Photolithography simulation method, training method, device, equipment, medium and product

Abstract

This disclosure provides a lithography simulation method, training method, apparatus, device, medium, and product, which can be applied to the fields of artificial intelligence and semiconductor lithography technology. The lithography simulation method includes: in response to a lithography simulation request, acquiring a mask image to be processed and process parameters; and generating a lithography image using a spatial image obtained based on the mask image and process parameters as a guide, wherein the spatial image is a mask pattern represented by the mask image, and the light intensity distribution is formed on the photoresist indicated by the process parameters through optical imaging.

Description

Technical Field

[0001] This disclosure relates to the fields of artificial intelligence and semiconductor lithography technology, and more specifically, to a lithography simulation method, training method, apparatus, equipment, medium, and product. Background Technology

[0002] As semiconductor process nodes continue to shrink, the feature size of integrated circuits is gradually approaching its physical limits. In order to accurately transfer the circuit design layout onto the semiconductor chip, it is necessary to finely control the mask pattern and process conditions.

[0003] Photolithography simulation aims to simulate the photolithography process, that is, to simulate and generate the circuit pattern after photolithography based on the mask image and process parameters. It is a key means to discover process defects in a timely manner and iteratively optimize process parameters. It can replace actual photolithography experiments, thereby reducing mask costs and improving R&D efficiency. Summary of the Invention

[0004] In view of this, this disclosure provides a photolithography simulation method, training method, apparatus, equipment, medium, and product.

[0005] According to one aspect of this disclosure, a photolithography simulation method is provided, comprising: in response to a photolithography simulation request, acquiring a mask image to be processed and process parameters; and generating a photolithography image guided by a spatial image obtained based on the mask image and the process parameters, wherein the spatial image is a mask pattern represented by the mask image, and a light intensity distribution formed on a photoresist indicated by the process parameters by optical imaging.

[0006] According to another aspect of this disclosure, a method for training a photolithography simulation model is provided, comprising: inputting a sample mask image and sample process parameters into a model to be trained, so that the model to be trained generates an output photolithography image guided by a sample space image obtained based on the sample mask image and the sample process parameters, wherein the sample space image is a light intensity distribution formed on a photoresist indicated by the sample process parameters by optical imaging of a sample mask pattern represented by the sample mask image; and training the model to be trained using the output photolithography image and the reference photolithography image corresponding to the sample mask image and the sample process parameters to obtain a photolithography simulation model.

[0007] According to another aspect of this disclosure, a photolithography simulation apparatus is provided, comprising: an acquisition module for acquiring a mask image to be processed and process parameters in response to a photolithography simulation request; and a first generation module for generating a photolithography image guided by a spatial image obtained based on the mask image and the process parameters, wherein the spatial image is a mask pattern represented by the mask image, and a light intensity distribution formed on a photoresist indicated by the process parameters by optical imaging.

[0008] According to another aspect of this disclosure, a training apparatus for a photolithography simulation model is provided, comprising: a second generation module for inputting a sample mask image and sample process parameters into a model to be trained, such that the model to be trained generates an output photolithography image guided by a sample spatial image obtained based on the sample mask image and the sample process parameters, wherein the sample spatial image is a light intensity distribution formed on a photoresist indicated by the sample process parameters by optical imaging of a sample mask pattern represented by the sample mask image; and a training module for training the model to be trained using the output photolithography image and a reference photolithography image corresponding to the sample mask image and the sample process parameters to obtain a photolithography simulation model.

[0009] According to another aspect of this disclosure, an electronic device is provided, comprising: one or more processors; and a memory for storing one or more instructions, wherein, when executed by the one or more processors, the one or more processors cause the one or more processors to perform the method as described in this disclosure.

[0010] According to another aspect of this disclosure, a computer-readable storage medium is provided having executable instructions stored thereon, which, when executed by a processor, cause the processor to perform the methods described in this disclosure.

[0011] According to another aspect of this disclosure, a computer program product is provided, which includes computer-executable instructions that, when executed, are used to perform the methods described in this disclosure. Attached Figure Description

[0012] The above and other objects, features, and advantages of this disclosure will become clearer from the following description of embodiments of the present disclosure with reference to the accompanying drawings, in which:

[0013] Figure 1 This illustration schematically shows a system architecture for which photolithography simulation methods and training methods can be applied according to embodiments of the present disclosure;

[0014] Figure 2 A flowchart illustrating a photolithography simulation method according to an embodiment of the present disclosure is shown schematically.

[0015] Figure 3A This illustration schematically shows an example of a process for generating a photolithographic image based on a spatial image obtained from a mask image and process parameters, according to an embodiment of the present disclosure.

[0016] Figure 3BThe illustration shows an example of a process according to an embodiment of the present disclosure, in which the light intensity distribution of a mask pattern is determined by optical imaging onto a photoresist based on a mask image and process parameters to obtain a spatial image.

[0017] Figure 3C This schematically illustrates an example of a process for determining the morphological changes of photoresist produced by photolithography reaction based on a spatial image, according to an embodiment of the present disclosure, to obtain a photolithographic image.

[0018] Figure 4A This illustration schematically shows an example of a process for generating a photolithographic image based on a spatial image obtained from a mask image and process parameters, according to another embodiment of the present disclosure.

[0019] Figure 4B This illustration schematically shows an example of a process for generating a photolithographic image based on a spatial image obtained from a mask image and process parameters, according to yet another embodiment of the present disclosure.

[0020] Figure 5 A flowchart illustrating a method for training a lithography simulation model according to an embodiment of the present disclosure is shown schematically.

[0021] Figure 6 The illustration shows an example schematic diagram of the training process of a lithography simulation model according to an embodiment of the present disclosure;

[0022] Figure 7 The illustration shows an example schematic diagram of the training process of a lithography simulation model according to another embodiment of the present disclosure;

[0023] Figure 8 A block diagram of a photolithography simulation apparatus according to an embodiment of the present disclosure is shown schematically;

[0024] Figure 9 A block diagram schematically illustrates a training apparatus for a photolithography simulation model according to an embodiment of the present disclosure; and

[0025] Figure 10 A block diagram of an electronic device suitable for implementing a photolithography simulation method and a training method according to an embodiment of the present disclosure is shown schematically. Detailed Implementation

[0026] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0027] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0028] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0029] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0030] In the technical solution of this invention, the user information (including but not limited to user personal information, user image information, user device information, such as location information) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, storage, use, processing, transmission, provision, disclosure, and application of related data all comply with relevant laws, regulations, and standards, take necessary confidentiality measures, do not violate public order and good morals, and provide corresponding operation entry points for users to choose to authorize or refuse.

[0031] In one example, lithography simulation methods can include numerical modeling-based approaches and deep learning-based approaches.

[0032] Numerical modeling refers to physical modeling of each stage of the photolithography process using partial differential equations. This approach offers strong model interpretability, but the modeling process is complex, computationally intensive, requires high hardware resources, has slow simulation speed, and is difficult to flexibly adapt to different process platforms.

[0033] Deep learning-based approaches involve constructing an end-to-end mapping from mask to photoresist morphology using a data-driven method. However, the black-box nature of this approach limits the model's generalization and transferability. Furthermore, deep learning-based approaches require spatial images as training support. However, spatial images are theoretical data, and precise real-world values ​​cannot be obtained experimentally. Approximate values ​​must be obtained using additional physical simulation software, but the parameter tuning process for this software is cumbersome and cannot accurately describe the complex multi-frequency coupled lithography imaging process. Therefore, the accuracy of the spatial image approximation significantly impacts the model training performance.

[0034] Therefore, this disclosure provides a lithography simulation method, training method, apparatus, device, medium, and product that can be applied to the fields of artificial intelligence and semiconductor lithography technology. The lithography simulation method includes: in response to a lithography simulation request, acquiring a mask image to be processed and process parameters; and generating a lithography image using a spatial image obtained based on the mask image and process parameters as a guide, wherein the spatial image is a mask pattern represented by the mask image, and the light intensity distribution is formed on the photoresist indicated by the process parameters through optical imaging.

[0035] Figure 1 The illustration schematically depicts a system architecture for applying photolithography simulation methods and training methods according to embodiments of the present disclosure. It should be noted that... Figure 1 The examples shown are merely examples of system architectures that can be applied to the embodiments of this disclosure, in order to help those skilled in the art understand the technical content of this disclosure, but do not mean that the embodiments of this disclosure cannot be used in other devices, systems, environments or scenarios.

[0036] like Figure 1 As shown, the system architecture 100 according to this embodiment may include a first terminal device 101, a second terminal device 102, a third terminal device 103, a network 104, and a server 105. The network 104 serves as a medium for providing communication links between different devices.

[0037] It should be noted that the lithography simulation method and training method provided in this embodiment can generally be executed by the server 105. Accordingly, the lithography simulation device and training device provided in this embodiment can generally be located in the server 105.

[0038] Alternatively, the lithography simulation method and training method provided in the embodiments of this disclosure can also be executed by the first terminal device 101, the second terminal device 102, or the third terminal device 103. Correspondingly, the lithography simulation apparatus and training apparatus provided in the embodiments of this disclosure can also be disposed in the first terminal device 101, the second terminal device 102, or the third terminal device 103.

[0039] It should be understood that Figure 1The number of terminal devices, networks, and servers shown is merely illustrative. Depending on implementation needs, any number of terminal devices, networks, and servers can be included.

[0040] It should be noted that the sequence numbers of the operations in the following methods are for descriptive purposes only and should not be considered as indicating the execution order of the operations. Unless explicitly stated otherwise, the method does not need to be executed in the exact order shown.

[0041] The foregoing section described the system architecture provided in this disclosure, which allows for the application of photolithography simulation methods and training methods for photolithography simulation models. The following section will use... Figure 2 As an example, the photolithography simulation process of this disclosure will be further explained.

[0042] Figure 2 A flowchart illustrating a photolithography simulation method according to an embodiment of the present disclosure is shown schematically.

[0043] like Figure 2 As shown, the photolithography simulation method 200 may include operations S210~S220.

[0044] In operation S210, in response to a lithography simulation request, the mask image to be processed and the process parameters are acquired.

[0045] In operation S220, a lithographic image is generated using a spatial image obtained based on a mask image and process parameters as a guide. The spatial image is a mask pattern represented by the mask image, and the light intensity distribution is formed on the photoresist indicated by the process parameters through optical imaging.

[0046] A lithography simulation request is a trigger signal initiated by a user or upper-level system, indicating the execution of a lithography process simulation task. For example, after completing the layout design in an Electronic Design Automation (EDA) tool, an integrated circuit design engineer can click the "Run Lithography Simulation" button. The EDA tool then sends a lithography simulation request containing the mask image and process parameters to the simulation engine. Alternatively, during batch iterations, process optimization scripts automatically initiate lithography simulation requests to the simulation service via API calls.

[0047] A photomask image is a digital graphic representation of the circuit pattern to be manufactured. It describes the geometric distribution of transparent and opaque areas on a photomask in the form of a grayscale or binary image. Each pixel value in the photomask image corresponds to the light transmission property of the corresponding location on the photomask. For example, a polysilicon gate line with a width of 45 nanometers will appear as a bright stripe about 1 to 3 pixels wide surrounded by dark areas in a photomask image with a resolution of 512×512 and a field of view of 30 micrometers.

[0048] Process parameters refer to a set of quantitative indicators describing the conditions of a photolithography process. They can be used to specify the physical conditions that affect imaging and photoresist response during the photolithography process. In one embodiment, process parameters may include at least one of the following: photoresist type, photoresist thickness, and light source exposure.

[0049] Photoresist type designation is a specific category identifier for photoresist, used to distinguish photoresists with different chemical formulations, photosensitivity characteristics, and process suitability. It's important to note that different photoresist types differ in physicochemical properties such as photoacid generation efficiency, acid diffusion coefficient, catalytic deprotection reaction rate, development contrast, and resolution limit. These differences affect the final photoresist morphology. Therefore, by using the photoresist type as a process parameter in photolithography simulation, it's possible to differentiate the varying response behaviors of different photoresists.

[0050] Photoresist thickness is the physical thickness of the photoresist film spin-coated onto the wafer surface in the vertical direction, measured in nanometers (nm). It's important to note that thickness determines the optical path length of light propagating within the photoresist. Different photoresist thicknesses affect the intensity and period of the standing wave effect, the total number of photons absorbed by the photoacid generator (PAG) during exposure, the effective diffusion distance of acid molecules during post-baking, and the kinetics of developer penetration and dissolution during development. Therefore, by using thickness as a process parameter in photolithography simulation, it becomes possible to predict these thickness-dependent morphology deviations.

[0051] The exposure dose of a light source is the total light energy applied to a unit area of ​​the photoresist surface by the lithography machine during the exposure process, expressed in millijoules per square centimeter (mJ / cm²). It's important to note that the exposure dose determines the total amount of photoacid-generating agents in the photoresist absorb photons and decompose to generate photoacid molecules; for example, a higher exposure dose results in a higher initial acid concentration per unit area. Based on this, by using the exposure rate as a process parameter in lithography simulation, it becomes possible to learn the modulation law of morphology caused by the exposure dose by studying the differences in output lithographic images under different exposure doses.

[0052] In the embodiments of this disclosure, since the process parameters include at least one of the photoresist type, photoresist thickness, and light source exposure, the entire process from spatial image generation to photoresist morphology prediction is adapted to specific process conditions, thereby improving the generalization and transferability of the photolithography simulation method.

[0053] In photolithography, a spatial image is a two-dimensional distribution of light intensity on the photoresist surface after the mask pattern undergoes diffraction and interference through a projection optical system including a light source, condenser lens, mask plate, and projection lens. Regions of high light intensity in the spatial image represent vigorous chemical reactions in the photoresist, while regions of low light intensity represent weak reactions. For example, taking a 45-nanometer line mask as an example, its corresponding spatial image shows the highest light intensity at the center of the line, gradually decreasing towards the edge, forming a smooth intensity distribution curve. The light intensity distribution is the essence of the spatial image, describing the light intensity value at each coordinate point (x, y) on the photoresist surface in the form of a two-dimensional scalar field.

[0054] In one embodiment, the spatial image can be calculated using the Hopkins diffraction integral or the Abbe imaging model; in another embodiment, the spatial image can be generated autonomously by the Fourier neural operator module, without limitation.

[0055] A mask pattern is the actual geometric layout on the mask plate corresponding to a mask image, used to modulate incident light. The geometry, size, and spacing of the mask pattern determine the spectral distribution of the diffracted light. For example, a mask pattern can be various geometric elements of integrated circuit layouts, such as periodic dense lines, isolated lines, contact hole arrays, and L-shaped corner structures.

[0056] Optical imaging is the physical process by which ultraviolet / deep ultraviolet (UV / Deep Ultraviolet, DUV) or extreme ultraviolet (EUV) light emitted from a light source is diffracted by a photomask, and then the diffraction orders are collected by a projection lens and re-interfered and superimposed on the photoresist surface to form a spatial image. This process is essentially a diffraction-limited low-pass filter, meaning that the objective lens pupil only allows diffracted light within a limited spatial frequency range to pass through; details of the mask pattern outside this frequency range cannot be transferred to the photoresist surface.

[0057] Photoresist is a photosensitive polymer material coated on the surface of a semiconductor wafer. The photoresist undergoes a photochemical reaction in the exposed area, followed by acid-catalyzed reaction and diffusion during the post-baking stage, and then selectively dissolves in the developer, ultimately forming a three-dimensional relief morphology corresponding to the mask pattern.

[0058] A lithography image is the final output of the lithography simulation process, representing the actual circuit pattern morphology formed on the photoresist after the complete lithography process, including exposure, baking, and development. The lithography image can be a binary image, where a pixel value of 1 represents the area where the photoresist is retained, and a pixel value of 0 represents the area where the photoresist is removed by development. For example, taking a polysilicon gate layer as an example, the position and width of the photoresist lines retained in the lithography image determine the actual size of the silicon gate after subsequent etching processes. The specific method of generating the lithography image using spatial images as guides can be configured according to actual business needs and is not limited here.

[0059] For example, the spatial image module can receive the tensor concatenated from the mask image and process parameters, embed it into a high-dimensional feature space via convolution, and then output a predicted spatial image by passing it through a Fourier layer to simulate the frequency selection and filtering effects of an optical system. The photoresist module then uses this spatial image as input, and through reactive diffusion and development, progressively maps the light intensity distribution to the photoresist morphology. In this case, the spatial image serves as an explicit intermediate representation between the spatial image module and the photoresist module, guiding the photoresist model to focus on the chemical reaction intensity of the exposed area in the form of light intensity distribution.

[0060] Alternatively, frequency domain features can be extracted from the mask image and process parameters by a Fourier layer, the spatial image module maps the features into an implicit spatial image, and then the photoresist module maps the implicit spatial image into a photoresist image. In this case, the spatial image may not be explicitly output, and the training phase is constrained to meet the optical low-pass characteristics and spatial image smoothness, guiding the generation of the lithography image in a physically consistent manner.

[0061] In the embodiments of this disclosure, since the spatial image is obtained based on the mask image and process parameters, it characterizes the light intensity distribution formed on the photoresist after the mask pattern is diffracted and interfered by the optical system. By using this as a guide to generate the lithographic image, the physical laws of optical imaging are injected into the generation process as intermediate constraints. This makes the generation of the lithographic image not simply dependent on data-driven statistical fitting, but subject to the physical prior constraints of diffraction-limited imaging. This enhances the generalization and transfer capabilities of the lithography simulation, improves the accuracy of the lithography simulation process and the obtained lithography image, and enhances its consistency with the actual lithography results.

[0062] According to an embodiment of this disclosure, operation S220 may include the following operations: determining the light intensity distribution formed on the photoresist by optical imaging of the mask pattern based on the mask image and process parameters, to obtain a spatial image; and determining the morphological changes of the photoresist caused by the photolithography reaction based on the spatial image, to obtain a photolithography image.

[0063] Photolithography reaction refers to the physicochemical transformation process that photoresist undergoes throughout the entire photolithography process. For example, photolithography reaction may include the exposure stage in which the photoacid generator absorbs photons and decomposes to generate acid molecules, the post-baking stage in which the acid concentration is determined by the acid-catalyzed resin deprotection reaction and the thermal expansion of acid molecules, and the development stage in which the developer selectively dissolves the deprotected area to form the final morphology.

[0064] Morphological changes refer to the structural changes that occur when photoresist, initially in a uniform and flat state, undergoes the exposure, post-baking, and development stages, resulting in the partial dissolution and removal of some areas while others are retained. In photolithography simulation, morphological changes can be represented as a binary pattern, where the pixel value of the area where the photoresist is retained is marked as 1, and the pixel value of the area where the photoresist is removed is marked as 0, thus obtaining the photolithographic image.

[0065] In the embodiments of this disclosure, a spatial image is obtained by determining the light intensity distribution based on the mask image and process parameters. The physical laws of optical diffraction and interference are explicitly modeled as an intermediate characterization step in the simulation process. This ensures that the mask pattern is accurately preserved after processing corresponding to the process parameters, guaranteeing that the smoothness and spectral cutoff characteristics of the spatial image conform to the physical reality of diffraction-limited imaging, thus improving the generalization reliability of the lithography simulation. Furthermore, by determining the morphological changes of the photoresist after the lithography reaction based on the spatial image to obtain the lithography image, each physicochemical stage of the lithography process is incorporated into the morphological evolution modeling. This reduces the simulation morphological differences of the mask pattern under different process conditions, improving the accuracy of the lithography simulation.

[0066] In one embodiment of this disclosure, the process of generating a photolithographic image can be implemented based on a photolithographic simulation model M1, which will be described below.

[0067] According to embodiments of this disclosure, determining the light intensity distribution formed on photoresist by optical imaging of a mask pattern based on a mask image and process parameters to obtain a spatial image may include the following operations: performing convolution processing on a first stitched feature obtained by stitching the mask image and process parameters to obtain input features; processing the input features using M Fourier layers to obtain a first frequency domain feature, wherein the Fourier layers are used to jointly process the input features from the frequency domain and the spatial domain, and M is an integer greater than 1; performing convolution processing on the first frequency domain feature to obtain a spatial image.

[0068] The first stitching feature is a multi-channel tensor formed by stitching the pixel matrix of the mask image with the numerical matrix of the process parameters along the channel dimension. This stitching operation integrates the spatial geometric information indicated by the mask image and the process condition information indicated by the process parameters into a unified multi-dimensional feature expression at the data level, enabling subsequent processing to simultaneously perceive pattern shape and process conditions. For example, stitching a 512×512×1 mask image with a 512×512×1 exposure channel and a 512×512×1 adhesive thickness channel yields a 512×512×3 first stitching feature.

[0069] After obtaining the first concatenated feature, it can be convolved to obtain the input feature. The convolution process is a process of performing a local weighted summation operation on the first concatenated feature using a learnable convolution kernel. The input feature is a high-dimensional hidden layer feature tensor obtained after convolution of the first concatenated feature. Its spatial resolution is consistent with the mask image, but the number of channels has been expanded to the hidden layer dimension.

[0070] In one embodiment, the mask image and process parameters can be concatenated along the channel dimension to obtain the first concatenated feature. Subsequently, a 1×1 convolution kernel is used to convolve the first concatenated feature. This 1×1 convolution projects the low-dimensional first concatenated feature to a 64-dimensional high-dimensional space using a pixel-by-pixel channel-wise linear combination, obtaining the input feature. The number of input channels for this 1×1 convolution is the total number of channels after concatenation, and the number of output channels is the hidden layer dimension (64), stride=1, and padding=0.

[0071] For the input features, they can be fed into M cascaded Fourier layers. The first frequency domain feature is obtained by performing frequency and spatial domain processing on the input features using the Fourier layers. The Fourier layer corresponds to the physical law of a photolithography optical system, which manifests as a product of transfer functions in the frequency domain. Each Fourier layer can include two parallel branches: a frequency domain branch and a spatial domain branch, to simultaneously perform frequency and spatial domain operations on the input features and fuse the results of the two branches. It should be noted that M represents the number of stacked Fourier layers; the output of one Fourier layer becomes the input of the next. Since M > 1, the photolithography imaging process can be refined layer by layer, thus helping to improve the accuracy of the spatial image.

[0072] The frequency domain is a representation space with spatial frequency as the independent variable after Fourier transform. In the frequency domain, the geometric features of the mask pattern are decomposed into complex amplitudes of different frequency components. Low-frequency components correspond to the macroscopic outline of the pattern, while high-frequency components correspond to fine edges and sharp corners. The frequency domain branch can be used to transform the input features to the frequency domain through Fourier transform, apply learnable linear operators for frequency selection and filtering within the truncated low-frequency modes, and then perform an inverse transform back to the spatial domain.

[0073] The spatial domain is the original representation space with pixel spatial coordinates as independent variables. In the spatial domain, feature maps directly present the geometry and local texture of a pattern as a two-dimensional image. Spatial domain branches can apply linear transformations directly to the spatial domain to capture local details.

[0074] After obtaining the features output by each of the two parallel branches, the two features can be added together and output as the first frequency domain feature after passing through a nonlinear activation function. The first frequency domain feature is a deep feature tensor output after the input features are processed layer by layer by M Fourier layers. Its spatial resolution and number of channels are consistent with the input features, but it contains rich semantic information after multi-level frequency domain filtering and spatial domain refinement. This first frequency domain feature can be understood as an implicit joint expression of the frequency and spatial domains of the mask pattern after diffraction imaging by an optical system.

[0075] After obtaining the first frequency domain features, the 64-channel high-dimensional features can be mapped into a spatial image through convolution. This convolution can be implemented using 1×1 convolution, i.e., pixel-wise linear projection; or kernel-small convolution (such as 3×3), with 64 input channels and 1 output channel. The output is a spatial image with the same resolution as the mask image, where each pixel value represents the light intensity at that location.

[0076] In the embodiments of this disclosure, input features are obtained by convolving the first stitched features of the mask image and process parameters. Spatial geometric information and process condition information are nonlinearly fused and embedded in a high-dimensional space in the channel dimension, so that the local morphology of the mask pattern and its specific process environment are coupled at the feature expression level. The first frequency domain feature is obtained by using M Fourier layers to jointly process the input features in the frequency and spatial domains, thereby achieving efficient simulation while maintaining physical interpretability. On this basis, a spatial image is obtained by convolving the first frequency domain feature. The rich implicit representation jointly encoded by multiple Fourier layers in the frequency and spatial domains is compressed and mapped into an explicit spatial image, so that the spatial image retains the band-limited smoothness characteristics of diffraction imaging and has the ability to respond to changes in mask pattern and process.

[0077] In the above embodiments, the process of generating the photolithographic image is implemented based on the photolithographic simulation model M1. The following will utilize... Figure 3A The process is illustrated by example.

[0078] Figure 3A The illustration shows an example schematic diagram of a process for generating a photolithographic image based on a spatial image obtained from a mask image and process parameters, according to an embodiment of the present disclosure.

[0079] like Figure 3AAs shown, in Example 300A, the process of generating a lithographic image is illustrated by taking the processing of a mask image 301 and process parameters 302 using a lithography simulation model M1 as an example. The lithography simulation model M1 may include a spatial image module M11 and a photoresist module M12.

[0080] For the spatial image module M11, the first stitched feature obtained by stitching the mask image 301 and the process parameters 302 can be convolved to obtain the input feature; the input feature can be processed using M Fourier layers to obtain the first frequency domain feature; the first frequency domain feature can be convolved to obtain the spatial image 303.

[0081] According to embodiments of this disclosure, the process parameters include at least one sub-parameter, and the channel size of each sub-parameter is the same as the size of the mask image; after obtaining the mask image to be processed and the process parameters, the method further includes: using the mask image as the first channel and each sub-parameter as the other channels, stitching the mask image and the process parameters in the channel dimension to obtain a first stitching feature, wherein the number of channels of the first stitching feature is the sum of the number of channels of the mask image and the number of sub-parameters.

[0082] In the embodiments of this disclosure, the data input to the photolithography simulation model includes mask images and process parameters. Since the mask image is a binary distribution of the mask's transmittance / opaqueness properties, it can essentially be fully represented by a single channel. Because the spatial image characterizes the light intensity distribution on the photoresist surface—that is, each location uses a numerical value to represent the light intensity—the spatial image is also a single-channel grayscale image. Similarly, because the photolithography image characterizes the binary state of photoresist retention / removal, it is also a single-channel grayscale image. Therefore, the mask image input to the model is single-channel, the spatial image of the intermediate model product is single-channel, and the final photolithography image output by the model is also single-channel; all three maintain inherent consistency in channel semantics.

[0083] Before inputting the mask image and process parameters into the spatial imaging module, the single-channel mask image data and process parameters can be concatenated along the channel dimension to obtain the first concatenated feature across multiple channels. Subsequently, a 1×1 convolution operation is used to map this low-dimensional concatenated tensor from a smaller number of channels to a higher-dimensional hidden layer space, such as mapping from three channels to a hidden layer dimension of 64, thus achieving high-dimensional feature space embedding. This expansion of the number of channels from low to high dimensions provides sufficient feature degrees of freedom for subsequent frequency domain transformations, enabling the learning of modulation patterns for different frequency components in a 64-dimensional high-dimensional space, thereby more richly characterizing the complex transmission relationships of multi-frequency coupling in the lithography optical system.

[0084] For the photoresist module M12, the light intensity distribution represented by the spatial image 303 can be used as the initial acid concentration distribution. For N time steps, the changes in the acid concentration distribution in the time and spatial dimensions during the photolithography process are determined to obtain the target acid concentration distribution. The target acid concentration distribution is then binarized and mapped to obtain the photolithography image 304.

[0085] The above text provides an example of how to obtain a lithographic image using a lithographic simulation model M1. The following text will describe how to obtain a spatial image based on the lithographic simulation model M1.

[0086] According to an embodiment of this disclosure, for the m-th Fourier layer, the following operations are performed: the m-th first frequency domain feature corresponding to the (m-1)-th intermediate feature is processed to obtain the m-th frequency domain branch feature, wherein the (m-1)-th intermediate feature is the feature output by the (m-1)-th Fourier layer, and the 0th intermediate feature is the input feature; a local linear transformation is performed on the (m-1)-th intermediate feature to obtain the m-th spatial domain branch feature; the m-th frequency domain branch feature and the m-th spatial domain branch feature are fused to obtain the m-th intermediate feature.

[0087] The m-th Fourier layer refers to the m-th layer in an M-layer cascaded Fourier layer structure, where m ranges from 2 to M. The m-th Fourier layer receives the intermediate features output from the (m-1)-th layer, processes them to generate the m-th intermediate feature, and then passes it to the (m+1)-th Fourier layer. For example, when M=4, m=2 corresponds to the 2nd Fourier layer, m=3 corresponds to the 3rd Fourier layer, and m=4 corresponds to the 4th Fourier layer. The 2nd Fourier layer receives the first intermediate feature output from the 1st Fourier layer as input, processes it, and outputs the second intermediate feature to the 3rd Fourier layer for further processing.

[0088] It should be noted that the larger M is, the stronger the ability of the M Fourier layers to represent multi-frequency coupling relationships, but the number of parameters and computational overhead also increase accordingly. Therefore, the specific value of M can be configured according to actual business needs and is not limited here.

[0089] The (m-1)th intermediate feature is the feature tensor output after processing by the (m-1)th Fourier layer, and it is also the input of the mth Fourier layer. The spatial resolution and number of channels of the intermediate feature remain consistent with the input feature, but its internal features have accumulated the joint refinement results of the first (m-1)th layers in the frequency and spatial domains. For example, when m=2, the first intermediate feature is a 512×512×64 feature tensor output by the first Fourier layer after performing joint frequency and spatial domain processing on the input feature; it carries coarse-grained information about the light intensity distribution after the first round of frequency domain filtering. When m=3, the second intermediate feature has further refined the details based on the first layer.

[0090] The m-th first frequency domain feature refers to the frequency domain representation of the (m-1)-th intermediate feature in its frequency domain branch after Fourier transform. Specifically, the (m-1)-th intermediate feature is transformed from the spatial domain to the frequency domain using a two-dimensional Fourier transform (FFT) to obtain the first frequency domain feature in the form of a complex matrix. This first frequency domain feature is organized in the frequency domain according to the spatial frequency, with low-frequency components clustered at the center of the frequency domain matrix and high-frequency components distributed at the edges.

[0091] After obtaining the m-th first frequency domain feature, the frequency domain branch and spatial domain branch of the Fourier layer can be used in parallel to process the m-th first frequency domain feature, thereby fusing the processing results of the two branches into the m-th intermediate feature.

[0092] For the frequency domain branch, the first frequency domain feature is processed by modal truncation and linear transformation, and then returned to the spatial domain by inverse Fourier transform to obtain the m-th frequency domain branch feature. This m-th frequency domain branch feature represents the learnable linear modulation applied by the m-th layer to the input (m-1)-th intermediate feature from the frequency domain perspective to filter or suppress high-frequency components.

[0093] For the spatial domain branch, the m-th spatial domain branch feature is obtained by performing a local linear transformation on the (m-1)-th intermediate feature. A local linear transformation refers to a linear mapping operation that relies only on local neighboring pixels in the input feature; for example, it can be performed using 1×1 or 3×3 convolution. This m-th spatial domain branch feature encodes the local adjustment result of the input feature from a spatial domain perspective at the m-th layer, capturing the local geometric details of the mask pattern and providing supplementary spatial domain information for subsequent fusion with the frequency domain branch feature.

[0094] After obtaining the m-th frequency domain branch feature and the m-th spatial domain branch feature, the features of the two branches can be fused into the m-th intermediate feature, so that the global frequency domain modulation result of the frequency domain branch and the local detail adjustment result of the spatial domain branch are superimposed in the same feature space. For example, the features of the two branches can be added element-wise, that is, the two tensors of the same dimension are directly added at their corresponding spatial positions and channels.

[0095] The m-th intermediate feature is the feature tensor output after processing by the m-th Fourier layer. It is obtained by fusing the m-th frequency domain branch feature and the m-th spatial domain branch feature and then applying a nonlinear activation function. This m-th intermediate feature simultaneously carries the global diffraction coupling information extracted from the frequency domain and the local geometric details captured from the spatial domain by the current layer. It is the result of joint processing in the frequency and spatial domains and is passed on as the input to the (m+1)-th Fourier layer.

[0096] For example, when m=2, the second intermediate feature is obtained by element-wise addition of the second frequency domain branch feature and the second spatial domain branch feature, followed by nonlinear mapping using the GELU activation function. This feature further corrects the frequency response in the mid-frequency band based on the first intermediate feature, making the light intensity distribution of the spatial image closer to the true diffraction imaging result.

[0097] In one embodiment, the process of using M Fourier layers to process the input features and obtain the first frequency domain features can be shown by the following formula (1).

[0098] (1)

[0099] in, Characterizes the (m-1)th intermediate feature; The m-th intermediate feature represents the output of the m-th Fourier layer; Characterizes the Fourier transform operation; Characterizes the inverse Fourier transform operation; Characterize learnable linear operators in the frequency domain; The representation space domain can learn linear transformation weights; Characterize nonlinear activation functions, including but not limited to the rectified linear unit (ReLU) or the Gaussian error linear unit (GELU), to introduce nonlinear expressive power.

[0100] In the embodiments of this disclosure, the m-th first frequency domain feature corresponding to the (m-1)-th intermediate feature is processed to obtain the m-th frequency domain branch feature. Frequency domain transformation, mode truncation, and learnable linear modulation are continuously performed in the 2nd to Mth Fourier layers, so that each layer can refine the modulation method of different spatial frequency components layer by layer based on the frequency features extracted in the previous layer. This breaks through the bottleneck of the single-layer Fourier layer being able to perform only low-order approximations, so that the frequency domain response after multi-layer progression can approximate the multi-frequency cross-coupling relationship described by the complete Hopkins model, thereby improving the prediction accuracy of spatial images.

[0101] By performing a local linear transformation on the (m-1)th intermediate feature to obtain the mth spatial domain branch feature, the spatial domain local geometric details are preserved in each layer. This allows the spatial domain branch to compensate for and repair the fine pattern edge information that may be lost when the frequency domain branch filters out high-frequency noise, thereby avoiding the blurring effect of pattern details caused by simple frequency domain truncation.

[0102] Based on this, the m-th frequency domain branch feature and the m-th spatial domain branch feature are fused to obtain the m-th intermediate feature. This allows the intermediate feature output by each layer to carry two complementary types of information: the overall diffraction effect of the pattern and the local morphological fine-tuning, and pass them to the next layer for further processing. After multi-layer stacking, the model can achieve the optimal balance between global consistency in the frequency domain and local fidelity in the spatial domain.

[0103] According to embodiments of this disclosure, processing the m-th first frequency domain feature corresponding to the (m-1)-th intermediate feature to obtain the m-th frequency domain branch feature may include the following operations: performing modal truncation on the m-th first frequency domain feature according to a preset modal truncation parameter to obtain the m-th truncated frequency domain feature, wherein the preset modal truncation parameter is used to limit the number of modes retained in the frequency domain transformation; performing a linear transformation on the m-th truncated frequency domain feature to obtain the m-th frequency domain branch feature.

[0104] The preset mode cutoff parameter (i.e., n_modes) can be used to limit the number of low-frequency modes retained after Fourier transform in the frequency domain. The preset mode cutoff parameter determines the side length of the square region centered at zero frequency in the frequency domain complex matrix, and all frequency components outside this region are set to zero. In one embodiment, the preset mode cutoff parameter can correspond to the band-limited physical constraint of the photolithography optical system due to the finite numerical aperture (NA), that is, the pupil only allows diffraction orders with spatial frequencies lower than the cutoff frequency (≈2NA / λ) to pass through.

[0105] For example, the preset mode truncation parameter can be set to 32, meaning that only a 32×32 low-frequency square region centered at zero frequency is retained in the 512×512 complex matrix in the frequency domain, while the remaining high-frequency components are truncated to zero. If the preset mode truncation parameter is set to a larger value, such as 64, more mid-to-high frequency information is retained, resulting in richer spatial image details, but the number of parameters increases. If the preset mode truncation parameter is set to a smaller value, such as 16, the strong filtering effect makes the spatial image smoother, but fine pattern information may be lost.

[0106] Modal truncation is an operation in the frequency domain that retains only the frequency coefficients within a preset modal truncation parameter range centered at zero frequency, while forcibly setting the high-frequency coefficients outside this range to zero. Specifically, it is equivalent to applying an ideal two-dimensional rectangular low-pass filter, where the coefficients passing through the central region are 1 and those passing through the edge regions are 0. The modal truncation operation simulates the physical blocking effect of a projection lens pupil on high-frequency diffracted light; that is, the finite aperture of the pupil can only collect diffracted light with a propagation angle smaller than a specific threshold.

[0107] For example, the modal phase process is explained below using a 512×512 resolution and n_modes=32 as an example: First, the center of the frequency domain matrix can be located, and the zero frequency can be moved to the center of the matrix (index=256,256) by FFT Shift; then, with the center as the origin, the frequency coefficients within ±16 positions along the row and column directions can be retained, that is, a 32×32 square area with row index [25616, 256+15] (32 rows) and column index [25616, 256+15] (32 columns) can be retained; then, all frequency coefficients outside the 32×32 area are assigned a value of 0; thus, the truncated frequency domain features contain only 1,024 non-zero modes (32×32), forming a highly sparse frequency domain representation.

[0108] The m-th truncated frequency domain feature is the result of modal truncation of the m-th first frequency domain feature. That is, in the complete frequency domain complex matrix, only the low-frequency central region retains non-zero complex values, while the rest are 0. This m-th truncated frequency domain feature preserves the frequency information within the band-limited range of the photolithography optical system, eliminates high-frequency components that are physically impossible to pass through the projection lens, and provides a dimension-reduced and physically consistent frequency domain input for subsequent linear transformations.

[0109] After obtaining the m-th truncated frequency domain feature, a linear transformation can be performed to obtain the m-th frequency domain branch feature. The linear transformation involves applying a learnable linear operator to the truncated frequency domain feature, linearly combining and scaling the complex values ​​of each retained frequency mode. By applying independent gain and phase shift to different frequency components in the frequency domain, the linear transformation simulates the frequency domain product effect of the optical system's transfer function.

[0110] For example, the linear transformation process is described below: First, a learnable frequency domain linear operator, which is a trainable complex weight matrix corresponding to the truncated mode size, can be applied to the m-th truncated frequency domain feature to preserve each frequency position within the region, and the complex vectors of all channels at that position are linearly combined by multiplying them by the corresponding weights; then, an inverse fast Fourier transform can be performed on the linearly modulated truncated frequency domain feature to transform the frequency domain complex representation back to the m-th frequency domain branch feature in the spatial domain.

[0111] In the embodiments of this disclosure, the m-th first frequency domain feature is modally truncated according to preset modal truncation parameters to obtain the truncated frequency domain feature. This explicit simulation of the physical blocking effect of the projection lens pupil on high-frequency diffraction orders via hard frequency truncation ensures that modal components exceeding the cutoff frequency are excluded in subsequent processing. This guarantees that the spatial image features output by the frequency domain branch strictly satisfy the band-limited physical constraints of the diffraction-constrained optical system, improving processing efficiency in large-scale photolithography simulations. Furthermore, by performing a linear transformation on the m-th truncated frequency domain feature, the resulting m-th frequency domain branch feature conforms to diffraction physics and possesses adaptability to process conditions.

[0112] The following will combine Figure 3B The specific structure of the spatial image module M11 and the process of obtaining spatial images are explained.

[0113] Figure 3B The illustration shows an example of a process according to an embodiment of the present disclosure, in which the light intensity distribution of a mask pattern is determined by optical imaging onto a photoresist based on a mask image and process parameters to obtain a spatial image.

[0114] like Figure 3B As shown, in embodiment 300B, the mask image 301 and the process parameters 302 can be stitched together to obtain a first stitched feature; and the first stitched feature is convolved to obtain input feature 305.

[0115] The input feature 305 is processed using M Fourier layers to obtain the first frequency domain feature 306. The M Fourier layers may include Fourier layers M11_1, ..., M11_M. Taking the m-th Fourier layer as an example, it may include a frequency domain branch and a spatial domain branch.

[0116] Specifically, the frequency domain branch can perform the following operations: Modal truncation is applied to the m-th first frequency domain feature 307 according to preset modal truncation parameters to obtain the m-th truncated frequency domain feature 308; a linear transformation is performed on the m-th truncated frequency domain feature 308 to obtain the m-th frequency domain branch feature 310. The spatial domain branch can perform the following operations: Local linear transformation is performed on the (m-1)-th intermediate feature 307 to obtain the m-th spatial domain branch feature 311; the m-th frequency domain branch feature 310 and the m-th spatial domain branch feature 311 are fused to obtain the m-th intermediate feature 312.

[0117] The above processing procedure is repeated for each Fourier layer until the Mth intermediate feature is obtained, and the Mth intermediate feature is determined as the first frequency domain feature 306. The first frequency domain feature 306 is convolved to obtain the spatial image 303.

[0118] The process of obtaining a spatial image based on the spatial image module M11 has been illustrated above. The process of obtaining a photolithographic image based on the photoresist module M12 will be described below.

[0119] According to this embodiment of photolithography, based on the spatial image, the morphological changes of the photoresist caused by the photolithographic reaction are determined to obtain a photolithographic image, including: processing the spatial image using a photoresist module to simulate the morphological changes in the photoresist formed based on the photochemical reaction and development process after exposure, thereby obtaining a photolithographic image.

[0120] In this embodiment, the photoresist module is a model component that receives a spatial image as input, simulates the internal physicochemical processes of the photoresist, and outputs a photolithographic image. The physicochemical processes simulated by the photoresist module include, but are not limited to: the photoacid generator absorbing photons and decomposing to produce acid during the exposure stage; the spatiotemporal evolution of acid concentration determined by the acid-catalyzed deprotection reaction and the thermal diffusion of acid molecules during the post-baking stage; and the selective dissolution of the deprotected region by the developer during the development stage.

[0121] It should be noted that the essential function of the photoresist module is to map the light intensity distribution characterized by the optical spatial image into a photolithographic image representing the final morphology of the photoresist through the modeling of the aforementioned physical and chemical processes.

[0122] According to this embodiment of photolithography, based on the spatial image, the morphological changes of the photoresist produced by the photolithography reaction are determined to obtain a photolithographic image, which may include the following operations: using the light intensity distribution represented by the spatial image as the initial acid concentration distribution, determining the changes of the acid concentration distribution in the time and spatial dimensions during the photolithography process for N time steps to obtain the target acid concentration distribution, where N is an integer greater than 1; and performing binarization mapping on the target acid concentration distribution to obtain the photolithographic image.

[0123] The initial acid concentration distribution refers to the initial concentration distribution of photoacid molecules at various spatial locations within the photoresist at the start of the Post Exposure Bake (PEB) stage. In actual photolithography processes, PAG absorbs photons and decomposes to produce acid during the exposure stage. The amount of acid generated is approximately proportional to the local light intensity; therefore, the light intensity distribution can be used as an approximation of the initial acid concentration distribution.

[0124] For example, if the light intensity at a certain location in the spatial image is I=0.8, using this light intensity as the initial acid concentration indicates that a relatively high concentration of acid molecules has accumulated at that location after exposure. If the light intensity at another location is I=0.1, it indicates a lower acid concentration in the dark area. It should be noted that the initial acid concentration can also be set to 0, and the spatial image can be used as the input condition for the reaction rate network to indirectly drive the increase in acid concentration. This method can also describe the evolution of acid concentration within the photoresist.

[0125] A time step is a discrete time interval in the discretization solution of acid concentration evolution. Within each time step, the acid concentration distribution is updated from the current time t to the next time t+Δt according to the reaction-diffusion equation. For example, taking Δt=0.05 as an example, the nth time step corresponds to the time interval [t_n, t_n+Δt]. Within this step, the diffusion term causes the acid to migrate from the high concentration region to the low concentration region, and the reaction term causes the acid to be catalytically amplified in the region of high light intensity. The superposition of these two terms updates the acid concentration distribution to Cⁿ⁺¹.

[0126] N represents the total number of time steps in the acid concentration evolution process, and is an integer greater than 1, representing the asymptotic evolution characteristics of reaction diffusion kinetics. For example, N can be 20. It should be noted that the value of N determines the fineness of time discretization. If N is larger, the time step is smaller and the numerical solution accuracy is higher, but the computational cost is also greater.

[0127] By processing through the aforementioned N time steps, the changes in acid concentration distribution in both the temporal and spatial dimensions during photolithography can be simulated to obtain the target acid concentration distribution. The temporal dimension change refers to the variation of the acid concentration distribution over time, i.e., the increase or decrease in acid concentration at each spatial location over time. The spatial dimension change refers to the differences and gradients in acid concentration between different spatial locations at the same moment. The target acid concentration distribution is the final two-dimensional acid concentration distribution obtained at the end of the PEB stage after the acid concentration has evolved through N time steps. This distribution is used as input to the subsequent development module to determine the final dissolved or retained state of the photoresist.

[0128] After obtaining the target acid concentration distribution, it can be binarized to obtain a photolithographic image. Binarization is the operation of converting a continuous target acid concentration distribution into a binary photoresist morphology image. For example, nonlinear functions such as the sigmoid function can be used to map continuous acid concentration values ​​to a binary output of 0 or 1. Through binarization, the selective dissolution behavior of the developer on the deprotected regions during the development process can be simulated, i.e., regions with acid concentrations above a certain threshold are dissolved and removed, while regions below the threshold are retained.

[0129] In one embodiment, the processing procedure for the above N time steps is shown in the following formula (2).

[0130] (2)

[0131] in, Characterizing acid concentration distribution; The partial derivative of acid concentration with respect to time represents the instantaneous rate of change of acid concentration at time t. Characterized by the diffusion coefficient, D=0.2, used to control the intensity of thermal diffusion of acid molecules; Characterizes the Laplacian operator acting on the acid concentration distribution, representing the local curvature of the acid concentration space surface; Characterizes the reaction rate function.

[0132] In the embodiments of this disclosure, the light intensity distribution characterized by a spatial image is used as the initial acid concentration distribution. This pre-positions the physical process of photon absorption and acid production during the exposure stage as the initial condition for the reaction diffusion evolution, ensuring that the initial state of the acid concentration evolution in the post-baking stage is consistent with the actual physical state of photolithography. The target acid concentration distribution is obtained by processing the initial acid concentration distribution over N time steps. A multi-step iterative discretization method is used to explicitly model the changes in the acid concentration distribution in the time and spatial dimensions during photolithography. Based on this, the target acid concentration distribution is binarized to obtain the photolithographic image, enabling the image to accurately reflect the morphological deviations of the pattern during photolithography, thereby improving the accuracy of the photolithography simulation.

[0133] According to embodiments of this disclosure, determining the changes in acid concentration distribution in the time and spatial dimensions during photolithography for N time steps to obtain a target acid concentration distribution includes: based on the reaction-diffusion equation, simulating the changes in acid concentration under the influence of acid catalysis and acid molecule diffusion after chemical amplification of the photoresist to obtain the target acid concentration distribution.

[0134] In the post-baking stage of chemically amplified photoresist, the photoacid molecules generated during exposure act as catalysts, catalyzing the resin to undergo a deprotection reaction, causing the acid concentration to increase in a nonlinear, self-amplifying manner; at the same time, the acid molecules diffuse from the high concentration region to the low concentration region under thermal drive.

[0135] The coupling process of the acid-catalyzed reaction and acid molecule diffusion described above determines the final acid concentration distribution at the end of the post-baking process, thus directly affecting the geometric characteristics of the photoresist morphology after development. In this case, the reaction-diffusion equation is a mathematical description of this coupling process, used to simulate the acid concentration changes under the influence of acid-catalyzed reaction and acid molecule diffusion after chemical amplification of the photoresist.

[0136] According to an embodiment of this disclosure, for the nth time step, the following operations are performed: the acid concentration distribution of the (n-1)th time step is convolved to obtain the nth diffusion term, wherein the acid concentration distribution of the 0th time step is the light intensity distribution represented by the spatial image; the second stitching feature obtained by stitching the acid concentration distribution of the (n-1)th time step with the spatial image is convolved to obtain the nth reaction term; the acid concentration distribution of the nth time step is determined based on the acid concentration distribution of the (n-1)th time step, the nth diffusion term, the nth reaction term, and the preset time step length.

[0137] N is the total number of time steps for discretizing the acid concentration evolution, and its value is an integer greater than 1. N determines the number of equal segments into which the total physical time of the post-baking stage is divided; that is, the larger N is, the smaller the time span of each step, the higher the numerical accuracy, but the greater the computational cost. The nth time step is the computational unit for the nth discrete time interval in the evolution of the acid concentration distribution, and the value of n ranges from 2 to N. Within each time step, based on the acid concentration distribution of the previous step, the contributions of the diffusion term and the reaction term to the change in acid concentration can be calculated separately, and then the acid concentration distribution of the current step is obtained by advancing the time steps. The nth time step inherits the result of the (n-1)th step and propagates it to the (n+1)th step.

[0138] For example, when N=20, n takes the values ​​2, 3, ..., 20 sequentially. The second time step uses the acid concentration distribution C¹ output from the first time step as input, calculates the diffusion and reaction contributions, and outputs C². This process continues until the 20th time step is the final step, outputting C². 0 That is, the target acid concentration distribution.

[0139] The acid concentration distribution at time step (n-1) is the acid concentration distribution obtained at the end of the previous time step. This distribution records the current accumulated acid concentration value at each pixel location, carrying the cumulative effect of the entire reaction-diffusion evolution process of the previous n-1 steps. For example, when n=3, the acid concentration distribution C² at time step 2 is the input for time step 3. C² is compared to the initial light intensity distribution C. 0 The reaction has undergone two steps of catalysis and diffusion smoothing, the acid concentration in the patterned region has increased and the edge diffusion has partially unfolded.

[0140] For the acid concentration distribution at time step (n-1), a predefined discrete Laplace convolution kernel can be used to perform a convolution operation on it to approximate the Laplace operator, yielding the nth diffusion term. This nth diffusion term represents the contribution of the acid concentration change caused by the thermal diffusion of acid molecules at time step (n), and is obtained by multiplying the diffusion coefficient D by the Laplace convolution result. It describes the physical effect of the natural migration of acid from high-concentration regions to low-concentration regions. The diffusion term flattens the concentration gradient and reduces the sharpness of the pattern edges.

[0141] For example, at a certain pixel location, if its acid concentration is lower than the average of its four neighboring regions, ∇²C>0, the diffusion term is positive, indicating that acid molecules from the neighboring regions diffuse to that location, increasing its concentration; if its concentration is higher than that of its four neighboring regions, ∇²C<0, the diffusion term is negative, indicating that acid diffuses to the neighboring regions, decreasing its concentration.

[0142] For the acid concentration distribution at the (n-1)th time step, it can be stitched with the spatial image to obtain a second stitched feature. The first channel of this second stitched feature can be the current acid concentration, and the second channel can be the light intensity. After obtaining the second stitched feature, it can be aligned and convolved to obtain the nth reaction term. This nth reaction term is the contribution of the acid concentration change caused by the acid-catalyzed deprotection chemical reaction at the nth time step.

[0143] For example, at a position where light intensity I = 0.9 and the current acid concentration Cⁿ⁻¹ = 0.6, a higher reaction rate (e.g., 0.15) may be output, meaning that the acid concentration will increase significantly due to catalytic amplification in this step; in the dark region where light intensity I = 0.1 and Cⁿ⁻¹ = 0.05, the output can be close to 0, and the acid concentration hardly increases.

[0144] After obtaining the nth diffusion term and the nth reaction term, the acid concentration distribution at the nth time step can be determined based on the acid concentration distribution at the (n-1)th time step, the nth diffusion term, the nth reaction term, and the preset time step size. The preset time step size Δt is the time span corresponding to each time step in the discretization solution. Δt and the total number of time steps N together determine the total physical simulation time: T_total = N × Δt. It should be noted that the value of Δt needs to balance accuracy and efficiency; that is, too large a Δt will lead to increased discretization error and possible numerical instability; while too small a Δt, although high in accuracy, will increase the number of calculation steps.

[0145] In one embodiment, the operation performed at the nth time step can be shown in the following formulas (3) to (5).

[0146] (3)

[0147] (4)

[0148] (5)

[0149] in, Characterizes the acid concentration distribution at the nth time step; Characterizes the acid concentration distribution at the (n-1)th time step; Characterizes the preset time step; Characterizes the nth diffusion term; Characterizes the nth reaction term; Characterizes the discrete Laplacian convolution kernel.

[0150] In the embodiments of this disclosure, the nth diffusion term is obtained by convolving the acid concentration distribution at the (n-1)th time step, ensuring the parameter-free physical determinism of the diffusion term calculation and improving the consistency of cross-process migration. The nth reaction term is obtained by convolving the acid concentration distribution at the (n-1)th time step with the second stitching feature obtained by stitching the spatial image, enabling the reaction term to flexibly capture the nonlinear self-amplification dynamics in the chemically amplified photoresist, thereby accurately restoring the differentiated acid concentration growth curves caused by the difference in catalytic regeneration rate between different light intensity regions. Based on this, the nth acid concentration distribution is determined by superimposing the acid concentration distribution, diffusion term, reaction term, and preset time step, ensuring that the acid concentration update at each step is a natural continuation of the combined effect of the diffusion and reaction in the previous step. This effectively restores the complete spatiotemporal dynamics of the chemically amplified photoresist post-baking process, thereby helping to improve the accuracy of the lithography image.

[0151] The following will combine Figure 3C The specific structure of the photoresist module M12 and the process of obtaining photolithographic images are explained.

[0152] Figure 3C The illustration shows an example schematic diagram of a process for obtaining a photolithographic image by determining the morphological changes of photoresist produced by the photolithographic reaction based on a spatial image according to an embodiment of the present disclosure.

[0153] like Figure 3C As shown, in Example 300C, the light intensity distribution characterized by spatial image 303 can be used as the initial acid concentration distribution 313. The changes in acid concentration distribution in the time and spatial dimensions during the photolithography process are determined for N time steps to obtain the target acid concentration distribution 314. The N time steps may include time steps M12_1, ..., M12_N.

[0154] For the nth time step, the following operations can be performed: convolve the acid concentration distribution 315 of the (n-1)th time step to obtain the nth diffusion term 316; convolve the second stitching feature 317 obtained by stitching the acid concentration distribution 315 of the (n-1)th time step with the spatial image 303 to obtain the nth reaction term 318; and determine the acid concentration distribution 319 of the nth time step based on the acid concentration distribution 315 of the (n-1)th time step, the nth diffusion term 316, the nth reaction term 318, and the preset time step size.

[0155] Repeat the above operations until the acid concentration distribution at the Nth time step is obtained, and define the acid concentration distribution at the Nth time step as the target acid concentration distribution 314. Perform binarization mapping on the target acid concentration distribution 314 to obtain the lithographic image 304.

[0156] In another embodiment of this disclosure, the process of generating a photolithographic image can be implemented based on a photolithographic simulation model M2, which will be described below.

[0157] According to embodiments of this disclosure, determining the light intensity distribution formed on photoresist by optical imaging of a mask pattern based on a mask image and process parameters to obtain a spatial image may include the following operations: processing the mask image and process parameters using P Fourier layers to obtain a second frequency domain feature, where P is an integer greater than 1; mapping the second frequency domain feature to a light intensity distribution in the spatial domain to obtain a spatial image; wherein the model parameters of the model used to perform frequency domain feature extraction and spatial domain mapping are constrained by a preset loss during the training phase to simulate the low-pass filtering characteristics of the photolithography process.

[0158] P Fourier layers refer to P cascaded and stacked Fourier neural operators, where P is an integer greater than 1. Each Fourier layer processes the input features in parallel in the frequency and spatial domains. Specifically, the frequency domain branch transforms the features to the frequency domain using Fourier transform, applies learnable linear operators for frequency selection and filtering within the truncated low-frequency modes, and then performs an inverse transform back to the spatial domain. The spatial domain branch applies local linear transforms in the spatial domain to capture local details. For example, P can be 4, meaning four cascaded Fourier layers, each with a cutoff frequency of 32 and 64 hidden channels.

[0159] The second frequency domain feature is a deep feature tensor output after the mask image and process parameters are processed by a cascade of P Fourier layers. The spatial resolution of this second frequency domain feature is consistent with the input mask image, the number of channels is the hidden layer dimension, and it contains rich semantic information after multi-layer frequency domain filtering and spatial domain refinement.

[0160] The following describes the process of obtaining the second frequency domain features by processing the mask image and process parameters using P Fourier layers: First, the mask image and process parameters can be concatenated along the channel dimension to obtain a multi-channel tensor, which serves as the input to the first Fourier layer. Then, each Fourier layer contains two parallel branches. The frequency domain branch performs a two-dimensional FFT transformation on the input to the frequency domain, truncating and retaining the low-frequency 32×32 modes. A learnable frequency domain linear operator R is applied for frequency selection and filtering, and then the input is returned to the spatial domain via an inverse fast Fourier transform (IFFT). The spatial domain branch processes local features through linear transformations (such as 1×1 convolution). The results of the two branches are added element-wise and output as the second frequency domain features after passing through a nonlinear activation function.

[0161] The model used for frequency domain feature extraction and spatial domain mapping can receive an input of 256×256×(1+number of process parameter channels), which is processed through four Fourier layers to extract a second frequency domain feature of 256×256×64, and then mapped to a spatial image of 256×256×1 through two convolutional layers. During the training phase, the model is constrained by a preset loss, which refers to the loss that imposes physical constraints on the implicit spatial image.

[0162] The pre-defined loss ensures that the spatial image generated by the model can still conform to the physical laws of photolithographic diffraction imaging, even without supervision from a real spatial image. For example, the pre-defined loss may include a low-pass loss to constrain the amplitude of high-frequency components in the frequency domain of the spatial image to approach zero, and a total variational loss to constrain the smoothness of adjacent pixels in the spatial domain of the spatial image.

[0163] After obtaining the second frequency domain features, they can be mapped to a single-channel spatial image using two convolutional layers. After P Fourier layers complete the joint processing of the frequency and spatial domains, the output features still maintain a high number of channels. To ensure that the output is consistent with the physically single-channel spatial image, the multi-channel features need to be converged into a single-channel output. This convergence process can be achieved by gradually reducing the number of channels through convolutional layers.

[0164] For example, the first convolutional layer can be a 3×3 convolution with padding=1, which further extracts local features and performs inter-channel interactions on the second frequency domain features to maintain spatial resolution and number of channels; the second convolutional layer can be a 1×1 convolution or a 3×3 convolution, which compresses the multi-channel features from high dimension to a single channel, and the output is a single-channel spatial image with the same resolution as the input mask image, where each pixel value represents the light intensity at that spatial location.

[0165] Through the aforementioned path of changing the number of channels—single-channel input, channel splicing, low-dimensional to high-dimensional embedding, high-dimensional frequency domain processing, high-dimensional to single-channel convergence, and single-channel output—the model undergoes a process of first increasing and then decreasing the dimensionality in terms of channel dimension. Specifically, the dimensionality-increasing stage provides ample expression space for frequency domain processing and physical feature extraction, while the dimensionality-decreasing stage converges the implicit representations of multiple channels into a single-channel spatial image with clear physical meaning. This ensures the consistency of the intermediate representations and the final output in terms of physical meaning while maintaining the depth of the model's expressive power.

[0166] In the embodiments of this disclosure, a second frequency domain feature is obtained by processing the mask image and process parameters using P Fourier layers. This multi-layered cascaded frequency and spatial domain joint processing overcomes the accuracy bottleneck of a single Fourier layer, which can only perform low-order approximations. This allows for the refinement of multi-frequency coupling relationships in lithography imaging layer by layer, thereby achieving efficient feature extraction while maintaining physical interpretability. Based on this, a spatial image is obtained by mapping the second frequency domain feature to a spatial intensity distribution. The rich implicit representation jointly encoded by the Fourier layers in the frequency and spatial domains is compressed into an explicit intensity distribution, ensuring that the implicit spatial images generated under various process conditions accurately reflect the low-pass smoothness of diffraction-limited imaging.

[0167] According to embodiments of this disclosure, determining the morphological changes of photoresist produced by photolithography based on a spatial image to obtain a photolithographic image may include the following operation: performing linear transformations on the pixel values ​​in the spatial image to obtain the photolithographic image.

[0168] Each pixel value is a scalar value I(i, j) of light intensity at each coordinate position (i, j) in the spatial image. A linear transformation refers to the operation of applying a function mapping to the input scalar. For each pixel value, the same linear transformation can be applied independently to map the light intensity to an intermediate logit value of the photoresist morphology.

[0169] For example, a lightweight 1×1 convolution can be used to map the spatial image to the lithographic image. This 1×1 convolution kernel is a learnable scalar w with a bias of b, essentially performing the same linear transformation on each pixel I(i,j) of the spatial image. During training, w and b can be optimized to be optimal parameters that reasonably map light intensity to the photoresist retention / removal tendency.

[0170] In the embodiments of this disclosure, a photolithographic image is obtained by performing linear transformation on each pixel value in the spatial image. The light intensity distribution of the spatial image is directly converted into a photoresist retention / removal decision by mapping each pixel independently. The essential physical logic of the photoresist response is modeled, so that the simulation results are consistent with the real photoresist development behavior while having high interpretability.

[0171] The following will utilize Figure 4A The specific structure of the lithography simulation model M2 and the process of obtaining a lithography image using the lithography simulation model M2 are illustrated by example.

[0172] Figure 4A The illustration shows an example schematic diagram of a process for generating a photolithographic image based on a spatial image obtained from a mask image and process parameters, according to another embodiment of the present disclosure.

[0173] like Figure 4AAs shown, in Example 400A, the process of generating a lithographic image is illustrated by using a lithography simulation model M2 to process a mask image 401 and process parameters 402. The lithography simulation model M2 may include a Fourier module M21, a spatial image module M22, and a photoresist module M23.

[0174] For the Fourier module M21, P Fourier layers can be used to process the mask image 401 and process parameters 402 to obtain the second frequency domain features. For the spatial image module M22, the second frequency domain features can be mapped to the light intensity distribution in the spatial domain to obtain the spatial image 403. For the photoresist module M23, linear transformations can be performed on each pixel value in the spatial image 403 to obtain the lithographic image 404.

[0175] The following will combine Figure 4B The specific structures of the Fourier module M21, the spatial image module M22, and the photoresist module M23, the process of obtaining the spatial image, and the process of obtaining the photolithographic image are explained.

[0176] Figure 4B The illustration shows an example schematic diagram of a process for generating a photolithographic image based on a spatial image obtained from a mask image and process parameters, according to yet another embodiment of the present disclosure.

[0177] like Figure 4B As shown, in embodiment 400B, taking the Fourier module M21 as including P Fourier layers, namely Fourier layers M21_1, ..., Fourier layer M21_P, the P Fourier layers can be used to process the mask image 401 and process parameters 402 step by step to obtain the second frequency domain feature 405.

[0178] The spatial image module M22 may include a convolutional layer M221, an activation function layer M222, a convolutional layer M223, and an activation function layer M224. Based on this, the second frequency domain feature 405 can be input into the convolutional layer M221, and processed sequentially by the convolutional layer M221, the activation function layer M222, the convolutional layer M223, and the activation function layer M224 to obtain the spatial image 403.

[0179] The photoresist module M23 may include a convolutional layer M231 and an activation function layer M232. Based on this, the spatial image 403 can be input into the convolutional layer M231, and processed sequentially by the convolutional layer M231 and the activation function layer M232 to obtain the photolithographic image 404.

[0180] The above are merely exemplary embodiments, but are not limited thereto. Other photolithography simulation methods known in the art may also be included, as long as they can improve the accuracy of the photolithography simulation process and the obtained photolithography image.

[0181] The above has described the photolithography simulation method provided in this disclosure. The following will use... Figure 5 As an example, the training process of the lithography simulation model of this disclosure will be further explained.

[0182] Figure 5 A flowchart illustrating a method for training a lithography simulation model according to an embodiment of the present disclosure is shown.

[0183] like Figure 5 As shown, the training method 500 for the photolithography simulation model may include operations S510~S520.

[0184] In operation S510, the sample mask image and sample process parameters are input into the model to be trained, so that the model to be trained generates an output lithography image guided by the sample spatial image obtained based on the sample mask image and sample process parameters. The sample spatial image represents the light intensity distribution formed on the photoresist indicated by the sample process parameters through optical imaging of the sample mask pattern represented by the sample mask image.

[0185] By operating the S520, the model to be trained is trained using the output lithography image and the reference lithography image to obtain the lithography simulation model.

[0186] For explanations regarding sample mask images, sample process parameters, sample spatial images, output lithographic images, and sample mask patterns, please refer to the above-mentioned content on mask images, process parameters, spatial images, lithographic images, and mask patterns, which will not be repeated here.

[0187] The reference lithography image serves as a supervision label in the training samples, representing the final morphology of the photoresist that should be obtained after a complete lithography process, given the sample mask pattern and process parameters corresponding to that set of samples. The reference lithography image acts as an optimization target during training, ensuring that the output lithography image of the model approximates this reference image as closely as possible. For example, the reference lithography image can be generated through actual lithography experiments or high-precision physical simulation software.

[0188] The model to be trained is a model that has been built before training begins, but whose parameters have not yet been optimized. During training, the model parameters of the model to be trained are gradually optimized through backpropagation of the loss function, eventually becoming a lithography simulation model that can accurately simulate lithography. This lithography simulation model can be directly used for inference, that is, inputting a mask image and process parameters, and outputting a predicted lithography image end-to-end.

[0189] In the embodiments of this disclosure, by inputting sample mask images and sample process parameters into the model to be trained, the model can use the sample spatial image generated based on the sample mask images and sample process parameters as an intermediate guide between optical imaging and photoresist response to generate the output lithography image. Based on this, the model to be trained is obtained by using the output lithography image and a reference lithography image to obtain a lithography simulation model. This allows the parameters of each module in the model to converge collaboratively to the global optimum under a unified training objective. The final lithography simulation model can directly predict the lithography image with high accuracy from the mask image and process parameters in an end-to-end manner.

[0190] In one embodiment of this disclosure, a lithography simulation model M1 can be trained using a lithography simulation model training method. The training process will be described below.

[0191] According to embodiments of this disclosure, the model to be trained may include a first spatial image module, the sample spatial image may include the first spatial image, and the training samples may further include a reference spatial image. A sample mask image and sample process parameters are input into the first spatial image module to obtain the first spatial image; based on a first difference between the first spatial image and the reference spatial image, the first spatial image module is trained to obtain an intermediate spatial image module.

[0192] The first spatial image is the predicted light intensity distribution output by the first spatial image module during training, based on the current sample mask image and sample process parameters. The reference spatial image is the spatial image supervision label in the training samples, i.e., the true light intensity distribution calculated by the physical simulation software using a physical model for the mask pattern and process parameters of this set of samples.

[0193] The first spatial image module is a sub-network in the model to be trained that generates a first spatial image based on the sample mask image and sample process parameters. In this case, the goal of training is to continuously adjust the parameters of the first spatial image module through backpropagation, so that the first spatial image gradually approximates the reference spatial image.

[0194] The following describes the process of using the first spatial image module to process the sample mask image and sample process parameters to obtain the first spatial image: First, the sample mask image and sample process parameters can be concatenated in the channel dimension to obtain a multi-channel input tensor; then, the number of channels is mapped from the low dimension to the hidden layer dimension of 64 through a 1×1 convolution to obtain the sample input features; next, the sample input features are processed layer by layer through M Fourier layers to obtain the sample frequency domain features; finally, the sample frequency domain features are mapped to the first spatial image through a convolutional layer.

[0195] The first difference is a measure of the difference between the first spatial image and the reference spatial image, used to drive parameter updates in the first spatial image module. The first difference quantifies the degree of deviation between the light intensity distribution predicted by the model indicated by the first spatial image and the physically true light intensity distribution indicated by the reference spatial image; that is, the greater the difference, the less accurate the model's modeling of the optical imaging process.

[0196] According to embodiments of this disclosure, the first spatial image and the reference spatial image have the same size. Same size means that the first spatial image and the reference spatial image have the same spatial resolution, i.e., they have the same height H and the same width W.

[0197] The first difference characterizes the difference in pixel values ​​at corresponding positions between the first spatial image and the reference spatial image. Corresponding positions refer to pixel pairs with the same coordinates (i, j) in the first and reference spatial images. Since the first and reference spatial images describe the light intensity distribution of the same sample mask pattern under the same sample process parameters, the pixel at coordinates (100, 150) in the first spatial image and the pixel at coordinates (100, 150) in the reference spatial image correspond to the same physical location on the photoresist surface.

[0198] The pixel value difference refers to the deviation between the pixel value at a certain location in the first spatial image and the pixel value at the corresponding location in the reference spatial image. For example, the first difference can be calculated by summing the squared differences of the deviations between the pixel values ​​at each location in the first and reference spatial images and dividing by the total number of pixels. In this case, each location contributes equally to the total difference, allowing the model to approximate the label evenly across the entire image.

[0199] In one embodiment, the first difference can be determined using the following formula (6).

[0200] (6)

[0201] in, Characterize the first difference; The pixel value at coordinates (i,j) represents the first spatial image. The pixel value of the reference space image at coordinates (i,j) represents the pixel value of the reference space image.

[0202] In the embodiments of this disclosure, since the first spatial image and the reference spatial image have the same size, it is ensured that the light intensity distribution predicted by the model is spatially aligned with the actual light intensity distribution generated by the physical simulation. Based on this, a first difference is determined by the difference in pixel values ​​at corresponding positions between the first spatial image and the reference spatial image. The optimization objective is set to minimize the numerical deviation between the predicted light intensity and the actual light intensity at all positions. This allows the parameter adjustment of the first spatial image module to be refined to the light intensity prediction accuracy at each independent position, thus helping to improve the simulation accuracy of the entire process from mask to photoresist morphology.

[0203] The intermediate spatial image module is a spatial image generation sub-network obtained after training the first spatial image module, with parameters that have initially converged. The intermediate spatial image module already has the ability to accurately predict spatial images from mask images and process parameters. In the future, it will be connected with the photoresist model for end-to-end joint fine-tuning for further optimization.

[0204] In embodiments of this disclosure, a first spatial image is obtained by inputting a sample mask image and sample process parameters into a first spatial image module, enabling the model to learn the mapping from mask pattern and process conditions to light intensity distribution in a data-driven manner. Based on this, an intermediate spatial image module is obtained by training the first spatial image module based on a first difference between the first spatial image and a reference spatial image, allowing the intermediate spatial image module to accurately reproduce the light intensity distribution described by the Hopkins diffraction integral or Abbe imaging model.

[0205] According to embodiments of this disclosure, the model to be trained may further include a first photoresist module; operation S520 may include the following operations: while keeping the model parameters of the intermediate spatial image module unchanged, the first photoresist module is trained based on the second difference between the output lithography image and the reference lithography image to obtain an intermediate photoresist module; based on the second difference between the output lithography image and the reference lithography image, the intermediate spatial image module and the intermediate photoresist module are jointly fine-tuned until a predetermined termination condition is met to obtain a lithography simulation model.

[0206] The first photoresist module is a sub-network in the model to be trained, used to generate a photoresist morphology image from the spatial image. The first photoresist module can receive the spatial image output by the intermediate spatial image module, obtain the target acid concentration distribution through reaction-diffusion iteration, and then obtain the output photoresist image through two layers of convolution and development processing.

[0207] The second difference is a measure of the difference between the output lithography image and the reference lithography image, which quantifies the deviation between the model-predicted photoresist morphology and the actual photoresist morphology in the form of a loss function value.

[0208] According to embodiments of this disclosure, the output lithographic image and the reference lithographic image have the same size. Same size means that the output lithographic image and the reference lithographic image have the same spatial resolution, i.e., both have the same height H and the same width W.

[0209] The second difference may include at least one of the first sub-difference and the second sub-difference; the first sub-difference represents the difference between the output lithographic image and the reference lithographic image in the edge contour, and the second sub-difference represents the difference between the output lithographic image and the reference lithographic image in the pixel value at the corresponding position.

[0210] The first sub-difference can be used to measure the difference in edge contours between the output lithographic image and the reference lithographic image. Edge contours refer to the boundary between the photoresist-retained and removed areas in the lithographic image, i.e., the geometric boundary of the circuit pattern. For example, the first sub-difference can be obtained by first extracting the edge maps of the two images using an edge extraction operator, and then comparing the differences between the two edge maps.

[0211] The second sub-difference can be used to measure the difference in pixel values ​​between the output lithographic image and the reference lithographic image at all corresponding positions. Corresponding positions refer to pixel pairs in the output and reference lithographic images that have the same coordinates (i, j). For example, the second sub-difference can be obtained by a pixel-by-pixel global comparison of the original pixel values ​​of the two images.

[0212] In one embodiment, the first sub-difference, the second sub-difference, and the second difference can be determined using the following formulas (7) to (9).

[0213] (7)

[0214] (8)

[0215] (9)

[0216] in, Characterizing the second difference; Characterize the first sub-difference (i.e., contour loss); Characterizes the second sub-difference (i.e., binarization loss); Used to control the relative contribution ratio of the first sub-difference to the second difference; Used to control the relative contribution ratio of the second sub-difference to the second difference; Characterize the output lithographic image; Characterize the reference lithography image; Characterizes the Sigmoid function.

[0217] In the embodiments of this disclosure, since the output lithography image and the reference lithography image have the same size, it is ensured that the morphology of the photoresist predicted by the model is spatially aligned with the morphology of the actual photoresist. Based on this, by using a first sub-difference to characterize the difference in edge contours between the output lithography image and the reference lithography image, the model is driven to optimize the precise matching of pattern geometric boundaries during training, thereby ensuring that the edge positions of the pattern predicted by the final lithography simulation model are highly consistent with the edge positions of the actual lithography results. By using a second sub-difference to characterize the difference in pixel values ​​at corresponding positions between the output lithography image and the reference lithography image, it is ensured that the predicted morphology has clear binarization features globally, thus making the simulation results visually and physically correspond to the actual state of the photoresist.

[0218] The intermediate photoresist module is a sub-network obtained by training the first photoresist module based on the second difference, while keeping the parameters of the intermediate spatial image module unchanged. The intermediate photoresist module already has the ability to predict lithographic images from spatial images, and will be further optimized by end-to-end joint fine-tuning after being concatenated with the spatial image model.

[0219] After the intermediate spatial image module and the intermediate photoresist module have been independently trained and converged, the two modules can be cascaded, and end-to-end overall parameter fine-tuning can be performed with the second difference as the optimization target. Joint fine-tuning allows the parameters of the two modules to be adjusted collaboratively within a small range to compensate for the overall prediction bias caused by the accumulation of serial errors between modules during their independent training.

[0220] The predetermined termination condition is the criterion for determining when the joint fine-tuning phase ends. For example, the predetermined termination condition may include at least one of the following: reaching a preset maximum number of training epochs, the second difference no longer decreasing significantly over a number of consecutive epochs, or the second difference falling below a preset threshold.

[0221] In the embodiments of this disclosure, by training the first photoresist module based on the second difference between the output lithography image and the reference lithography image while keeping the model parameters of the intermediate spatial image module unchanged, an intermediate photoresist module is obtained. This decouples the reaction diffusion and development modeling of the photoresist from the complete lithography simulation process for training. This allows the parameter updates of the photoresist module to focus on learning the accurate mapping of the acid-catalyzed deprotection reaction rate and the nonlinear response of development, without being disturbed by the gradient of the spatial image module. This ensures that the intermediate photoresist module can accurately model the chemical amplification and development processes based on accurate spatial image input. Furthermore, by jointly fine-tuning the intermediate spatial image module and the intermediate photoresist module based on the second difference until a predetermined termination condition is met, a lithography simulation model is obtained. The two modules are then connected in series to collaboratively optimize all parameters in an end-to-end manner. This effectively eliminates the overall prediction accuracy loss caused by the accumulation of serial errors when the two modules are trained independently. The final lithography simulation model can directly output the predicted lithography image from the mask image and process parameters in an end-to-end forward propagation manner during inference, achieving convenient and efficient lithography simulation.

[0222] The following will utilize Figure 6 The training process of the above-mentioned photolithography simulation model M1 is illustrated by example.

[0223] Figure 6 The illustration shows an example schematic diagram of the training process of a lithography simulation model according to an embodiment of the present disclosure.

[0224] like Figure 6 As shown, in embodiment 600, the model to be trained may include a first spatial image module M11 and a first photoresist module M12. The training samples may include a sample mask image 601, a reference spatial image 605, a reference lithography image 607, and sample process parameters 602 related to the reference lithography image. The training process may include three stages, and each stage will be described exemplarily below.

[0225] In the first stage, the sample mask image 601 and the sample process parameters 602 are input into the first spatial image module M11 to obtain the first spatial image 603; based on the first difference 606 between the first spatial image 603 and the reference spatial image 605, the first spatial image module M11 is trained to obtain the intermediate spatial image module.

[0226] In the second stage, while keeping the model parameters of the intermediate spatial image module unchanged, the first photoresist module M12 is trained based on the second difference 608 between the output lithography image 604 and the reference lithography image 607 to obtain the intermediate photoresist module.

[0227] In the third stage, based on the second difference 608 between the output lithography image 604 and the reference lithography image 607, the intermediate spatial image module and the intermediate photoresist module are jointly fine-tuned until the predetermined termination condition is met, and the lithography simulation model M1 is obtained.

[0228] In another embodiment of this disclosure, a lithography simulation model M2 can be trained using a training method for a lithography simulation model. The training process will be described below.

[0229] According to an embodiment of this disclosure, the model to be trained may include a second spatial image module and a second photoresist module; operation S520 may include the following operation: based on a third difference between the output lithography image and the reference lithography image and a fourth difference between the second spatial image, the model parameters of the second spatial image module and the second photoresist module are adjusted end-to-end until a predetermined termination condition is met, thereby obtaining a lithography simulation model.

[0230] The second spatial image module is a sub-network in the model to be trained that maps the frequency domain features extracted by the Fourier layers to an implicit second spatial image. The second spatial image is an implicit light intensity distribution generated by the second spatial image module based on the frequency domain features output by the Fourier layers, mapped through two convolutional layers. For example, the second spatial image module may include two convolutional layers: the first convolutional layer can be a 3×3 convolution with padding=1, and the second convolutional layer can be a 1×1 convolution or a 3×3 convolution.

[0231] The second photoresist module is a sub-network in the model to be trained that maps the implicit second spatial image to the output photoresist image. For example, the second photoresist module may include a 1×1 convolutional kernel that performs a pixel-by-pixel linear transformation on the second spatial image and maps it to the output photoresist image via a sigmoid function.

[0232] The third difference is used to measure the deviation between the output lithographic image and the reference lithographic image, and can drive parameter updates of the second spatial image module and the second photoresist module. In one embodiment, the third difference may include photoresist L1 loss and edge loss. Specifically, the photoresist L1 loss is used to measure the L1 norm deviation between the two images at all pixel locations, and the edge loss is used to calculate the L1 loss between the edge images after first extracting the edges of the two images separately using the Sobel operator.

[0233] The fourth difference can be used to constrain the physical plausibility of the second spatial image, directly measuring the degree to which the second spatial image deviates from physical expectations. In one embodiment, the fourth difference may include total variational loss and low-pass loss. Specifically, the total variational loss is used to constrain the minimization of the differences between adjacent pixel values ​​in the spatial image to ensure spatial domain smoothness, and the low-pass loss is used to constrain the mean amplitude of the high-frequency components in the frequency domain of the spatial image to approach zero to ensure that it meets the optical low-pass filtering characteristics.

[0234] In one embodiment, the loss function used to adjust the model parameters of the second spatial image module and the second photoresist module can be shown in the following formula (10).

[0235] (10)

[0236] in, Characterizes the total difference in model parameters used to adjust the second spatial image module and the second photoresist module; and Together they constitute the third difference; and Together they constitute the fourth difference.

[0237] After obtaining the third and fourth differences, the total difference obtained based on the third and fourth differences can be used to backpropagate gradients and update all model parameters simultaneously. For example, the Adam optimizer can be used with a learning rate set to 1×10⁻. 4 After 100 iterations of training, Adam's adaptive learning rate mechanism is suitable for simultaneously optimizing complex parameters in the frequency domain and real parameters in the spatial domain.

[0238] In the embodiments of this disclosure, model parameter adjustment is driven by a third difference between the output lithography image and the reference lithography image, simultaneously optimizing the pixel-level prediction accuracy of the photoresist morphology and the geometric matching accuracy of the edge contour. This ensures that the final lithography simulation model can predict the lithography image with high fidelity in both the internal region and edge positions of the pattern. A fourth difference based on the second spatial image is used to synchronously constrain the model parameter adjustment, ensuring that the implicit spatial image generated by the model satisfies a reasonable light intensity distribution. Furthermore, by combining the third and fourth differences to synchronously adjust the model parameters of the second spatial image module and the second photoresist module until a predetermined termination condition is met, the supervised learning of the photoresist morphology and the self-supervised constraint of the physical rationality of the spatial image are unified in an end-to-end training framework. This allows the second spatial image module and the second photoresist module to adapt to each other in collaborative optimization, and the resulting lithography simulation model can directly predict the photoresist morphology with high accuracy during inference using a single end-to-end forward propagation. Moreover, since the training process does not require a spatial image as a label, data preparation costs and time are reduced, achieving efficient, convenient, and physically reliable lithography simulation.

[0239] According to embodiments of the present disclosure, the output lithographic image and the reference lithographic image have the same size, and the third difference includes at least one of a third sub-difference and a fourth sub-difference; the third sub-difference characterizes the difference between the output lithographic image and the reference lithographic image in the corresponding pixel values, and the fourth sub-difference characterizes the difference between the output lithographic image and the reference lithographic image in the edge contour.

[0240] The third sub-difference can be used to measure the difference between the output lithographic image and the reference lithographic image at corresponding pixel values. For example, the third sub-difference can summarize the deviations between the pixel values ​​at each pixel position in the output lithographic image and the corresponding pixel values ​​in the reference lithographic image. It focuses on global pixel-level numerical consistency, so that each pixel value in the output lithographic image is as close as possible to the pixel value used as a label in the reference lithographic image.

[0241] In one embodiment, the third sub-difference can be determined using the following formula (11).

[0242] (11)

[0243] in, Characterizes the height of the output lithographic image and the reference lithographic image; Characterizes the width of the output lithographic image and the reference lithographic image; The pixel value at position (i,j) of the output lithographic image is represented. The pixel value at the corresponding position (i,j) of the reference lithographic image is represented.

[0244] The fourth sub-difference measures the difference in edge contours between the output lithographic image and the reference lithographic image. For example, the fourth sub-difference can first extract the gradient magnitude distribution at the geometric boundaries of the pattern in the output lithographic image and the reference lithographic image respectively using an edge extraction operator, and then compare the differences between the gradient magnitude distributions, focusing on the geometric boundary matching accuracy of the circuit pattern.

[0245] In the embodiments of this disclosure, since the output lithography image and the reference lithography image have the same size, it is ensured that the photoresist morphology predicted by the model is pixel-aligned with the reference photoresist morphology used as a label. Because the third sub-difference characterizes the difference in pixel values ​​at corresponding positions between the output lithography image and the reference lithography image, it is ensured that there are no large areas of misclassified pixels in the pattern interior region and the background region of the lithography image, providing global pixel-level morphology fidelity for lithography simulation. Because the fourth sub-difference characterizes the difference in edge contours between the output lithography image and the reference lithography image, the model can be constrained during training to accurately match the geometric boundary positions of the pattern, thereby ensuring that the circuit geometric features in the lithography image produced by the final lithography simulation model match the actual lithography results.

[0246] According to embodiments of this disclosure, the fourth difference may include at least one of a fifth sub-difference and a sixth sub-difference; the fifth sub-difference is determined based on the sum of the absolute values ​​of the gradients of the second spatial image in the horizontal and vertical directions, and the sixth sub-difference is determined based on the high-frequency components of the second spatial image.

[0247] The fifth sub-difference is used to constrain the smoothness of the second spatial image in the spatial domain. For example, the fifth sub-difference can be determined based on the sum of the absolute values ​​of the gradients of adjacent pixels in the horizontal and vertical directions of the second spatial image. The gradient in the horizontal direction refers to the change in pixel value between adjacent pixels along the x-axis in the second spatial image, i.e., I(i, j+1) - I(i, j). The horizontal gradient describes the rate and direction of change of light intensity distribution from one column to the next in the horizontal direction. The gradient in the vertical direction refers to the change in pixel value between adjacent pixels along the y-axis in the second spatial image, i.e., I(i+1, j) - I(i, j). The vertical gradient describes the spatial rate of change of light intensity distribution in the vertical direction.

[0248] Specifically, the absolute values ​​of the differences between each pair of horizontally adjacent pixels (i,j) and (i,j+1) in the second spatial image, and the absolute values ​​of the differences between each pair of vertically adjacent pixels (i,j) and (i+1,j), can be taken. Then, the absolute values ​​of all horizontal and vertical gradients in the entire image are summed. The smaller the value of the fifth sub-difference, the smoother the second spatial image and the more continuous the transition between adjacent pixels.

[0249] In one embodiment, the fifth sub-difference can be determined using the following formula (12).

[0250] (12)

[0251] in, Characterizes the gradient in the vertical direction; It represents the gradient in the horizontal direction.

[0252] The sixth sub-difference is used to constrain the loss of low-pass characteristics in the frequency domain of the second spatial image. For example, the sixth sub-difference can be determined based on the high-frequency components of the second spatial image. Specifically, the amplitudes of these high-frequency components can be extracted and their average values ​​calculated; this average value is the value of the sixth sub-difference. The smaller the sixth sub-difference, the fewer high-frequency components the second spatial image contains, which better matches the inherent low-pass filtering characteristics of a diffraction-limited optical system.

[0253] High-frequency components refer to the spatial frequency components in the frequency domain that are outside the predetermined low-frequency region after the second spatial image has undergone a Fourier transform. In photolithography physics, high-frequency components correspond to rapid spatial changes in light intensity distribution—such as sharp edges, noise spikes, and detailed textures. Since the projection lens pupil acts as a low-pass filter, diffracted light with spatial frequencies higher than the cutoff frequency cannot pass through the pupil to reach the photoresist surface. Therefore, the real spatial image should not contain high-frequency components exceeding the system cutoff frequency.

[0254] In the embodiments of this disclosure, since the fifth sub-difference is determined based on the sum of the absolute values ​​of the gradients of the second spatial image in the horizontal and vertical directions, a global smoothing constraint is applied to the second spatial image in the spatial domain by accumulating the absolute values ​​of the light intensity differences of adjacent pixels. This ensures that any pixel value jump in the second spatial image is quantitatively processed, thereby driving the light intensity distribution generated by the model to have the continuous and smooth characteristics that diffraction interference superposition should have in space. This ensures that the light intensity distribution pattern of the spatial image maintains the physical and realistic gradual continuity in the pattern edge transition zone and background area.

[0255] Since the sixth sub-difference is determined by the high-frequency components of the second spatial image, a band-limited low-pass constraint can be applied to the second spatial image in the frequency domain, so that the spectral distribution of the second spatial image strictly matches the pupil cutoff characteristics of the diffraction-limited optical system. Thus, without relying on the annotation data of the reference spatial image, the implicit spatial image generated by the model naturally possesses the physical fidelity of optical imaging.

[0256] According to embodiments of this disclosure, high-frequency components can be obtained by: frequency-domain shifting the third frequency domain feature so that the low-frequency component in the third frequency domain feature is located at the center of the frequency domain, thereby obtaining the shifted frequency domain feature; using a preset mask, extracting the high-frequency component in the shifted frequency domain feature, wherein the target region in the preset mask is a first value, and the other regions in the preset mask other than the target region are second values, and the target region is the region within a preset radius with the spatial image center as the origin.

[0257] The third frequency domain feature is the frequency domain complex matrix obtained after the second spatial image is Fourier transformed. In this matrix, low-frequency components are located at the four corners of the matrix by default, and high-frequency components are located at the center of the matrix. It encodes the amplitude and phase information of each spatial frequency component in the spatial image in complex form.

[0258] For the third frequency domain feature, a frequency domain shift can be performed, that is, the third frequency domain feature is rearranged into quadrants so that the low-frequency components at the four corners of the matrix are swapped to the center of the matrix, and the high-frequency components at the center of the matrix are swapped to the four corners and the edges. In the shifted frequency domain feature, the closer the position is to the center of the matrix, the lower the spatial frequency, and the farther the position is from the center of the matrix, the higher the spatial frequency, forming a radial frequency distribution with zero frequency as the origin.

[0259] In one embodiment, the frequency domain shift operation can be represented by the following formula (13).

[0260] (13)

[0261] in, Characterizes the third frequency domain features; Characterizes frequency domain shift operations; Characterizes the frequency domain features after shifting.

[0262] After obtaining the shifted frequency domain features, high-frequency components can be extracted using a preset mask. The preset mask is a two-dimensional binary matrix of the same size as the shifted frequency domain features, and can be used to selectively extract specific frequency components from the shifted features. For example, the target region in the preset mask can be assigned a first value, and other regions can be assigned a second value; the first value can be 1, and the second value can be 0. By multiplying the preset mask element-wise with the shifted frequency domain features, the frequency components within the target region are multiplied by the first value, and the components in other regions are multiplied by the second value, thereby achieving selective retention or filtering of frequency components.

[0263] For example, the preset mask can be a 256×256 binary matrix. The first value is assigned to a circular area centered at (128, 128) with a radius r = 0.25 × 256 = 64 pixels, and the second value is assigned to the area outside the circular area. After multiplying this mask element-wise with the shifted frequency domain features, all high-frequency components within the central circular area are preserved, while all low-frequency components outside the circular area are filtered out, thus completing the extraction of high-frequency components.

[0264] In one embodiment, the sixth sub-difference can be determined using the following formula (14).

[0265] (14)

[0266] in, Characterizes the frequency domain features after shifting; Represents the preset mask.

[0267] In the embodiments of this disclosure, by frequency-domain shifting the third frequency domain feature to center the low-frequency component in the frequency domain, a mapping relationship is formed between the radial distance from any position in the frequency domain matrix to the center and its corresponding spatial frequency. Based on this, by using a preset mask to extract the high-frequency component from the shifted frequency domain feature, low-frequency suppression and high-frequency passage in the entire frequency domain can be completed in one step using element-wise multiplication of the binary mask, improving the computational speed and accuracy of the high-frequency component extraction operation. Furthermore, by defining the target region as a region within a preset radius with the spatial image center as the origin, the circular aperture of the pupil in the lithography optical system is modeled in the form of a frequency domain circular mask, ensuring that the extraction boundary of the high-frequency component has a clear lithographic physical meaning. This further improves the interpretability of the constraint of the sixth sub-difference on the physical rationality of the spatial image.

[0268] The following will utilize Figure 7 The training process of the above-mentioned photolithography simulation model M2 is illustrated by example.

[0269] Figure 7The illustration shows an example schematic diagram of the training process of a lithography simulation model according to another embodiment of the present disclosure.

[0270] like Figure 7 As shown, in embodiment 700, the model to be trained may include a Fourier module M21, a second spatial image module M22, and a second photoresist module M23. The training samples may include a sample mask image 701, a reference lithography image 705, and sample process parameters 702 related to the reference lithography image 705. The training process of this model will be illustrated below.

[0271] For the Fourier module M21, P Fourier layers can be used to process the sample mask image 701 and the sample process parameters 702 to obtain the second frequency domain features. For the spatial image module M22, the second frequency domain features can be mapped to the light intensity distribution in the spatial domain to obtain the second spatial image 703. For the photoresist module M23, linear transformations can be performed on each pixel value in the second spatial image 703 to obtain the output photolithography image 704.

[0272] Based on the third difference 706 between the output lithography image 704 and the reference lithography image 705, and the fourth difference 707 between the second spatial image 707, the model parameters of the Fourier module M21, the second spatial image module M22, and the second photoresist module M23 are adjusted until the predetermined termination condition is met, thus obtaining the lithography simulation model M2.

[0273] The above are merely exemplary embodiments, but are not limited thereto. Other training methods for lithography simulation models known in the art may also be included, as long as they can predict lithography images with high accuracy.

[0274] Based on the above-described photolithography simulation method, this invention also provides a photolithography simulation apparatus. The following will be combined with... Figure 8 The device is described in detail.

[0275] Figure 8 A block diagram of a photolithography simulation apparatus according to an embodiment of the present disclosure is shown schematically.

[0276] like Figure 8 As shown, the photolithography simulation apparatus 800 may include an acquisition module 810 and a first generation module 820.

[0277] The acquisition module 810 is used to acquire the mask image and process parameters to be processed in response to the photolithography simulation request.

[0278] The first generation module 820 is used to generate a photolithography image guided by a spatial image obtained based on a mask image and process parameters, wherein the spatial image is a mask pattern represented by the mask image, and the light intensity distribution is formed on the photoresist indicated by the process parameters through optical imaging.

[0279] Based on the above-described training method for the photolithography simulation model, this invention also provides a training device for the photolithography simulation model. The following will combine... Figure 9 The device is described in detail.

[0280] Figure 9 A block diagram of a training apparatus for a lithographic simulation model according to an embodiment of the present disclosure is shown schematically.

[0281] like Figure 9 As shown, the training device 900 for the photolithography simulation model may include a second generation module 910 and a training module 920.

[0282] The second generation module 910 is used to input the sample mask image and sample process parameters into the model to be trained, so that the model to be trained can generate an output lithography image based on the sample spatial image and sample process parameters. The sample spatial image represents the light intensity distribution formed on the photoresist indicated by the sample process parameters by optical imaging of the sample mask pattern represented by the sample mask image.

[0283] Training module 920 uses the output lithography image, the reference lithography image corresponding to the sample mask image and the sample process parameters to train the model to be trained, and obtain the lithography simulation model.

[0284] Any one or more of the modules according to embodiments of this disclosure, or at least part of the functionality of any one or more of them, can be implemented in one module. Any one or more of the modules according to embodiments of this disclosure can be implemented by dividing them into multiple modules. Any one or more of the modules according to embodiments of this disclosure can be at least partially implemented as hardware circuitry, such as a field-programmable gate array (FPGA), a programmable logic array (PLA), a system-on-a-chip, a system-on-a-substrate, a system-on-package, an application-specific integrated circuit (ASIC), or implemented in hardware or firmware by any other reasonable means of integrating or packaging circuitry, or implemented in software, hardware, or firmware, or in any suitable combination of any of these three implementation methods. Alternatively, one or more of the modules according to embodiments of this disclosure can be at least partially implemented as computer program modules, which, when run, can perform corresponding functions.

[0285] It should be noted that the lithography simulation apparatus section in the embodiments of this disclosure corresponds to the lithography simulation method section in the embodiments of this disclosure. For a detailed description of the lithography simulation apparatus section, please refer to the lithography simulation method section, which will not be repeated here. Similarly, the training apparatus section for the lithography simulation model in the embodiments of this disclosure corresponds to the training method section for the lithography simulation model in the embodiments of this disclosure. For a detailed description of the training apparatus section for the lithography simulation model, please refer to the training method section for the lithography simulation model, which will not be repeated here.

[0286] Figure 10 A block diagram of an electronic device suitable for implementing a photolithography simulation method and a training method according to an embodiment of the present disclosure is shown schematically. Figure 10 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0287] like Figure 10 As shown, a computer electronic device 1000 according to an embodiment of the present disclosure includes a processor 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage portion 1009 into a random access memory (RAM) 1003. The processor 1001 may include, for example, a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or an associated chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 1001 may also include onboard memory for caching purposes. The processor 1001 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0288] RAM 1003 stores various programs and data required for the operation of electronic device 1000. Processor 1001, ROM 1002 and RAM 1003 are interconnected via bus 1004.

[0289] According to embodiments of this disclosure, the electronic device 1000 may further include an input / output (I / O) interface 1005, which is also connected to a bus 1004. The electronic device 1000 may also include one or more of the following components connected to the input / output (I / O) interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to the input / output (I / O) interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on the drive 1010 as needed so that computer programs read from it can be installed into the storage section 1008 as needed.

[0290] This disclosure also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the photolithography simulation method and training method according to the embodiments of this disclosure.

[0291] In this disclosure, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0292] Embodiments of this disclosure also include a computer program product comprising a computer program containing program code for performing the methods provided in the embodiments of this disclosure. When the computer program product is run on an electronic device, the program code is used to enable the electronic device to implement the lithography simulation method and training method provided in the embodiments of this disclosure.

[0293] When the computer program is executed by the processor 1001, it performs the functions defined in the system / apparatus of this disclosure embodiments. According to embodiments of this disclosure, the systems, apparatuses, modules, units, etc., described above can be implemented by computer program modules.

[0294] According to embodiments of this disclosure, program code for executing computer programs provided in embodiments of this disclosure can be written in any combination of one or more programming languages.

[0295] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. It should also be noted that in some alternative implementations, the functions indicated in the boxes may occur in a different order than those shown in the drawings.

[0296] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. The scope of this disclosure is defined by the appended claims and their equivalents. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A photolithography simulation method, comprising: In response to a lithography simulation request, the mask image and process parameters to be processed are obtained; as well as A photolithography image is generated using a spatial image obtained based on the mask image and the process parameters as a guide, wherein the spatial image is a mask pattern represented by the mask image, and the light intensity distribution is formed on the photoresist indicated by the process parameters by optical imaging.

2. The method according to claim 1, wherein, The step of generating a photolithography image based on a spatial image obtained from the mask image and the process parameters includes: Based on the mask image and the process parameters, the light intensity distribution formed by optical imaging of the mask pattern on the photoresist is determined to obtain the spatial image; and Based on the spatial image, the morphological changes of the photoresist caused by the photolithography reaction are determined, and the photolithographic image is obtained.

3. The method according to claim 2, wherein, The step of determining the light intensity distribution formed on the photoresist by optical imaging of the mask pattern based on the mask image and the process parameters to obtain the spatial image includes: The first stitched feature obtained by stitching the mask image and the process parameters is subjected to convolution processing to obtain the input feature; The input features are processed using M Fourier layers to obtain the first frequency domain features, wherein the Fourier layers are used to jointly process the input features from the frequency and spatial domains, and M is an integer greater than 1; and The spatial image is obtained by convolution processing the first frequency domain feature.

4. The method according to claim 3, wherein, The process parameters include at least one sub-parameter, and the size of the channel of each sub-parameter is the same as the size of the mask image; After acquiring the mask image to be processed and the process parameters, the process further includes: Using the mask image as the first channel and each of the sub-parameters as other channels, the mask image and the process parameters are stitched together in the channel dimension to obtain the first stitching feature, wherein the number of channels in the first stitching feature is the sum of the number of channels in the mask image and the number of the sub-parameters.

5. The method according to claim 3, wherein, For the m-th Fourier layer, perform the following operations, m=2,…,M: The m-th first frequency domain feature corresponding to the (m-1)-th intermediate feature is processed to obtain the m-th frequency domain branch feature, wherein the (m-1)-th intermediate feature is the feature output by the (m-1)-th Fourier layer, and the 0th intermediate feature is the input feature; A local linear transformation is performed on the (m-1)th intermediate feature to obtain the m-th spatial domain branch feature; and By fusing the m-th frequency domain branch feature and the m-th spatial domain branch feature, the m-th intermediate feature is obtained.

6. The method according to claim 4, wherein, The process of processing the m-th first frequency domain feature corresponding to the (m-1)-th intermediate feature to obtain the m-th frequency domain branch feature includes: According to preset mode truncation parameters, the m-th first frequency domain feature is modally truncated to obtain the m-th truncated frequency domain feature, wherein the preset mode truncation parameters are used to limit the number of modes retained in the frequency domain transform; and A linear transformation is performed on the m-th truncated frequency domain feature to obtain the m-th frequency domain branch feature.

7. The method according to any one of claims 2 to 6, wherein, The step of determining the morphological changes of the photoresist resulting from the photolithography reaction based on the spatial image, and obtaining the photolithographic image, includes: The spatial image is processed using a photoresist module to simulate the morphological changes within the photoresist after exposure, based on photochemical reactions and the development process, to obtain the photolithographic image.

8. The method according to claim 7, wherein, The process of processing the spatial image using a photoresist module to simulate the morphological changes within the photoresist after exposure based on photochemical reactions and development processes, thereby obtaining the photolithographic image, includes: Using the light intensity distribution represented by the spatial image as the initial acid concentration distribution, the changes in acid concentration distribution in the time and spatial dimensions during the photolithography process are determined for N time steps to obtain the target acid concentration distribution, where N is an integer greater than 1; and The target acid concentration distribution is binarized and mapped to obtain the lithographic image.

9. The method according to claim 8, wherein, The process of determining the changes in acid concentration distribution in the time and spatial dimensions during photolithography for N time steps to obtain the target acid concentration distribution includes: Based on the reaction-diffusion equation, the acid concentration change under the acid catalytic reaction and acid molecule diffusion of the photoresist after chemical amplification is simulated to obtain the target acid concentration distribution.

10. The method according to claim 9, wherein, For the nth time step, perform the following operations, n=2, ...,N: The acid concentration distribution at the (n-1)th time step is convolved to obtain the nth diffusion term, where the acid concentration distribution at the 0th time step is the light intensity distribution characterized by the spatial image. The second stitched feature obtained by stitching the acid concentration distribution at the (n-1)th time step with the spatial image is convolved to obtain the nth reaction term; and The acid concentration distribution at the nth time step is determined based on the acid concentration distribution at the (n-1)th time step, the nth diffusion term, the nth reaction term, and the preset time step size.

11. The method according to claim 2, wherein, The step of determining the light intensity distribution formed on the photoresist by optical imaging of the mask pattern based on the mask image and the process parameters to obtain the spatial image includes: Using P Fourier layers, the mask image and the process parameters are processed to obtain the second frequency domain features, where P is an integer greater than 1; and The second frequency domain feature is mapped to the light intensity distribution in the spatial domain to obtain the spatial image; The model parameters of the model used to perform frequency domain feature extraction and spatial domain mapping are constrained by a preset loss during the training phase to simulate the low-pass filtering characteristics of the photolithography process.

12. The method according to claim 2 or 11, wherein, The step of determining the morphological changes of the photoresist resulting from the photolithography reaction based on the spatial image, and obtaining the photolithographic image, includes: The lithographic image is obtained by performing linear transformations on each pixel value in the spatial image.

13. The method according to claim 1, wherein, The process parameters include at least one of the following: photoresist type, photoresist thickness, and light source exposure.

14. A training method for a photolithography simulation model, comprising: The sample mask image and sample process parameters are input into the model to be trained, so that the model generates an output photolithography image guided by the sample spatial image obtained based on the sample mask image and the sample process parameters. The sample spatial image is a sample mask pattern represented by the sample mask image, and the light intensity distribution formed on the photoresist indicated by the sample process parameters is optically imaged. The model to be trained is obtained by using the output lithography image, the reference lithography image corresponding to the sample mask image and the sample process parameters.

15. The method according to claim 14, wherein, The model to be trained includes a first spatial image module, and the sample spatial image includes the first spatial image; The method further includes: The sample mask image and the sample process parameters are input into the first spatial image module to obtain the first spatial image; and Based on the first difference between the first spatial image and the reference spatial image, the first spatial image module is trained to obtain the intermediate spatial image module.

16. The method according to claim 15, wherein, The model to be trained also includes a first photoresist module; The step of training the model to be trained using the output lithographic image and the reference lithographic image to obtain a lithographic simulation model includes: While keeping the model parameters of the intermediate spatial image module unchanged, the first photoresist module is trained based on the second difference between the output lithographic image and the reference lithographic image to obtain the intermediate photoresist module; and Based on the second difference between the output lithography image and the reference lithography image, the intermediate spatial image module and the intermediate photoresist module are jointly fine-tuned until a predetermined termination condition is met, thereby obtaining the lithography simulation model.

17. The method according to claim 15, wherein, The first spatial image and the reference spatial image have the same size; the first difference characterizes the difference in pixel values ​​at corresponding positions between the first spatial image and the reference spatial image.

18. The method according to claim 16, wherein, The output lithographic image and the reference lithographic image have the same size, and the second difference includes at least one of the first sub-difference and the second sub-difference; The first sub-difference characterizes the difference between the output lithographic image and the reference lithographic image in terms of edge contours, and the second sub-difference characterizes the difference between the output lithographic image and the reference lithographic image in terms of pixel values ​​at corresponding positions.

19. The method of claim 14, wherein, The model to be trained includes a second spatial image module and a second photoresist module, and the sample spatial image includes the second spatial image; The step of training the model to be trained using the output lithographic image and the reference lithographic image to obtain a lithographic simulation model includes: Based on the third difference between the output lithography image and the reference lithography image, and the fourth difference between the second spatial image, the model parameters of the second spatial image module and the second photoresist module are adjusted end-to-end until the predetermined termination condition is met, thereby obtaining the lithography simulation model.

20. The method according to claim 19, wherein, The output lithographic image and the reference lithographic image have the same size, and the third difference includes at least one of a third sub-difference and a fourth sub-difference; The third sub-difference characterizes the difference between the output lithographic image and the reference lithographic image in the corresponding pixel values, and the fourth sub-difference characterizes the difference between the output lithographic image and the reference lithographic image in the edge contour.

21. The method according to claim 19, wherein, The fourth difference includes at least one of a fifth sub-difference and a sixth sub-difference; the fifth sub-difference is determined based on the sum of the absolute values ​​of the gradients of the second spatial image in the horizontal and vertical directions, and the sixth sub-difference is determined based on the high-frequency components of the second spatial image.

22. The method according to claim 21, wherein, The high-frequency components are obtained through the following method: The third frequency domain feature is frequency-shifted so that the low-frequency component in the third frequency domain feature is located at the center of the frequency domain, thus obtaining the shifted frequency domain feature; as well as Using a preset mask, high-frequency components in the shifted frequency domain features are extracted. The target region in the preset mask is a first value, and the other regions in the preset mask besides the target region are second values. The target region is the region within a preset radius with the center of the spatial image as the origin.

23. A photolithography simulation apparatus, comprising: The acquisition module is used to acquire the mask image and process parameters to be processed in response to the photolithography simulation request; as well as The first generation module is used to generate a photolithography image guided by a spatial image obtained based on the mask image and the process parameters, wherein the spatial image is a mask pattern represented by the mask image, and the light intensity distribution is formed on the photoresist indicated by the process parameters by optical imaging.

24. A training device for a photolithography simulation model, comprising: The second generation module is used to input a sample mask image and sample process parameters into the model to be trained, so that the model to be trained generates an output photolithography image guided by a sample spatial image obtained based on the sample mask image and the sample process parameters. The sample spatial image is a sample mask pattern represented by the sample mask image, and the light intensity distribution formed on the photoresist indicated by the sample process parameters through optical imaging. The training module uses the output lithography image and the reference lithography image to train the model to be trained, thereby obtaining a lithography simulation model.

25. An electronic device, comprising: One or more processors; Memory, used to store one or more computer programs. The characteristic feature is that the one or more processors execute the one or more computer programs to implement the steps of the method according to any one of claims 1 to 22.

26. A computer-readable storage medium having a computer program or instructions stored thereon, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 22.

27. A computer program product comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 22.

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