Method for generating simulated images and image processing method

Abstract

This technology provides the ability to generate simulated images of patterns with variations in shape that can be generated from the same CAD pattern. [Solution] The simulated image generation method generates a reconstructed pattern contour 70 using pattern variation models L2 and L3, generates a reconstructed segment map 80 from the reconstructed pattern contour 70, inputs the reconstructed segment map 80 to the pattern image estimation model L1, and outputs a simulated pattern image 90 from the pattern image estimation model L1.

Description

[Technical Field]

[0001] The present invention relates to a method for generating a simulated image of a pattern formed on a workpiece used in the manufacture of semiconductor devices such as wafers, substrates, and panels. [Background technology]

[0002] Segmentation is the process of extracting the shape of a pattern from SEM images generated by a scanning electron microscope. Deep learning is sometimes used in this segmentation. For example, as shown in Figure 17, the SEM image 501 of pattern 500 is input to an inference model built using deep learning, and a pattern segment 503 containing a pattern contour 502 that shows the shape of pattern 500 is output.

[0003] Training data used in deep learning includes pattern images and ground truth masks that accurately represent the patterns. For good sensitivity and robust segmentation, it is desirable that the training data include pattern images with variations in pattern shape, such as line width variations, displacements, and other fluctuations. This is because variations in the training data improve the versatility and robustness of the functions that utilize deep learning. However, test samples used to obtain training data images may not contain patterns with sufficient variation. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2019-174940 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] Therefore, the present invention provides a technology that can generate simulated images of patterns with variations in shape that can be generated from the same CAD pattern. [Means for solving the problem]

[0006] In one embodiment, a method for generating a simulated image is provided, which involves generating multiple real pattern images by capturing multiple real patterns manufactured according to a CAD pattern using an image generation device, performing a pattern contour extraction process on the multiple real patterns on the multiple real pattern images to generate multiple pattern contours corresponding to the multiple real patterns, generating multiple training segment maps from the multiple pattern contours, creating a pattern image estimation model that estimates a pattern image from a segment map by performing machine learning using training data including the multiple training segment maps and the multiple real pattern images, creating a pattern variation model that simulates the variation of the multiple pattern contours, generating a reconstructed pattern contour using the pattern variation model, generating a reconstructed segment map from the reconstructed pattern contour, inputting the reconstructed segment map into the pattern image estimation model, and outputting a simulated pattern image from the pattern image estimation model.

[0007] In one embodiment, the pattern contour extraction process is a contour extraction process using a dynamic contour model. In one embodiment, the pattern variation model includes a centroid variation model that simulates the variation in the centroids of the plurality of pattern contours. In one embodiment, the centroid fluctuation model is created based on the distribution of multiple centroids of the multiple pattern contours. In one embodiment, the centroid fluctuation model is a mathematical model that includes the mean and standard deviation of the multiple centroids and random numbers.

[0008] In one embodiment, the pattern variation model includes a contour variation model that simulates the variation in the shapes of the plurality of pattern contours. In one embodiment, the contour variation model is created based on the distribution of multiple contour vertices that constitute the multiple pattern contours. In one embodiment, the contour variation model is a mathematical model that includes at least one principal component obtained from principal component analysis of the plurality of contour vertices, the positions of each of the plurality of average vertices that constitute the average contour which is the average of the shapes of the plurality of pattern contours, and random numbers. In one embodiment, the at least one principal component is a plurality of principal components from the first principal component to the Mth principal component (where M is a natural number), and the cumulative contribution rate, which is the sum of the contribution rates from the first principal component to the Mth principal component, is greater than or equal to a predetermined value. In one embodiment, the average contour is the average of the shapes of the plurality of pattern contours when the centroids of the plurality of pattern contours are combined. In one embodiment, the position of each of the plurality of average vertices is the average of the positions of the corresponding plurality of contour vertices of the plurality of pattern contours. In one embodiment, the contour variation model includes a Fourier descriptor model and an inverse transform model, wherein the Fourier descriptor model includes at least one principal component obtained from principal component analysis of a plurality of Fourier descriptors transformed from the plurality of contour vertices, a mean Fourier descriptor, and a random number, the mean Fourier descriptor being the frequency-wise average of the plurality of Fourier descriptors transformed from the plurality of contour vertices constituting the plurality of pattern contours, and the inverse transform model generates the pattern contour by inverse transforming the plurality of reconstructed Fourier descriptors calculated by the Fourier descriptor model.

[0009] In one embodiment, an image processing method is provided which generates multiple reconstructed segment maps and multiple simulated pattern images by repeatedly generating reconstructed pattern contours using the pattern variation model, generating reconstructed segment maps, and outputting simulated pattern images from the pattern image estimation model, and then creates a segmentation model that generates segment maps from real pattern images by performing machine learning using training data including the multiple reconstructed segment maps and the multiple simulated pattern images. In one embodiment, the image processing method further includes inputting a real pattern image in which the pattern appears into the segmentation model, and outputting a segment map from the segmentation model that includes a pattern contour showing the outline of the pattern.

[0010] In one embodiment, an image processing method is provided which generates multiple reconstructed pattern contours and multiple simulated pattern images by repeatedly generating reconstructed pattern contours using the pattern variation model, generating reconstructed segment maps, and outputting simulated pattern images from the pattern image estimation model, and creates a pattern contour extraction model that generates pattern contours from real pattern images by performing machine learning using training data including the multiple reconstructed pattern contours and the multiple simulated pattern images. In one embodiment, the image processing method further includes inputting a real pattern image in which the pattern appears into the pattern contour extraction model, and outputting a pattern contour indicating the contour of the pattern from the pattern contour extraction model. [Effects of the Invention]

[0011] The reconstructed pattern contour generated using the pattern variation model can represent the variability of the actual pattern created according to the CAD pattern. Therefore, a simulated pattern image that mimics the actual pattern can be generated from the reconstructed pattern contour.

[0012] Machine learning using training data that includes simulated pattern images and reconstructed segment maps that reflect the variability of real patterns can build robust segmentation models. These segmentation models can generate accurate segment maps from real pattern images.

[0013] Machine learning using training data including simulated pattern images that reflect variations of actual patterns and reconstructed pattern contours can construct a robust pattern contour extraction model. This pattern contour extraction model can extract accurate pattern contours from actual pattern images. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] [Figure 1] It is a schematic diagram showing an embodiment of an image processing apparatus. [Figure 2] It is a flowchart for describing an embodiment of a simulated image generation method for generating a simulated pattern image. [Figure 3] It is a schematic diagram showing an example of a CAD pattern. [Figure 4] It is a diagram showing examples of a plurality of actual pattern images of a plurality of actual patterns generated according to the CAD pattern shown in FIG. 3. [Figure 5] It is a diagram for describing an embodiment of executing pattern contour extraction processing on an actual pattern on an actual pattern image. [Figure 6] It is a diagram showing examples of a plurality of pattern contours generated by the pattern contour extraction processing. [Figure 7] It is a diagram showing examples of a plurality of training segment maps. [Figure 8] It is a diagram showing a plurality of pattern contours with a plurality of centroids aligned. [Figure 9] It is a graph showing examples of principal components calculated by principal component analysis, the contribution rate of each principal component, and the cumulative contribution rate. [Figure 10] It is a diagram showing an example of a reconstructed pattern contour. [Figure 11] It is a diagram showing an example of a reconstructed segment map. [Figure 12] It is a diagram for describing an embodiment of generating a simulated pattern image from a reconstructed segment map using a pattern image estimation model. [Figure 13] It is a diagram showing an example of a first CAD pattern and a second CAD pattern that partially overlap each other. [Figure 14] This figure shows examples of actual pattern images of the first and second actual patterns created according to the first and second CAD patterns shown in Figure 13. [Figure 15] This figure illustrates one embodiment of generating the pattern contours of a first real pattern and a second real pattern by performing a pattern contour extraction process. [Figure 16] This figure shows an example of a training segment map. [Figure 17] This diagram illustrates an example of segmentation using an inference model. [Modes for carrying out the invention]

[0015] Embodiments of the present invention will be described below with reference to the drawings. Figure 1 is a schematic diagram showing one embodiment of an image processing apparatus. The image processing apparatus includes a scanning electron microscope 1, which is an example of an image generation apparatus that generates an image of a workpiece W, and a processing system 5 that processes the image generated by the scanning electron microscope 1. Examples of workpiece W include wafers, masks, panels, and substrates used in the manufacture of semiconductor devices.

[0016] The processing system 5 consists of at least one computer. The processing system 5 includes a storage device 5a in which a program is stored, and an arithmetic unit 5b that performs calculations according to the instructions contained in the program. The storage device 5a includes main memory such as RAM and auxiliary storage such as a hard disk drive (HDD) or solid-state drive (SSD). Examples of arithmetic units 5b include a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit). However, the specific configuration of the processing system 5 is not limited to these examples.

[0017] The processing system 5 may be an edge server connected to the scanning electron microscope 1 via a communication line, a cloud server connected to the scanning electron microscope 1 via a communication network such as the internet or a local network, or a fog computing device (gateway, fog server, router, etc.) installed within the network connected to the scanning electron microscope 1. The processing system 5 may be a combination of multiple servers. For example, the processing system 5 may be a combination of edge servers and cloud servers connected to each other via a communication network such as the internet or a local network.

[0018] The scanning electron microscope 1 includes an electron gun 15 that emits an electron beam, a focusing lens 16 that focuses the electron beam emitted from the electron gun 15, an X-deflector 17 that deflects the electron beam in the X direction, a Y-deflector 18 that deflects the electron beam in the Y direction, an objective lens 20 that focuses the electron beam onto a workpiece W, which is an example of a sample, and a stage 31 that supports the workpiece W. The configuration of the electron gun 15 is not particularly limited. For example, a field emitter type electron gun or a semiconductor photocathode type electron gun can be used as the electron gun 15.

[0019] The electron beam emitted from the electron gun 15 is focused by the focusing lens 16, then deflected by the X-deflector 17 and Y-deflector 18, and finally focused by the objective lens 20 to irradiate the surface of the workpiece W. When the primary electrons of the electron beam irradiate the workpiece W, secondary electrons and backscattered electrons are emitted from the workpiece W. The electrons emitted from the workpiece W are detected by the electron detector 26. The electron detection signal from the electron detector 26 is input to the image acquisition device 28 and converted into an image. In this way, the scanning electron microscope 1 generates an image of the surface of the workpiece W. The image acquisition device 28 is connected to the processing system 5, and the image of the workpiece W is sent to the processing system 5.

[0020] The following describes one embodiment of a method for generating a pseudo-pattern image using an image processing device equipped with a scanning electron microscope 1 and a processing system 5. The pseudo-pattern image is an image that simulates the actual image of the pattern on the workpiece W, generated by the scanning electron microscope 1. The pattern on the workpiece W is formed based on design data (also called CAD data). CAD is an abbreviation for computer-aided design.

[0021] Figure 2 is a flowchart illustrating one embodiment of a simulated image generation method for generating simulated pattern images. Each step of the flowchart will be described in detail below.

[0022] In step 1, the scanning electron microscope 1 generates multiple real pattern images by imaging multiple real patterns manufactured according to the CAD pattern. The CAD pattern is a virtual pattern created by the processing system 5 based on the pattern information contained in the design data, and has a polygon shape. The design data includes pattern information such as the coordinates of the pattern vertices, the position, shape, and size of the pattern, and the layer number to which the pattern belongs. The pattern design data is pre-stored in the storage device 5a. The processing system 5 can read the pattern design data from the storage device 5a.

[0023] Figure 3 is a schematic diagram showing an example of a CAD pattern. In the example shown in Figure 3, the CAD pattern 40 has a rectangular shape. However, the shape of the CAD pattern 40 is not limited to the example shown in Figure 3. In one embodiment, the CAD pattern 40 may have a shape that has been subjected to corner rounding, which rounds the corners of the CAD pattern 40, and / or scaling, which enlarges or reduces the CAD pattern 40, and / or offset, which expands or shrinks the CAD pattern 40. Furthermore, in one embodiment, the CAD pattern 40 may be multiple partially overlapping CAD patterns formed in multiple layers.

[0024] The scanning electron microscope 1 generates multiple real pattern images by imaging multiple real patterns manufactured according to the CAD pattern 40 shown in Figure 3. The multiple real patterns manufactured according to the CAD pattern 40 shown in Figure 3 may be formed on a single workpiece or on multiple workpieces. In this specification, the pattern actually formed on a workpiece according to the CAD pattern 40 is referred to as a real pattern.

[0025] Figure 4 shows examples of multiple real pattern images 50 of multiple real patterns 49 formed according to the CAD pattern 40 shown in Figure 3. As can be seen from Figure 4, even real patterns 49 created from the same CAD pattern 40 have variations in their shapes.

[0026] In step 2, the processing system 5 performs pattern contour extraction on multiple real patterns 49 on multiple real pattern images 50 to generate multiple pattern contours corresponding to the multiple real patterns 49.

[0027] Figure 5 illustrates one embodiment of performing pattern contour extraction processing on a real pattern 49 on a real pattern image 50. In this embodiment, the pattern contour extraction processing is a contour extraction processing using a dynamic contour model. The dynamic contour model is a process that determines the final contour 54 that is closest to the contour of pattern 49 by deforming (contracting) the initial contour 53 toward the pattern 49. The initial contour 53 and the final contour 54 are composed of multiple vertices shown by black circles. That is, a contour is composed of multiple vertices. The final contour 54 is the contour extracted for pattern 49, and in the following description, the final contour 54 will be referred to as the pattern contour 54.

[0028] The processing system 5 performs pattern contour extraction processing on the actual patterns 49 on each actual pattern image 50 shown in Figure 4, generating multiple pattern contours 54 as shown in Figure 6. The symbol G in Figure 6 indicates the centroid of each pattern contour 54.

[0029] In step 3, the processing system 5 generates multiple training segment maps from multiple pattern contours 54 by assigning different numerical values ​​to the inner and outer regions of each of the multiple pattern contours 54 shown in Figure 6. The numerical values ​​are assigned to distinguish the inner and outer regions of each pattern contour 54, and any numerical values ​​(e.g., 0 and 1) can be used. Figure 7 shows an example of multiple training segment maps 60. The processing system 5 generates multiple training segment maps 60 by assigning a first numerical value to the inner region 56 of each pattern contour 54 and a second numerical value different from the first numerical value to the outer region 57 of each pattern contour 54.

[0030] In step 4, the processing system 5 creates a pattern image estimation model L1 that estimates pattern images from segment maps by performing machine learning using training data that includes multiple training segment maps 60 (see Figure 7) generated in step 3 and multiple real pattern images 50 (see Figure 4) generated in step 1. The pattern image estimation model L1 constructed by machine learning is stored in the memory device 5a of the processing system 5. An example of machine learning is deep learning, particularly deep learning using a convolutional neural network (CNN).

[0031] The multiple training segment maps 60 shown in Figure 7 are generated based on the multiple real pattern images 50 shown in Figure 4, and each corresponds to one of the multiple real pattern images 50. That is, the real pattern images 50 shown in Figure 2 are converted into the training segment maps 60 shown in Figure 7 after the pattern contour extraction process in step 2 and the assignment of numerical values ​​in step 3.

[0032] The machine learning process used to create the pattern image estimation model L1 is a supervised machine learning method that uses multiple training segment maps 60 (shown in Figure 7) as explanatory variables and multiple real pattern images 50 (shown in Figure 4) as the target variable. The pattern image estimation model L1 learns the correlation between the multiple training segment maps 60 and the multiple real pattern images 50. That is, the processing system 5 inputs each training segment map 60 into the pattern image estimation model L1 and adjusts the parameters (weights, biases, etc.) of the pattern image estimation model L1 so that the real pattern image 50 corresponding to the input training segment map 60 is output from the pattern image estimation model L1. As a result of this machine learning, the pattern image estimation model L1 is created as a trained model.

[0033] Next, the processing system 5 creates a pattern variation model that simulates the variation in position and shape of multiple pattern contours 54 (see Figure 6) that represent the contours of multiple actual patterns 49. The pattern variation model is a model that represents the variation of actual patterns 49 manufactured according to the CAD pattern 40. That is, multiple actual patterns 49 manufactured from the same CAD pattern 40 have variations in their position and shape, as shown in Figure 4. The pattern variation model is a model that simulates such variation of actual patterns 49. In this embodiment, the pattern variation model includes a centroid variation model L2 and a contour variation model L3, which are described below.

[0034] In step 5, the processing system 5 creates a center of gravity fluctuation model L2 that simulates the variation in the center of gravity G of the multiple pattern contours 54 (see Figure 6) generated in step 2. The actual pattern 49 manufactured on the workpiece according to the CAD pattern 40 (see Figure 3) not only deforms in its contour, as shown in Figure 4, but the center of gravity of the actual pattern 49 also fluctuates. Therefore, there is variation in the center of gravity G of the multiple pattern contours 54 generated in step 2. The center of gravity fluctuation model L2 is configured to simulate the variation in the center of gravity G of the pattern contours 54.

[0035] The processing system 5 creates a centroid fluctuation model L2 based on the distribution of multiple centroids G of the multiple pattern contours 54 generated in step 2. The centroid fluctuation model L2 is stored in the storage device 5a of the processing system 5. In one embodiment, the centroid fluctuation model L2 is a mathematical model that includes the mean and standard deviation of the multiple centroids G and random numbers. In this embodiment, the centroid fluctuation model L2 is expressed by the following equation. Center of gravity fluctuation model L2 = Gav + Ra·Gsd·Co (1) However, Gav represents the average of the positions G of multiple centroids, Ra represents a random number, Gsd represents the standard deviation of the positions G of multiple centroids, and Co represents a preset coefficient. By changing Co, the magnitude of centroid variation in the generated pattern can be adjusted. In one embodiment, the random number Ra is a value generated by a Gaussian distribution with mean 0 and standard deviation 1.

[0036] In step 6, the processing system 5 creates a contour variation model L3 that simulates the variations in the shapes of the multiple pattern contours 54 (see Figure 6) generated in step 2. The actual pattern 49 manufactured on the workpiece according to the CAD pattern 40 (see Figure 3) has a deformed contour, as shown in Figure 4. Therefore, there is variation in the shapes of the multiple pattern contours 54 generated in step 2. The contour variation model L3 is configured to simulate the variations in the shapes of the pattern contours 54.

[0037] The processing system 5 creates a contour variation model L3 based on the distribution of multiple contour vertices (black circles that make up the final contour 54 as a pattern contour in Figure 5) that constitute the multiple pattern contours 54 generated in step 2. The contour variation model L3 is stored in the storage device 5a of the processing system 5. The contour variation model L3 calculates the shape of the pattern contour that simulates the variation in the shape of the actual pattern contour 54. In this embodiment, the contour variation model L3 is a mathematical model that includes at least one principal component obtained from principal component analysis of the multiple contour vertices, the positions of each of the multiple average vertices that constitute the average contour which is the average of the shapes of the multiple pattern contours 54, and random numbers.

[0038] As shown in Figure 5, the position of each contour vertex constituting the pattern contour 54 (i.e., the black circles that constitute the final contour 54 as a pattern contour) can be represented by the X and Y coordinates on the XY coordinate system. Each contour vertex has information on the X and Y coordinates. As shown in Figure 8, the processing system 5 aligns the multiple centroids G of the multiple pattern contours 54 shown in Figure 6. Furthermore, the processing system 5 performs principal component analysis on the multiple contour vertices constituting the multiple pattern contours 54 (shown as the black circles that constitute the final contour 54 as a pattern contour in Figure 5) and calculates the first principal component, second principal component, third principal component, ...

[0039] In one embodiment, the processing system 5 creates a data matrix by combining the X and Y coordinates of multiple contour vertices that constitute multiple pattern contours 54 with their centroid G aligned. Each row of the data matrix contains the X and Y coordinate values ​​of the multiple contour vertices that constitute each pattern contour 54. Therefore, the number of rows in the data matrix matches the number of multiple pattern contours 54, and the number of columns in the data matrix is ​​twice the number of contour vertices. The processing system 5 performs principal component analysis on the coordinates representing the positions of the multiple contour vertices that constitute the multiple pattern contours 54.

[0040] The average contour is the average of the shapes of multiple pattern contours 54 when their centroids G are combined. In Figure 8, the average contour is indicated by the symbol Cav. The processing system 5 calculates the average vertices, which are the average of the positions of the corresponding contour vertices of the multiple pattern contours 54, and determines the average contour Cav from the multiple average vertices. More specifically, the processing system 5 calculates the nth average vertex, which is the average of the positions of the nth contour vertices of the multiple pattern contours 54 (n=1,2,3,...,N, where N is the total number of contour vertices of each pattern contour 54). The position of each of the multiple average vertices that make up the average contour Cav is the average of the positions of the corresponding contour vertices of the multiple pattern contours 54.

[0041] The contour variation model L3 is expressed by the following equation, which includes at least one principal component obtained from principal component analysis of multiple contour vertices, the positions of the multiple average vertices that constitute the average contour Cav, and random numbers. Contour variation model L3 = Pav(n) + Co·Ra1·PC1 + Co·Ra2·PC2 + ... + Co·Ra M PC M (2) However, n represents the number of the multiple contour vertices that make up each pattern contour 54 (n=1,2,3,...,N, where N is the total number of multiple contour vertices of each pattern contour 54), Pav(n) represents the position of the nth average vertex, Co represents a predetermined coefficient, Ra1,Ra2,...,Ra M represents a random number, PC1, PC2, ..., PC M These represent the first principal component, second principal component, ..., Mth principal component calculated by principal component analysis. By changing Co, the magnitude of variation in the generated pattern shape can be adjusted. In one embodiment, random numbers Ra1, Ra2, ..., Ra M This value is generated by a Gaussian distribution with a mean of 0 and a standard deviation of 1.

[0042] The upper limit of M (a natural number) for the Mth principal component included in the contour variation model L3 is determined based on the cumulative contribution rate, which is the sum of the contribution rates from the first to the Mth principal components. The contribution rate of each principal component is an indicator of how well each principal component explains the variance of multiple contour vertices that constitute multiple pattern contours 54, and is calculated according to a known method.

[0043] Figure 9 is a graph showing an example of principal components calculated by principal component analysis, the contribution rate of each principal component, and the cumulative contribution rate. In Figure 9, the horizontal axis represents the principal components, and the vertical axis represents the contribution rate of each principal component. Processing system 5 processes from the first principal component PC1 to the Mth principal component PC M The Mth principal component is determined if its cumulative contribution rate up to a certain point is greater than or equal to a predetermined value. The predetermined value is, for example, a number within the range of 0.8 to 0.9. In one example, the Mth principal component may be the first principal component PC1 or the second principal component PC2.

[0044] Next, another embodiment of the contour variation model L3 will be described. In the embodiments described so far, the processing system 5 performs principal component analysis on a plurality of contour vertices (indicated by black circles constituting the final contour 54 as the pattern contour in FIG. 5) constituting the plurality of pattern contours 54. However, in the present embodiment, the processing system 5 converts the plurality of contour vertices constituting the plurality of pattern contours 54 into a plurality of Fourier descriptors, and performs principal component analysis on these Fourier descriptors.

[0045] In the present embodiment, first, as shown in FIG. 8, the processing system 5 aligns the plurality of centroids G of the plurality of pattern contours 54 shown in FIG. 6. Next, the processing system 5 represents the coordinates x(n), y(n) of the plurality of contour vertices constituting each pattern contour 54 as a complex number z(n) as follows. z(n)=x(n)+y(n)j, n=0,1,2,...,N-1 (3) j is the imaginary unit, n is the number of the plurality of contour vertices constituting each pattern contour 54, and is an integer from 0 to N-1. N is the total number of the plurality of contour vertices constituting each pattern contour 54. The complex number z(n) represents the position of the n-th contour vertex constituting each pattern contour 54.

[0046] Next, the processing system 5 applies a Discrete Fourier Transform (DFT) to the complex number z(n) to obtain the Fourier descriptor Z represented by the following formula k to calculate. [Formula]

[0047] Next, the processing system 5 combines the real part and the imaginary part of the Fourier descriptor Z k to create a data matrix. Each row of the data matrix arranges the real part and the imaginary part of the Fourier descriptor Z representing the positions of the plurality of contour vertices constituting each pattern contour 54 k . Therefore, the number of rows of the data matrix matches the number of the plurality of pattern contours 54, and the number of columns of the data matrix is twice the number of the plurality of contour vertices. The processing system 5 uses the Fourier descriptor Z kPrincipal component analysis is performed on the result to calculate the first principal component, second principal component, third principal component, and so on.

[0048] In this embodiment, the contour variation model L3 includes a Fourier descriptor model and an inverse transform model. The Fourier descriptor model consists of multiple Fourier descriptors Z transformed from multiple contour vertices. k It can be expressed by the following equation, which includes at least one principal component obtained from principal component analysis of , a mean Fourier descriptor, and random numbers. Z' k =Fav+Co·Ra1·PC1+Co·Ra2·PC2+...+ Co·Ra M PC M (5) Here, Fav represents the mean Fourier descriptor, Co represents a predetermined coefficient, Ra1, Ra2, ..., Ra M represents a random number, PC1, PC2, ..., PC M This is the Fourier descriptor Z k This represents the first principal component, second principal component, ..., Mth principal component calculated by principal component analysis on . By changing Co, the magnitude of variation in the generated pattern shape can be adjusted. The mean Fourier descriptor is a set of Fourier descriptors Z transformed from multiple contour vertices that make up multiple pattern contours 54. k This is the average for each frequency. In one embodiment, random numbers Ra1, Ra2, ..., Ra M This value is generated by a Gaussian distribution with a mean of 0 and a standard deviation of 1.

[0049] The Fourier descriptor model is a mathematical model constructed from equation (5) above, and according to equation (5) above, multiple reconstructed Fourier descriptors Z' k The inverse transform model uses multiple reconstructed Fourier descriptors Z'. k This is a mathematical model configured to generate (reconstruct) the shape of the pattern contour by performing an inverse transform. The inverse transform model is expressed by the following equation.

number

[0050] Next, in step 7, the processing system 5 generates a reconstructed pattern contour using the centroid fluctuation model L2 and contour fluctuation model L3 described above. Figure 10 shows an example of the reconstructed pattern contour 70. The processing system 5 calculates the centroid using the centroid fluctuation model L2 represented by equation (1) above, and calculates the shape of the pattern contour using the contour fluctuation model L3 represented by equation (2) or equations (5) and (6) above. Then, the processing system 5 generates the reconstructed pattern contour 70 by matching the centroid of the shape of the pattern contour calculated by the contour fluctuation model L3 with the centroid calculated by the centroid fluctuation model L2. The reconstructed pattern contour 70 is placed within a frame 72 that represents the size and shape of the actual pattern image.

[0051] In step 8, the processing system 5 generates a reconstructed segment map from the reconstructed pattern contour 70 by assigning different numerical values ​​to the inner and outer regions of the reconstructed pattern contour 70 shown in Figure 10. Figure 11 shows an example of the reconstructed segment map 80. The processing system 5 generates the reconstructed segment map 80 by assigning a first numerical value to the inner region 74 of the reconstructed pattern contour 70 and a second numerical value different from the first numerical value to the outer region 75 of the reconstructed pattern contour 70. The numerical values ​​are assigned to distinguish between the inner region 74 and the outer region 75 of the reconstructed pattern contour 70, and any numerical values ​​(for example, 0 and 1) can be used.

[0052] In step 9, the processing system 5 generates a simulated pattern image from the reconstructed segment map 80 (see Figure 11) using the pattern image estimation model L1 created in step 4. Figure 12 illustrates one embodiment of generating a simulated pattern image 90 from the reconstructed segment map 80 using the pattern image estimation model L1. As shown in Figure 12, the processing system 5 inputs the reconstructed segment map 80 into the pattern image estimation model L1 and outputs a simulated pattern image 90 from the pattern image estimation model L1. This simulated pattern image 90 is an image that simulates the actual image generated by the scanning electron microscope 1.

[0053] The centroid variation model L2 simulates variations in the centroid of the pattern, and the contour variation model L3 simulates variations in the shape of the pattern. The reconstructed pattern contour 70 generated using the centroid variation model L2 and the contour variation model L3 can represent the variations in the actual pattern created according to the CAD pattern. Therefore, the processing system 5 can generate a simulated pattern image 90 that simulates the actual pattern from the reconstructed pattern contour 70.

[0054] The processing system 5 can generate multiple reconstructed segment maps and multiple simulated pattern images by repeatedly generating reconstructed pattern contours using the centroid fluctuation model L2 and the contour fluctuation model L3, generating reconstructed segment maps, and outputting simulated pattern images from the pattern image estimation model L1. In other words, by repeating steps 2 to 9 shown in Figure 2 multiple times, the processing system 5 can create multiple reconstructed segment maps and multiple simulated pattern images without the scanning electron microscope 1 generating new images.

[0055] Furthermore, the processing system 5 creates a segmentation model L4 by performing machine learning using training data that includes multiple reconstructed segment maps 80 and multiple simulated pattern images 90. In this machine learning, the multiple reconstructed segment maps 80 included in the training data are used as ground truth labels. The segmentation model L4 is configured to generate segment maps containing pattern contours from real pattern images, as shown in Figure 11. An example of machine learning is deep learning, particularly deep learning using convolutional neural networks. The segmentation model L4 constructed by machine learning is stored in the memory device 5a of the processing system 5.

[0056] The processing system 5 inputs the actual pattern image in which the pattern appears into the segmentation model L4, and outputs a segment map containing the pattern contour that shows the outline of the pattern from the segmentation model L4.

[0057] Machine learning using training data that includes simulated pattern images and reconstructed segment maps that reflect the variability of real patterns can construct a robust segmentation model L4. This segmentation model L4 can generate accurate segment maps from real pattern images.

[0058] In another embodiment, the processing system 5 creates a pattern contour extraction model L5 by performing machine learning using training data that includes multiple reconstructed pattern contours 70 and multiple simulated pattern images 90. In this machine learning, the multiple reconstructed pattern contours included in the training data are used as ground truth labels. The pattern contour extraction model L5 is configured to generate pattern contours from real pattern images as shown in Figure 10. Examples of machine learning include deep learning, particularly deep learning using convolutional neural networks. Since the coordinates of the pattern contours generated by the pattern contour extraction model L5 are real numbers with smaller granularity than integer pixel coordinates, the pattern contour extraction model L5 can extract pattern contours with higher accuracy. The pattern contour extraction model L5 constructed by machine learning is stored in the storage device 5a of the processing system 5.

[0059] The processing system 5 inputs the actual pattern image in which the pattern appears to the pattern contour extraction model L5, and outputs a pattern contour from the pattern contour extraction model L5 that indicates the pattern on the actual pattern image.

[0060] The line width of the actual pattern can be obtained from the shape of the pattern obtained by pattern contour or segmentation. Line width is an important indicator in semiconductor process control and process equipment monitoring. Similarly, the overlay between layers of the actual pattern is also an important indicator. In recent years, it has been pointed out that measuring the local roughness (fluctuation) of the shape of the line pattern is important in semiconductor process control. In roughness measurement, line edge roughness (LER) and line width roughness (LWR) are among the indicators used.

[0061] The pattern contours output from segmentation model L4 or pattern contour extraction model L5 can be used to measure the patterns on the actual pattern image described above. In one example, the processing system 5 measures the line width of the pattern on the actual pattern image based on the pattern contour output from the segmentation model L4 or the pattern contour extraction model L5. In one example, the processing system 5 measures the overlay between pattern layers on the actual pattern image based on the pattern contours output from the segmentation model L4 or the pattern contour extraction model L5. In one example, the processing system 5 measures the line edge roughness of the pattern on the actual pattern image based on the pattern contour output from the segmentation model L4 or the pattern contour extraction model L5. In one example, the processing system 5 measures the line width roughness of the pattern on the actual pattern image based on the pattern contour output from the segmentation model L4 or the pattern contour extraction model L5.

[0062] In the embodiments described above, the pattern variation model consists of a centroid variation model L2 and a contour variation model L3, but the pattern variation model is not limited to the embodiments described above. For example, the pattern variation model may be a model that vectorizes the actual pattern on the image and performs principal component analysis without using contour extraction, or a generative model that simulates the variation of the actual pattern (such as a variational autoencoder).

[0063] In the embodiments described so far, a simulated pattern image 90 is generated from a CAD pattern 40 in a single layer. However, the processing system 5 can also generate a simulated pattern from multiple overlapping CAD patterns existing in multiple layers, as described below.

[0064] Figure 13 shows an example of partially overlapping first CAD pattern 101 and second CAD pattern 102, and Figure 14 shows an example of actual pattern images 110 of the first actual pattern 105 and second actual pattern 106 created according to the first CAD pattern 101 and second CAD pattern 102 shown in Figure 13.

[0065] The second real pattern 106 overlaps a portion of the first real pattern 105. In step 2 of the flowchart shown in Figure 2, the processing system 5 separately performs pattern contour extraction processing on the first real pattern 105 and the second real pattern 106 on the real pattern image 111 to generate the pattern contour 114 of the first real pattern 105 and the pattern contour 116 of the second real pattern 106.

[0066] Figure 15 illustrates one embodiment of generating the pattern contour 114 of the first actual pattern 105 and the pattern contour 116 of the second actual pattern 106 by performing a pattern contour extraction process using a dynamic contour model. Since a portion of the first actual pattern 105 is covered by the second actual pattern 106, the actual contour of this portion of the first actual pattern 105 is unknown. Therefore, as shown in Figure 15, the processing system 5 omits the vertices of the portion of the first actual pattern 105 that is covered by the second actual pattern 106, and generates the pattern contour 114 of the first actual pattern 105 from the vertices (represented by black circles) of the portion of the first actual pattern 105 that is not covered by the second actual pattern 106.

[0067] On the other hand, the entirety of the second actual pattern 106 is located above the first actual pattern 105. Therefore, the processing system 5 generates the pattern contour 116 of the second actual pattern 106 from the vertices (represented by black circles) of the second actual pattern 106. The processing system 5 superimposes the pattern contour 116 of the second actual pattern 106 on top of the pattern contour 114 of the first actual pattern 105. In this way, in step 2 of the flowchart shown in Figure 2, the pattern contour 114 of the first actual pattern 105 and the pattern contour 116 of the second actual pattern 106 are generated.

[0068] Next, in step 3 of the flowchart shown in Figure 2, the processing system 5 generates a training segment map 120 as shown in Figure 16 by assigning different numerical values ​​to the inner and outer regions of the pattern contour 114 of the first real pattern 105 and the pattern contour 116 of the second real pattern 106. Subsequently, steps 4 to 9 of the flowchart shown in Figure 2 are executed in the same manner.

[0069] The embodiments described above are intended to enable persons with ordinary skill in the art to implement the present invention. Various modifications of the above embodiments can be made naturally by those skilled in the art, and the technical idea of ​​the present invention can be applied to other embodiments as well. Therefore, the present invention is not limited to the embodiments described, but is to be interpreted in the broadest sense according to the technical idea defined by the claims. [Explanation of symbols]

[0070] W Workpiece 1. Scanning electron microscope 5 Processing System 5a Storage device 5b Arithmetic unit 15. Electron gun 16 Focusing lens 17X deflector 18 Y deflector 20 Objective lenses 26 Electron detectors 28 Image acquisition device 31 stages 40 CAD patterns 49 Actual Patterns 50 Actual Pattern Images 53 Initial contour 54 Pattern contour (final contour) 56 Inner area 57 Outer area 60 Training Segment Map L1 Pattern Image Estimation Model L2 Center of Gravity Fluctuation Model L3 contour variation model L4 Segmentation Model 70 Reconstructed Pattern Contours 72 frames 74 Inner area 75 Outer area 80 Reconstructed Segment Map 90 Simulated Pattern Images 101 First CAD Pattern 102 Second CAD Pattern 105 First Actual Pattern 106 Second Actual Pattern 110 Actual Pattern Images 114 Pattern Contours 116 Pattern Contours 120 Training Segment Map

Claims

1. Multiple physical patterns manufactured according to CAD patterns are captured by an image generation device to generate multiple physical pattern images. A pattern contour extraction process is performed on the multiple real patterns on the multiple real pattern images to generate multiple pattern contours corresponding to the multiple real patterns. Multiple training segment maps are generated from the aforementioned multiple pattern contours. By performing machine learning using the training data which includes the multiple training segment maps and the multiple real pattern images, a pattern image estimation model is created that estimates pattern images from the segment maps. A pattern variation model is created that simulates the variation of the aforementioned multiple pattern contours. Using the aforementioned pattern variation model, a reconstructed pattern contour is generated. A reconstructed segment map is generated from the aforementioned reconstructed pattern contour. A method for generating a simulated image, comprising inputting the reconstructed segment map into the pattern image estimation model and outputting a simulated pattern image from the pattern image estimation model.

2. The method for generating a simulated image according to claim 1, wherein the pattern contour extraction process is a contour extraction process using a dynamic contour model.

3. The method for generating a simulated image according to claim 1, wherein the pattern variation model includes a centroid variation model that simulates the variation in the centroids of the plurality of pattern contours.

4. The method for generating a simulated image according to claim 3, wherein the centroid fluctuation model is created based on the distribution of multiple centroids of the multiple pattern contours.

5. The method for generating a simulated image according to claim 4, wherein the centroid fluctuation model is a mathematical model that includes the mean and standard deviation of the plurality of centroids and random numbers.

6. The method for generating a simulated image according to claim 1, wherein the pattern variation model includes a contour variation model that simulates the variation in the shapes of the plurality of pattern contours.

7. The method for generating a simulated image according to claim 6, wherein the contour variation model is created based on the distribution of a plurality of contour vertices that constitute the plurality of pattern contours.

8. The method for generating a simulated image according to claim 7, wherein the contour variation model is a mathematical model that includes at least one principal component obtained from principal component analysis of the plurality of contour vertices, the positions of each of the plurality of average vertices that constitute the average contour which is the average of the shapes of the plurality of pattern contours, and random numbers.

9. The simulated image generation method according to claim 8, wherein the at least one principal component is a plurality of principal components from the first principal component to the Mth principal component (where M is a natural number), and the cumulative contribution rate, which is the sum of the contribution rates from the first principal component to the Mth principal component, is greater than or equal to a predetermined value.

10. The method for generating a simulated image according to claim 8, wherein the average contour is the average of the shapes of the plurality of pattern contours when the centroids of the plurality of pattern contours are combined.

11. The method for generating a simulated image according to claim 8, wherein the position of each of the plurality of average vertices is the average of the positions of the corresponding plurality of contour vertices of the plurality of pattern contours.

12. The contour variation model includes a Fourier descriptor model and an inverse transform model, The Fourier descriptor model includes at least one principal component obtained from principal component analysis of the multiple Fourier descriptors transformed from the multiple contour vertices, a mean Fourier descriptor, and random numbers. The averaged Fourier descriptor is the frequency-wise average of the multiple Fourier descriptors converted from the multiple contour vertices constituting the multiple pattern contours, The simulated image generation method according to claim 7, wherein the inverse transform model generates a pattern contour by performing an inverse transform on a plurality of reconstructed Fourier descriptors calculated by the Fourier descriptor model.

13. By repeatedly generating reconstructed pattern contours using the pattern variation model described in claims 1 to 12, generating reconstructed segment maps, and outputting simulated pattern images from the pattern image estimation model, multiple reconstructed segment maps and multiple simulated pattern images are generated. An image processing method for creating a segmentation model that generates segment maps from real pattern images by performing machine learning using training data that includes the aforementioned multiple reconstructed segment maps and the aforementioned multiple simulated pattern images.

14. The actual pattern image in which the pattern appears is input to the segmentation model. The image processing method according to claim 13, further comprising outputting a segment map from the segmentation model that includes a pattern contour showing the contour of the pattern.

15. By repeatedly generating reconstructed pattern contours using the pattern variation model described in claims 1 to 12, generating reconstructed segment maps, and outputting simulated pattern images from the pattern image estimation model, multiple reconstructed pattern contours and multiple simulated pattern images are generated. An image processing method for creating a pattern contour extraction model that generates pattern contours from real pattern images by performing machine learning using training data that includes the aforementioned multiple reconstructed pattern contours and the aforementioned multiple simulated pattern images.

16. The actual pattern image in which the pattern appears is input to the pattern contour extraction model. The image processing method according to claim 15, further comprising outputting a pattern contour representing the contour of the pattern from the pattern contour extraction model.

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