Mask optimization method, electronic equipment and computer readable storage medium

Abstract

The invention discloses a mask optimization method, electronic equipment and a computer readable storage medium, belongs to the field of semiconductors, and aims to solve the problems of nonlinearity and tradeoff between local and global performance. The sampled metal layer fragments are processed through an ILT engine, and a quasi-optimized continuous transmission mask (CTM) is generated and used for initializing regular distribution values; optimizing the rule distribution value by using an index natural evolution strategy of photoetching perception; the optimized rule distribution value is used for testing the generation sub-resolution auxiliary features (SRAF) of the pattern segment and the model-based optical proximity effect correction (OPC), and the effect is that the photoetching performance and the calculation efficiency can be improved.

Description

Technical Field

[0001] The invention belongs to the field of semiconductors, and relates to a mask optimization method, an electronic device and a computer-readable storage medium, and in particular to an OPC rule extraction method based on an inverse lithography technology engine. Background Art

[0002] Model-based optical proximity correction (OPC) and its sub-resolution assist feature (SRAF) generation are key standard methods to compensate for lithography distortions in integrated circuit manufacturing at advanced technology nodes. Typical model-based OPC and SRAF algorithms involve user-controlled selection of rule parameters. Traditionally, these rules are usually determined through heuristic methods and applied globally across the correction region, which is time-consuming and requires expert knowledge of the tool. In addition, the relationship between rule parameters and the optimization goal is highly non-linear. All these factors make designing a high-performance OPC engine for complex metals a very complex task.

[0003] Over the past few decades, advances in semiconductor manufacturing technology have continuously pushed the boundaries of chip design, leading to an increasing demand for more sophisticated computational lithography techniques. Therefore, applying resolution enhancement techniques (RET), such as sub-resolution assist feature (SRAF) insertion and optical proximity correction (OPC), to adjust layout patterns has become critical to obtain high pattern fidelity and mask manufacturability.

[0004] As an important resolution enhancement technology, optical proximity correction (OPC) solves the problem of unnecessary wafer image distortion by pre-correcting the graphic distortion on the lithography mask. The current rapidly developing OPC methods mainly include model-based OPC, inverse lithography technology (ILT) and deep learning-based OPC. The model-based OPC method relies on complex simulation to accurately adjust the mask layout, mainly through edge segmentation and movement, combined with the strategic placement of sub-resolution auxiliary features (SRAF) to optimize the lithography process. The ILT method regards mask optimization as a pixel-based inverse imaging problem, and continuously optimizes the mask layout through iteration until the simulated wafer image is highly consistent with the target pattern. It is particularly good at processing complex design graphics and generating masks that can take into account optical and process effects. Finally, deep learning-based OPC predicts the initial mask solution through a deep learning model, and then uses the ILT engine for subsequent optimization, which accelerates the mask optimization process.

[0005] However, these techniques face challenges in dealing with complex, large-scale industrial graphics. The complexity of the ILT method requires a lot of computing resources, making it too long to run in large-scale designs. In addition, the masks generated by ILT are difficult to actually manufacture due to their pixel-based nature. For deep learning-based OPC, the accuracy of its generated models is highly dependent on the amount and quality of training data. These models may not generalize well on different graphic areas, and their black-box nature makes it difficult to understand and diagnose OPC results.

[0006] Currently, model-based OPC methods are still the mainstream methods in the industry, mainly because they can handle complex graphic geometries and adapt to advanced lithography technologies. The key lies in the optimization of mask edge segmentation and segment movement rules, which control how to segment the edge into different segments and the displacement of the segments in each OPC iteration. In the SRAF insertion process, the rules are mainly divided into two categories: the distance between the SRAF and the main feature, and the size of the SRAF. Optimizing these rule parameters is crucial to achieve an excellent OPC solution with excellent lithography performance and high efficiency. In industrial applications, the current common methods mainly rely on OPC engineers to manually configure the rule values, which requires both rich domain knowledge and a lot of manpower. However, fine-tuning these parameters in high-dimensional space is complex and challenging, mainly due to their indirect and non-analytical impact on lithography performance, and the subtle trade-off between local and global performance. To address these challenges, genetic algorithms have been used to adjust SRAF generation rules and OPC parameters. These methods model rule parameter adjustment as a complete black-box optimization problem without considering information in the lithography process. This optimization process may lead to drastic changes in the gene combination, making it easy for the search algorithm to fall into a local optimal solution. Summary of the invention

[0007] In order to solve the above problem, in a first aspect, a mask optimization method according to some embodiments of the present application includes determining a rule set;

[0008] The sampled metal layer fragments are processed by the ILT engine to generate a quasi-optimized continuous transmission mask (CTM) for regular distribution value initialization;

[0009] Optimizing regular distribution values ​​using a lithography-aware exponential natural evolution strategy;

[0010] The optimized regularly distributed values ​​are used to generate sub-resolution assist features (SRAF) and model-based optical proximity correction (OPC) of the test pattern fragments.

[0011] According to the mask optimization method in some embodiments of the present application, the optimization target of the ILT engine includes the wafer image under nominal conditions and the target image R* (m), and the area of ​​the process variation band; the loss function l(M) of a given regular distribution vector m is a function of mask M, expressed by the following formula:

[0012] l(M)=||R(M)-R * (M)||2+β||R out (M)-R in (M)|| 2

[0013] In the formula, R(M) represents the printed image, R * (M) represents the target image, M represents the mask corresponding to the printed image, β is the weight coefficient, R out (M) indicates the outermost contour, R in (M) indicates the innermost contour;

[0014] By iteratively updating the unconstrained intermediate variable M' to minimize the loss function l(M), a quasi-optimal continuous transmission mask (CTM) is generated, which is expressed by the following formula:

[0015]

[0016] Where M′ represents an unconstrained intermediate variable, Δ t represents the iterative update step size parameter; where, α M′ represents the gradient parameter for the transformation from M' to M.

[0017] According to the mask optimization method in some embodiments of the present application, the method of iteratively updating the continuous transmission mask (CTM) includes:

[0018] After average pooling and downsampling, fast optimization is performed with low resolution r_L;

[0019] Upsample twice and optimize in detail with higher resolution r_H;

[0020] The optimization is expressed as follows:

[0021]

[0022] The constraints are:

[0023] In the formula, represents the final optimized continuous projection mask (CTM), Indicates that The initial high-resolution continuous transmission mask obtained by upsampling, represents the continuous transmission mask (CTM) obtained by iterative updating at low resolution, Represents the continuous transmission mask (CTM) obtained by iterative updating at high resolution; the Upscale(M,k) function indicates that the mask M is upsampled by a scale factor k using nearest neighbor interpolation.

[0024] According to the mask optimization method in some embodiments of the present application, a lithography-aware exponential natural evolution strategy is used to optimize the rule distribution, including:

[0025] Optimizing regular distribution parameters through a lithography-aware natural gradient method; wherein natural gradient updating is performed through natural exponential expansion;

[0026] Modeling a relative ranking based fitness function where adaptive sampling is performed on test graph fragments.

[0027] According to the mask optimization method in some embodiments of the present application, in optimizing the regular distribution parameters by the lithography-aware natural gradient method, the regular distribution parameters θ are updated in a direction that minimizes the expected lithography cost, while imposing constraints on the information gain at each step;

[0028] The natural gradient is formalized as the solution to the constrained lithography rule value optimization problem:

[0029]

[0030] Where, L(θ-δθ) represents the expected lithography cost after the parameter θ changes by δθ, L(θ) represents the expected lithography cost under the regular distribution parameter, δθ represents the parameter change, Represents the gradient of the loss function with respect to the parameters;

[0031] The constraints are:

[0032] D(θ-δθ||θ)=∈

[0033] Where D(θ-δθ||θ) represents the distance between the distribution with θ-δθ as parameter and the distribution with θ as parameter, and ∈ represents an arbitrarily small quantity;

[0034] In the case where δθ→0, the natural distance metric is:

[0035]

[0036] Where D KL (θ-δθ||θ) represents the KL divergence between parameter distribution θ and θ-δθ, and F(θ) is the Fisher information matrix of a given rule parameter family, which is expressed as:

[0037]

[0038] In the formula, P(m|θ) represents the probability distribution, and E[·] represents the average of the rule vector m.

[0039] By substituting the direction of the natural gradient into the Lagrange multiplier method of the constrained optimization problem, the update step is expressed as:

[0040]

[0041] Where γ represents the scale factor;

[0042] The natural gradient is determined to be in the same direction as δθ and is calculated as:

[0043]

[0044] In the formula, represents the natural gradient of the loss function with respect to the regular distribution parameter θ, F -1 represents the inverse of the Fisher information matrix;

[0045] Update parameters:

[0046]

[0047] Where η represents the update step size of the regular distribution parameters.

[0048] According to the mask optimization method in some embodiments of the present application, natural gradient updating is performed by natural exponential expansion, and the updating formula is as follows:

[0049]

[0050] Where δ and W represent the direction of natural gradient update, μ′ represents the mean of the updated distribution θ, and Q′ represents the standard deviation of the updated distribution θ.

[0051] In the natural gradient coordinate system, the Fisher matrix F(θ) is the identity matrix with respect to the orthogonal basis (δ, W), and the current search distribution It is encoded as (δ,W)=(0,0), and the logarithmic expression of the probability density is:

[0052]

[0053] In the formula, tr(Q) represents the trace operation of the matrix Q, m represents the rule parameter to be optimized, and μ represents the mean of the distribution of m;

[0054] For sample m n =μ+Q·t n , where t n~N(0,I) represents the loss function, I represents the identity matrix;

[0055] The sample generation follows the following formula:

[0056] Calculation of the natural gradient of δ:

[0057]

[0058] In the formula, Represents the gradient of the loss function of the current distribution state to the distribution parameter θ, (0,0) represents the current distribution state, n represents the nth sample, and N represents the total number of samples in each cycle to update the distribution parameter. represents the gradient of the orthogonal basis δ;

[0059] Calculation of the natural gradient of W:

[0060]

[0061] In the formula, represents the natural gradient of W, Represents the gradient of the loss function with respect to the orthogonal basis W;

[0062] Decompose the transformation matrix Q = σ·U into steps of length σ∈R + and a normalized matrix U satisfying det(U)=1;

[0063] Gradient of σ It is expressed as:

[0064]

[0065] Gradient of U It is expressed as:

[0066]

[0067] In the formula, d represents the total dimension of the parameter;

[0068] The natural gradient is O(d 3 ) is calculated with the complexity of .

[0069] According to the mask optimization method in some embodiments of the present application, a relative ranking-based fitness function is shaped to correct the gradient estimation to maintain scale invariance and ranking invariance between different graphic fragments, the lithography cost is converted into a utility value u1≥u2≥…≥uN, and individuals are ranked according to the cost, wherein when arranged in ascending order of cost, the i-th highest ranked individual is m i , and m1 is the rule parameter with the lowest cost, m N is the parameter with the highest cost, expressed as:

[0070]

[0071] Where N represents the total number of samples in each cycle to update the distribution parameters, P(m n |θ) means that under the distribution parameter θ, the nth parameter takes m n The posterior distribution of ;

[0072] Choose the utility value u i The utility function u is given by the following formula n express:

[0073]

[0074] According to the mask optimization method in some embodiments of the present application, in the adaptive sampling on the test pattern fragment, the layout is divided into overlapping tiles, and the width and height of each tile are calculated:

[0075]

[0076] In the formula, Λ w and Λ h Represent the width and height of the complete layout, λ w and λ h Indicates the width and height of the crop tile, s w and h represents the stride in width and height, k w and k h Respectively represent the number of tiles.

[0077] In the second aspect, an embodiment of the present application also provides an electronic device, comprising: one or more processors, a memory, and one or more programs; wherein the one or more programs are stored in the memory, and the one or more programs include instructions, which, when executed by the electronic device, enable the electronic device to execute the first aspect and any possible technical solution of the first aspect.

[0078] On the third aspect, an embodiment of the present application also provides a computer-readable storage medium, which includes a computer program. When the computer program runs on an electronic device, the electronic device executes the first aspect and any possible technical solution of the first aspect.

[0079] Beneficial effects: The present invention proposes a comprehensive mask optimization system and method called RuleLearner, which is specifically used for SRAF generation and model-based OPC in real industrial scenarios. The framework is learned through an information-enhanced inverse lithography technology (ILT) engine. Although this engine can handle complex designs, it is expensive to generate optimized masks for the entire set of design fragments. Considering the nonlinearity and trade-offs between local and global performance, the extracted rule value distribution is further optimized by a customized natural gradient. Complex SRAF generation, edge segmentation and movement are all guided by rule parameters. Experimental results show that RuleLearner can be applied in different complex design patterns and achieve optimal lithography performance and computational efficiency. Additional aspects and advantages of the present invention will be given in part in the description below, and in part will become apparent from the description below, or will be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a continuous transmittance mask generation process with efficient updating of multiple resolution levels.

[0081] Figure 2 It is a flowchart of parameter distribution update.

[0082] Figure 3 This is a visualization of the mask optimization results of four samples. Each row corresponds to a sample, where (a) is the target pattern, (b) is the optimized mask, (c) is the pattern printed on the wafer, and (d) is the process variation bandwidth. DETAILED DESCRIPTION

[0083] The following describes the embodiments of the present application in detail with reference to the accompanying drawings, examples of which are shown in the accompanying drawings. The present application provides a method and an electronic device. The method and the device are based on the same technical concept. Since the principles of solving problems by the method and the device are similar, the implementation of the device and the method can refer to each other, and the repeated parts will not be repeated.

[0084] I. Overview

[0085] The present invention combines information obtained from the ILT engine to optimize the parameters of rules for complex two-dimensional metal designs. To this end, the present invention proposes a comprehensive mask optimization system called RuleLearner, which aims to improve lithography performance by extracting and optimizing rule parameters and can be applied to various mask fragments. The present invention develops a customized ILT engine that uses hierarchical enhancement information to quickly generate quasi-optimized continuous transmission masks (CTMs) for small-scale design fragments in a small number of iterations, and the expression intensity map derived from it can provide guidance for the initial rule value distribution. Unlike binary masks that use binary values ​​to represent each grid position as fully transparent or fully blocked, CTMs assign a floating intensity value to each position, providing a spectrum from fully blocked (value 0) to fully transparent (value 1). The intensity value gradient in the CTM provides a more refined representation than traditional binary encoding. To address the lack of a direct analytical relationship between rule values ​​and lithography performance results, and to achieve a better balance between local and global performance, the present invention introduces an exponential extension of lithography-aware natural gradients. The present invention uses this parameterized search distribution to generate a batch of rule parameters for pattern segments, then creates SRAFs based on the sampled rule parameters and applies model-based OPC to these segments. The lithography performance of each pattern segment is evaluated as fitness, and a natural gradient is estimated to update the rule parameter distribution accordingly. By identifying reusable lithography-aware mask update and SRAF generation criteria, the present invention is able to simplify the complexity of mask generation to the application of these rules, thereby achieving efficient, scalable and manufacturable OPC correction while maintaining accuracy.

[0086] II. Preliminary Knowledge

[0087] A. Compact ruleset

[0088] In this study, we focus on a compact rule set suitable for industrial-grade SRAF generation and model-based OPC. The considered rule parameters and their descriptions are listed in Table I. It is worth noting that this framework can be easily extended to consider other rule parameters.

[0089] SRAF generation rules. SRAFs are strategically placed near isolated target patterns to increase spatial frequency without actually being printed on the wafer. This technique significantly improves the imaging fidelity of the target pattern. Figure 2 On the left side of the figure, this study follows an industrial-grade SRAF generation process. When SRAF is deployed on an edge with a side length of LLL, the rules are as follows:

[0090] 1. If the main graphic is within the vertical distance r0, SRAF will not be inserted. This range is called the SRAF insertion restricted area.

[0091] 2. Otherwise, if the main figure is within the distance r1, insert a width w0 and length l at the center between the nearest opposite edges. SRAF1 ×L rectangular SRAF.

[0092] 3. If there is no other main figure within the distance r2, insert two main figures with widths w1 and w2 and length l at distances d1 and d2 respectively. SRAF2 ×L and ll SRAF3 ×L SRAF.

[0093] Therefore, the rule parameters generated by SRAF are defined as a vector containing the above parameters:

[0094] m SRAF =[r0,r1,r2,w0,w1,w2,l SRAF1 ,l SRAF2 ,l SRAF3 ,d1,d2].

[0095] Model-based OPC rules. The model-based OPC considered consists of two steps: edge segmentation and segment movement, as detailed in Figure 2 Right part.

[0096] 4. In the segmentation stage, when there is another main figure in the projection area and its vertical distance is within the projection threshold distance d p Then, if the edge length L exceeds the threshold L tr , then a length of L is generated at the corner c The remaining edges are evenly divided into pieces of length L u On the contrary, if L is less than or equal to L tr , the edges are evenly segmented without considering the corners. After segmentation, the length of the segments is fixed.

[0097] 5. In the subsequent movement phase, each iteration adjusts the segment inward or outward to correct the distortion of the pattern printed on the wafer. If the printed contour matches the target shape well, the corresponding segment remains unchanged. The movement step lengths of the projection segment, corner segment, and uniform segment are s and s, respectively. p 、s c and u .

[0098] Therefore, the set of rules that define the OPC process is:

[0099] m OPC =[d p ,L tr ,L c ,L u ,s p ,sc ,s u ]

[0100] The complete rule set is a combination of SRAF and OPC rules, and its rule vector is represented as the concatenation of these two parts:

[0101]

[0102] B. Search Gradient Method

[0103] The basic idea of ​​the search gradient method is to use the sampled gradient of the expected loss as the search gradient to update the search distribution parameters. Without loss of generality, the present invention assumes that the rule parameter search process obeys the multivariate normal distribution. Let θ represent the parameters of the probability density function P(m|θ), and let l(m) represent the lithography cost of the sampled rule vector m, which will be described in detail in Section III-A. The expected cost under the search distribution is:

[0104] L(θ)=E θ [l(m)]=∫l(m)P(m|θ)dm

[0105] In order to update the distribution parameters θ to reduce the expected cost, the direct derivative of the expected loss L(θ) with respect to the distribution parameters can be derived by the log-likelihood technique:

[0106]

[0107] In the last step, the search gradient is estimated using a Monte Carlo sampling strategy with a sample size NNN. The gradient of this expected cost allows direct gradient descent to be used to iteratively search for distribution updates:

[0108]

[0109] where η is the learning rate.

[0110] C. Formalization of the problem

[0111] In this study, we built a comprehensive mask optimization system focusing on extracting and optimizing rule values ​​to improve lithography performance of SRAF and model-based OPC. To evaluate the quality of the final lithography simulation results, we used edge position error (EPE) and process variation band (PVBand) as criteria:

[0112] Definition 1 (Edge Position Error EPE): The edge position error refers to the vertical or horizontal misalignment between the lithography profile under nominal conditions and the target pattern profile, which is usually measured by the Manhattan distance between the two, such as Figure 3(a). The measurement points are evenly distributed on the contour of the target figure. The present invention uses two indicators to comprehensively evaluate the fidelity of the figure:

[0113] oTotal EPE length (EPE Sum ): The sum of the EPE distances of all measured points, providing a comprehensive quantification of the overall mask fidelity.

[0114] oMaximum EPE (EPE Max ): The maximum EPE value among all measurement points, indicating the most serious image distortion.

[0115] Definition 2 (PVBand): In the actual lithography process, process variation may cause deviation of the printed image, which in turn causes printing failure. The process variation band (PVBand) is composed of the XOR area between multiple contours under different process conditions, such as Figure 3 (b) as shown.

[0116] Based on the above-mentioned lithography performance evaluation index, the present invention can formally propose SRAF and model-based OPC rule optimization problems.

[0117] Problem 1 (Mask Optimization Based on Rule Learning): Given a small portion of metal layer fragments from a large-scale design and a specific rule pattern, the goal is to design a mask optimization system that can extract and optimize the rule values And apply it to other unseen metal segments so that the total EPE length (EPE Sum )、Maximum EPE(EPE Max ) and process variation band (PVBand) area, while shortening the OPC run time as much as possible.

[0118] III. RuleLearner Framework

[0119] The workflow of the RuleLearner framework is as follows Figure 1 As shown. After determining the rule set to be considered, a portion of the sampled metal layer fragments are processed through a customized ILT engine and quasi-optimized to generate a continuous transmission mask (CTM) for rule value initialization. The rules are then evaluated based on the corrected mask quality and the rule distribution is optimized using a lithography-aware exponential natural evolution strategy. Finally, the optimized rules can be used to guide SRAF and model-based OPC for other test pattern fragments.

[0120] A. Potential Information Extraction

[0121] Compared to binary masks that usually use binary values ​​to indicate whether each grid point is completely transparent or completely blocked, the information-enhanced CTM provides a more complex indication of spatial frequencies, allowing higher frequency diffraction components to participate in the imaging process. In addition, it preserves the latent information of the usually structureless SRAF. In the framework of the present invention, the generation of CTM relies on a customized ILT engine.

[0122] Forward lithography simulation converts the mask M(x,y) into a wafer image R(x,y), where the light passing through the mask produces a light intensity image I(x,y) on the wafer. The light intensity I(x,y) is converted to the wafer image R(x,y) through the photoresist model by comparing the air intensity with the intensity threshold of the photoresist:

[0123]

[0124] Among them I th is the intensity threshold of the binary image on the wafer plane. This forward lithography process can usually be expressed as R = Γ(M). Where Γ is the lithography engine. ILT considers the pattern on the target wafer and the parameters of the lithography system to calculate the optimal transmission value for each mask grid point. The optimization target considers the wafer image under nominal conditions and the target image R * (m), and the area of ​​the process variation band. For a given rule vector m, its loss function l(·) is also a function of the binary mask M:

[0125] l(M)=||R(M)-R*(M)||2+β||R out (M)-R in (M)|| 2

[0126] In the formula, R(M) represents the printed image, R * (M) represents the target image, M represents the mask corresponding to the printed image, β is the weight coefficient, R out (M) indicates the outermost contour, R in (M) indicates the innermost contour.

[0127] To update the binary mask using gradient descent, an unconstrained intermediate variable M' is used:

[0128]

[0129] In the formula, α M′ represents the gradient parameter for the transformation from M' to M.

[0130] Due to foundry manufacturing limitations, only binary masks can be produced. Previous work has used larger steepness to achieve a clear binary transition. M′To smooth the transition, it helps to better express the transmission distribution of light and enrich the gradient details. The information-enhanced CTM is optimized by iteratively updating M' to minimize the loss function:

[0131]

[0132] Where M′ represents an unconstrained intermediate variable, Δ t Represents the iterative update step size parameter.

[0133] In order to better balance the accuracy and efficiency of spatial transmission calculation, the information-enhanced CTM is updated in a hierarchical manner. The target design is first downsampled by 8×8 average pooling, quickly optimized at low resolution r_L, and then upsampled by two times, and optimized in detail at higher resolution r_H. The optimization process can be expressed as:

[0134]

[0135] The constraints are:

[0136]

[0137] In the formula, represents the final optimized continuous projection mask (CTM), Indicates that The initial high-resolution continuous transmission mask obtained by upsampling, represents the continuous transmission mask (CTM) obtained by iterative updating at low resolution, Represents the continuous transmission mask (CTM) obtained by iterative updating at high resolution; the Upscale(M,k) function indicates that the mask M is upsampled by a scale factor k using nearest neighbor interpolation.

[0138] The generated CTM significantly enhances the latent information. The transmission distribution pattern near the edge of the main pattern shows dynamic contraction and expansion, which closely matches the changes at the segment level. For the i-th segment, the OPC parameter m OPC The initialization of will be close to the generated CTM shape. Accordingly, the SRAF parameter m SRAF Initially it is adjusted to match the corresponding high transmission area in the CTM. The transmission distribution guides the rule value initialization, which greatly improves the efficiency of the optimization process.

[0139] B. Rule parameter optimization based on lithography-aware natural evolution strategy

[0140] The generated CTM is a quasi-optimized mask, but the potential information it provides may be implicit and may not generalize across different graphic fragments, which requires further optimization. In addition, the lack of a direct analytical relationship between rule parameters and final lithography performance is also one of the main challenges. The influence of rule parameter values ​​is non-differentiable, discrete, and highly random, so it is not possible to directly update each rule vector m using a gradient descent-based algorithm.

[0141] However, a straightforward implementation of the regular search gradient, as discussed in Section II-B, leads to unstable and suboptimal performance even in simple quadratic cases. It seeks the direction of steepest descent in the space of rule parameters θ, treats the parameter space as Euclidean, and uses the Euclidean metric to measure the distance between parameter vectors. This metric is parameterization dependent, which means that different reparameterizations can lead to different gradients and update directions in complex rule optimization problems.

[0142] To address this problem, the natural gradient method provides a more powerful alternative approach to effectively address these challenges by optimizing the distribution parameters of the rule values. Next, this section will introduce how to incorporate the guidance of lithography performance into the update process of rule parameters to further improve the efficiency of the mask optimization task.

[0143] B1 Lithography-aware Natural Gradient: The key idea is to remove the dependency on parameterization by relying on a more “natural” distance D(θ'||θ) between the probability distributions P(m|θ) and P(m|θ'). The update of the parameter θ should be done in the direction that minimizes the expected lithography cost while imposing constraints on the information gain at each step. The natural gradient can be formalized as the solution to the constrained lithography rule value optimization problem:

[0144]

[0145] Where, L(θ-δθ) represents the expected lithography cost after the parameter θ changes by δθ, L(θ) represents the expected lithography cost under the regular distribution parameter, δθ represents the parameter change, Represents the gradient of the loss function with respect to the parameters.

[0146] The constraints are:

[0147] D(θ-δθ||θ)=∈

[0148] where D(θ-δθ||θ) represents the distance between the distribution parameterized by θ-δθ and the distribution parameterized by θ, and ∈ represents an arbitrarily small quantity.

[0149] In the above formula, L(θ) is the expected lithography cost under regular distribution parameters. A common natural distance metric is the Kullback-Leibler (KL) divergence between two probability distributions. In the case of δθ→0, the natural distance metric is:

[0150]

[0151] Where D KL (θ-δθ||θ) represents the KL divergence between parameter distribution θ and θ-δθ, and F(θ) is the Fisher information matrix of a given rule parameter family, which is expressed as

[0152]

[0153] Where P(m|θ) represents the probability distribution and E[·] represents the average of the rule vector m.

[0154] By substituting the direction of the natural gradient into the Lagrange multiplier method of the constrained optimization problem, the update step is obtained:

[0155]

[0156] Where γ represents the scale factor.

[0157] The natural gradient can be determined to be in the same direction as δθ and is calculated as:

[0158]

[0159] In the formula, represents the natural gradient of the loss function with respect to the regular distribution parameter θ, F -1 represents the inverse of the Fisher information matrix.

[0160] Therefore, the parameters can be updated:

[0161]

[0162] Where η represents the update step size of the regular distribution parameters.

[0163] B2 Relative ranking-based fitness function shaping: The mask optimization problem is a highly non-convex problem, and the optimization path may be different for different rule vectors θ on the same mask fragment. In addition, different design pattern fragments have different geometric complexities, resulting in large differences in the lithography performance after mask optimization between different fragments. These changes in mask optimization may distort the gradient estimation due to the fluctuating lithography cost.

[0164] To solve this problem, the RuleLearner of the present invention converts the photolithography cost into a utility value u1≥u2≥…≥uN and ranks the individuals according to the cost, wherein when the individuals are ranked in ascending order of cost, the i-th highest ranked individual is m i , and m1 is the rule parameter with the lowest cost, m N is the parameter with the highest cost. This approach fixes the gradient estimate in the formula to maintain scale invariance and rank invariance between different graph fragments:

[0165]

[0166] Based on the previous experience of covariance matrix adaptive evolution strategy (CMA-ES), the utility value u is selected i

[0167]

[0168] B3 Natural Exponential Expansion: In a d-dimensional multivariate Gaussian distribution, the parameters θ = (μ, ∑), where μ is the mean vector and ∑ is the covariance matrix. When updating ∑, it is necessary to maintain its positive definiteness, which cannot be guaranteed a priori. In addition, the dimension of the distribution parameters θ = (μ, ∑) is d + d (d + 1) / 2 ∈ O (d 2 ), while the dimension of the Fisher information matrix in the previous formula (12) is O(d 4 ). Therefore, the complexity of calculating its inverse matrix reaches O(d 6 ), which is very computationally expensive. To address these challenges, the present invention introduces an exponential mapping method for the covariance matrix and uses natural coordinates to update the distribution vector. Specifically, the present invention does not directly calculate the new mean and covariance parameters (μ', ∑'), but instead decomposes the covariance matrix into , and update it on the tangent space of the parameter manifold. The update formula is as follows:

[0169]

[0170] Where δ and W represent the direction of the natural gradient update, μ′ represents one of the quantities represented by the updated distribution θ: mean (in Gaussian distribution, distribution parameter θ = (μ, Σ) is the mean and variance), and Q′ represents the standard deviation represented by the updated distribution θ.

[0171] In this formula, δ and W represent the direction of the natural gradient update. In this way, the positive definiteness of the matrix is ​​automatically maintained, and the natural gradient can be updated efficiently. In addition, this update method can significantly reduce the complexity and avoid directly processing large-scale Fisher information matrix inversion operations.

[0172] This natural exponential expansion not only solves the problem of computational complexity, but also ensures the stability and efficiency of distribution updates. In the process of rule parameter optimization, this method can achieve faster and more stable distribution adjustments.

[0173] The present invention also utilizes a natural gradient coordinate system, in which the Fisher matrix F(θ) is the identity matrix with respect to the orthogonal basis (δ, W). In the new coordinate system, the current search distribution is encoded as (δ,W) = (0,0). In this coordinate system, the logarithmic expression of the probability density is:

[0174]

[0175] Where tr(Q) represents the trace operation of the matrix Q, m represents the rule parameter to be optimized, and μ represents the mean of the distribution of m.

[0176] By this method, the generation of samples follows the following formula: n =μ+Q·t n , where t n The computation of the natural gradient of δ with the ~N(0,I) loss function becomes more efficient, where I represents the identity matrix:

[0177]

[0178] In the formula, Represents the gradient of the loss function of the current distribution state to the distribution parameter θ, (0,0) represents the current distribution state, n represents the nth sample, and N represents the total number of samples in each cycle to update the distribution parameter. represents the gradient of the orthogonal basis δ.

[0179] Approximately, the gradient with respect to w can be derived as:

[0180]

[0181] In the formula, represents the natural gradient of W, Represents the gradient of the loss function with respect to the orthogonal basis W.

[0182] To further improve efficiency, the transformation matrix Q = σ·U is decomposed into a step size σ∈R +and a normalized matrix U satisfying det(U)=1. The gradients of σ and U are:

[0183]

[0184] Where d represents the total dimension of the parameter (the number of elements in the m vector).

[0185] Finally, the natural gradient can be calculated as O(d 3 ) is calculated with the complexity of . After the above discussion, the overall algorithm can be summarized as:

[0186]

[0187] B4: Adaptive Sampling on Unseen Pattern Fragments Sampling-based rule-distributed updates take into account geometric properties and aim to improve performance in complex metal patterns. However, mask optimization using this rule is fragment-based due to computational limitations, and optimizing the full mask of a complex VLSI design on a single system is not feasible.

[0188] In the lithography process, the capability of the optical projection system is determined by factors such as light wavelength and numerical aperture, which limit the line width and focus depth. As the design node shrinks, the diffraction effect becomes more significant. Therefore, the mask optimization of the layout tile also needs to consider the influence of adjacent tiles. To this end, the present invention divides the layout into overlapping tiles, as mentioned in the literature, and calculates the width and height of each tile based on the following considerations:

[0189]

[0190] Among them, Λ w and Λ h denote the width and height of the complete layout, respectively, and λ w and λ h Indicates the width and height of the crop tile. w and h Indicates the stride in the width and height directions, which is a predefined constant. k w ×k h Respectively represent the number of tiles.

[0191] The rule distribution is updated after lithography engine simulation and natural evolution optimization. In order to effectively generalize across various pattern complexities, pattern fragment sampling must be adaptive based on the distribution characteristics. If the rules favor denser SRAFs and coarser segmentation and more aggressive fragment movement, the sampled fragments may appear sparse and simple. Therefore, the next iteration of sampling should prioritize complex fragments with higher metal area ratio. Conversely, if the rules involve smaller SRAFs and more complex model-based OPC processes, subsequent sampling should focus on sparse and simple fragments to maintain a balance.

[0192] C. General Mask Optimization Process

[0193] In the present invention, the proposed rules are applied to an industrial-level mask optimization flow, which includes rule-based SRAF insertion and model-based OPC.

[0194] The key elements of SRAF generation are position and size information. Compared with simple single-level rule SRAF insertion methods, the rules considered in the present invention are able to adapt to the inherent geometric relationships in complex main graphics. Since auxiliary features (SRAFs) are crucial for isolated graphics, in the rule set of the present invention, the sparsity near the boundary of each main graphic is first checked. The optimized parameters r0, r1, and r2 are used to characterize this isolation and determine whether SRAF can be inserted and how many levels of SRAF should be inserted. Depending on the specific circumstances of each case, the position rule parameters d1 and d2 are used to define the distance between the SRAF and the edge of the main graphic. Next, the configuration of the SRAF is determined by the shape rule parameters w0, w1, w2, and l SRAF1 ,l SRAF2 ,l SRAF3 The generated SRAF will be fixed in the following model-based OPC process. It is worth noting that RuleLearner can be easily extended to accommodate more complex rules without a lot of work.

[0195] After generating the SRAF, the model-based OPC modifies the complex master pattern to compensate for the imaging distortion. In the new complex segment, the edge of the master pattern is adaptively segmented according to the influence of the neighboring master patterns: the influence of the neighboring master patterns may affect the lithography result, especially at the threshold distance d. p If the edge length is less than l tr , the corners are ignored; otherwise, the edge will be split into a length of l at the corner c ,

[0196] The remaining part is evenly divided into pieces of length l uIn each iteration, the deviation of the wafer image from the target edge guides the shift of the segment: if the wafer image shrinks, the segment is shifted in a fixed step size s according to the segment type. p ,s c ,s u If a protrusion appears, the segment shrinks accordingly. It is worth mentioning that in addition to the mask optimization process designed by the present invention, the lithography-aware natural evolution strategy in RuleLearner can be extended to consider other lithography-related rule parameters in a specific mask optimization process. This iterative process will stop when the cost is less than a predefined threshold or the maximum number of iterations is reached.

[0197] IV. Experiment

[0198] A. Experimental Setup

[0199] The RuleLearner framework of the present invention is implemented in PyTorch, and all experiments are performed on a Linux system with an Nvidia GeForceRTX 3090 GPU. The present invention uses a Calibre-compatible lithography simulator to perform the lithography process, which contains an optical and compact photoresist model from the industry with a reference threshold of 0.25. The relevant Calibre OPC script comes from an industry partner. Referring to the most advanced OPC methods, such as AdaOPC and LithoBench, the present invention cuts a large number of layout tiles from a 45nm design synthesized by the IC design tool OpenROAD. Given a GDS-II layout file, the present invention uses KLayout to cut the layout into 1024nm×1024nm tiles with a step of 256nm×256nm, and extracts the first metal layer. Each tile contains a part of the entire design pattern, and the local geometric characteristics may be simple (metal area ratio is less than 0.25) or complex (metal area ratio is greater than 0.35). The present invention selects 5 simple tiles and 5 complex tiles to test the performance of the optimization rules. Detailed pattern area per reference (nm 2 ) and area ratios are in Table I.

[0200] Similar to previous work, the performance evaluation is based on the final wafer image, and the evaluation metrics used include process variation band area (PVB, unit: square nanometers), sum of edge position errors (EPESum, unit: nanometers), maximum edge position error (EPEMax, unit: nanometers), and runtime (RT, unit: seconds). The detection points of edge position error are evenly distributed on the target edge, and the distance between each detection point is 40 nanometers. The total number of detection points in each test case is listed in the last column of Table II. PVB is the XOR area between wafer profiles under different process conditions. The defocus value is selected from the set {-10nm, 0nm, 10nm}, where the nominal focus corresponds to 0nm, and the exposure dose value is selected from the set {0.95, 1.0, 1.05}, and the nominal dose value is set to 1.0.

[0201] Table 1. Statistics of benchmark tiles

[0202]

[0203] B. Comparison with different model-based OPC approaches

[0204] In the first experiment, we evaluated the mask quality after RuleLearner optimization and compared it with other model-based OPC methods. We compared the results with the industrial tool Calibre and two state-of-the-art model-based OPC methods that can adapt to metal layer patterns. AccOPC performs mask optimization by inserting a single-level SRAF, and CAMO is a reinforcement learning-based OPC method that uses a graph-based mask encoding to consider geometric associations and serializes segment moves through a recurrent neural network (RNN).

[0205] As shown in Table II, RuleLearner exhibits excellent mask optimization performance. Thanks to the more complex SRAF insertion decision and fragment control mechanism, the results of the present invention reduce the PVB area by 8% compared to AccOPC, the total length of EPESum is significantly reduced by 18%, and the maximum EPE value is reduced by 15%. Compared with CAMO using reinforcement learning strategy, RuleLearner shows better scalability when processing complex two-dimensional patterns, with a 6% reduction in PVB area, an 8% reduction in EPE sum, and a 21% reduction in maximum EPE length. Even compared with the commercial tool Calibre, RuleLearner improves PVB area, EPE sum, and maximum EPE by 6%, 3%, and 7%, respectively.

[0206] Mask optimization is a complex iterative process that occurs in a highly non-convex space, and different methods require different numbers of iterations to reach the optimal result. In addition to mask quality metrics, the adaptive flexibility inherent in RuleLearner accelerates the convergence of mask optimization. Compared with Calibre, AccOPC, and CAMO, RuleLearner achieves 1.55x, 2.23x, and 1.51x speedups, respectively.

[0207] The present invention also evaluates the mask segmentation times of different methods, which represents the average number of rectangle segmentations required to accurately reproduce the optimized mask. The results show that the mask segmentation times of RuleLearner are slightly higher than those of other model-based OPC engines because RuleLearner introduces a more complex edge segmentation and SRAF insertion process to achieve higher wafer image quality.

[0208] Table II compares different OPC engines

[0209]

[0210] C. Comparison with different rule optimization methods

[0211] In the second experiment, we evaluate the quality of the rules generated by RuleLearner by evaluating the quality of the final optimized mask.

[0212] To the best of the present invention's knowledge, this is the first model-based OPC framework that considers rule optimization in both the SRAF generation stage and the OPC stage. Therefore, the present invention compares the developed RuleLearner with different parameter optimization methods and tests the generated rules using the same rule-based SRAF and model-based OPC. Experts manually sample different rule value candidates and select the optimal candidate based on parameter adjustment experience. This approach mimics the behavior of experts in selecting appropriate rule values. The covariance matrix adaptive evolution strategy (CMA-ES) focuses on adjusting the covariance matrix of the sampling distribution, enabling the algorithm to learn the shape of the objective function landscape. GA-Rule uses a genetic algorithm to optimize the SRAF insertion rules. For a fair comparison, the present invention re-implemented the algorithm and optimized the SRAF and OPC rules. The number of iterations of the above method was set to 50.

[0213] As shown in Table IV, RuleLearner optimizes the rules in these test cases and achieves the best mask quality. Compared with the expert-adjusted rules, the RuleLearner of the present invention reduces the PVB area by 9%, the total EPESum by 17%, and the maximum EPE by 11%. Compared with CMA-ES, RuleLearner significantly improves the update efficiency of rule values ​​through natural gradient and adaptive evaluation, reducing the PVB area by 7%, the total EPESum by 12%, and the maximum EPE by 10%. In addition, RuleLearner uses a customized ILT engine to guide the optimization process, which improves the PVB area and the total EPESum by 13% and 24% respectively, and reduces the maximum EPE by 19% compared with GA-rule.

[0214] The rules generated by RuleLearner also enable the fastest convergence time for mask optimization. Compared with the other methods listed, the mask optimization runtime of the present invention is improved by 58%, 43%, and 47%, respectively. This advantage may be more significant when implemented on a large-scale set of mask fragments.

[0215] The number of mask segmentation times for different rule optimization methods is comparable. The differences mainly come from the chosen segment length and SRAF insertion decision.

[0216] Table III Comparison with different rule optimization algorithms

[0217]

[0218] D. Visualization of Lithography Performance

[0219] In order to more intuitively demonstrate the lithography performance of the mask after RuleLearner optimization, the present invention compares the optimized mask profile with the final imaging effect on the wafer, such as Figure 3 As shown. The imaging results of each pattern are based on the mask generated by the optimal rule set. The dotted line in the figure represents the design target pattern, the black solid line represents the nominal focal length imaging profile of the wafer image, and the red area is the process variation band (PVBand). The present invention shows the lithography results of three representative metal patterns with different geometric complexity and large differences in edge characteristics.

[0220] from Figure 3 It can be seen that RuleLearner can generate high-quality masks on different patterns, showing a small process variation band (PVBand), and the wafer imaging profile matches the target pattern very well. This shows that RuleLearner can optimize masks to obtain excellent lithography performance under different geometric complexity conditions.

[0221] E. Ablation Study on CTM Engine Guidance and Adaptation

[0222] Ablation studies were performed to evaluate the role of the CTM engine in the optimization performance, and the results are shown in Table V. In the first row, the rule values ​​are randomly initialized and then the same natural evolution optimization process is used. The results clearly show that the rules initialized using the customized CTM engine outperform the randomly initialized rules in terms of PVB area, EPE sum length, maximum EPE length, and optimization time.

[0223] In addition, the adaptive adjustment function in the RuleLearner framework is also verified, and the results are shown in the second row of Table V. Applying adaptive adjustment to RuleLearner can effectively prevent premature convergence and numerical instability in the rule optimization process, ultimately leading to better mask optimization results.

[0224] Table V Ablation Experiment

[0225]

[0226] V. Conclusion

[0227] The present invention focuses on optimizing rule values ​​in complex SRAF generation and model-based OPC processes. In the present invention, the present invention proposes RuleLearner, an innovative automation framework that utilizes an ILT engine to extract latent features and optimizes rule values ​​using a natural evolution strategy. To the best of the present invention's knowledge, this is the first work that has been able to extract rules from small parts of a complex design and generalize them to other parts. Experimental results show that the present invention's approach exhibits superior practical performance on more complex metal layers. The present invention believes that the rule extraction strategy implemented in RuleLearner will play a key role in the evolution of modern lithography mask optimization.

[0228] References:

[0229] [2] B. Jiang, H. Zhang, J. Yang, and EF Young, "A fast machine learning based mask printability predictor for OPC acceleration," in IEEE / ACM Asia and South Pacific Design Automation Conference (ASPDAC), 2019, pp. 412–419.

[0230] [4]

[0231]

[19] Y.Xu, B.Zhang, C.Wang, W.Wilkinson, and J.Bolton, "The performance improvement of SRAF placement rules using GA optimization," in Proceedings ofSPIE, vol.9985, 2016.

[0232]

[31] N. Hansen and A. Ostermeier, "Completely derandomized selfadaptation in evolution strategies," Evolutionary computation, vol.9, no.2, pp.159–195, 2001.

[0233] Based on the above embodiments, the embodiments of the present application further provide a computer program, which, when executed on a computer, enables the computer to execute the methods provided in the above embodiments.

[0234] Based on the above embodiments, the embodiments of the present application further provide a computer storage medium, in which a computer program is stored. When the computer program is executed by a computer, the computer executes the method provided in the above embodiments.

[0235] The storage medium may be any available medium that can be accessed by a computer. For example, but not limited to, a computer-readable medium may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer.

[0236] Based on the above embodiments, an embodiment of the present application further provides a chip, which is used to read a computer program stored in a memory to implement the method provided in the above embodiments.

[0237] Based on the above embodiments, an embodiment of the present application provides a computer program product. When the computer program product is run on an electronic device, the method provided in the above embodiments is implemented.

[0238] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0239] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0240] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0241] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0242] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A mask optimization method, characterized in that: include Determine the rule set; The sampled metal layer fragments are processed by the ILT engine to generate a quasi-optimized continuous transmission mask (CTM) for regular distribution value initialization; Optimizing regular distribution values ​​using a lithography-aware exponential natural evolution strategy; The optimized regularly distributed values ​​are used to generate sub-resolution assist features (SRAF) and model-based optical proximity correction (OPC) of the test pattern fragments.

2. The mask optimization method according to claim 1, characterized in that: The optimization objectives of the ILT engine include the wafer image under nominal conditions and the target image R * (m), and the area of ​​the process variation band; the loss function l(M) of a given regular distribution vector m is a function of mask M, expressed by the following formula: l(M)=||R(M)-R * (M)||2+β||R out (M)-R in (M)|| 2 Where R(M) represents the printed image, R * (M) represents the target image, M represents the mask corresponding to the printed image, β is the weight coefficient, R out (M) indicates the outermost contour, R in (M) indicates the innermost contour; By iteratively updating the unconstrained intermediate variable M' to minimize the loss function l(M), a quasi-optimal continuous transmission mask (CTM) is generated, which is expressed by the following formula: Where M′ represents an unconstrained intermediate variable, Δ t represents the iterative update step size parameter; where, α M′ represents the gradient parameter for the transformation from M' to M.

3. The mask optimization method according to claim 2, characterized in that: in, The continuous transmission mask (CTM) iterative update method includes After average pooling and downsampling, fast optimization is performed with low resolution r_L; Upsample twice and optimize in detail with higher resolution r_H; The optimization is expressed as follows: The constraints are: In the formula, represents the final optimized continuous projection mask (CTM), Indicates that The initial high-resolution continuous transmission mask obtained by upsampling, represents the continuous transmission mask (CTM) obtained by iterative updating at low resolution, Represents the continuous transmission mask (CTM) obtained by iterative updating at high resolution; the Upscale(M,k) function indicates that the mask M is upsampled by a scale factor k using nearest neighbor interpolation.

4. The mask optimization method according to claim 1, characterized in that: Optimize regular distributions using a lithography-aware exponential natural evolution strategy, including Optimizing regular distribution parameters through a lithography-aware natural gradient method; wherein natural gradient updating is performed through natural exponential expansion; Modeling a relative ranking based fitness function where adaptive sampling is performed on test graph fragments.

5. The mask optimization method according to claim 4, characterized in that: in, In optimizing the regular distribution parameters by the lithography-aware natural gradient method, the regular distribution parameters θ are updated in the direction of minimizing the expected lithography cost, while imposing constraints on the information gain at each step; The natural gradient is formalized as the solution to the constrained lithography rule value optimization problem: Where, L(θ-δθ) represents the expected lithography cost after the parameter θ changes by δθ, L(θ) represents the expected lithography cost under the regular distribution parameter, δθ represents the parameter change, Represents the gradient of the loss function with respect to the parameters; The constraints are: D(θ-δθ||θ)=∈ Where D(θ-δθ||θ) represents the distance between the distribution with θ-δθ as parameter and the distribution with θ as parameter, and ∈ represents an arbitrarily small quantity; In the case where δθ→0, the natural distance metric is: Where D KL (θ-δθ||θ) represents the KL divergence between parameter distribution θ and θ-δθ, and F(θ) is the Fisher information matrix of a given rule parameter family, which is expressed as: In the formula, P(m|θ) represents the probability distribution, and E[·] represents the average of the rule vector m. By substituting the direction of the natural gradient into the Lagrange multiplier method of the constrained optimization problem, the update step is expressed as: Where γ represents the scale factor; The natural gradient is determined to be in the same direction as δθ and is calculated as: In the formula, represents the natural gradient of the loss function with respect to the regular distribution parameter θ, F -1 represents the inverse of the Fisher information matrix; Update parameters: Where η represents the update step size of the regular distribution parameters.

6. The mask optimization method according to claim 5, characterized in that: in, The natural gradient update is performed through natural exponential expansion. The update formula is as follows: Where δ and W represent the direction of natural gradient update, μ′ represents the mean of the updated distribution θ, and Q′ represents the standard deviation of the updated distribution θ. In the natural gradient coordinate system, the Fisher matrix F(θ) is the identity matrix with respect to the orthogonal basis (δ, W), and the current search distribution It is encoded as (δ,W)=(0,0), and the logarithmic expression of the probability density is: In the formula, tr(Q) represents the trace operation of the matrix Q, m represents the rule parameter to be optimized, and μ represents the mean of the distribution of m; For sample m n =μ+Q·t n , where t n ~N(0,I) represents the loss function, I represents the identity matrix; The sample generation follows the following formula: Calculation of the natural gradient of δ: In the formula, Represents the gradient of the loss function of the current distribution state to the distribution parameter θ, (0,0) represents the current distribution state, n represents the nth sample, and N represents the total number of samples in each cycle to update the distribution parameter. represents the gradient of the orthogonal basis δ; Calculation of the natural gradient of W: In the formula, represents the natural gradient of W, Represents the gradient of the loss function with respect to the orthogonal basis W; Decompose the transformation matrix Q = σ·U into steps of length σ∈R + and a normalized matrix U satisfying det(U)=1; Gradient of σ It is expressed as: Gradient of U It is expressed as: In the formula, d represents the total dimension of the parameter; The natural gradient is O(d 3 ) is calculated with the complexity of .

7. The mask optimization method according to claim 5, characterized in that: in, The relative ranking-based fitness function is used to modify the gradient estimation to maintain scale invariance and rank invariance between different graph fragments. The lithography cost is converted into a utility value u1≥u2≥…≥uN. Individuals are ranked according to their cost, where the i-th highest ranked individual is m when sorted in ascending order of cost. i , and m1 is the rule parameter with the lowest cost, m N is the parameter with the highest cost, expressed as: Where N represents the total number of samples in each cycle to update the distribution parameters, P(m n |θ) means that under the distribution parameter θ, the nth parameter takes m n The posterior distribution of Choose the utility value u i The utility function u is given by the following formula n express:

8. The mask optimization method according to claim 7, characterized in that: in, In Adaptive Sampling on a Test Graphics Fragment, the layout is divided into overlapping tiles, and the width and height of each tile is calculated: In the formula, Λ w and Λ h Respectively represent the width and height of the complete layout, λ w and λ h Indicates the width and height of the crop tile, s w and h represents the stride in width and height, k w and k h Respectively represent the number of tiles.

9. An electronic device, comprising: One or more processors, a memory, and one or more programs; wherein the one or more programs are stored in the memory, and the one or more programs include instructions, which, when executed by the electronic device, enable the electronic device to perform the method described in any one of claims 1-8.

10. A computer-readable storage medium, comprising a computer program, and when the computer program is executed on an electronic device, the electronic device is enabled to execute the method according to any one of claims 1 to 8.

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