SMO method based on abbe-hopkins unified framework
Patent Information
- Application Number
- CN202611197148.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-07
- Publication Date
- 2026-11-03
AI Technical Summary
Existing light source mask optimization methods suffer from mismatch and computational redundancy issues introduced by the optimization between models, leading to a decrease in lithography performance.
We employ the Abbe-Hopkins unified framework, perform fast optical imaging calculations through convolution using the Hopkins kernel function, optimize light source intensity by combining sparse hotspots and the TF-Hopkins model, and achieve collaborative optimization of the light source and mask using gradient descent and the chain rule.
It avoids systematic errors introduced by model inconsistency, stably converges to the global optimum, improves computational efficiency and lithography performance, expands the exposure focus and process window, and enhances the yield and stability of chip manufacturing.
Smart Images
Figure CN123029754A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of semiconductor manufacturing technology, and in particular to an SMO method based on the Abbe-Hopkins unified framework. Background Technology
[0002] In the post-Moore's Law era, to meet the demands for smaller chip feature sizes and ever-increasing performance, photolithography calculations are required during chip design and manufacturing. Due to various limitations in photolithography technology, the smallest achievable feature size per pattern has reached its limit. Furthermore, with increasing design scale requirements, the demands on photolithography resolution are rising, making the research of more efficient resolution enhancement algorithms in photolithography an inevitable trend. Source Mask Optimization (SMO), as an advanced resolution enhancement technique, can simultaneously optimize both the illumination source and the mask. Compared to traditional resolution enhancement methods, it offers greater freedom, enabling optimization schemes that approach the global optimum. SMO has become a key technology for improving process windows in chip manufacturing.
[0003] SMO (Simulation Modeling) iterates between two optimization stages: Mask Optimization (MO) and Source Optimization (SO), using both the Abbe and Hopkins models for lithography calculations. The Abbe model models the extended light source as a series of independent point sources, calculates the intensity pattern of each point source on the image plane, and incoherently superimposes the intensity contributions of all point sources to obtain the overall spatial intensity distribution. It is advantageous for simulating optical systems with dynamically changing illumination and projection parameters and is commonly used to characterize optical systems and address source optimization problems. The Hopkins model, on the other hand, mathematically rewrites the Abbe model, decoupling the transmission properties of the optical system from the mask function. The Hopkins model is suitable for imaging calculations with different masks under fixed light source and projection parameters, and offers a significant speed improvement over the Abbe model. Therefore, in industrial software systems, these two models are often integrated into different software architectures. This model separation makes cross-model verification difficult and inefficient.
[0004] In existing technologies, different physical models or approximation methods are typically used to improve the computational efficiency of MO and SO. This leads to model mismatch issues after the introduction of models during the optimization process, making it difficult for alternating optimization to truly converge to the global optimum, ultimately affecting lithography performance. Furthermore, in existing SMO methods, the MO and SO steps are usually executed in an alternating iterative manner. This results in the mask already being in an optimal imaging state when the MO stage converges, while the subsequent SO stage generates a large amount of redundant computation on the already well-imaged mask region. Therefore, existing light source-mask co-optimization methods lead to problems such as optimization mismatch between models and redundant optimization computation. Summary of the Invention
[0005] The purpose of this invention is to provide a solution that addresses the shortcomings of the aforementioned background technology by resolving issues such as model mismatch and computational redundancy in existing light source mask optimization methods.
[0006] To achieve the above objectives, the present invention provides a method for collaborative optimization of light source masks, comprising the following steps: S1, initialize the basic parameters of the integrated circuit photolithography process, and obtain the initial light source distribution and initial mask pattern; S2, based on the basic parameters, the MO stage obtains the pre-generated Hopkins kernel function under the Abbe-Hopkins unified framework; S3 utilizes the convolution of the mask pattern with the Hopkins kernel function to perform fast optical imaging calculations, performs mask optimization, and iteratively optimizes to obtain the converged mask pattern; In the S4 and SO stages, the set of points whose errors exceed a preset threshold in the converged mask pattern is determined based on the converged light intensity distribution, and the set of points is determined as a sparse hot spot set. S5, based on hotspots in a sparse hotspot set, uses the TF-Hopkins model to quickly calculate the intensity of hotspot imaging within the Abbe-Hopkins unified framework; S6. Define the loss function with the hot spot light intensity and the target value, determine the gradient of the loss function with respect to the light source intensity based on the chain rule, and update the light source intensity using the gradient descent method to obtain the converged light source intensity distribution. S7 uses the SMO convergence index to judge the converged mask pattern and the converged light source intensity. When both the converged mask pattern and the converged light source intensity satisfy the SMO convergence index, the converged mask pattern and the converged light source intensity are output as the collaborative optimization result.
[0007] Furthermore, S3 utilizes convolution of mask patterns with the Hopkins kernel function for fast optical imaging calculations, including: The mask transmission function is fast convolved with the Hopkins kernel function in the frequency domain to calculate the full-field light intensity distribution.
[0008] Furthermore, in S4, based on the converged light intensity distribution, the set of points in the converged mask pattern whose errors exceed a preset threshold is determined, and this set of points is identified as a sparse hotspot set, including: The converged light intensity distribution is compared with the target image, and sampling points with errors exceeding a preset threshold are selected from the image contour point set.
[0009] Furthermore, in S5, based on hotspots in a sparse hotspot set, and within the Abbe-Hopkins unified framework, the TF-Hopkins model is used for rapid calculation of hotspot imaging intensity, including: The TF-Hopkins model is used to optimize the light source and transform it into a linear representation of the light source intensity, enabling rapid calculation of hotspot light intensity, including: Construct an offset mask function based on hotspots in a sparse hotspot set; Construct a point spread function, multiply the point spread function with the offset mask function point by point, and perform a two-dimensional Fourier transform and vectorization to obtain a frequency domain vector; Construct a weight vector based on the frequency domain vector; Based on the weight vector, the hot spot light intensity is represented as a linear form of the light source intensity; Furthermore, S6 includes: Construct a weighted squared error loss function; The gradient of the loss function with respect to the light source is calculated using the chain rule; The light source intensity is updated using the gradient descent method; Determine whether the light source intensity meets the convergence condition. If it does, output the converged light source intensity distribution. If it does not, continue iterating until convergence.
[0010] This invention also provides a method for constructing the Abbe-Hopkins unified framework, comprising the following steps: S01, determine a unified spatial sampling grid and frequency sampling grid; S02, based on a unified spatial sampling grid and a unified frequency sampling grid, obtain the intensity distribution data of the illumination source, the transmittance distribution data of the mask pattern, and the frequency domain characterization data of the point spread function or pupil function of the projection optical system, respectively. S03, based on the intensity distribution data of the illumination source and the frequency domain characterization data of the point spread function or pupil function of the projection optical system, perform Abbe imaging simulation under a unified frequency sampling grid and obtain the TCC operator on the pupil surface; S04. Perform eigenvalue decomposition on the TCC operator, extract a preset number of eigenfunctions and their corresponding eigenvalues, and determine all extracted eigenfunctions as the Hopkins kernel function of the Abbe-Hopkins unified framework, thus completing the construction of the Abbe-Hopkins unified framework.
[0011] Furthermore, in S02, the frequency domain characterization data of the point spread function or pupil function of the projection optical system are obtained, including: Constructing the first linear operator It satisfies the following relationship:
[0012] in, This indicates a window cutoff due to limited space. This indicates frequency domain finite window truncation. and These represent the Fourier transform and the inverse Fourier transform, respectively. Applying the constructed first linear operator to the starting point spread function yields a point spread function that is simultaneously constrained in both the spatial and spectral domains. Performing a Fourier transform on the simultaneously constrained point spread function yields the corresponding pupil function that is simultaneously constrained in both the spatial and frequency domains. Alternatively, construct a second linear operator. The second linear operator satisfies the following relation:
[0013] The constructed second linear operator is applied to the initial pupil function to obtain a pupil function that is simultaneously constrained in both the spatial and spectral domains. An inverse Fourier transform is then performed on the simultaneously constrained pupil function to obtain the corresponding point spread function that is simultaneously constrained in both the spatial and frequency domains.
[0014] Furthermore, in S04, the TCC operator is modified using the Lanczos tridiagonalization method. Perform eigenvalue decomposition, including: Generate initial block vector Set the initial parameters for iteration. , The initial block vector is normalized to obtain the normalized vector. The expression is: ; Set iteration metrics The Lanczos tridiagonalization method is iterated and looped based on the iterative index. After the iteration is completed, we get Real symmetric tridiagonal matrix For real symmetric tridiagonal matrix Perform standard feature decomposition; Before selection The largest eigenvalues and corresponding feature vectors Construct intrinsic kernel functions The expression is:
[0015] in, The linear transformation matrix representing the Lanczos vector; The TCC operator, determined based on the intrinsic kernel function, is expressed as follows:
[0016] in, Describes an optical system, from a point Time The coherent transport characteristics, This represents the conjugate transpose of a matrix.
[0017] Furthermore, the Lanczos tridiagonalization method is iterated and looped based on the iterative index, including: Calculate the matrix-vector product of the TCC operator and the Lanczos vector. The expression is:
[0018] Calculate the diagonal elements of a triangular matrix The expression is:
[0019] matrix-vector product To perform orthogonalization, the expression is:
[0020] in, Let be the second diagonal element of a tridiagonal matrix, and
[0021] Calculate the second diagonal element If the second diagonal element If the condition is met, the current loop terminates and the algorithm restarts; otherwise, the next iteration vector is generated, satisfying the following relation:
[0022] After the iteration is completed, we get Real symmetric tridiagonal matrix The expression is: .
[0023] Furthermore, for real symmetric tridiagonal matrices Perform standard eigenvalue decomposition, the expression is:
[0024] in, Represents the eigenvector matrix, This represents the conjugate transpose of a matrix. Let represent the eigenvalue diagonal matrix, and .
[0025] The above-described solution of the present invention has the following beneficial effects: The SMO method based on the Abbe-Hopkins unified framework provided by this invention achieves light source mask optimization through the Abbe-Hopkins unified framework, ensuring that MO and SO are performed under completely identical physical models and numerical conditions, fundamentally avoiding system errors introduced by model inconsistency. From the perspective of system performance, the Abbe-Hopkins unified framework ensures that the alternating optimization algorithm can stably converge to the global optimum, avoiding oscillations or divergences caused by model switching. From the perspective of computational efficiency, in the MO stage, efficient feature decomposition of the TCC operator is performed based on Lanczos to obtain an efficient Hopkins kernel function. The mask is then rapidly convolved with the Hopkins kernel function for optical imaging calculation, achieving efficient computation of the Hopkins model. In the SO stage, a fast TF-Hopkins model is used to precisely control the light source by utilizing sparse hotspots. The optimized process achieves the optimal solution in terms of computational efficiency and physical accuracy, thereby significantly expanding the exposure focus and process window, and improving the yield and stability of chip manufacturing. Other beneficial effects of the present invention will be described in detail in the following detailed description section. Attached Figure Description
[0026] Figure 1 This is a flowchart illustrating the overall steps of the present invention; Figure 2 This is a flowchart of the iterative loop of the Lanczos tridiagonalization method based on iterative indices according to the present invention. Detailed Implementation
[0027] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.
[0028] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.
[0029] It should also be noted that the illustrations provided in the following embodiments are merely schematic representations of the basic concept of this disclosure. The illustrations only show components relevant to this disclosure and are not drawn according to the actual number, shape, and size of components in implementation. In actual implementation, the type, quantity, and proportion of each component can be arbitrarily changed, and the component layout may be more complex. Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.
[0030] like Figure 1 As shown, embodiments of the present invention provide a method and system for collaborative optimization of light source masks, comprising the following steps: S1 initializes the basic parameters of the integrated circuit photolithography process, and obtains the initial light source distribution and initial mask pattern.
[0031] In this embodiment, S1 provides physically accurate and numerically executable initial conditions for all subsequent calculations, including several key sub-tasks such as physical abstraction and numerical discretization of the basic parameters of the circuit lithography process and initial pattern generation.
[0032] S2, based on the basic parameters, obtains the pre-generated Hopkins kernel function under the Abbe-Hopkins unified framework in the MO stage.
[0033] In this embodiment, the construction steps of the Abbe-Hopkins unified framework specifically include: determining a unified spatial sampling grid and a unified frequency sampling grid; based on the unified spatial sampling grid and the unified frequency sampling grid, acquiring the intensity distribution data of the illumination source, the transmittance distribution data of the mask pattern, and the frequency domain characterization data of the point spread function or pupil function of the projection optical system, respectively; performing Abbe imaging simulation under the unified frequency sampling grid according to the intensity distribution data of the illumination source and the frequency domain characterization data of the point spread function or pupil function of the projection optical system, and obtaining the TCC operator on the pupil surface; performing feature decomposition on the TCC operator, extracting a preset number of eigenfunctions and their corresponding eigenvalues, and determining all extracted eigenfunctions as the Hopkins kernel function of the Abbe-Hopkins unified framework, thus completing the construction of the Abbe-Hopkins unified framework.
[0034] It should be noted that the construction process of the point spread function includes one of the following two methods: Method 1, constructing the first linear operator. The expression is as follows:
[0035] in, This indicates a window cutoff due to limited space. This indicates frequency domain finite window truncation. This represents the inverse Fourier transform. The first linear operator constructed... The point spread function is applied to the starting point spread function to obtain a point spread function that is both spatially and spectrally constrained. If necessary, a Fourier transform is then performed to convert the obtained point spread function, which is both spatially and spectrally constrained, into the corresponding pupil function.
[0036] Method 2: Construct a second linear operator, as shown in the following expression:
[0037] The constructed second linear operator is applied to the initial pupil function to obtain a pupil function that is both spatially and spectrally restricted. If necessary, an inverse Fourier transform is then performed to convert the obtained spatially and spectrally restricted pupil function into the corresponding point spread function.
[0038] In this embodiment, the TCC operator is constructed based on the traditional Hopkins model, which is a positive definite Hermitian operator that acts on... Block vector, expressed as:
[0039] in, Represents the TCC operator. Indicates that the incident light is In the polarized component of the emitted (or transmitted) light The propagation of polarization components, Indicates the incident light is When the polarization component is in the emitted light Kernel function of polarization component, Indicates that the incident light is When the polarization component is in the emitted light Kernel function of polarization component, Indicates that the incident light is When the polarization component is in the emitted light Kernel function of polarization component, Indicates the corresponding point.
[0040] In this embodiment, the process of obtaining the kernel function by eigenvalue decomposition of the TCC operator using the Lanczos tridiagonalization method is as follows: Generate initial block vector Set the initial parameters for iteration. , The initial block vector is normalized to obtain the normalized vector. The expression is as follows:
[0041] It should be noted that, , It does not appear directly in the formula, but is set to zero as a historical term in the recursion to ensure the correctness of subsequent iterations.
[0042] Set iteration metrics Based on the iterative index, an iterative loop is performed using the Lanczos tridiagonalization method. Please also refer to [the relevant documentation / reference]. Figure 2 This step includes: Calculate the matrix-vector product of the TCC operator and the Lanczos vector. The expression is:
[0043] Calculate the diagonal elements of a triangular matrix The expression is:
[0044] matrix-vector product To perform orthogonalization, the expression is:
[0045] in, Let be the second diagonal element of a tridiagonal matrix, and
[0046] Calculate the second diagonal element If the second diagonal element If the condition is met, the current loop terminates and the algorithm restarts; otherwise, the next iteration vector is generated, satisfying the following relation:
[0047] After the iteration is completed, we get Real symmetric tridiagonal matrix The expression is as follows:
[0048] In this embodiment, for a real symmetric tridiagonal matrix Perform standard eigenvalue decomposition, as shown in the following expression:
[0049] in, Represents the eigenvector matrix, This represents the conjugate transpose of a matrix. Let represent the eigenvalue diagonal matrix, and , Represents the eigenvalue.
[0050] Before selection The largest eigenvalues and corresponding feature vectors Construct intrinsic kernel functions The expression is as follows:
[0051] in, Let represent the linear transformation matrix. Therefore, the TCC operator obtained from the representation is determined based on the intrinsic kernel function, and its expression is as follows:
[0052] It should be noted that this expression represents the eigenvalue approximation decomposition process of the TCC operator. Describes an optical system, from a point Time The coherent transfer characteristics of the TCC operator encompass all coherent information about the light source, mask, and projection. This expression allows us to obtain the output kernel function of the TCC operator. That is, the Hopkins kernel function.
[0053] S3 utilizes the convolution of the mask pattern with the Hopkins kernel function to perform fast optical imaging calculations, performs mask optimization, and iteratively optimizes to obtain the converged mask pattern.
[0054] In this embodiment, the mask transmission function and the Hopkins kernel function are subjected to fast frequency domain convolution to calculate the full-field light intensity distribution. The expression is:
[0055] in, This represents the mask transmission function, which describes the transmission function of each point on the mask plane. Modulation of the complex amplitude of the incident light.
[0056] Therefore, in this embodiment, the convergence of mask optimization is determined by performing a fast frequency-domain convolution between the mask transmission function and the Hopkins kernel function. If convergence is not achieved, iteration continues; if convergence is achieved, iteration stops, and the converged light intensity distribution and the converged mask pattern are output. Specifically, the convergence of mask optimization can be determined based on changes in the mask pattern: in two consecutive iterations, the mask transmission function... The change in intensity, such as the pixel flip ratio or root mean square error, is below a preset threshold; changes in light intensity distribution: calculate the light intensity of the current iteration and the previous iteration. If the difference is less than a threshold, convergence is considered achieved; the objective function is stable: if the optimization process minimizes a certain objective, such as light intensity error, it stops when the objective function value no longer decreases or the decrease is extremely small after several consecutive iterations. Of course, if the maximum number of iterations is reached, it can be forcibly stopped to prevent infinite loops.
[0057] In the S4 and SO stages, the set of points whose errors exceed a preset threshold in the converged mask pattern is determined based on the converged light intensity distribution, and the set of points is identified as a sparse hot spot set.
[0058] In this embodiment, the converged light intensity distribution is compared with the target image, and the light intensity distribution is compared with the target image contour point set. Sampling points with errors exceeding a preset threshold are selected based on the following relationship:
[0059] in, This represents the selected set of points, i.e., the set of hotspots. Represents the set of points representing the outline of a figure A single sampling point in the middle, Indicates the light intensity threshold. This indicates the allowable error, thus retaining the selected hotspot set as a sparse hotspot set.
[0060] S5, based on hotspots in a sparse hotspot set, utilizes the TF-Hopkins model, i.e., the Hopkins model without TCC decomposition (TCC-FreeHopkins, TF-Hopkins), within the Abbe-Hopkins unified framework to rapidly calculate hotspot imaging intensity.
[0061] In this embodiment, the TF-Hopkins model is used to optimize the light source and transform it into a linear representation of the light source intensity, enabling rapid calculation of the hotspot light intensity. Specifically, this includes: The offset mask function is constructed based on the hotspots in the sparse hotspot set, as shown in the following expression:
[0062] in, Indicates hot topics The offset mask function is equal to the original mask function in coordinates. The value at that location.
[0063] Construct a point spread function, multiply the point spread function by the offset mask function point by point, and perform a two-dimensional Fourier transform and vectorization to obtain the frequency domain vector, as shown in the following expression:
[0064] in, Represents a frequency domain vector. Represents the point spread function. Indicates Fourier transform, Vectorization is represented.
[0065] The weight vector is constructed based on the frequency domain vector, as shown in the following expression:
[0066] in, Represents the weight vector. Indicates the component index of the vector.
[0067] Based on the weight vector, the hotspot light intensity is represented as a linear form of the light source intensity, as shown in the following expression:
[0068] in, express The intensity of the hot spot light, It represents the light source intensity, and thus outputs the hot spot light intensity in a linear form based on the light source intensity.
[0069] Therefore, in the SO process, the light intensity of each hotspot is simply represented as the dot product of the light source intensity and the hotspot coefficient vector in the mask, thus transforming the SO problem into a linear representation of the light source intensity. The TF-Hopkins model makes each light source update involve only a small amount of computation, significantly improving computational efficiency. Furthermore, the application of the TF-Hopkins model is not limited to the SMO optimization process; it is applicable to all imaging processes involving a single point in the mask, such as verifying the consistency between Abbe and Hopkins calculation results by randomly sampling points.
[0070] S6 defines the loss function based on the hot spot light intensity and the target value, determines the gradient of the loss function with respect to the light source intensity based on the chain rule, and updates the light source intensity using the gradient descent method to obtain the converged light source intensity distribution.
[0071] It should be noted that the light source intensity distribution is defined as a discretized light source intensity distribution function within the pupil plane. Therefore, this step specifically includes: The weighted squared error loss function is constructed as follows:
[0072] in, Indicates the first The proportion coefficient of each hotspot is used to adjust the contribution ratio of different hotspots in the loss function. This represents the light intensity threshold.
[0073] The gradient of the loss function with respect to the light source is calculated using the chain rule, and the expression is as follows:
[0074] in, This indicates the sensitivity of the hot spot light intensity to the intensity of the light source.
[0075] The light source intensity is updated using the gradient descent method, as shown in the following expression:
[0076] in, Indicates the number of iterations. This represents the learning rate. This method is used to determine whether the light source intensity meets the convergence condition. If it does, the converged light source intensity distribution is output; otherwise, iterative convergence continues.
[0077] S7 uses the SMO convergence index to judge the converged mask pattern and the converged light source intensity. When both the converged mask pattern and the converged light source intensity satisfy the SMO convergence index, the converged mask pattern and the converged light source intensity are output as the collaborative optimization result.
[0078] In this embodiment, the global convergence index is determined based on the preset number of iterations. If the SMO convergence index is met, the convergence iteration is stopped, and the converged mask pattern and the converged light source intensity are output as the collaborative optimization result. If the SMO convergence index is not met, the mask optimization is performed again in S3 with the converged light source intensity until the convergence condition is met.
[0079] Therefore, the light source mask collaborative optimization method provided in this embodiment implements SMO through a unified framework of traditional Hopkins and TF-Hopkins, ensuring that MO and SO are performed under completely identical physical models and numerical conditions, fundamentally avoiding system errors introduced by model inconsistency. From the perspective of system performance, the unified framework ensures that the alternating optimization algorithm can stably converge to the global optimum, avoiding oscillations or divergences caused by model switching. From the perspective of computational efficiency, in the MO stage, efficient feature decomposition of the TCC operator based on Lanczos is performed to obtain an efficient Hopkins kernel. Optical imaging calculations are performed by fast convolution of the mask and the Hopkins kernel, realizing efficient computation of the Hopkins model. In the SO stage, a fast TF-Hopkins model is used to accurately control the light source by utilizing sparse hotspots. The optimized process achieves the optimal solution in terms of computational efficiency and physical accuracy, thereby significantly expanding the exposure focus and process window, and improving the yield and stability of chip manufacturing.
[0080] Based on the same inventive concept, this embodiment also provides a light source mask collaborative optimization system, including a parameter and graphics initialization module, and an Abbe module. The Hopkins unified framework includes modules for building the mask, full-image imaging, hotspot extraction and analysis, hotspot intensity calculation, light source gradient optimization, and collaborative convergence judgment and result output. The parameter and pattern initialization module loads and verifies basic lithography parameters, reads or generates initial light source intensity distributions and initial mask patterns, and outputs standardized data structures for direct use by subsequent modules. Hopkins Unified Framework Builder module is used to build Abbe The Hopkins unified framework includes: performing mask optimization based on the traditional Hopkins model, implementing the Lanczos tridiagonalization algorithm, performing feature decomposition on the TCC operator, and extracting a finite number of Hopkins kernel functions. The mask optimization and full-image imaging module receives the Hopkins kernel function and the current mask image, calculates the full-field light intensity distribution through kernel convolution for fast imaging, defines a cost function based on the difference between the light intensity and the target image, calculates the gradient, updates the mask using the optimization algorithm, iterates until convergence, and outputs the converged mask image and the corresponding light intensity distribution. In the light source optimization stage, the hotspot extraction and analysis module, based on the converged light intensity distribution from the mask stage, judges point by point according to a preset error threshold, filters all points that do not meet the requirements, and forms a sparse hotspot set. The hotspot intensity calculation module is based on Abbe. Hopkins unified framework, through TF The Hopkins model, for sparse hotspot coordinates, directly and rapidly calculates and outputs the hotspot light intensity point-by-point using the light source, mask spectrum, and pupil function. The light source gradient optimization module defines a loss function based on the hotspot light intensity and the target value, calculates the gradient of the loss with respect to the light source intensity distribution using the chain rule, updates the light source intensity using a constrained gradient descent method, iterates until convergence, and outputs the final optimized light source intensity distribution. The collaborative convergence judgment and result output module jointly judges the output converged mask pattern and the output converged light source intensity, and simultaneously records and outputs the final mask pattern, light source distribution, and key process indicators.
[0081] The system provided by this invention has the same inventive concept and beneficial effects as the aforementioned method, which will not be repeated here.
[0082] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0083] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.
Claims
1. An SMO method based on the Abbe-Hopkins unified framework, characterized in that, Includes the following steps: S1, initialize the basic parameters of the integrated circuit photolithography process, and obtain the initial light source distribution and initial mask pattern; S2, based on the basic parameters, the MO stage obtains the pre-generated Hopkins kernel function under the Abbe-Hopkins unified framework; S3 utilizes the convolution of the mask pattern with the Hopkins kernel function to perform fast optical imaging calculations, performs mask optimization, and iteratively optimizes to obtain the converged mask pattern; In the S4 and SO stages, the set of points whose errors exceed a preset threshold in the converged mask pattern is determined based on the converged light intensity distribution, and the set of points is determined as a sparse hot spot set. S5, based on hotspots in a sparse hotspot set, uses the TF-Hopkins model to quickly calculate the intensity of hotspot imaging within the Abbe-Hopkins unified framework; S6. Define the loss function with the hot spot light intensity and the target value, determine the gradient of the loss function with respect to the light source intensity based on the chain rule, and update the light source intensity using the gradient descent method to obtain the converged light source intensity distribution. S7 uses the SMO convergence index to judge the converged mask pattern and the converged light source intensity. When both the converged mask pattern and the converged light source intensity satisfy the SMO convergence index, the converged mask pattern and the converged light source intensity are output as the collaborative optimization result.
2. The SMO method based on the Abbe-Hopkins unified framework according to claim 1, characterized in that, S3 utilizes convolution of mask patterns with Hopkins kernel functions for fast optical imaging calculations, including: The mask transmission function is fast convolved with the Hopkins kernel function in the frequency domain to calculate the full-field light intensity distribution.
3. The SMO method based on the Abbe-Hopkins unified framework according to claim 1, characterized in that, In S4, the set of points in the converged mask pattern whose errors exceed a preset threshold are determined based on the converged light intensity distribution, and this set of points is identified as a sparse hotspot set, including: The converged light intensity distribution is compared with the target image, and sampling points with errors exceeding a preset threshold are selected from the image contour point set.
4. The SMO method based on the Abbe-Hopkins unified framework according to claim 1, characterized in that, S5 uses hotspots from a sparse hotspot set and, within the Abbe-Hopkins unified framework, leverages the TF-Hopkins model for rapid calculation of hotspot imaging intensity, including: The TF-Hopkins model is used to optimize the light source and transform it into a linear representation of the light source intensity, enabling rapid calculation of hotspot light intensity, including: Construct an offset mask function based on hotspots in a sparse hotspot set; Construct a point spread function, multiply the point spread function with the offset mask function point by point, and perform a two-dimensional Fourier transform and vectorization to obtain a frequency domain vector; Construct a weight vector based on the frequency domain vector; Based on the weight vector, the hot spot light intensity is represented as a linear form of the light source intensity.
5. The SMO method based on the Abbe-Hopkins unified framework according to claim 1, characterized in that, S6 include: Construct a weighted squared error loss function; The gradient of the loss function with respect to the light source is calculated using the chain rule; The light source intensity is updated using the gradient descent method; Determine whether the light source intensity meets the convergence condition. If it does, output the converged light source intensity distribution. If it does not, continue iterating until convergence.
6. A method for constructing the Abbe-Hopkins unified framework, characterized in that, Includes the following steps: S01, determine a unified spatial sampling grid and frequency sampling grid; S02, based on a unified spatial sampling grid and a unified frequency sampling grid, obtain the intensity distribution data of the illumination source, the transmittance distribution data of the mask pattern, and the frequency domain characterization data of the point spread function or pupil function of the projection optical system, respectively. S03, based on the intensity distribution data of the illumination source and the frequency domain characterization data of the point spread function or pupil function of the projection optical system, perform Abbe imaging simulation under a unified frequency sampling grid and obtain the TCC operator on the pupil surface; S04. Perform eigenvalue decomposition on the TCC operator, extract a preset number of eigenfunctions and their corresponding eigenvalues, and determine all extracted eigenfunctions as the Hopkins kernel function of the Abbe-Hopkins unified framework, thus completing the construction of the Abbe-Hopkins unified framework.
7. The method for constructing the Abbe-Hopkins unified framework according to claim 6, characterized in that, In S02, the frequency domain characterization data of the point spread function or pupil function of the projection optical system are obtained, including: Constructing the first linear operator It satisfies the following relationship: in, This indicates a window cutoff due to limited space. This indicates frequency domain finite window truncation. and These represent the Fourier transform and the inverse Fourier transform, respectively. Applying the constructed first linear operator to the starting point spread function yields a point spread function that is simultaneously constrained in both the spatial and spectral domains. Performing a Fourier transform on the simultaneously constrained point spread function yields the corresponding pupil function that is simultaneously constrained in both the spatial and frequency domains. Alternatively, construct a second linear operator. The second linear operator satisfies the following relation: The constructed second linear operator is applied to the initial pupil function to obtain a pupil function that is simultaneously constrained in both the spatial and spectral domains. An inverse Fourier transform is then performed on the simultaneously constrained pupil function to obtain the corresponding point spread function that is simultaneously constrained in both the spatial and frequency domains.
8. The method for constructing the Abbe-Hopkins unified framework according to claim 6, characterized in that, In S04, the TCC operator is modified using the Lanczos tridiagonalization method. Perform eigenvalue decomposition, including: Generate initial block vector Set the initial parameters for iteration. , The initial block vector is normalized to obtain the normalized vector. The expression is: ； Set iteration metrics The Lanczos tridiagonalization method is iterated and looped based on the iterative index. After the iteration is completed, we get Real symmetric tridiagonal matrix For real symmetric tridiagonal matrix Perform standard feature decomposition; Before selection The largest eigenvalues and corresponding feature vectors Construct intrinsic kernel functions The expression is: in, The linear transformation matrix representing the Lanczos vector; The TCC operator, determined based on the intrinsic kernel function, is expressed as follows: in, Describes an optical system, from a point Time The coherent transport characteristics, This represents the conjugate transpose of a matrix.
9. The method for constructing the Abbe-Hopkins unified framework according to claim 8, characterized in that, The Lanczos tridiagonalization method is iterated based on iterative metrics, including: Calculate the matrix-vector product of the TCC operator and the Lanczos vector. The expression is: Calculate the diagonal elements of a triangular matrix The expression is: matrix-vector product To perform orthogonalization, the expression is: in, Let be the second diagonal element of a tridiagonal matrix, and Calculate the second diagonal element If the second diagonal element If the condition is met, the current loop terminates and the algorithm restarts; otherwise, the next iteration vector is generated, satisfying the following relation: After the iteration is completed, we get Real symmetric tridiagonal matrix The expression is: 。 10. The method for constructing the Abbe-Hopkins unified framework according to claim 8, characterized in that, Real symmetric tridiagonal matrix Perform standard eigenvalue decomposition, the expression is: in, Represents the eigenvector matrix, Represents the conjugate transpose of a matrix. Let represent the eigenvalue diagonal matrix, and .