin, NILS, MEEF) into two-dimensional characteristic parameters (such as the first statistical parameter and the second statistical parameter) to simplify data and make subsequent grouping operations easier to perform.

Next, in steps S350 and S360, the computing device 110 performs a grouping operation on a plurality of feature data to generate grouped feature data. In one embodiment, the computing device 110 may perform step S350 and step S360 on multiple feature data into groups twice. Specifically, in step S350, the computing device 110 may first use one of Gaussian mixture model (Gaussian mixture model, GMM) and averaging algorithm (K-means) to perform the first grouping of multiple feature data to generate Temporary group. Next, in step S360, the computing device 110 uses one of GMM and K-means to perform a second grouping on the temporary group to generate a plurality of grouped feature data. In step S370, the computing device 110 may sample a plurality of grouped feature data to generate a plurality of sampled data. Since step S350 and step S360 have performed two groupings, the total number of groups of the grouped characteristic data will be greater than the total number of temporary groups. Moreover, when the grouping is finer, it will be beneficial to the data representativeness of the sampling operation in step S370, thereby reducing the number of samples. For example, each group can collect a representative number of data, thereby reducing the sampling time.

Figure 4 illustrates an OPC model generation method according to an embodiment of the present invention. flow chart. Referring to FIG. 4, in step S410, the computing device 110 may receive OPC data. Next, in step S420, the computing device 110 may add the adjustment terms including the weight operation and the penalty operation to the cost function to generate an adjusted cost function. In step S430, the computing device 110 may perform a regression operation on the OPC data according to the adjusted cost function to generate an OPC model.

To sum up, the present invention can increase the accuracy of the OPC model and improve the generation speed of the OPC model by adding adjustment terms with weight operation and penalty operation to the cost function to generate the OPC model, and further reduce the over-fitting effect. On the other hand, grouping data through machine learning operations can reduce the sampling data required by the OPC model and increase the sampling speed.

Although the present invention has been disclosed above through embodiments, they are not intended to limit the present invention. Anyone with ordinary knowledge in the technical field may make some modifications and modifications without departing from the spirit and scope of the present invention. Therefore, The protection scope of the present invention shall be determined by the appended patent application scope.

S410-S430: Steps

Claims (12)

A method for generating an optical proximity correction model, including: generating optical proximity correction data through machine learning operations; adding an adjustment term to a cost function to generate an adjusted cost function, wherein the adjustment term includes a cost weight term, a specification penalty term and a normal normalization penalty term, wherein the cost weight term is used to perform a weighting operation, the specification penalty term and the normalization penalty term are used to perform a penalty operation; the optical proximity correction data is regressed according to the adjusted cost function Operation is performed to generate an optical proximity correction model, wherein the machine learning operation includes: performing feature transformation on a plurality of four-dimensional optical parameters, so that the plurality of four-dimensional optical parameters are dimensionally reduced to form a plurality of two-dimensional feature parameters. The generation method according to claim 1, wherein generating the optical proximity correction data through the machine learning operation includes: receiving a plurality of preset data corresponding to a plurality of test points in the test mask pattern; using the machine learning Operations include sampling the plurality of preset data to generate a plurality of sampling data; measuring a plurality of test points to generate a plurality of measurement data; and calculating differences between the plurality of sampling data and the plurality of measurement data. values to generate the optical proximity correction data. The generation method as described in claim 2, wherein generating the plurality of measurement data includes: The test mask pattern is measured using a critical dimension measurement scanning electron microscope (CD-SEM) to generate the plurality of measurement data. The generation method as described in claim 2, wherein the machine learning operation includes: dividing the plurality of preset data into a plurality of training data and a plurality of test data; optically performing optical processing on the plurality of training data according to exposure conditions. operating to generate a plurality of optical parameters; preprocessing the plurality of optical parameters to generate a plurality of feature data; performing a grouping operation on the plurality of feature data to generate a plurality of grouped feature data; and performing a grouping operation on the plurality of grouped feature data; Sampling is performed through the clustered characteristic data to generate the plurality of sampling data. The generation method according to claim 4, wherein the preprocessing of the plurality of optical parameters includes: performing at least one of a feature scaling operation and an outlier detection operation on the plurality of optical parameters to generate a plurality of The first transient parameter. The generation method as described in claim 1, wherein the step of performing feature transformation on the plurality of four-dimensional optical parameters includes: performing principal component analysis (Principal Component Analysis) on a plurality of first transient parameters to generate the Multiple two-dimensional feature parameters. The production method as described in claim 4, wherein the grouping operation includes: Performing a first grouping, the first grouping is to use one of a Gaussian mixture model and an average algorithm to group the plurality of feature data to generate a temporary group; and performing a second grouping, the third grouping is performed. The secondary grouping is to use one of the Gaussian mixture model and the averaging algorithm to group the temporary groups generated by the first grouping to generate the plurality of grouped feature data. The production method as described in claim 1, wherein the cost weight item _Wi is:

Where i is the mask pattern type, Si is the calibration specification of each mask pattern type, Qi is the number of data for each mask pattern type, and m is the number of mask pattern types. The production method as described in claim 1, wherein the specification penalty term αμ(f) is:

where α is the penalty coefficient, m is the number of mask types, n is the number of test points that exceed the preset specifications, i is the mask pattern type, and j is the test points that exceed the preset specifications in each mask pattern type. fi,j is the fitting error of test points that exceed the preset specifications, and Si is the correction specification for each mask pattern type. The generation method as described in claim 1, wherein the regularization penalty term λ Ω ( Wi ) is:

Where λ is the normalization coefficient, i is the mask pattern type, m is the number of mask pattern types, and Wi is the weight. The generation method of claim 1 further includes: after generating the optical proximity correction model, determining whether the optical proximity correction model meets preset specifications. The generation method of claim 11, wherein when the optical proximity correction model meets the preset specifications, the optical proximity correction model is output and used for verification by multiple test data. When the optical proximity correction model Adjust the adjustment items when they do not meet the preset specifications.

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