Photolithography mask multi-objective robust optimization method, system, computer device, and medium

Abstract

Embodiments of the present application relate to the field of photolithography, and provide a photolithography mask multi-target robust optimization method, system, computer device and medium, wherein the method comprises: determining wafer patterns obtained by an initial mask under N kinds of process parameters based on a photolithography simulation model, N being an integer greater than 1; constructing N loss functions based on deviations between the wafer patterns obtained by various process parameters and a target pattern, each loss function corresponding to a process parameter; performing multi-round iteration optimization on the initial mask until all loss functions converge and reach equilibrium, obtaining an optimized mask. The optimized mask obtained according to the embodiments of the present application has good adaptability and high robustness to different process parameters.

Description

Technical Field

[0001] This application relates to photolithography technology, and more particularly to a multi-objective robust optimization method for photolithography masks, a multi-objective robust optimization system for photolithography masks, a computer device, and a computer-readable storage medium. Background Technology

[0002] Chip manufacturing mainly includes wafer preparation, deposition, photolithography, and etching. Among these, photolithography directly determines the minimum size of the pattern that can be manufactured, representing the advancement of the manufacturing technology, and is the most critical step. A photolithography system consists of a light source, a mask, a projection system, photoresist, and a wafer. During photolithography, the light source penetrates the mask, passes through the projection system, and is transmitted to the wafer. When the light intensity exceeds a certain threshold, the chemical properties of the photosensitive photoresist material change, ultimately forming a circuit pattern on the wafer. With the shrinking of node technologies, optical proximity effects, such as optical diffraction, become very significant when the light source passes through the mask. This causes significant distortion in the photoresist and subsequent optical imaging on the wafer, reducing chip production yield. Currently, the technology to mitigate this effect is Optical Proximity Correction (OPC), which compensates for this distortion by modifying the mask pattern beforehand, thus obtaining the correct pattern.

[0003] Reverse lithography, as one of the mainstream methods of OPC (Optical Processing), achieves high-precision wafer patterns through pixel-level mask optimization and lithography modeling. This method first rasterizes the mask pattern and optimizes the mask by flipping each discretized pixel. Typically, gradient descent-based methods are used for mask updates until the upper limit of the number of iterations is reached or the desired evaluation accuracy is achieved. Evaluation accuracy is generally measured by edge placement error (EPE) and process window (PW). However, existing reverse lithography techniques mostly only consider the optimization of specific process parameters, and the robustness of the mask remains to be addressed. Summary of the Invention

[0004] This application provides a multi-objective robust optimization method, a multi-objective robust optimization system for photolithography masks, a computer device, and a computer-readable storage medium, aiming to obtain photomasks with stable quality under different process parameters and improve the robustness of the photomasks.

[0005] In a first aspect, embodiments of this application provide a multi-objective robust optimization method for photolithographic masks, the method comprising the following steps:

[0006] Based on the photolithography simulation model, the wafer patterns obtained by the initial mask under N process parameters are determined respectively, where N is an integer greater than 1;

[0007] Based on the deviation between the wafer pattern and the target pattern obtained from various process parameters, N loss functions are constructed, each loss function corresponding to one of the process parameters;

[0008] The initial mask is iteratively optimized multiple times until all loss functions converge and reach equilibrium, resulting in the optimized mask.

[0009] In the scheme of this application embodiment, the wafer pattern obtained by the initial mask under different process parameters is first determined by a photolithography simulation model. Then, based on the deviation between the wafer pattern obtained by different process parameters and the target pattern, a loss function corresponding to each process parameter is constructed. The initial mask is iteratively optimized in multiple rounds until all loss functions converge and reach equilibrium, thus obtaining the optimized mask. The optimized mask obtained according to the scheme of this application embodiment has good adaptability and high robustness to different process parameters.

[0010] In one possible implementation, each round of iterative optimization includes:

[0011] Obtain the gradient vectors corresponding to the N loss functions respectively;

[0012] Gradient conflict pairs are determined from the N gradient vectors, and conflict mitigation is performed on each gradient conflict pair;

[0013] After mitigating the conflicts of all the gradient conflict pairs, the updated gradient vectors corresponding to each gradient vector are obtained.

[0014] The first gradient fusion vector is determined based on the N updated gradient vectors;

[0015] The parameters in the initial mask are updated based on the first gradient fusion vector.

[0016] In one possible implementation, determining gradient conflict pairs from the N gradient vectors includes:

[0017] A gradient vector set is constructed by randomly selecting a portion of the gradient vectors from the N gradient vectors.

[0018] The gradient conflict pairs are determined from the set of gradient vectors.

[0019] In one possible implementation, determining gradient conflict pairs includes:

[0020] If the angle between two gradient vectors is greater than 90°, then the two gradient vectors are determined to be the gradient conflict pair.

[0021] In one possible implementation, the conflict mitigation for each of the gradient conflict pairs includes:

[0022] The two gradient vectors in the gradient conflict pair are respectively denoted as the first gradient vector and the second gradient vector;

[0023] Calculate the first projection of the first gradient vector onto the orthogonal direction of the second gradient vector, and obtain the updated gradient vector corresponding to the first gradient vector based on the first projection;

[0024] Calculate the second projection of the second gradient vector onto the orthogonal direction of the first gradient vector, and obtain the updated gradient vector corresponding to the second gradient vector based on the second projection.

[0025] In one possible implementation, determining the first gradient fusion vector based on the N updated gradients includes:

[0026] The N updated gradient vectors are summed to obtain the second gradient fusion vector;

[0027] The second gradient fusion vector is normalized to obtain the third gradient fusion vector;

[0028] The gradient fusion vector magnitude is determined based on the vector with the largest gradient magnitude among the N updated gradient vectors.

[0029] The first gradient fusion vector is determined based on the third gradient fusion vector and the magnitude of the gradient fusion vector.

[0030] In one possible implementation, determining the wafer pattern obtained from the initial mask under N process parameters based on the photolithography simulation model includes:

[0031] For each of the process parameters, the K lithography kernels corresponding to the process parameters are subjected to a dot product weighted operation with the initial mask to obtain a lithography intensity map;

[0032] The photolithography intensity map is processed based on the photolithography simulation model to obtain the wafer pattern corresponding to the process parameters.

[0033] Secondly, embodiments of this application provide a multi-objective robust optimization system for photolithographic masks, including:

[0034] The determination module is used to determine the wafer pattern obtained by the initial mask under N process parameters based on the photolithography simulation model, where N is an integer greater than 1;

[0035] The construction module is used to construct N loss functions based on the deviation between the wafer pattern and the target pattern obtained from various process parameters, and each loss function corresponds to one of the process parameters;

[0036] The iterative optimization module is used to perform multiple rounds of iterative optimization on the initial mask until all the loss functions converge and reach equilibrium, thus obtaining the optimized mask.

[0037] Thirdly, embodiments of this application provide a computer device, including:

[0038] Memory, used to store programs;

[0039] A processor for executing a program stored in the memory, wherein when the processor executes the program stored in the memory, the processor is configured to perform the method described in the first aspect above.

[0040] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions for performing the method described in the first aspect above.

[0041] The solutions provided in the second to fourth aspects above are used to implement or cooperate with the methods provided in the first aspect above, and therefore can achieve the same or corresponding beneficial effects as the first aspect, which will not be elaborated here.

[0042] It should be understood that the above general description and the following detailed description are merely exemplary and do not limit this application. Attached Figure Description

[0043] Figure 1 A flowchart illustrating a multi-objective robust optimization method for photolithographic masks provided in this application embodiment;

[0044] Figure 2 A schematic diagram of an iterative optimization process provided for an embodiment of this application;

[0045] Figure 3 A schematic diagram illustrating the process of determining a first gradient fusion vector provided in an embodiment of this application;

[0046] Figure 4 A schematic diagram of a multi-objective robust optimization system for photolithography masks provided in this application embodiment;

[0047] Figure 5 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0048] To make the objectives, technical methods, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0049] It should be noted that the meaning of "multiple" (or "more than") in the description of the embodiments of this application refers to two or more, and "greater than," "less than," "exceeding," etc. are understood to exclude the number itself, while "above," "below," "within," etc. are understood to include the number itself. If "first," "second," etc. are used in the description, they are only for the purpose of distinguishing technical features and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0050] In this application embodiment, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, or the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of singular or plural items. For example, at least one of a, b, and c can represent: the existence of a alone, the existence of b alone, the existence of c alone, the simultaneous existence of a and b, the simultaneous existence of a and c, the simultaneous existence of b and c, or the simultaneous existence of a, b, and c, where a, b, and c can be single or multiple.

[0051] The terms "substantially," "about," and similar terms used in the embodiments of this application are used as approximate terms, not as terms of degree, and are intended to take into account the inherent biases of measurements or calculations known to those skilled in the art. Furthermore, the term "may" used in describing the embodiments of this application refers to "one or more possible embodiments." The terms "use," "using," and "used" used in the embodiments of this application can be considered synonymous with the terms "utilize," "utilizing," and "utilized," respectively. Additionally, the term "exemplary" is intended to refer to an instance or illustration.

[0052] Chip manufacturing mainly includes wafer preparation, deposition, photolithography, and etching. Among these, photolithography directly determines the minimum size of the pattern that can be manufactured, representing the advancement of the manufacturing technology, and is the most critical step. A photolithography system consists of a light source, a mask, a projection system, photoresist, and a wafer. During photolithography, the light source penetrates the mask, passes through the projection system, and is transmitted to the wafer. When the light intensity exceeds a certain threshold, the chemical properties of the photosensitive photoresist material change, ultimately forming a circuit pattern on the wafer. With the shrinking of node technologies, optical proximity effects, such as optical diffraction, become very significant when the light source passes through the mask. This causes significant distortion in the photoresist and subsequent optical imaging on the wafer, reducing chip production yield. Currently, the technology to mitigate this effect is Optical Proximity Correction (OPC), which compensates for this distortion by modifying the mask pattern beforehand, thus obtaining the correct pattern.

[0053] Reverse lithography, as one of the mainstream methods of OPC (Optical Processing), achieves high-precision wafer patterns through pixel-level mask optimization, resulting in optimized masks that, after passing through a lithography model. This method first rasterizes the mask pattern and then optimizes the mask by flipping each discretized pixel. Typically, a gradient descent-based method is used for mask updates until the upper limit of the number of iterations is reached or the desired evaluation accuracy is achieved. Evaluation accuracy is generally measured using edge placement error (EPE) and the process window (PW).

[0054] One related technique proposes back-lithography considering the process window. First, it calculates the wafer pattern under different exposure doses and defocusing conditions using a lithography simulation model. Then, it calculates the edge placement error using the wafer pattern obtained under conventional process parameters and the target pattern, deriving the gradient backpropagation formula for mask iterative optimization. Next, it calculates the process variation band (PVB) using the wafer pattern obtained under two extreme process parameters and the target pattern. Finally, it obtains the optimization objective by linearly weighting the edge placement error and the PVB, and iteratively optimizes using a gradient descent algorithm to obtain the optimized mask. However, this technique only considers the optimization under ideal conditions and two extreme process parameters, and cannot be equated to optimizing the crucial process window. Furthermore, the subsequent objective function calculation, which simply linearly weights and sums the two loss values ​​into a single optimization objective, affects the final convergence. Ultimately, the mask obtained using this method does not achieve satisfactory process window performance.

[0055] Another related technique proposes a two-stage robust reverse lithography optimization method. First, assuming that the defocusing process perturbation exhibits a normal distribution, the expected value of the difference between the wafer pattern and the target pattern under various defocusing process perturbations is calculated statistically, thus obtaining the final optimization objective function. Simultaneously, to reduce computational costs, a smaller number of optical kernel functions are used in the first stage of simulation calculations based on the lithography simulation model, and a coarsely optimized mask is obtained through gradient descent. In the second stage, all optical kernel functions from the lithography simulation model are retained for simulation calculations, and the mask obtained in the first stage is optimized again. This stage requires only a small number of iterations to obtain a better mask pattern. However, this related technique uses a normal distribution as the weighting weight for the difference between the wafer pattern and the target pattern under different process parameters when designing the objective function. This heuristic weighting design may affect the optimization effect, easily getting trapped in local optima, and is not conducive to obtaining good process window performance under various process parameter perturbations.

[0056] Another related technique proposes robust reverse lithography through energy function optimization. First, a lithography simulation model is designed under defocused process parameters, from which a wafer pattern with process perturbations can be obtained. Then, Gaussian weights are used to sum the differences between the wafer pattern and the target pattern under different process parameters to obtain the optimized target form, and an energy function is designed for optimization based on this. Finally, the mask is updated using an iterative method. However, this technique only considers reverse lithography optimization under defocused process parameter perturbations and cannot fully reflect the optimization of the process window. Furthermore, its update method is overly complex, computationally intensive, and has many hyperparameters, making it unsuitable for practical algorithm deployment.

[0057] Based on the defects and deficiencies in related technologies, this application proposes a multi-objective robust optimization method, a multi-objective robust optimization system for photolithography masks, a computer device, and a computer-readable storage medium, aiming to obtain photomasks with stable quality under different process parameters and improve the robustness of the photomasks.

[0058] The multi-objective robust optimization method for lithographic masks provided in this application can be applied to terminals, servers, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, etc.; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDN), and big data and artificial intelligence platforms; the software can be an application implementing the multi-objective robust optimization method for lithographic masks, etc., but is not limited to the above forms.

[0059] The embodiments of this application can be used in numerous general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In a distributed computing environment, program modules can reside in local and remote computer storage media, including storage devices.

[0060] It should be noted that in various specific embodiments of this application, when processing data related to the characteristics of an object (such as a user's attribute information or a set of attribute information) is required, the permission or consent of the corresponding object will be obtained first. Furthermore, the collection, use, and processing of this data will comply with relevant laws and standards. In addition, when embodiments of this application need to obtain the attribute information of an object, separate permission or consent from the corresponding object will be obtained through pop-ups or redirection to a confirmation page. Only after obtaining the separate permission or consent of the corresponding object will the necessary object-related data for the normal operation of embodiments of this application be obtained.

[0061] See Figure 1 , Figure 1 The flowchart illustrates a multi-objective robust optimization method for photolithographic masks provided in this application embodiment. The method includes, but is not limited to, the following steps:

[0062] Step S110: Determine the wafer patterns obtained by the initial mask under N process parameters based on the photolithography simulation model, where N is an integer greater than 1.

[0063] In this embodiment, N different process parameters are predefined, for example, 6 or 10 process parameters are predefined as needed; an initial mask is fabricated based on the target pattern (i.e., the target chip pattern), which is the mask to be optimized; for each process parameter, the wafer pattern formed by the initial mask under that process parameter is obtained through a photolithography simulation model. Through the above process, this embodiment can obtain N wafer patterns corresponding one-to-one with the above N process parameters.

[0064] For example, process parameter 1, process parameter 2, ..., process parameter N are predefined; for each of the N process parameters, a corresponding lithography simulation model is constructed, namely, lithography simulation model 1 corresponding to process parameter 1, lithography simulation model 2 corresponding to process parameter 2, ..., lithography simulation model N corresponding to process parameter N; an initial mask is designed and fabricated based on the target pattern; the initial mask is simulated using the above-mentioned lithography simulation models (lithography simulation models 1 to N) corresponding to different process parameters, thereby obtaining wafer patterns corresponding to different process parameters, namely, wafer pattern 1 corresponding to process parameter 1, wafer pattern 2 corresponding to process parameter 2, ..., wafer pattern N corresponding to process parameter N.

[0065] For example, the above process parameters may include optical parameters, photoresist parameters, etc.

[0066] Step S120: Based on the deviation between the wafer pattern and the target pattern obtained from various process parameters, construct N loss functions, each loss function corresponding to a process parameter.

[0067] In this embodiment of the application, after obtaining N wafer patterns corresponding to different process parameters, the deviation between these N wafer patterns and the target pattern is calculated respectively, and a corresponding loss function is constructed based on the deviation, that is, a loss function 1 corresponding to process parameter 1, a loss function 2 corresponding to process parameter 2, ..., a loss function N corresponding to process parameter N is constructed.

[0068] For example, the loss function can be mean squared error (MSE), mean absolute error (MAE), cross-entropy loss, binary cross-entropy loss, logarithmic binary cross-entropy loss, Kullback-Leibler divergence, negative log-likelihood loss, or hinge loss, etc. The specific type of loss function is not limited in the embodiments of this application.

[0069] Step S130: Perform multiple rounds of iterative optimization on the initial mask until all loss functions converge and reach equilibrium, thus obtaining the optimized mask.

[0070] In this embodiment of the application, after obtaining N loss functions corresponding to different process parameters, the initial mask is iteratively optimized in multiple rounds with the goal of all N loss functions converging and reaching equilibrium.

[0071] It should be understood that during the iterative optimization process, the parameters of the mask are continuously adjusted through optimization algorithms (such as gradient descent) so that the value of the loss function gradually decreases until it reaches a minimum point or close to the minimum point. This point indicates that the deviation between the wafer pattern obtained by the current mask and the target pattern is minimized.

[0072] It should also be understood that after each round of iterative optimization, the values ​​of the above N loss functions are recalculated, and it is determined whether each loss function has converged and reached equilibrium. If so, the current mask is used as the final optimized mask. If not, the next round of iterative optimization continues, including adjusting the mask parameters based on the current values ​​of each loss function using optimization algorithms (such as gradient descent).

[0073] It should be noted that in the embodiments of this application, the iteration termination condition requires that the loss functions reach equilibrium, that is, the values ​​of the loss functions cannot differ too much, so as to ensure that the final optimized mask can meet the requirements of each optimization objective.

[0074] As can be seen, the embodiments of this application determine the wafer pattern obtained by the initial mask under different process parameters through a photolithography simulation model. Then, based on the deviation between the wafer pattern obtained by different process parameters and the target pattern, loss functions corresponding to each process parameter are constructed. The initial mask is iteratively optimized in multiple rounds until all loss functions converge and reach equilibrium, thus obtaining the optimized mask. Since the effects of various process parameter disturbances are considered in the optimization process, the optimized mask obtained can achieve good adaptability and high robustness to different process parameters.

[0075] For example, this application embodiment introduces multi-objective optimization theory to obtain a robust mask, wherein the optimized mask and its acquisition process can be expressed by the following calculation formula (1): (Equation 1)

[0076] in, and These represent the initial masks for binarization. Photolithography intensity maps and wafer lithography patterns obtained through photolithography simulation models under different process parameters. It is the first n The first process parameter One kernel, It is the first The weight of each kernel in a coherent system. This represents a photoresist model, showing the light intensity during photoresist exposure. Areas exceeding a certain threshold will form wafer patterns. By simultaneously minimizing these N types of wafer lithography patterns With target mask The deviations between them are used to obtain the optimized mask, i.e.: The above formula can take into account N kinds of process disturbances, thus obtaining an optical mask with good robustness.

[0077] For example, in specific implementations, optical kernel functions with different simulation parameters can be stitched together in a high dimension. Utilizing the efficient computing power of multiple GPUs, these kernels can be deployed to achieve parallel forward and backward lithography simulations under various process conditions. This acceleration method enhances the scalability of the design framework of the embodiments in this application.

[0078] For example, determining the wafer pattern obtained from the initial mask under N process parameters based on a photolithography simulation model includes, but is not limited to, the following steps:

[0079] Step S310: For each process parameter, perform a dot product weighted operation on the K lithography kernels corresponding to the process parameter and the initial mask to obtain the lithography intensity map;

[0080] Step S320: Process the photolithography intensity map based on the photolithography simulation model to obtain the wafer pattern corresponding to the process parameters.

[0081] In other words, in this embodiment, the photolithography simulation first determines the photolithography intensity map, and then uses the photoresist model to generate the corresponding wafer pattern based on the photolithography intensity map.

[0082] It should be noted that the above-mentioned photolithography simulation model that yields the photolithography intensity map and wafer photolithography pattern can also be replaced with other differentiable models, and this application embodiment does not limit this.

[0083] See Figure 2 , Figure 2 This is a schematic diagram of an iterative optimization process provided for embodiments of this application. In some embodiments of this application, each round of iterative optimization includes, but is not limited to, the following steps:

[0084] Step S510: Obtain the gradient vectors corresponding to the N loss functions respectively.

[0085] In this embodiment, a gradient descent algorithm is used to iteratively optimize the mask. During the iterative optimization process, a loss function is calculated based on the wafer pattern obtained from the current mask. The loss function measures the deviation between the wafer pattern obtained from the current mask and the target pattern. If the current loss function does not converge, a gradient vector is calculated based on the loss function to update the mask parameters according to the gradient vector and a preset learning rate (step size). The rule for parameter updating is to follow the opposite direction of the gradient vector to minimize the loss function.

[0086] It should be understood that, since there are N loss functions in this embodiment, it is necessary to calculate the corresponding gradient vector for each loss function. In specific implementation, the chain rule can be used to calculate the gradient vector of the loss function with respect to each parameter, and this embodiment does not limit this to that.

[0087] Step S520: Determine gradient conflict pairs from the N gradient vectors and perform conflict mitigation on each gradient conflict pair.

[0088] It should be understood that this application embodiment has N loss functions, i.e., N optimization objectives. However, there may be conflicts between the gradient vectors corresponding to the N loss functions, i.e., the directional deviations between some gradient vectors are large, which will affect the optimization efficiency and optimization effect of the mask. Therefore, it is necessary to identify the gradient conflict pairs among the N gradient vectors and then perform conflict mitigation on the gradient conflict pairs.

[0089] For example, a gradient conflict pair refers to two gradient vectors whose directions are too far apart, that is, the angle between the two gradient vectors is too large.

[0090] For example, identifying gradient conflict pairs includes, but is not limited to: if the angle between two gradient vectors is greater than 90°, then the two gradient vectors are identified as a gradient conflict pair.

[0091] In other words, if among N gradient vectors, there exist two gradient vectors whose angle is greater than 90°, then these two gradient vectors can be considered a gradient conflict pair. For example, the angle between gradient vector 1 and gradient vector 2 is 120°, therefore gradient vector 1 and gradient vector 2 can be determined as a conflicting gradient pair.

[0092] One possible implementation is to mitigate gradient conflict pairs by assessing the degree of conflict between them and dynamically adjusting the optimization direction of conflicting gradients accordingly. This allows for a comprehensive consideration of all objectives to arrive at the final optimization direction. This approach automatically balances different objectives and theoretically guarantees convergence to the average loss.

[0093] As another possible implementation, gradient conflict mitigation can be achieved by projecting the gradient vector of each target onto an orthogonal plane that merges with the first gradient vectors. Specifically, if the gradients generated by two targets conflict with each other, the gradients are adjusted by projecting the conflicting gradients to ensure that the gradient of each target is zero in the direction that conflicts with the gradients of other targets. In this way, each target only updates its parameters in the direction that does not conflict with the gradients of other targets.

[0094] Alternatively, gradient clipping can be used to mitigate gradient conflicts. Specifically, gradient boundaries are pre-defined, and when a gradient vector exceeds the gradient boundary, the gradient vector is forced to be set to a vector in the same direction as the boundary.

[0095] Step S530: After mitigating the conflict of all gradient conflict pairs, the updated gradient vectors corresponding to each gradient vector are obtained.

[0096] Step S540: Determine the first gradient fusion vector based on N updated gradient vectors.

[0097] After mitigating gradient conflicts, the final first gradient fusion vector is obtained by comprehensively considering N gradient vectors, thereby balancing the update directions of each objective.

[0098] Step S550: Update the parameters in the initial mask based on the first gradient fusion vector.

[0099] Specifically, the mask parameters are updated based on the first gradient fusion vector and the preset learning rate (step size). The rule for parameter updating is to update along the opposite direction of the gradient in order to minimize the loss function.

[0100] It should be noted that the learning rate can be adaptively adjusted during the optimization process. For example, in multiple rounds of iterative optimization, the learning rate can be gradually reduced according to a certain decay rate to improve training efficiency and mask performance.

[0101] As one possible implementation, gradient conflict pairs are determined from N gradient vectors, including but not limited to the following steps:

[0102] Step S710: Randomly select a portion of the gradient vectors from the N gradient vectors to construct a gradient vector set;

[0103] Step S720: Identify gradient conflict pairs from the set of gradient vectors.

[0104] It should be understood that the presence of multiple optimization objectives increases the likelihood of gradient conflicts between these objectives, which becomes the main computational bottleneck in the parameter update process. To improve overall optimization efficiency, a multi-objective sampling strategy can be introduced, which involves randomly sampling the gradients of some objectives in each iteration to accelerate the process. This can significantly improve optimization efficiency.

[0105] In a specific example, for the nth gradient vector Consider sampling R gradients from other target gradients for conflict mitigation, specifically expressed mathematically as follows: ,in This indicates that R samples are randomly and uniformly sampled from a set S, where S is the set excluding the gradient vector. The set of other gradient vectors besides the gradient vectors. The sampled R gradient vectors form a gradient vector set, and gradient conflict pairs are identified from this set. In this example, in each iteration, only a portion of the gradients are sampled for conflict mitigation to accelerate the iteration. After multiple iterations, the gradients of multiple objectives gradually balance out, and gradient conflicts are gradually alleviated, thereby improving the optimization efficiency.

[0106] As one possible implementation, conflict mitigation is performed on each gradient conflict pair, including but not limited to the following steps:

[0107] Step S910: Denote the two gradient vectors in the gradient conflict pair as the first gradient vector and the second gradient vector, respectively;

[0108] Step S920: Calculate the first projection of the first gradient vector onto the orthogonal direction of the second gradient vector, and obtain the updated gradient vector corresponding to the first gradient vector based on the first projection;

[0109] Step S930: Calculate the second projection of the second gradient vector in the orthogonal direction of the first gradient vector, and obtain the updated gradient vector corresponding to the second gradient vector based on the second projection.

[0110] See Figure 3 , Figure 3 This is a schematic diagram illustrating a process for determining a first gradient fusion vector, as provided in an embodiment of this application. Figure 3 It includes two gradient vectors. and ,when and The angle between <0 (i.e.) When >90°, and These are called "conflicting gradient pairs", such as Figure 3 As shown in (1) of the diagram. To alleviate the gradient conflict between the two, the gradient vectors are... Projected onto gradient vector In the orthogonal direction, the goal is to eliminate conflicts while preserving as much as possible along the gradient vector. The update step size and direction of the original gradient direction are obtained, thus realizing the gradient vector. The update yields the gradient vector. ,like Figure 3 As shown in (2) in the figure; a similar operation is used to transform the gradient vector. Projected onto gradient vector In the orthogonal direction, the gradient vector is realized. The update yields the gradient vector. ,like Figure 3 As shown in (3) of the text.

[0111] For example, a gradient vector Projected onto another gradient vector In the orthogonal direction, the updated vector is obtained. It can be calculated using the following formula:

[0112] (Equation 2)

[0113] It should be understood that by projecting one gradient vector in a gradient conflict pair onto the orthogonal direction of the other gradient vector, it is possible to eliminate the conflict while preserving the update step size and direction along the original gradient direction as much as possible.

[0114] It should be noted that, Figure 3 The number of gradient vectors in the diagram is only illustrative and may be much larger in real-world applications. Figure 3 Examples include more gradient vectors, and a gradient vector may conflict with multiple other gradient vectors. For example, At the same time with , In the event of a gradient conflict, in this case, we can let First with Gradient mitigation is performed to obtain the updated... Determine the updated and Are there still conflicts? If so, then update... and Gradient mitigation is implemented.

[0115] As one possible implementation, the first gradient fusion vector is determined based on N updated gradients, including but not limited to the following steps:

[0116] Step S1101: Add the N updated gradient vectors together to obtain the second gradient fusion vector.

[0117] Specifically, it can be calculated using the following formula:

[0118] (Equation 3)

[0119] Among them, the updated vector This represents the updated gradient vector n. This represents the second gradient fusion vector.

[0120] Step S1102: Normalize the second gradient fusion vector to obtain the third gradient fusion vector.

[0121] Specifically, it can be calculated using the following formula:

[0122] (Equation 4)

[0123] in, This represents the third gradient fusion vector.

[0124] It should be understood that normalizing the second gradient fusion vector is equivalent to calculating the unit vector of the second gradient fusion vector, and then denoteing this unit vector as the third gradient fusion vector.

[0125] Step S1103: Determine the gradient fusion vector magnitude based on the vector with the largest gradient magnitude among the N updated gradient vectors.

[0126] Specifically, it can be calculated using the following formula:

[0127] (Equation 5)

[0128] in, Denotes the gradient in the t-th iteration. amplitude, This represents the magnitude of the gradient fusion vector in the t-th iteration.

[0129] It should be understood that this application proposes a gradient magnitude balancing design to alleviate the problem of large gradient magnitudes dominating the update process. Since mask optimization in this application is based on gradient descent for iterative updates, determining an appropriate gradient magnitude or step size is crucial to the algorithm's convergence speed and final performance. A larger gradient magnitude can accelerate convergence, while reducing the gradient magnitude in subsequent iterations can fine-tune the results and find the Pareto optimal point. Based on the above idea, this application proposes that the balancing gradient magnitude for the t-th iteration is the maximum of multiple gradient magnitudes.

[0130] Step S1104: Determine the first gradient fusion vector based on the third gradient fusion vector and the magnitude of the gradient fusion vector.

[0131] It should be understood that summing the N updated gradient vectors yields the second gradient fusion vector, which determines the direction of the final first gradient fusion vector. Then, the second gradient fusion vector is normalized to obtain the unit vector in its direction (i.e., the third gradient fusion vector). Next, the equilibrium gradient magnitude of the t-th iteration is set to the maximum of the multiple gradient magnitudes to obtain the gradient fusion vector magnitude. Finally, multiplying the third gradient fusion vector by the gradient fusion vector magnitude determines the final first gradient fusion vector. This process achieves gradient balancing across multiple objectives, thereby improving optimization efficiency and the performance of the optimized mask.

[0132] like Figure 3 As shown in (4) above, the updated gradient vector and Add them together to get the gradient vector. Then determine and The maximum amplitude value in, here The amplitude value is the maximum value; finally, in The direction determines the final gradient fusion vector. , The amplitude value is equal to The amplitude value, such as Figure 3 As shown in (5) of the text.

[0133] It should be understood that as chip technology nodes continue to shrink, lithography precision faces significant challenges. Optical mask optimization technology is crucial for ensuring wafer pattern fidelity, improving chip performance, and reducing production costs, and is a key step in achieving high-precision chip manufacturing. In actual lithography, perturbations in process parameters can severely affect the imaging quality of the final wafer pattern, reducing chip production yield. This application's embodiments introduce multi-objective optimization theory, combined with the basic principles of lithography models, to consider the effects of various process parameter perturbations during mask optimization, improving the quality and robustness of masks with different levels of complexity. Furthermore, this application's embodiments explore fast gradient update calculation methods and efficient mask correction from two aspects: utilizing multi-GPU deployment and efficient algorithm design.

[0134] The methods of the embodiments of this application have been described above. The system of the embodiments of this application is provided below.

[0135] Please see Figure 4 , Figure 4 This is a schematic diagram of a multi-objective robust optimization system for photolithography masks provided in an embodiment of this application. This system has the function of implementing the multi-objective robust optimization method for photolithography masks provided in any of the above embodiments. The function can be implemented in hardware or by hardware executing corresponding software. The hardware or software includes one or more modules corresponding to the above functions.

[0136] In one possible implementation, the lithography mask multi-objective robust optimization system includes:

[0137] The determination module is used to determine the wafer pattern obtained by the initial mask under N process parameters based on the photolithography simulation model, where N is an integer greater than 1;

[0138] The module is used to construct N loss functions based on the deviation between the wafer pattern obtained from various process parameters and the target pattern, with each loss function corresponding to a process parameter.

[0139] The iterative optimization module is used to perform multiple rounds of iterative optimization on the initial mask until all loss functions converge and reach equilibrium, resulting in the optimized mask.

[0140] It should be noted that the information interaction and execution process between the above modules / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0141] See Figure 5 This application also provides a computer device 300. The computer device 300 may be a server or a terminal, and its internal structure includes, but is not limited to:

[0142] Memory 310 is used to store programs;

[0143] The processor 320 is used to execute the program stored in the memory 310. When the processor 320 executes the program stored in the memory 310, the processor 320 is used to execute the photolithography mask multi-objective robust optimization method as in any of the preceding embodiments.

[0144] The processor 320 and memory 310 can be connected via a bus or other means.

[0145] The memory 310, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs, such as the photolithography mask multi-objective robust optimization method described in any embodiment of this application. The processor 320 implements the photolithography mask multi-objective robust optimization method as described in any of the preceding embodiments by running the non-transitory software program and instructions stored in the memory 310.

[0146] The memory 310 may include a program storage area and a data storage area. The program storage area may store the operating system and application programs required for at least one function. The data storage area may store the execution of the aforementioned photolithographic mask multi-objective robust optimization method. Furthermore, the memory 310 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory 310 may optionally include memory remotely located relative to the processor 320, and these remote memories may be connected to the processor 320 via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0147] The non-transient software program and instructions required to implement the above-described multi-objective robust optimization method for photolithography masks are stored in memory 310. When executed by one or more processors 320, the multi-objective robust optimization method for photolithography masks provided in any embodiment of this application is executed.

[0148] This application also provides a computer-readable storage medium storing computer-executable instructions for executing the above-described photolithography mask multi-objective robust optimization method.

[0149] In one embodiment, the storage medium stores computer-executable instructions that are executed by one or more control processors, such as one or more processors 320 in the computer device 300, which can cause the one or more processors 320 to perform the photolithographic mask multi-objective robust optimization method provided in any embodiment of this application.

[0150] The embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0151] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically include computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0152] Furthermore, one embodiment of this application also provides a computer program product, including a computer program that, when executed by a processor, implements the photolithographic mask multi-objective robust optimization method as described in any of the preceding embodiments.

[0153] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0154] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The protection scope of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in this application, or make equivalent substitutions for some of the technical features. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the protection scope of this application.

Claims

1. A robust multi-objective optimization method for photolithographic masks, characterized in that, The method includes the following steps: Based on the photolithography simulation model, the wafer patterns obtained by the initial mask under N process parameters are determined respectively, where N is an integer greater than 1; Based on the deviation between the wafer pattern and the target pattern obtained from various process parameters, N loss functions are constructed, each loss function corresponding to one of the process parameters; The initial mask is iteratively optimized in multiple rounds until all loss functions converge and reach equilibrium, resulting in the optimized mask. Each round of iterative optimization includes: Obtain the gradient vectors corresponding to the N loss functions respectively; Gradient conflict pairs are determined from the N gradient vectors, and conflict mitigation is performed on each gradient conflict pair; After mitigating the conflicts of all the gradient conflict pairs, the updated gradient vectors corresponding to each gradient vector are obtained. The N updated gradient vectors are summed to obtain the second gradient fusion vector; The second gradient fusion vector is normalized to obtain the third gradient fusion vector; The gradient fusion vector magnitude is determined based on the vector with the largest gradient magnitude among the N updated gradient vectors. The first gradient fusion vector is determined based on the third gradient fusion vector and the magnitude of the gradient fusion vector; The parameters in the initial mask are updated based on the first gradient fusion vector.

2. The method according to claim 1, characterized in that, Determining gradient conflict pairs from the N gradient vectors includes: A gradient vector set is constructed by randomly selecting a portion of the gradient vectors from the N gradient vectors. The gradient conflict pairs are determined from the set of gradient vectors.

3. The method according to claim 1 or 2, characterized in that, The determination of gradient conflict pairs includes: If the angle between two gradient vectors is greater than 90°, then the two gradient vectors are determined to be the gradient conflict pair.

4. The method according to claim 3, characterized in that, The conflict mitigation for each of the gradient conflict pairs includes: The two gradient vectors in the gradient conflict pair are respectively denoted as the first gradient vector and the second gradient vector; Calculate the first projection of the first gradient vector onto the orthogonal direction of the second gradient vector, and obtain the updated gradient vector corresponding to the first gradient vector based on the first projection; Calculate the second projection of the second gradient vector onto the orthogonal direction of the first gradient vector, and obtain the updated gradient vector corresponding to the second gradient vector based on the second projection.

5. The method according to claim 1, characterized in that, The determination of wafer patterns obtained from the initial mask under N process parameters based on the photolithography simulation model includes: For each of the process parameters, the K lithography kernels corresponding to the process parameters are subjected to a dot product weighted operation with the initial mask to obtain a lithography intensity map; The photolithography intensity map is processed based on the photolithography simulation model to obtain the wafer pattern corresponding to the process parameters.

6. A multi-objective robust optimization system for photolithographic masks, characterized in that, include: The determination module is used to determine the wafer pattern obtained by the initial mask under N process parameters based on the photolithography simulation model, where N is an integer greater than 1; The construction module is used to construct N loss functions based on the deviation between the wafer pattern and the target pattern obtained from various process parameters, and each loss function corresponds to one of the process parameters; The iterative optimization module is used to perform multiple rounds of iterative optimization on the initial mask until all the loss functions converge and reach equilibrium, thus obtaining the optimized mask. Each round of iterative optimization includes: Obtain the gradient vectors corresponding to the N loss functions respectively; Gradient conflict pairs are determined from the N gradient vectors, and conflict mitigation is performed on each gradient conflict pair; After mitigating the conflicts of all the gradient conflict pairs, the updated gradient vectors corresponding to each gradient vector are obtained. The N updated gradient vectors are summed to obtain the second gradient fusion vector; The second gradient fusion vector is normalized to obtain the third gradient fusion vector; The gradient fusion vector magnitude is determined based on the vector with the largest gradient magnitude among the N updated gradient vectors. The first gradient fusion vector is determined based on the third gradient fusion vector and the magnitude of the gradient fusion vector; The parameters in the initial mask are updated based on the first gradient fusion vector.

7. A computer device, characterized in that, include: Memory, used to store programs; A processor for executing a program stored in the memory, wherein when the processor executes the program stored in the memory, the processor is configured to perform the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The device stores computer-executable instructions for performing the method as described in any one of claims 1 to 5.

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