Method, apparatus, and storage medium for assisted graph optimization

Abstract

According to example embodiments of the present disclosure, methods, devices and storage media for assisting with graph optimization are provided. The method includes obtaining an initial mask pattern, the initial mask pattern including a main graph and at least one initial assist graph; obtaining a plurality of candidate assist graph groups, one of the plurality of candidate assist graph groups including at least one candidate assist graph corresponding to the main graph; determining respective imaging costs of the plurality of candidate assist graph groups; and determining at least one target assist graph for optimizing the initial mask pattern based on the respective imaging costs of the plurality of candidate assist graph groups. In this way, the imaging performance of the mask pattern under different process conditions can be improved.

Description

Technical Field

[0001] The embodiments of this disclosure primarily relate to the field of integrated circuit technology, and more specifically, to methods, apparatus, and storage media for assisting in graphics optimization. Background Technology

[0002] As semiconductor manufacturing processes continue to evolve towards smaller feature sizes and higher integration densities, the imaging accuracy requirements during photolithography have significantly increased. However, due to the resolution limitations of optical systems and the combined influence of various factors such as photoresist, exposure light source, and mask pattern, the actual image of the mask pattern on the wafer often differs from the designed pattern.

[0003] To reduce this imaging deviation, Optical Proximity Correction (OPC) technology is commonly used. By introducing auxiliary structures into the mask pattern or correcting the edges of the pattern, the imaged wafer pattern is made closer to the target design pattern. However, this traditional edge-adjustment-based OPC method is gradually facing bottlenecks in terms of efficiency and manufacturability. How to ensure image quality while considering process constraints and manufacturing feasibility has become a crucial issue in lithography optimization. Summary of the Invention

[0004] In a first aspect of this disclosure, a method for optimizing auxiliary patterns is provided. The method includes: acquiring an initial mask pattern, the initial mask pattern including a main pattern and at least one initial auxiliary pattern; acquiring a plurality of candidate auxiliary pattern groups, one of the candidate auxiliary pattern groups including at least one candidate auxiliary pattern corresponding to the main pattern; determining the corresponding imaging costs of the plurality of candidate auxiliary pattern groups; and determining at least one target auxiliary pattern for optimizing the initial mask pattern based on the corresponding imaging costs of the plurality of candidate auxiliary pattern groups.

[0005] In a second aspect of this disclosure, a method for generating auxiliary graphics is provided. The method includes: acquiring an initial mask pattern, the initial mask pattern including a main graphic and at least one initial auxiliary graphic; acquiring multiple sets of control parameters, one set of control parameters including multiple parameters for controlling the auxiliary graphic in different dimensions; and generating multiple candidate auxiliary graphic groups based on the multiple sets of control parameters and the initial mask pattern, one of the candidate auxiliary graphic groups including at least one candidate auxiliary graphic corresponding to the main graphic.

[0006] In a third aspect of this disclosure, an electronic device is provided. The electronic device includes a processor and a memory coupled to the processor. The memory has instructions stored therein, which, when executed by the processor, cause the electronic device to perform a method according to a first or second aspect of this disclosure.

[0007] In a fourth aspect of this disclosure, a computer-readable storage medium is provided. A computer program is stored on the computer-readable storage medium. When executed by a processor, the computer program implements the method according to a first or second aspect of this disclosure.

[0008] As will be understood from the following description, according to embodiments of this disclosure, an initial mask pattern is first determined, comprising a main pattern and at least one initial auxiliary pattern. Further, a plurality of candidate auxiliary pattern groups are obtained, one of which includes at least one candidate auxiliary pattern corresponding to the main pattern. Further still, the corresponding imaging costs of the plurality of candidate auxiliary pattern groups are determined. Based on the corresponding imaging costs of the plurality of candidate auxiliary pattern groups, at least one target auxiliary pattern is determined for optimizing the initial mask pattern. In this manner, the imaging performance of the mask pattern under different process conditions can be improved.

[0009] It should be understood that the content described in this summary section is not intended to limit the key or essential features of the embodiments of this disclosure, nor is it intended to restrict the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0010] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0011] Figure 1 A schematic diagram of an example environment in which the various embodiments of this disclosure can be implemented is shown;

[0012] Figure 2 A schematic diagram illustrating a process for optimizing an auxiliary image according to some embodiments of the present disclosure is shown;

[0013] Figure 3A A schematic diagram of an initial mask pattern according to some embodiments of the present disclosure is shown;

[0014] Figure 3B A schematic diagram illustrating the process of generating a candidate auxiliary graphic group according to some embodiments of the present disclosure is shown;

[0015] Figure 4 A schematic diagram illustrating the process of determining the imaging cost of candidate auxiliary graphics groups according to some embodiments of the present disclosure is shown;

[0016] Figure 5 A flowchart illustrating a process for assisting graphics optimization according to some embodiments of the present disclosure is shown;

[0017] Figure 6 A flowchart illustrating a process for generating auxiliary graphics according to some embodiments of the present disclosure is shown; and

[0018] Figure 7 A block diagram of an electronic device in which one or more embodiments of the present disclosure may be implemented is shown. Detailed Implementation

[0019] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0020] In the description of embodiments of this disclosure, the term "comprising" and similar terms should be understood as open-ended inclusion, i.e., "including but not limited to". The term "based on" should be understood as "at least partially based on". The term "one embodiment" or "the embodiment" should be understood as "at least one embodiment". The terms "first", "second", etc., may refer to different or the same objects. Other explicit and implicit definitions may also be included below.

[0021] The following will describe in detail various example implementations of this scheme with reference to the accompanying drawings.

[0022] First see Figure 1 It illustrates a schematic diagram of an example environment 100 in which the various embodiments of this disclosure can be implemented. For example... Figure 1 As shown, the example environment 100 may generally include electronic device 110.

[0023] In some embodiments, the electronic device 110 can interact with other devices (not shown). For example, the electronic device 110 can receive input information from other devices and output feedback information to other devices. In some embodiments, the input information from other devices can be design layout data 120. The electronic device 110 can perform corresponding mathematical operations on the design layout data and output the corresponding operation results 130 to other devices. In some embodiments, the operation results can be corrected layout data.

[0024] In example environment 100, electronic device 110 can be any type of computing-capable device, including terminal devices or server devices. Terminal devices can be any type of mobile terminal, fixed terminal, or portable terminal, including mobile phones, desktop computers, laptop computers, notebook computers, netbook computers, tablet computers, media computers, multimedia tablets, personal communication system (PCS) devices, personal navigation devices, personal digital assistants (PDAs), audio / video players, digital cameras / camcorders, positioning devices, television receivers, radio receivers, e-book devices, gaming devices, or any combination of the foregoing, including accessories and peripherals of these devices or any combination thereof. Server devices can include, for example, computing systems / servers, such as mainframes, edge computing nodes, computing devices in cloud environments, and so on.

[0025] It should be understood that the structure and function of the example environment 100 are described for illustrative purposes only and do not imply any limitation on the scope of this disclosure. Example embodiments according to this disclosure will now be described in detail with reference to the accompanying drawings.

[0026] As briefly mentioned above, optical proximity correction is an important means to improve the precision of photolithography processes in semiconductor manufacturing. However, with the continuous increase in design complexity and manufacturing precision, simply correcting the main pattern often cannot guarantee imaging stability under different process conditions (e.g., focal length shift or exposure dose fluctuations). Therefore, introducing auxiliary patterns into the mask pattern has become an important means to improve photolithography performance. For example, sub-resolution assist features (SRAFs) are tiny auxiliary structures that cannot be directly developed during the imaging process. By adding sub-resolution assist features to the mask pattern, the light field distribution can be improved, the pattern contrast can be enhanced, and the process window (PW) can be expanded, thereby enhancing the overall photolithography robustness.

[0027] Traditionally, OPC technology typically only modifies the main pattern while keeping the auxiliary patterns unchanged. While this approach allows the imaging contour to fit the target under standard process conditions, it is difficult to simultaneously optimize comprehensive performance indicators such as lithography depth bandwidth (PV Band), normalized image log slope (NILS), and process window.

[0028] Furthermore, iterative inverse lithography (ILT) technology can directly optimize patterns on the mask layer using methods such as gradient descent. However, this approach relies on a continuously differentiable objective function and cannot effectively handle situations with hard constraints. For example, the process window lacks a computable gradient, making it impossible for ILT to optimize using this as a cost function. Mask rule check (MRC) constraints are discontinuous geometric constraints, lacking differentiable gradient information, making it difficult for ILT to consider manufacturing feasibility. Edge-moving-based optimization methods also cannot dynamically adjust the number of auxiliary patterns, potentially leading to redundant auxiliary structures in some areas and increasing the risk of misprinting.

[0029] To address this, embodiments of this disclosure propose a scheme for auxiliary pattern optimization. According to embodiments of this disclosure, firstly, an initial mask pattern is determined, comprising a main pattern and at least one initial auxiliary pattern. Further, multiple candidate auxiliary pattern groups are obtained, one of which includes at least one candidate auxiliary pattern corresponding to the main pattern. Further still, the corresponding imaging costs of the multiple candidate auxiliary pattern groups are determined. Based on the corresponding imaging costs of the multiple candidate auxiliary pattern groups, at least one target auxiliary pattern is determined for optimizing the initial mask pattern.

[0030] In the embodiments of this disclosure, multiple candidate auxiliary pattern groups are obtained for the auxiliary patterns in the mask pattern, and the imaging results of each candidate auxiliary pattern group are simulated and the imaging cost is evaluated. In this way, the imaging performance can be compared among multiple candidate distributions to determine the optimal target auxiliary pattern. This method does not rely on traditional gradient-based optimization solutions, but achieves global optimization of imaging performance through parallel evaluation of multiple candidate schemes. Through this approach, the solution of this disclosure can improve the imaging stability of the mask pattern under different process conditions and the consistency of lithographic imaging performance with the overall process window, while satisfying mask manufacturing constraints, thereby effectively improving the final imaging quality.

[0031] The following describes various example implementations of this scheme in further detail with reference to the accompanying drawings. In some embodiments, the process of determining the mask pattern described above can be performed by, for example... Figure 1 The electronic device 110 shown is performing this operation. The following is in conjunction with... Figure 1 Let me explain in detail.

[0032] Figure 2 A schematic diagram of a process 200 for optimizing an auxiliary image according to some embodiments of the present disclosure is shown. Figure 2As shown, the electronic device 110 can acquire an initial mask pattern 205. The initial mask pattern 205 may include a main pattern and at least one initial auxiliary pattern.

[0033] In some embodiments, the master pattern can be used to form a target design pattern during the photolithography process, and its shape can be determined based on the target design pattern. Initial auxiliary patterns can include auxiliary structures that are not directly developed during the imaging process, used to improve photolithography imaging performance. For example, at least one initial auxiliary pattern can include at least one sub-resolution auxiliary pattern. The initial auxiliary patterns can be generated based on empirical rules, or they can be generated through model calculation or prediction; this disclosure does not limit this.

[0034] Continue to refer to Figure 2 In box 210, the electronic device 110 can acquire multiple candidate auxiliary pattern groups (e.g., candidate auxiliary pattern groups 215-1 to 215-N). One of the multiple candidate auxiliary pattern groups includes at least one candidate auxiliary pattern corresponding to the main pattern. The purpose of acquiring multiple candidate auxiliary pattern groups is to explore different auxiliary pattern distribution schemes in order to evaluate their imaging performance and select the optimal auxiliary pattern distribution in subsequent imaging simulations.

[0035] In some embodiments, candidate auxiliary graphic groups can be obtained based on the auxiliary graphic generation method provided in this disclosure, or they can be obtained independently of the generation method through other means. This disclosure does not limit this. For example, electronic device 110 can generate multiple candidate auxiliary graphic groups based on at least one initial auxiliary graphic. Alternatively or additionally, electronic device 110 can obtain multiple candidate auxiliary graphic groups from an external system or database. These candidate auxiliary graphic groups can be distributions of auxiliary graphics generated through other optimization algorithms, empirical rules, or predefined templates.

[0036] In some embodiments, a candidate auxiliary graphic set can be a collection of auxiliary graphics generated based on a set of control parameters for use in simulated imaging in conjunction with the main graphic. In other words, a candidate auxiliary graphic set can correspond to a specific distribution of auxiliary graphics in the mask pattern. Each candidate auxiliary graphic set can be viewed as an alternative for mask pattern optimization. The differences between these candidate auxiliary graphic sets may lie in the number, position, width, or spacing of the auxiliary graphics.

[0037] In some embodiments, the electronic device 110 can acquire multiple sets of control parameters. For example, the electronic device 110 can utilize a heuristic algorithm to generate multiple sets of control parameters. One set of control parameters includes multiple parameters for controlling the auxiliary graphic in different dimensions. The heuristic algorithm may include, but is not limited to, global search algorithms that do not rely on gradient calculation, such as genetic algorithms, evolutionary algorithms, and particle swarm optimization. Each set of control parameters may include multiple values ​​for controlling the auxiliary graphic in different dimensions (e.g., position, width, or spacing). These parameters can be understood as feature quantities describing the shape and distribution of the auxiliary graphic, used to adjust the specific geometric features of the auxiliary graphic during the optimization process.

[0038] Alternatively or additionally, the electronic device 110 may acquire multiple sets of control parameters from an external system or a pre-set database. For example, the electronic device 110 may receive a set of control parameters provided by a training model, historical optimization results, or manual settings as initial search parameters or partial reference parameters. In this way, external empirical knowledge or existing optimization results can be introduced into the current auxiliary graph generation process, thereby improving the initial quality and convergence efficiency of the search.

[0039] As an example, for the initial auxiliary graphic, multiple sets of control parameters can be randomly generated initial values. These initial values ​​do not depend on the specific shape of the initial auxiliary graphic, but only on the number of currently valid auxiliary graphics. In subsequent iterations, the heuristic algorithm can update the control parameters, causing their values ​​to gradually approach the global optimum.

[0040] Furthermore, for each set of control parameters, the electronic device 110 can adjust at least one initial auxiliary pattern based on that set of control parameters to generate a candidate auxiliary pattern set corresponding to that set of control parameters. Each candidate auxiliary pattern set can represent a different auxiliary pattern distribution scheme for subsequent imaging simulation and performance evaluation.

[0041] In some embodiments, the electronic device 110 may determine at least one layout unit of an initial auxiliary graphic based on one or more features of the initial mask pattern. This layout unit can be used to limit the optimization range of the auxiliary graphic in order to reduce computational load while maintaining overall geometric regularity.

[0042] As an example, Figure 3A A schematic diagram of an initial mask pattern 301 according to some embodiments of the present disclosure is shown. For example... Figure 3AAs shown, the initial mask pattern 301 is periodically distributed and symmetrical in the horizontal direction. In this case, the electronic device 110 can determine the basic regions with the same pattern distribution in the initial mask pattern 301 based on at least one of the geometric or structural features of the initial mask pattern. Further, the electronic device 110 can use this basic region as a basic unit for auxiliary pattern optimization (e.g., layout unit 305).

[0043] The layout unit 305 can be understood as the smallest structural unit of the mask pattern 301, which can represent the repetitive features of the entire pattern in terms of shape and spacing. By performing optimization operations only within the layout unit 305 and expanding it in subsequent steps using the periodicity and symmetry of the structure, the number of auxiliary graphics to be optimized can be significantly reduced, thereby reducing computational complexity and accelerating algorithm convergence.

[0044] In some embodiments, within layout unit 305, electronic device 110 can adjust at least one portion of an initial auxiliary graphic belonging to the layout unit based on the set of control parameters to generate candidate auxiliary graphics. Adjustment of the auxiliary graphic portion in layout unit 305 may include changing geometric properties such as the position or width of the auxiliary graphic within the layout unit.

[0045] As an example, Figure 3B A schematic diagram of a process 300 for generating a candidate auxiliary graphic group according to some embodiments of the present disclosure is shown. A first parameter in the control parameters can be used to control the position of the auxiliary graphic, and a second parameter can be used to control the width of the auxiliary graphic. For example... Figure 3B As shown, the electronic device 110 can calculate and update the coordinates and shape data of the auxiliary graphic in the layout unit 305 according to these parameters. For example, the auxiliary graphic portion is moved to the boundary of the layout unit 305.

[0046] Furthermore, the electronic device 110 can generate one of a plurality of candidate auxiliary graphic groups by performing at least one of copying or transforming the generated candidate auxiliary graphics. The copying operation can be used to reuse candidate auxiliary graphics in a periodic structure. The transformation operation can include operations such as symmetrical flipping, translation, or rotation to ensure that the spatial distribution of the auxiliary graphics within the entire main graphic area conforms to the expected geometric relationship.

[0047] Continue to refer to Figure 3BAfter generating a candidate auxiliary graphic by adjusting the initial auxiliary graphic in the layout unit 305, the electronic device 110 can generate a corresponding candidate auxiliary graphic group 315 by performing a horizontal flip operation on the auxiliary graphic and copying it periodically. The auxiliary graphic portion in the layout unit 305 and the graphics generated by performing copying or transformation operations belong to the same candidate auxiliary graphic group. In this way, the distribution of auxiliary graphics within a periodic unit can be adjusted using a very small number of control variables (e.g., two control parameter values), thereby significantly reducing the search space and accelerating the convergence speed of the optimization algorithm. Similar to the aforementioned process, the electronic device 110 can adjust the auxiliary graphics in the layout unit based on multiple sets of generated control parameters, and generate corresponding candidate auxiliary graphic groups through operations such as copying or flipping.

[0048] After generating multiple candidate auxiliary graphic groups, the electronic device 110 can perform geometric consistency checks on the graphics in the candidate auxiliary graphic groups and adjust the number of auxiliary graphics in the candidate auxiliary graphic groups. This ensures that the generated auxiliary graphics meet predetermined spatial constraints and manufacturing requirements.

[0049] In some embodiments, if there are at least two candidate auxiliary graphics in the first candidate auxiliary graphics group among a plurality of candidate auxiliary graphics groups that are less than a threshold distance, the electronic device 110 may merge the at least two candidate auxiliary graphics.

[0050] As an example, continue to refer to Figure 3B When a candidate auxiliary graphic is moved in layout unit 305 and then flipped and copied to generate a complete candidate auxiliary graphic group, auxiliary graphics in adjacent units may overlap, intersect, or be too close together. In this case, electronic device 110 can merge two auxiliary graphics with a distance below a threshold into a new auxiliary graphic, thereby obtaining a new candidate auxiliary graphic group 325. The candidate auxiliary graphic group 325 obtained in this way includes auxiliary graphic structures that satisfy manufacturing rules.

[0051] In some embodiments, if a first candidate auxiliary graphic exists in a second candidate auxiliary graphic group among a plurality of candidate auxiliary graphic groups, and the first candidate auxiliary graphic is located outside a predetermined area or has a width less than a threshold width, the electronic device 110 may remove the first candidate auxiliary graphic from the second candidate auxiliary graphic group.

[0052] As an example, the values ​​of some control parameters may cause the generated auxiliary graphics to be moved outside the layout unit range, or to have unreasonable situations such as negative widths. In this case, the electronic device 110 can identify these auxiliary graphics that do not meet spatial constraints or geometric conditions and remove them from the corresponding candidate auxiliary graphics group. This ensures the accuracy of subsequent simulation calculations and the validity of manufacturing data.

[0053] In the embodiments of this disclosure, by performing geometric consistency checks on the graphics in the candidate auxiliary graphic group, the number of auxiliary graphics that do not conform to manufacturing rules can be effectively reduced. During the optimization process, by identifying and merging auxiliary graphics that are too close together and deleting illegal auxiliary graphics, imaging accuracy and process window can be improved without violating manufacturing rules. Compared with traditional edge-movement-based correction methods that can only continuously adjust existing boundaries, the method in the embodiments of this disclosure can adjust the number of auxiliary graphics and provide greater adjustment space for subsequent mask rule checks, avoiding structures on the final mask that are unmanufacturable or pose printing risks.

[0054] Return to reference Figure 2 The electronic device 110 can determine the corresponding imaging costs of multiple candidate auxiliary pattern groups. For example, for candidate auxiliary pattern groups 215-1 to 215-N, the electronic device 110 can determine the corresponding imaging costs 220-1 to 220-N. The imaging costs can be used to evaluate the imaging performance of the corresponding candidate auxiliary pattern groups. By determining the imaging cost of each candidate auxiliary pattern group, a quantitative evaluation of different auxiliary pattern distribution schemes can be achieved, thereby helping to select the auxiliary pattern layout with the best imaging performance. In other words, by calculating the imaging costs, the electronic device 110 can numerically measure the effect of each auxiliary pattern distribution in lithographic imaging, and screen and optimize candidate schemes based on the evaluation results, thereby helping to determine the optimal auxiliary pattern layout.

[0055] In some embodiments, for one of a plurality of candidate auxiliary pattern groups, the electronic device 110 may first perform optical proximity correction on the main pattern. The purpose of optical proximity correction is to reduce errors in the photolithography process by correcting the geometry of the main pattern, thereby ensuring that the main pattern can be imaged more accurately. It should be noted that the aforementioned optical proximity correction process can be implemented using any suitable optical proximity correction technique or algorithm, such as model-driven correction methods or rule-based correction methods, and this disclosure does not limit it.

[0056] Furthermore, the electronic device 110 can perform optical imaging simulation on the corrected main pattern and the candidate auxiliary pattern group to obtain the simulation results of the candidate auxiliary pattern group. The optical imaging simulation can be based on a photolithography imaging model to numerically simulate the imaging process of the mask pattern in the photolithography system. Through simulation calculations, the imaging characteristics of the mask pattern under different illumination conditions, exposure doses, and focal length shifts can be obtained, thereby predicting the imaging performance of the candidate auxiliary pattern group under actual photolithography conditions.

[0057] In some embodiments, based on simulation results, electronic device 110 can determine the imaging cost of the candidate auxiliary graphic group. The imaging cost can be used to comprehensively reflect the manufacturability and imaging performance of the candidate auxiliary graphic group, serving as an objective function for auxiliary graphic optimization. By calculating the imaging cost, electronic device 110 can determine the degree of deviation between the imaging performance of the candidate auxiliary graphic group and the target design, under the premise of meeting manufacturing constraints, thereby providing a basis for subsequent optimization updates.

[0058] Figure 4 A schematic diagram of a process 400 for determining the imaging cost of candidate auxiliary graphics groups according to some embodiments of the present disclosure is shown. Figure 4 As shown, taking candidate auxiliary pattern group 215-1 among multiple candidate auxiliary pattern groups as an example, the electronic device 110 can first perform a manufacturing rule check on candidate auxiliary pattern group 215-1. The manufacturing rule check can also be called a mask rule check, which can be used to verify whether the pattern meets the mask preparation process requirements.

[0059] In frame 410, electronic device 110 can determine whether the corresponding spacing between multiple candidate auxiliary graphics in candidate auxiliary graphic group 215-1 and the corrected main graphic 402, as well as the corresponding width of the multiple auxiliary graphics, conform to predetermined manufacturing rules.

[0060] As an example, manufacturing rules may include minimum spacing thresholds between main and auxiliary graphics, minimum spacing thresholds between different auxiliary graphics, and minimum width thresholds for auxiliary graphics. These parameters can be set by the user according to specific manufacturing process requirements. Electronic device 110 can determine whether the spacing d1 between the main graphic 402 and candidate auxiliary graphics is greater than the minimum spacing between the main graphic and auxiliary graphics, whether the spacing d2 between candidate auxiliary graphics is greater than the minimum spacing between auxiliary graphics, and whether the width d3 of the candidate auxiliary graphics is greater than the minimum width of the auxiliary graphics. Through these checks, electronic device 110 can determine the number of candidate auxiliary graphics that violate the manufacturing rules.

[0061] In some embodiments, if the result of the manufacturing rule check indicates that there is at least one candidate auxiliary graphic in candidate auxiliary graphic group 215-1 whose spacing or width does not conform to the predetermined manufacturing rule, process 400 may proceed to block 430.

[0062] In box 430, electronic device 110 can calculate the corresponding imaging cost 220-1 based on the number of at least one candidate auxiliary graphic and a first weight. For example, electronic device 110 can calculate the imaging cost 220-1 as the product of the number of candidate auxiliary graphics that violate manufacturing rules and the first weight. The first weight can be set according to the specific optimization objective and is used to assign the highest priority to manufacturing rule constraints during the optimization process. In this case, electronic device 110 can directly output the calculated imaging cost without performing subsequent imaging simulation or performance calculation steps. In this way, auxiliary graphic distribution schemes that do not meet manufacturing constraints can be quickly screened out in the early stage of optimization, thereby reducing invalid calculations and improving the computational efficiency of the overall optimization process.

[0063] In some embodiments, if the detection results indicate that there are no auxiliary graphics in candidate auxiliary graphic group 215-1 that violate predetermined manufacturing rules, process 400 can proceed to block 420. In block 420, electronic device 110 can determine whether there are any unexpected contours outside the expected imaging area in the simulation results. That is, electronic device 110 can perform a print contour check.

[0064] As an example, electronic device 110 can determine, based on the simulation results of candidate auxiliary pattern group 215-1, whether there are imaging contours outside the target design pattern, i.e., unexpected contours. Unexpected contours can represent brightness contour lines or exposure areas appearing outside the target boundary in photolithography simulation, corresponding to the phenomenon of the auxiliary pattern being partially developed during photolithography. In other words, if a new light intensity distribution contour is detected outside the expected imaging area in the simulation results, it indicates that the auxiliary pattern may be partially printed on the silicon wafer. This is a situation that is desirable to avoid in the design.

[0065] In some embodiments, the electronic device 110 can perform a print profile check under different focal length offsets or exposure doses according to user-defined simulation conditions to ensure that auxiliary patterns are not developed under different process fluctuations. If the print profile check indicates that there are unexpected profiles in the candidate auxiliary pattern group 215-1, process 400 can proceed to box 430.

[0066] In box 430, electronic device 110 can calculate imaging cost 220-1 based on the number of unexpected contours and a second weight. For example, electronic device 110 can calculate the product of the number of unexpected contours and the second weight as imaging cost 220-1. The second weight can be less than the first weight to reflect the optimization order in which manufacturing rule constraints take precedence over printing risk constraints. In other words, during the auxiliary pattern optimization process, electronic device 110 can prioritize eliminating candidate auxiliary pattern groups that violate manufacturing rules, and then eliminate candidate auxiliary pattern groups that pose printing risks. In this way, candidate auxiliary pattern distribution schemes with potential printing risks can be further screened out, so that only candidate auxiliary pattern groups that meet manufacturing constraints and will not produce unexpected exposures are retained in subsequent optimizations.

[0067] Continue to refer to Figure 4 If the detection results indicate that there are no auxiliary graphics in candidate auxiliary graphic group 215-1 that do not conform to the manufacturing rule inspection, and there are no unexpected contours in the simulation results that do not conform to the printing contour inspection, process 400 can proceed to box 430. In box 430, electronic device 110 can calculate at least one index to represent imaging performance based on the simulation results, as imaging cost 220-1.

[0068] In some embodiments, at least one metric may include Edge Placement Error (EPE), which measures the degree of deviation of the simulated imaging profile from the target design boundary.

[0069] In some embodiments, at least one metric may include a normalized logarithmic slope of light intensity, used to reflect the contrast and sharpness of the edges of the photolithographic image. A larger value of the normalized logarithmic slope of light intensity indicates sharper edge imaging and better process stability.

[0070] Alternatively or additionally, at least one indicator may include a process window, which describes the range of processes that maintain imaging accuracy under varying focal length shifts and exposure doses. A larger process window value indicates greater imaging robustness.

[0071] In some embodiments, the electronic device 110 can select one or more of the above-mentioned indicators and combine them according to the optimization objectives set by the user, so as to comprehensively characterize the imaging performance of the candidate auxiliary pattern group. In this way, while ensuring manufacturing rules and printing safety, the optimal auxiliary pattern distribution scheme can be further found based on the lithography performance indicators.

[0072] In some embodiments, the electronic device 110 may determine at least one target auxiliary pattern for optimizing the initial mask pattern based on the corresponding imaging costs of a plurality of candidate auxiliary pattern groups.

[0073] Return to referenceFigure 2 In step 230, the electronic device 110 can determine whether there exists a candidate auxiliary graphic group among multiple candidate auxiliary graphic groups whose corresponding imaging cost value meets predetermined conditions. Predetermined conditions may include, but are not limited to: the imaging cost reaching a minimum value, the cost change rate being lower than a preset threshold, or the cost meeting a set convergence criterion. For example, after multiple optimization iterations, when the imaging cost value of a certain candidate auxiliary graphic group changes less than a threshold compared to the previous iteration, it can be considered that the group of auxiliary graphics has met the predetermined conditions and reached a stable optimization state.

[0074] In some embodiments, if the imaging cost value of the third candidate auxiliary graphic group among a plurality of candidate auxiliary graphic groups meets a predetermined condition, process 200 may proceed to block 240. In block 240, the electronic device 110 may determine at least one auxiliary graphic included in the third candidate auxiliary graphic group as at least one target auxiliary graphic. The at least one target auxiliary graphic may be considered as an auxiliary graphic distribution that has the optimal imaging performance under the current optimization conditions and satisfies manufacturing constraints.

[0075] In some embodiments, if the corresponding imaging costs in multiple candidate auxiliary pattern sets do not meet predetermined conditions, process 200 can be restarted to block 210. In block 210, electronic device 110 can reacquire multiple candidate auxiliary pattern sets. For example, if the imaging performance of all current candidate auxiliary pattern sets has not yet reached the expected target, electronic device 110 can continue the next round of optimization search by updating control parameters and regenerating the auxiliary pattern distribution to obtain better imaging results.

[0076] In some embodiments, the electronic device 110 can update multiple sets of control parameters used to generate multiple candidate auxiliary image groups based on the corresponding imaging cost. For example, a heuristic algorithm can adaptively adjust the control parameters used in the current iteration according to the corresponding imaging cost of each candidate auxiliary image group. For instance, for candidate auxiliary image groups with low imaging costs, the heuristic algorithm can retain or amplify their control parameter characteristics. For candidate auxiliary image groups with high imaging costs, new control parameter values ​​can be generated through parameter perturbation, mutation, or resampling.

[0077] In some embodiments, based on updated sets of control parameters, the electronic device 110 can regenerate multiple candidate auxiliary graphic groups. Further, the electronic device 110 can determine at least one target auxiliary graphic based on the corresponding imaging costs of the regenerated multiple candidate auxiliary graphic groups.

[0078] As an example, similar to the aforementioned process, electronic device 110 can readjust features such as the number, size, or spacing of the initial auxiliary graphics using updated control parameters. This allows electronic device 110 to generate new candidate auxiliary graphic distribution schemes. For these newly generated candidate auxiliary graphic groups, electronic device 110 can perform imaging simulation and calculate the corresponding imaging cost. Subsequently, based on the updated imaging costs of multiple candidate auxiliary graphic groups, electronic device 110 can determine whether there exists an auxiliary graphic layout that meets predetermined conditions. If a suitable auxiliary graphic layout exists, electronic device 110 can identify it as at least one target auxiliary graphic. If not, electronic device 110 can continue to the next iteration.

[0079] In this process, electronic device 110 can utilize the stochastic search characteristics of heuristic algorithms to determine the control parameters for the next iteration based on imaging cost. By adjusting the control parameters, the optimization direction shifts towards a solution space with better imaging performance and more reasonable manufacturing constraints. This parameter update mechanism based on cost feedback embodies the core idea of ​​heuristic algorithms: in the absence of gradient information, it gradually approaches the global optimum through multiple rounds of trial-and-error searches. In this way, the optimization process can adaptively adjust the search direction, thereby achieving efficient global optimization of the auxiliary image distribution.

[0080] In some embodiments, at least one target auxiliary pattern can be applied to the mask pattern for subsequent photolithography processes. For example, electronic device 110 can combine the determined target auxiliary pattern with a master pattern after optical proximity correction to generate an optimized mask pattern for photolithography. In this way, the mask pattern can achieve better imaging performance while maintaining manufacturing feasibility.

[0081] Alternatively or additionally, once at least one target auxiliary pattern is determined, the electronic device 110 can output the corresponding imaging performance indicators and related parameters for evaluation of the optimization effect. In this way, the optimization results of the auxiliary pattern can not only be reflected in the improvement of the mask structure, but also provide reference data for subsequent process window evaluation and mask correction.

[0082] In summary, the auxiliary pattern optimization scheme of the embodiments of this disclosure achieves global search and adaptive optimization of the auxiliary pattern through heuristic algorithm-based control parameter generation and imaging cost feedback iteration. This approach enables global search and optimization of the auxiliary pattern without relying on gradient information. Furthermore, by introducing manufacturing rule checks and printing contour checks during the auxiliary pattern optimization process, the risk of misprinting of the auxiliary pattern can be reduced while maintaining mask manufacturing feasibility. This improves the overall imaging consistency and process robustness of the mask design.

[0083] Figure 5 A flowchart of a process 500 for assisting graphics optimization according to some embodiments of the present disclosure is shown. In some embodiments, process 500 may be performed by, for example... Figure 1 The illustrated electronic device 110 performs this operation. It should be understood that process 500 may also include additional boxes not shown and / or one (or some) of the boxes shown may be omitted; the scope of this disclosure is not limited in this respect. The following is in conjunction with… Figure 1 The process 500 is described in detail.

[0084] like Figure 5 As shown, in box 510, electronic device 110 acquires an initial mask pattern, which includes a main pattern and at least one initial auxiliary pattern.

[0085] In box 520, electronic device 110 acquires multiple candidate auxiliary graphic groups. One of the candidate auxiliary graphic groups includes at least one candidate auxiliary graphic corresponding to the main graphic.

[0086] In box 530, electronic device 110 determines the corresponding imaging cost of multiple candidate auxiliary graphic groups.

[0087] In box 540, electronic device 110 determines at least one target auxiliary pattern for optimizing the initial mask pattern based on the corresponding imaging costs of multiple candidate auxiliary pattern groups.

[0088] In some embodiments, determining the corresponding imaging cost of a plurality of candidate auxiliary graphic groups includes: performing optical proximity correction on the main graphic for one of the candidate auxiliary graphic groups; performing optical imaging simulation on the corrected main graphic and the candidate auxiliary graphic group to obtain the simulation result of the candidate auxiliary graphic group; and determining the imaging cost of the candidate auxiliary graphic group based on the simulation result.

[0089] In some embodiments, determining the imaging cost of a plurality of candidate auxiliary graphic groups includes: for one of the plurality of candidate auxiliary graphic groups, determining whether the corresponding spacing between the plurality of candidate auxiliary graphics and the corrected main graphic and the corresponding width of the plurality of auxiliary graphics conform to predetermined manufacturing rules; in response to the spacing and corresponding width conforming to predetermined manufacturing rules and the absence of unexpected contours outside the expected imaging area in the simulation results, calculating at least one index to represent imaging performance as the imaging cost based on the simulation results.

[0090] In some embodiments, determining the imaging cost of the candidate auxiliary pattern group further includes: in response to the presence of at least one candidate auxiliary pattern in the candidate auxiliary pattern group whose spacing or width does not conform to a predetermined manufacturing rule, calculating the imaging cost based on the number of at least one candidate auxiliary pattern and a first weight; or in response to the presence of an unexpected contour, calculating the imaging cost based on the number of unexpected contours and a second weight, wherein the second weight is less than the first weight.

[0091] In some embodiments, determining at least one target auxiliary graphic includes: in response to a predetermined condition being met by the imaging cost value of a third candidate auxiliary graphic group among a plurality of candidate auxiliary graphic groups, determining at least one auxiliary graphic included in the third candidate auxiliary graphic group as at least one target auxiliary graphic.

[0092] In some embodiments, determining at least one target auxiliary graphic includes: in response to a predetermined condition that the corresponding imaging cost of a plurality of candidate auxiliary graphic groups does not meet the predetermined condition, updating a plurality of control parameters used to generate the plurality of candidate auxiliary graphic groups based on the corresponding imaging cost; regenerating the plurality of candidate auxiliary graphic groups based on the updated plurality of control parameters; and determining at least one target auxiliary graphic based on the corresponding imaging cost of the regenerated plurality of candidate auxiliary graphic groups.

[0093] Figure 6 A flowchart of a process 600 for generating auxiliary graphics according to some embodiments of the present disclosure is shown. In some embodiments, process 600 may be performed by, for example... Figure 1 The illustrated electronic device 110 performs this operation. It should be understood that process 600 may also include additional boxes not shown and / or some (or more) of the boxes shown may be omitted; the scope of this disclosure is not limited in this respect. The following is in conjunction with... Figure 1 The process 600 is described in detail.

[0094] like Figure 6 As shown, in box 610, electronic device 110 acquires an initial mask pattern, which includes a main pattern and at least one initial auxiliary pattern.

[0095] In box 620, electronic device 110 acquires multiple sets of control parameters. One set of control parameters includes multiple parameters used to control the auxiliary graphics in different dimensions.

[0096] In box 630, electronic device 110 generates multiple candidate auxiliary graphic groups based on multiple sets of control parameters and an initial mask pattern. One of the candidate auxiliary graphic groups includes at least one candidate auxiliary graphic corresponding to the main graphic.

[0097] In some embodiments, generating multiple candidate auxiliary graphic groups includes: for each of the multiple sets of control parameters, adjusting at least one initial auxiliary graphic based on the set of control parameters to generate a candidate auxiliary graphic group corresponding to the set of control parameters.

[0098] In some embodiments, adjusting at least one initial auxiliary graphic includes: determining a layout unit of at least one initial auxiliary graphic based on one or more features of an initial mask pattern; adjusting a portion of the at least one initial auxiliary graphic belonging to the layout unit based on the set of control parameters in the layout unit to generate a candidate auxiliary graphic; and generating one of a plurality of candidate auxiliary graphic groups by performing at least one of copying or transforming on the generated candidate auxiliary graphic.

[0099] In some embodiments, process 600 further includes: merging at least two candidate auxiliary graphics in a first candidate auxiliary graphics group of a plurality of candidate auxiliary graphics groups where the distance is less than a threshold.

[0100] In some embodiments, process 600 further includes: in response to the existence of a first candidate auxiliary graphic located outside a predetermined region or with a width less than a threshold width in a second candidate auxiliary graphic group among a plurality of candidate auxiliary graphic groups, deleting the first candidate auxiliary graphic from the second candidate auxiliary graphic group.

[0101] In some embodiments, determining at least one layout unit of an initial auxiliary graphic includes: determining a basic region in the initial mask pattern that has the same graphic distribution based on at least one of the geometric or structural features of the initial mask pattern; and determining the basic region as a layout unit.

[0102] Figure 7 A block diagram is shown of an electronic device 700 in which one or more embodiments of the present disclosure may be implemented. The electronic device 700 may, for example, be used to implement... Figure 1 The electronic device 110 shown. It should be understood that, Figure 7 The electronic device 700 shown is merely exemplary and should not be construed as limiting the functionality and scope of the embodiments described herein.

[0103] like Figure 7As shown, electronic device 700 is in the form of a general-purpose electronic device. Components of electronic device 700 may include, but are not limited to, one or more processors 710 or processing units, memory 720, storage device 730, one or more communication units 740, one or more input devices 750, and one or more output devices 770. The processing unit may be a physical or virtual processor and is capable of performing various processes according to programs stored in memory 720. In a multiprocessor system, multiple processing units execute computer-executable instructions in parallel to improve the parallel processing capability of electronic device 700.

[0104] Electronic device 700 typically includes multiple computer storage media. Such media can be any available media accessible to electronic device 700, including but not limited to volatile and non-volatile media, removable and non-removable media. Memory 720 can be volatile memory (e.g., registers, cache, random access memory (RAM)), non-volatile memory (e.g., read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory), or some combination thereof. Storage device 730 can be a removable or non-removable medium and can include machine-readable media, such as flash drives, disks, or any other media that can be used to store information and / or data (e.g., training data for training) and can be accessed within electronic device 700.

[0105] Electronic device 700 may further include additional removable / non-removable, volatile / non-volatile storage media. Although not explicitly stated... Figure 7 As shown, disk drives for reading from or writing to removable, non-volatile disks (e.g., "floppy disks") and optical disk drives for reading from or writing to removable, non-volatile optical disks can be provided. In these cases, each drive can be connected to a bus (not shown) via one or more data media interfaces. Memory 720 may include computer program product 725 having one or more program modules configured to perform various methods or actions of various embodiments of this disclosure.

[0106] The communication unit 740 enables communication with other electronic devices via a communication medium. Additionally, the functionality of the components of the electronic device 700 can be implemented using a single computing cluster or multiple computing machines capable of communicating via communication connections. Therefore, the electronic device 700 can operate in a networked environment using logical connections to one or more other servers, network personal computers (PCs), or another network node.

[0107] Input device 750 can be one or more input devices, such as a mouse, keyboard, trackball, etc. Output device 770 can be one or more output devices, such as a monitor, speaker, printer, etc. Electronic device 700 can also communicate with one or more external devices (not shown) via communication unit 740 as needed. These external devices include storage devices, display devices, etc., and can communicate with one or more devices that enable user interaction with electronic device 700, or with any device that enables electronic device 700 to communicate with one or more other electronic devices (e.g., network card, modem, etc.). Such communication can be performed via input / output (I / O) interface (not shown).

[0108] According to an exemplary implementation of this disclosure, a computer-readable storage medium is provided that stores one or more computer instructions, wherein one or more computer instructions are executed by a processor to implement the methods described above.

[0109] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products implemented according to this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0110] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processing unit of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0111] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions that execute on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0112] 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. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing the specified logical function. In some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0113] Various implementations of this disclosure have been described above. The foregoing description is exemplary and not exhaustive, nor is it limited to the disclosed implementations. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described implementations. The terminology used herein is chosen to best explain the principles, practical applications, or improvements to technology in the market, or to enable others skilled in the art to understand the implementations disclosed herein.

Claims

1. A method for assisting graph optimization, characterized by, The method comprises: obtaining an initial mask pattern, the initial mask pattern comprising a main pattern and at least one initial auxiliary pattern; obtaining a plurality of candidate auxiliary pattern groups, each of the plurality of candidate auxiliary pattern groups comprising at least one candidate auxiliary pattern corresponding to the main pattern, wherein the plurality of candidate auxiliary pattern groups are generated based on a plurality of sets of control parameters, the plurality of sets of control parameters comprising a plurality of sets of initial values generated randomly, and each of the plurality of candidate auxiliary pattern groups represents a different auxiliary pattern distribution scheme; determining respective imaging costs of the plurality of candidate auxiliary pattern groups; and based on the respective imaging costs of the plurality of candidate auxiliary pattern groups, determining at least one target auxiliary pattern for optimizing the initial mask pattern. The determining the respective imaging costs of the plurality of candidate auxiliary pattern groups comprises:

2. The method for assisting graph optimization of claim 1, wherein, for one of the plurality of candidate auxiliary pattern groups, performing optical proximity correction on the main pattern; performing optical imaging simulation on the corrected main pattern and the one of the plurality of candidate auxiliary pattern groups to obtain a simulation result of the one of the plurality of candidate auxiliary pattern groups; and based on the simulation result, determining an imaging cost of the one of the plurality of candidate auxiliary pattern groups. The determining the respective imaging costs of the plurality of candidate auxiliary pattern groups comprises:

3. The method for assisting graph optimization of claim 1, wherein, for one of the plurality of candidate auxiliary pattern groups, determining whether respective spacings between the plurality of candidate auxiliary patterns in the one of the plurality of candidate auxiliary pattern groups and the main pattern after performing optical proximity correction and respective widths of the plurality of candidate auxiliary patterns satisfy predetermined manufacturing rules; in response to the spacings and the respective widths satisfying the predetermined manufacturing rules and an absence of an unintended contour outside an intended imaging area in a simulation result of optical imaging for the one of the plurality of candidate auxiliary pattern groups, calculating, based on the simulation result, at least one indicator representing imaging performance as the imaging cost. The method further comprises:

4. The method for assisting graph optimization of claim 3, wherein, in response to the one of the plurality of candidate auxiliary pattern groups having at least one candidate auxiliary pattern whose spacings or widths do not satisfy the predetermined manufacturing rules, calculating the imaging cost based on a number of the at least one candidate auxiliary pattern and a first weight; or in response to the presence of the unintended contour, calculating the imaging cost based on a number of the unintended contour and a second weight, the second weight being less than the first weight. The determining the at least one target auxiliary pattern comprises: in response to an imaging cost value of a third of the plurality of candidate auxiliary pattern groups satisfying a predetermined condition, determining at least one auxiliary pattern included in the third of the plurality of candidate auxiliary pattern groups as the at least one target auxiliary pattern.

5. The method for assisting graph optimization of claim 1, wherein, The determining the at least one target auxiliary pattern comprises: in response to the respective imaging costs of the plurality of candidate auxiliary pattern groups not satisfying a predetermined condition, updating, based on the respective imaging costs, the plurality of sets of control parameters used to generate the plurality of candidate auxiliary pattern groups; 6. The method for assisting graph optimization of claim 1, wherein, regenerating a plurality of candidate auxiliary pattern groups based on the updated plurality of sets of control parameters; and determining the at least one target auxiliary pattern based on respective imaging costs of the regenerated plurality of candidate auxiliary pattern groups. The method comprises: ​ 7. A method for generating an auxiliary graph, characterized by, ​ obtaining an initial mask pattern, the initial mask pattern comprising a main pattern and at least one initial auxiliary pattern; obtaining a plurality of sets of control parameters, one set of control parameters in the plurality of sets of control parameters comprising a plurality of parameters for controlling auxiliary patterns in different dimensions, and the plurality of sets of control parameters being a plurality of sets of initial values generated randomly; and generating a plurality of candidate auxiliary pattern sets based on the plurality of sets of control parameters and the initial mask pattern, each candidate auxiliary pattern set in the plurality of candidate auxiliary pattern sets comprising at least one candidate auxiliary pattern corresponding to the main pattern, and the each candidate auxiliary pattern set representing a different auxiliary pattern distribution scheme.

8. The method for generating an auxiliary graph according to claim 7, wherein, Generating the plurality of candidate auxiliary pattern sets comprises: for each set of control parameters in the plurality of sets of control parameters, adjusting the at least one initial auxiliary pattern based on the set of control parameters to generate a candidate auxiliary pattern set corresponding to the set of control parameters.

9. The method for generating an auxiliary graph according to claim 7 or 8, characterized in that, Adjusting the at least one initial auxiliary pattern comprises: determining a layout unit of the at least one initial auxiliary pattern based on one or more features of the initial mask pattern; in the layout unit, adjusting a portion of the at least one initial auxiliary pattern belonging to the layout unit based on the set of control parameters to generate a candidate auxiliary pattern; and generating one of the plurality of candidate auxiliary pattern sets by performing at least one of copying or transforming the generated candidate auxiliary pattern.

10. The method for generating an auxiliary graph of claim 7, wherein, Further comprising: in response to there being at least two candidate auxiliary patterns in a first candidate auxiliary pattern set in the plurality of candidate auxiliary pattern sets that are within a distance below a threshold, merging the at least two candidate auxiliary patterns.

11. The method for generating an auxiliary graph of claim 7, wherein, Further comprising: in response to there being a first candidate auxiliary pattern in a second candidate auxiliary pattern set in the plurality of candidate auxiliary pattern sets that is outside a predetermined area or has a width below a threshold width, deleting the first candidate auxiliary pattern from the second candidate auxiliary pattern set.

12. The method for generating an auxiliary graph of claim 9, wherein, Determining a layout unit of the at least one initial auxiliary pattern based on a feature of the initial mask pattern comprises: determining a basic area in the initial mask pattern having a same pattern distribution based on at least one of a geometric feature or a structural feature of the initial mask pattern; and determining the basic area as the layout unit.

13. An electronic device, comprising: comprising: at least one processing unit; and at least one memory coupled to the at least one processing unit and storing instructions for execution by the at least one processing unit, the instructions when executed by the at least one processing unit causing the electronic device to perform the method according to any one of claims 1-6 or claims 7-12. A computer program stored thereon, characterized in that the computer program is executable by a processor to implement the method according to any one of claims 1-6 or claims 7-12.

14. A computer-readable storage medium, characterized in that, ​

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