A machine learning assisted phase shift mask proximity correction method

Abstract

The application discloses a machine learning assisted phase shift mask proximity correction method and belongs to the technical field of semiconductor lithography. The method comprises the following steps: obtaining an initial phase shift mask pattern and a target imaging pattern; constructing and training a physically guided forward imaging prediction model, wherein the model adopts a hybrid neural-physical double-branch architecture, the physical branch uses a learnable parameterized effective thin mask to approximately compensate for the thick mask effect, the main branch learns the residual error, and the fusion output predicts the spatial image; taking the forward model as a differentiable simulator, performing reverse correction under the manufacturability constraint by using the accompanying sensitivity and controlled random disturbance, and obtaining a final phase shift mask pattern; and outputting the mask pattern data after design rule checking and local fine-tuning. The application takes into account the physical consistency and data-driven flexibility of imaging prediction, improves the reverse optimization quality, considers the mask manufacturability constraint, and is suitable for proximity correction of phase shift masks in EUV lithography.

Description

Technical Field

[0001] This invention relates to the field of semiconductor lithography technology, and more specifically to a machine learning-assisted phase-shift mask proximity correction method. Background Technology

[0002] In advanced semiconductor manufacturing processes, extreme ultraviolet (EUV) lithography is one of the key technologies for achieving nanoscale feature sizes. Phase-shifting masks, by introducing transparent regions with different phases, enhance imaging contrast through the interference effect of light, effectively improving lithographic resolution and widening the process window. However, the mask thickness effect and shadowing effect caused by tilted illumination in EUV lithography significantly affect spatial image quality, making it difficult for proximity correction methods based on traditional scalar imaging models to accurately predict photoresist patterns. Existing reverse lithography techniques driven by rigorous electromagnetic field simulation, while achieving high accuracy, suffer from enormous computational overhead, making it difficult to meet the needs of large-scale layout optimization at the whole-chip level. On the other hand, deep learning-based reverse lithography methods still have shortcomings in terms of training data dependence and physical consistency; when the input mask state differs from the training distribution, prediction reliability may decrease. Therefore, a machine learning-assisted phase-shifting mask proximity correction method is urgently needed to address the problems in existing technologies. Summary of the Invention

[0003] The purpose of this invention is to provide a machine learning-assisted phase-shift mask proximity correction method that balances the physical consistency of imaging prediction with data-driven flexibility, improves the quality of reverse optimization, and takes into account mask manufacturability constraints, making it suitable for proximity correction of phase-shift masks in EUV lithography.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A machine learning-assisted phase-shift mask proximity correction method includes: Step 1: Obtain the initial phase-shift mask pattern to be corrected and the predefined target imaging pattern; Step 2: Construct and train a physical-guided forward imaging prediction model. The forward imaging prediction model adopts a hybrid neural-physical dual-branch architecture. The physical branch is constructed based on a learnable parameterized effective thin mask approximation model to compensate for EUV thick mask effects and shadow effects. The main branch uses multi-layer Fourier neural operators to learn the residual correction of the prediction results of the physical branch. Step 3: Using the forward imaging prediction model as a differentiable imaging simulator, construct the inverse correction process from the target imaging pattern to the phase shift mask pattern. Under the constraint of mask manufacturability, continuously relax and optimize the phase shift mask using the accompanying sensitivity information and controlled random perturbation, and discretize the optimization results to obtain the final phase shift mask pattern. Step 4: Perform design rule checks and local manufacturability refinements on the final phase-shift mask pattern, and output a mask pattern data file that conforms to manufacturing specifications.

[0005] Further, in step 1, the initial phase shift mask pattern to be corrected is obtained, specifically as follows: Connectivity labeling is performed on the binary matrix obtained by rasterizing the target map, and bright region polygons are extracted; each bright region polygon is shrunk inward by a predetermined width to obtain a 0° phase shift opening region. When the distance between adjacent bright areas is less than a preset threshold, a 180° phase-shifted strip is generated at the central axis of the dark area; the remaining area is set as an opaque area, thus forming a three-value pixel matrix, with pixel values ​​corresponding to the 0° phase-transparent area, the 180° phase-transparent area, and the opaque area, respectively.

[0006] Furthermore, in step 1, the target imaging pattern is a continuous value matrix, representing the intensity distribution of the photoresist pattern to be formed on the wafer.

[0007] Furthermore, in step 2, the physical branch is constructed based on the Abbe partially coherent imaging model. Its equivalent mask complex transmittance is obtained by multiplying the original mask matrix with the learnable phase compensation map and then convolving it with the learnable Gaussian blur kernel. The learnable phase compensation map is generated by the convolutional network with the original mask matrix as input, and the standard deviation of the learnable Gaussian blur kernel is a learnable parameter.

[0008] Furthermore, in step 2, the single-channel intensity map output by the physical branch is mapped to a multi-channel feature map through a series of convolutional layers, and then concatenated with the final output features of the main branch in the channel dimension. The predicted normalized spatial image intensity distribution is generated through a convolutional projection layer and a Sigmoid activation function.

[0009] Furthermore, in step 2, the loss function used for training the forward imaging prediction model includes data fidelity loss, physical consistency loss, frequency domain energy conservation loss, and distribution bridging loss; wherein the distribution bridging loss is a prediction consistency constraint of the model on the ternary mask input and its continuous version input with noise, which is used to reduce the distribution offset of the model when facing continuous value input in the reverse correction stage.

[0010] Furthermore, in step 3, the reverse correction process employs an adjoint sensitivity Langevin dynamics optimizer for iterative updates, and the update steps include: Calculate the gradient of the principal loss of the inverse problem with respect to the original mask; The accompanying physical sensitivity factor is constructed by using the sum of the predicted spatial image intensities relative to the mask sensitivity matrix, and then multiplied element-wise with the original gradient to obtain the effective gradient. The mask is updated according to an update formula that includes an effective gradient, dynamic step size, and temperature-controlled random term, and the pixel values ​​are constrained to a continuous interval by a projection operator.

[0011] Furthermore, the principal loss of the inverse problem is the mean square error between the predicted spatial image and the target image; the effective gradient is also superimposed with the gradients of the total variation regularization term and the binarization penalty term; the dynamic step size is adaptively adjusted according to the mean of the discrete Laplacian absolute value of the current mask; and the temperature coefficient is gradually reduced from the initial value according to the cosine annealing strategy.

[0012] Further, in step 4, the local manufacturability finishing includes: Detect width violations, spacing violations, and redundant phase conflict hotspots in the final phase shift mask pattern; For each hotspot, extract the local mask module and target block, and perform fine-tuning optimization with local fidelity, manufacturability constraints and edge continuity as loss terms under the boundary transition zone constraint to obtain the repaired local mask and write it back to the global mask.

[0013] In summary, the beneficial technical effects of the present invention are as follows: The method provided in this invention deeply integrates a learnable physical model with Fourier neural operators. Through a hybrid neural-physical dual-branch architecture, the forward imaging prediction model possesses both physically guided extrapolation capabilities and data-driven fitting accuracy. A parameterized, effective thin-mask approximation model can compensate for the thick-mask effect and shadowing effect unique to EUV with relatively low computational cost, while the backbone network only needs to learn the residuals predicted by the physical model, reducing learning difficulty and improving model stability. In the inverse correction stage, the optimization strategy incorporating accompanying sensitivity information and controlled random perturbations helps to escape local minima in non-convex mask optimization, obtaining a better phase-shift mask configuration. The distributed bridging loss added during training mitigates the distribution offset problem of the model during continuous relaxation optimization. Based on this, combined with design rule-driven local manufacturability refinement, the final output phase-shift mask pattern ensures both imaging accuracy and good manufacturing compliance, providing a feasible solution for the rapid and high-precision design of phase-shift masks in EUV lithography. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0016] like Figure 1 As shown, this invention provides a machine learning-assisted phase-shift mask proximity correction method, comprising: Step 1: Obtain the initial phase-shift mask pattern to be corrected and the predefined target imaging pattern; Step 2: Construct and train a physical-guided forward imaging prediction model. The forward imaging prediction model adopts a hybrid neural-physical dual-branch architecture. The physical branch is constructed based on a learnable parameterized effective thin mask approximation model to compensate for EUV thick mask effects and shadow effects. The main branch uses multi-layer Fourier neural operators to learn the residual correction of the prediction results of the physical branch. Step 3: Using the forward imaging prediction model as a differentiable imaging simulator, construct the inverse correction process from the target imaging pattern to the phase shift mask pattern. Under the constraint of mask manufacturability, continuously relax and optimize the phase shift mask using the accompanying sensitivity information and controlled random perturbation, and discretize the optimization results to obtain the final phase shift mask pattern. Step 4: Perform design rule checks and local manufacturability refinements on the final phase-shift mask pattern, and output a mask pattern data file that conforms to manufacturing specifications.

[0017] Next, the above steps will be explained in detail with reference to specific parameter settings: In step 1, the initial phase-shift mask pattern to be corrected and the predefined target imaging pattern are obtained, specifically as follows: This step is performed in a computer, which serves as a photolithography mask data processing device. The computer contains at least a central processing unit, a graphics processing unit, a memory, and multiple input / output interfaces. The memory contains the EUV lithography target layout file exported by the layout design tool. This file, in standard GDSII or OASIS format, stores the polygonal geometry information of each layer of the circuit design. The following is a detailed description of this process, including the following sub-steps: Step 101: Target layout reading and rasterization The computer reads the target layout file through an input interface, parses out all closed polygons belonging to the current metal or polysilicon layer to be corrected, and rasterizes these polygons into a uniformly sampled two-dimensional grid matrix. The grid size is determined by the minimum design linewidth in the layout and the expected proximity correction accuracy, and is taken as one-tenth of the design linewidth. For example, for an EUV lithography layer with a critical dimension of 20 nanometers, each grid pixel represents a physical size of 2 nanometers.

[0018] After rasterization, a binary target image matrix is ​​obtained, which can be formally represented as: ; The value is The pixel represents the bright area where a photoresist pattern is expected to be formed on the wafer, and the value is... The pixels represent the dark areas where the photoresist is expected to be preserved. The grid side length is 256 or 512.

[0019] Step 102: Smoothing of the target image To eliminate the stepped jagged edges produced during rasterization, the computer... Perform a Gaussian low-pass filter once to obtain the smoothed target image: ; in Gaussian filter kernel: ; The standard deviation is 0.7 times the grid pixel size. This is the cutoff radius. After filtering. Normalize each pixel value in Within the interval. This matrix represents the predefined target imaging pattern, used for subsequent fidelity evaluation.

[0020] Important correction notes: It is only used as an imaging target in subsequent loss calculations; the polygonal geometry operations of the initial mask are not based on Instead, it is based on the original binary matrix. This involves connected component analysis to avoid the contradiction of no closed boundaries in grayscale images.

[0021] Step 103: Geometric generation of the initial phase-shift mask pattern Computer based on original binary matrix (rather than) The polygon geometry in the () is used to generate the initial phase-shift mask. The specific process is as follows: (1) To Perform connected component labeling and extract all values. The set of closed polygons Each polygon is represented by a clockwise sequence of boundary vertices.

[0022] (2) For each bright area polygon It shrinks inward by a fixed width along its edge. This width is equal to the optimal phase boundary offset estimated by the optical proximity correction model in the EUV lithography process, typically 0.2 times the design linewidth (for a 20nm design linewidth). (pixels). The shrinkage operation is implemented through a polygon clipping algorithm: for Each edge is translated inwards The intersection is then calculated to obtain the shrunken polygon. Assign a value to all shrunken polygon regions. , representing the mask opening region where the transmission phase is 0°.

[0023] (3) Perform phase-shift auxiliary feature insertion on the dark areas between adjacent bright areas. For any pair of bright area polygons and Calculate its shortest Euclidean distance. .like Less than the preset phase shift auxiliary feature insertion threshold (Typical value is 1.5 times the design line width), then in and A phase-shifted stripe is generated along the midline of the dark area between the two polygons. Specifically, the midline segment between the two polygons is extracted using a Voronoi diagram, and its width is symmetrically expanded along both sides of the midline. (Typical value is 0.4 times the design line width), assign the value to the extended area. , representing the phase shift region with a transmission phase of 180°.

[0024] (4) Assign values ​​to all remaining regions that have not yet been assigned. , representing a completely opaque chromium film masking area.

[0025] The output of the above operation is the initial phase-shift mask pattern matrix: ; Step 104: Output and Connection obtained in this way and Together, they constitute the output of step 1. These two components are then passed to step 2 via computer memory to define the training data format, and in step 3, they serve as the optimization objective and initial solution, respectively. The meshing, connected component analysis, polygon clipping, and Voronoi diagram calculations involved in step 1 are all accelerated and executed in parallel by the graphics processor according to the Computing Unified Device Architecture (CUDA) to ensure rapid processing of large-scale layouts at the full chip level.

[0026] In step 2, a physically guided forward imaging prediction model is constructed and trained. This forward imaging prediction model employs a hybrid neural-physical dual-branch architecture, specifically: Step 2 is executed offline on a workstation equipped with a graphics processing unit. The input information for Step 2 is the mask pixel representation (three-valued) defined in Step 1. The format of the training data is defined by information such as the pixel resolution (2 nanometers / pixel). The specific values ​​are not directly involved in training. The output of step 2 is a fully trained neural network model file, containing all trainable parameters. After being fixed, it is stored in the memory for use in the reverse correction process of steps 3 and 4. The following is a detailed explanation of the content involved in step 2: 1. Task definition of forward imaging prediction model The model The mapping from the phase-shift mask pattern to the intensity distribution of the EUV lithography spatial image is established, formalized as follows: ; in: The input is the phase-shift mask pixel matrix; For all trainable parameters of the model; The predicted normalized spatial image intensity distribution; A uniform 256 pixels is used, corresponding to a 512nm×512nm mask area.

[0027] 2. Hybrid neural-physical dual-branch architecture This invention designs a hybrid neural-physical architecture, consisting of a main branch (a learnable Fourier neural operator) and a physical branch (an improved efficient thin mask approximation model) operating in parallel. The outputs of the two branches are fused in the latent space to produce the final prediction. The physical branch introduces two learnable parameterized correction terms, namely, a phase shift compensation map. and adaptive fuzzy kernel This allows it to compensate for the thick masking and shadowing effects unique to EUV; the main branches only need to learn the corrected residuals, greatly reducing the learning difficulty and improving the reliability of extrapolation. This architecture is not a simple combination of existing Fourier neural operators or thin mask approximations, but rather achieves deep coupling between the two through learnable physical parameterization and latent space fusion, which will be explained below: (1) Main branches: Multilayer Fourier neural operators The input mask matrix first passes through a pixel embedding layer implemented by 1×1 convolutions, which boosts the single channel to a higher resolution. Channels, yielding initial features: ; Then they passed through in turn. Fourier layer. The first... layer( The operation of ) is: ; in: and These are the two-dimensional discrete Fourier transform and its inverse; Discrete coordinates in the frequency domain; For the first Layer at frequency The complex-valued weight matrix at the point, where each element is a learnable parameter that acts independently for each frequency mode; It is a spatial bias vector that can be learned; This is the GELU activation function.

[0028] The total number of learnable parameters of a Fourier layer is (The real and imaginary parts of the complex-valued matrix), by truncating the high-frequency modes (keeping only the first part) (each frequency mode) controls the actual parameter quantity to approximately Within the limits of GPU memory capacity, the truncation strategy is to retain only those that meet the following conditions. The frequency components.

[0029] (2) Physical branch: Improved parameterized effective thin mask approximation model This invention proposes an efficient thin mask model for parametric shadow-thick mask compensation, which is constructed based on Abbe partially coherent imaging theory and introduces a learnable correction term. The correct Abbe imaging formula is: for each source point... After translation and pupil truncation, the mask diffraction spectrum undergoes inverse transformation to obtain the spatial amplitude. The square of the modulus is then integrated weighted by the light source intensity. Based on this, the expression for the physical branch is: ; in: This is the set of discrete sampling points for the EUV ring light source, with a sampling step size of [value missing]. ; To normalize the light source intensity distribution, the ring illumination parameter is the external coherence factor. Internal coherence factor ,Right now: ; For aberration-free systems, the pupil function is: ; Numerical aperture, EUV wavelength; For the equivalent mask complex transmittance, the following learnable mapping is used to obtain the original mask. get: ; in: For small convolutional networks (called phase compensation networks) The parameterized phase shift compensation diagram of the network is used to... For input, output and Continuous phase corrections of the same size. The network structure is: 3×3 convolution (1 input channel, 16 output channels) → GELU → 3×3 convolution (16→16) → GELU → 3×3 convolution (16→1, no activation), with a total number of parameters of approximately ; Gaussian blur convolution kernel: ; For learnable parameters, initialize to Pixels, simulating the blurring effect caused by limited resolution; This represents a two-dimensional convolution operation; The physical meaning is: the phase of the original mask ( Corresponding to 0°, The additional phase shift caused by the thick mask superimposed on the 180° area.

[0030] Output of the physics branch Instead of directly using it as the final image intensity, it is input into two consecutive 3×3 convolutional layers (32 channels each, GELU activated), mapping each channel to... Channel feature map: ; (3) Feature fusion and final output The final output features of the main Fourier layer With physical branch output By splicing along the channel dimension, we obtain Channel fusion features. Then, a 1×1 convolutional projection layer is used to compress it back to a single channel, followed by a Sigmoid activation function to output the predicted spatial image: ; This fusion approach allows the network to spontaneously decide where to rely on physical knowledge and where to rely on data-driven residual correction.

[0031] 3. Training Dataset Preparation The training data was generated using a mixed-precision EUV lithography simulation process, balancing accuracy and efficiency. (1) Random mask generation: In 0° and 180° open polygons are randomly placed on the mesh, with line widths ranging from 16nm (8 pixels) to 100nm (50 pixels) and random spacing (20nm to 200nm). Simultaneously, scattering stripes with widths ranging from 8nm to 16nm are randomly inserted as auxiliary features with a 30% probability. A total of 20,000 ternary mask samples are generated. .

[0032] (2) Layered simulation strategy: For each sample, a rigorous electromagnetic field solver based on the waveguide method (RCWA) is used to calculate its spatial image as a label. To balance computational efficiency and accuracy, a fast simulation using thin mask approximation and edge correction is employed for simple graphics with linewidths ≥ 40 nm; while a fully rigorous simulation is used for graphics with linewidths < 40 nm or containing phase-shift boundaries. This hierarchical strategy reduces the total simulation time from an estimated several thousand GPU hours to approximately 500 GPU hours.

[0033] (3) Simulation parameters: EUV light source NA=0.33, ring illumination , ,wavelength nm, principal incident angle (Represented by inclined plane wave incidence in rigorous simulation), the mask stack consists of a 70nm tantalum absorber layer / 2.5nm ruthenium capping layer / Mo-Si multilayer film (40 periodic pairs). The calculated image intensity is normalized. ; (4) Data set partitioning: The dataset is randomly partitioned into a training set (16,000 samples), a validation set (2,000 samples), and a test set (2,000 samples) in a ratio of 8:1:1.

[0034] 4. Loss Function Design The total loss function comprises four terms: data fidelity loss, physical consistency loss, frequency domain energy conservation loss, and distributed bridging loss. ; (1) Data fidelity loss (Mean squared error): ; (2) Loss of physical consistency : Define two key regions: ①Opaque area ; ② Phase boundary region Defined as: for middle Region and Each region is subjected to a 3×3 morphological dilation, and the intersection of the two dilated regions is taken and then removed. ,Right now: ; The physical consistency loss constraint is: ; in As a weighting factor, This represents the highest normalized intensity allowed in the phase boundary region.

[0035] (3) Spectral energy conservation loss : ; (4) Distributed bridging loss : To address the distribution shift caused by the model being trained on ternary inputs but receiving continuous inputs in step 3, the input mask is used with a 50% probability during training. Replace with a noisy, continuous version: ; in The distributed bridging loss serves as a consistency constraint on the model's predictions for both clean ternary inputs and noisy continuous inputs. ; (5) Adaptive weight update rule: , , The initial values ​​are respectively set to , , Update according to the following rules after each epoch, and force it to remain at the lower bound. and the Upper Realm between: ; in , To adjust the step size, the target gradient ratio Set as follows , , .

[0036] 5. Training Process AdamW optimizer (weight decay) is used ), initial learning rate Batch size 16, training for 500 epochs. Learning rate decays using a cosine annealing strategy. ; in , , After each epoch, the average relative error on the validation set is calculated. If there is no improvement after 20 consecutive epochs, early stopping is triggered and the optimal model is saved. After training, the model weights are saved to the file forward_model.pt, which will serve as the differentiable imaging simulator in steps 3 and 4. use.

[0037] In step 3, the forward imaging prediction model is used as a differentiable imaging simulator to construct an inverse correction process from the target imaging pattern to the phase-shift mask pattern. Under the constraint of mask manufacturability, the phase-shift mask is continuously relaxed and optimized using accompanying sensitivity information and controlled random perturbations. The optimization results are then discretized to obtain the final phase-shift mask pattern. Specifically: Step 3 is run on a computing server equipped with the physically guided forward imaging prediction model trained in Step 2. The input is the predefined target imaging pattern provided in Step 1. and initial phase shift mask pattern The output is the final phase shift mask pattern after proximity correction. The following is a more detailed explanation of the content involved in step 3: 1. Mathematical Formulation of the Inverse Correction Problem The reverse correction problem is defined as finding an optimal phase-shift mask under mask manufacturability constraints. This minimizes the difference between its spatial image and the target image: ; in For the inverse problem loss function, For manufacturability regularization, For regularization weights. Because the mask values ​​are discrete, direct solution is extremely difficult, therefore... Continuous relaxation to Optimize and then discretize again.

[0038] 2. Hybrid Langevin Dynamics with Gradient Descent Algorithm This invention proposes an Adjoint-Sensitivity Langevin Dynamics (ASLD) optimizer. This algorithm incorporates controlled random perturbations and an adaptive step-size mechanism into traditional adjoint gradient descent, effectively escaping local minima in non-convex mask optimization. The update formula for the next iteration is: ; In the formula: Pixel-wise projection operator ; : Effective gradient matrix; Dynamic step size; Temperature coefficient, used to control the intensity of random disturbances; : A random perturbation matrix, where each element is independent and identically distributed, following a set pattern. ; (Continuization: The three values ​​are directly used as the initial continuous values).

[0039] 3. Components of an effective gradient The principal loss of the inverse problem is defined as the mean square error between the spatial image and the target image: ; Its original gradient pass Automatic differentiation backpropagation calculation.

[0040] (1) Accompanying physical sensitivity factors: Define scalar auxiliary quantities (That is, the sum of all pixels in the prediction spatial image), calculate its gradient with respect to the input mask, and obtain the sensitivity matrix: ; Indicates input mask pixels The average effect of a unit change in the intensity of the overall spatial image physically reflects the optical sensitivity at that location. The accompanying physical sensitivity factor is defined as: ; in These are scaling parameters. The gradient approaches 1 in the high-sensitivity region and approaches 0 in the low-sensitivity region, thus focusing the gradient onto the optical boundary.

[0041] (2) Effective gradient synthesis: ; in For element-wise multiplication, the regularization term It consists of two parts: ; Total variational regularization term: ; Binarization penalty term: ; , .

[0042] 4. Dynamic step size and temperature decay (1) Dynamic step size: The mean absolute value of the discrete Laplace of the current mask is taken as the curvature measure. : ; The discrete Laplace operator is: ; Mirror fill is used at the boundaries, with a step size defined as: ; in , .

[0043] (2) Cosine temperature coefficient annealing: ; in , .

[0044] 5. Iteration Termination and Discretization The convergence condition is checked every 50 iterations: if... The relative changes satisfy: ; Then terminate early, and denote the termination iteration index as... .

[0045] Obtain the final continuous mask Then, hard threshold discretization is performed. Discretization threshold The selection criteria are as follows Symmetrical boundary point: at Within the interval, exist Take the maximum value of 1 at that point. The minimum value is 0. and , arrive The distance (0.33) is less than the distance to 0 (0.67), therefore the threshold of 0.67 corresponds to... Gradient pointing Basin boundaries: ; Step 2 training results In this step, the parameters are frozen and used only as differentiable functions in the automatic differential gradient calculation. Distributed bridging loss. The introduction ensured For continuous values The predictive reliability. Step 1 provides direct as The output after optimization Proceed to step 4 for manufacturability finishing and GDSII output.

[0046] In step 4, the final phase-shift mask pattern undergoes design rule checks and local manufacturability refinements, outputting a mask pattern data file that conforms to manufacturing specifications. Specifically: Step 4 is executed on the same computing server. The input includes the discretized phase-shift mask output from Step 3. The target imaging image output in step 1 Step 2: Freezing the forward model And the digital constraint set of mask design rules provided by the contract manufacturer (minimum transmittance width) Minimum phase shift region width Minimum gap between openings of the same phase Minimum isolation distance for different phase openings (etc.). The output is a GDSII format mask data file final_psm_mask.gds that conforms to all manufacturing specifications. The following is a detailed description of each sub-step of step 4: Step 401: Rule Inspection and Violation Hotspot Extraction (1) Connected component labeling: for Median and Each region is subjected to 8-adjacent connected component labeling, resulting in... District polygon set and District polygon set Each polygon is represented by a clockwise sequence of boundary vertices.

[0047] (2) Width violation detection: For each polygon, use distance transformation to calculate its skeleton and the diameter of the inscribed circle along the skeleton. If there is an inscribed circle diameter smaller than... (right )or (right If the polygon is located in a certain position, then the location of the polygon will be marked as a width violation hotspot.

[0048] (3) Spacing violation detection: For in-phase polygon pairs ( Internal or (Internal), calculate the shortest Euclidean distance, if less than Then mark the spacing violation hotspots; for different phase polygon pairs (one from...) One from If the shortest distance is less than Then mark and isolate the violation hotspots. Each hotspot is recorded as a bounding rectangle (two polygons extending outwards from each other). (The bounding box of a pixel).

[0049] (4) Redundant phase conflict detection: For For each polygon in the equation, if it is in... If all target values ​​within the corresponding area are 0 (completely dark area), it is marked as a redundant phase conflict hotspot.

[0050] Finally, a hotspot set is generated. .

[0051] Step 402: Local Context Expansion and Mask Reconstruction For each hotspot Expand outward from the center of its circumscribed rectangle Pixels (covering 128nm), from Crop local mask module ,from Trim local target block Define width The boundary transition zone of a pixel; pixels within this transition zone are frozen during subsequent optimization. Set of active pixels. This removes all pixels from the transition band within a local block.

[0052] Step 403: Manufacturability-guided local secondary reverse correction For each local mask module Perform a miniaturized version of ASLD optimization. The local loss function is: ; (1) Local fidelity loss: ; (2) Loss due to manufacturability constraints: A soft binarization approximation is used to map the continuous mask into an approximate binary value for width estimation: ; in .right district and The differentiable width estimate is calculated separately for each region. Taking the district as an example, define .right For each connected component, the local width is estimated using differentiable morphological erosion: implement Secondary corrosion ( , (pixels), each erosion uses a differentiable approximation of a 3×3 structuring element (replacing the hard minimum with a soft minimum). If a pixel is at the ... If it disappears after the second corrosion, then its estimated width is... Pixels. Width violation penalty: ; in and After soft binarization and The pixel set of the region For pixels The estimated local width at that location.

[0053] Redundant phase cleanup items: ; This formula only applies when tend A penalty is incurred when there is a 180° phase shift and the target is a dark area.

[0054] The sum of the above two items: ; (3) Edge continuity loss: The ring at the boundary between the transition zone and the active zone Calculate the total variation within a width of 2 pixels: ; (4) Optimize parameters: , , , , After optimization, hard thresholding is performed (threshold is the same as in step 3), and the non-transition zone regions are written back to the global mask to obtain... .

[0055] Step 404: Full Chip Integration and GDSII Output (1) To In Region and The Marching Squares algorithm (contour lines) was used in different regions. and Extract closed polygons.

[0056] (2) Use the Douglas-Peucker algorithm with tolerance Pixel smoothing of polygon boundaries removes stepped jagged edges while ensuring that the displacement does not exceed half the pixel size.

[0057] (3) The polygon is written to the first data layer (Layer1, DATATYPE0) of the GDSII file. The polygon is written to the second data layer (Layer2, DATATYPE0), and the process identification text (Layer255) is embedded, indicating that Layer1 = 0° phase shift opening and Layer2 = 180° phase shift opening.

[0058] (4) The output file final_psm_mask.gds is stored in the storage device and delivered to the mask manufacturing plant.

[0059] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0060] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0061] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0062] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A machine learning-assisted phase-shift mask proximity correction method, characterized in that, include: Step 1: Obtain the initial phase-shift mask pattern to be corrected and the predefined target imaging pattern; Step 2: Construct and train a physical-guided forward imaging prediction model. The forward imaging prediction model adopts a hybrid neural-physical dual-branch architecture. The physical branch is constructed based on a learnable parameterized effective thin mask approximation model to compensate for EUV thick mask effects and shadow effects. The main branch uses multi-layer Fourier neural operators to learn the residual correction of the prediction results of the physical branch. Step 3: Using the forward imaging prediction model as a differentiable imaging simulator, construct the inverse correction process from the target imaging pattern to the phase shift mask pattern. Under the constraint of mask manufacturability, continuously relax and optimize the phase shift mask using the accompanying sensitivity information and controlled random perturbation, and discretize the optimization results to obtain the final phase shift mask pattern. Step 4: Perform design rule checks and local manufacturability refinements on the final phase-shift mask pattern, and output a mask pattern data file that conforms to manufacturing specifications.

2. The machine learning-assisted phase-shift mask proximity correction method according to claim 1, characterized in that, In step 1, the initial phase shift mask pattern to be corrected is obtained, specifically as follows: Connectivity labeling is performed on the binary matrix obtained by rasterizing the target map, and bright region polygons are extracted; each bright region polygon is shrunk inward by a predetermined width to obtain a 0° phase shift opening region. When the distance between adjacent bright areas is less than a preset threshold, a 180° phase-shifted strip is generated at the central axis of the dark area; the remaining area is set as an opaque area, thus forming a three-value pixel matrix, with pixel values ​​corresponding to the 0° phase-transparent area, the 180° phase-transparent area, and the opaque area, respectively.

3. The machine learning-assisted phase-shift mask proximity correction method according to claim 1, characterized in that, In step 1, the target imaging pattern is a continuous value matrix, representing the intensity distribution of the photoresist pattern to be formed on the wafer.

4. The machine learning-assisted phase-shift mask proximity correction method according to claim 1, characterized in that, In step 2, the physical branch is constructed based on the Abbe partially coherent imaging model. Its equivalent mask complex transmittance is obtained by multiplying the original mask matrix with the learnable phase compensation map and then convolving it with the learnable Gaussian blur kernel. The learnable phase compensation map is generated by the convolutional network with the original mask matrix as input, and the standard deviation of the learnable Gaussian blur kernel is a learnable parameter.

5. The machine learning-assisted phase-shift mask proximity correction method according to claim 4, characterized in that, In step 2, the single-channel intensity map output by the physical branch is mapped to a multi-channel feature map through a series of convolutional layers, and then concatenated with the final output features of the main branch in the channel dimension. The predicted normalized spatial image intensity distribution is generated through a convolutional projection layer and a Sigmoid activation function.

6. The machine learning-assisted phase-shift mask proximity correction method according to claim 5, characterized in that, In step 2, the loss functions used for training the forward imaging prediction model include data fidelity loss, physical consistency loss, frequency domain energy conservation loss, and distribution bridging loss. The distribution bridging loss is a prediction consistency constraint of the model on the ternary mask input and its continuous version input with added noise, which is used to reduce the distribution offset of the model when facing continuous value inputs in the reverse correction stage.

7. The machine learning-assisted phase-shift mask proximity correction method according to claim 6, characterized in that, In step 3, the reverse correction process uses the Langevin dynamics optimizer with adjoint sensitivity for iterative updates. The update steps include: Calculate the gradient of the principal loss of the inverse problem with respect to the original mask; The accompanying physical sensitivity factor is constructed by using the sum of the predicted spatial image intensities relative to the mask sensitivity matrix, and then multiplied element-wise with the original gradient to obtain the effective gradient. The mask is updated according to an update formula that includes an effective gradient, dynamic step size, and temperature-controlled random term, and the pixel values ​​are constrained to a continuous interval by a projection operator.

8. The machine learning-assisted phase-shift mask proximity correction method according to claim 7, characterized in that, The inverse problem main loss is the mean square error between the predicted spatial image and the target image; the effective gradient is also superimposed with the gradient of the total variation regularization term and the binarization penalty term; the dynamic step size is adaptively adjusted according to the mean of the discrete Laplacian absolute value of the current mask; the temperature coefficient is gradually reduced from the initial value according to the cosine annealing strategy.

9. The machine learning-assisted phase-shift mask proximity correction method according to claim 8, characterized in that, In step 4, the local manufacturability finishing includes: Detect width violations, spacing violations, and redundant phase conflict hotspots in the final phase shift mask pattern; For each hotspot, extract the local mask module and target block, and perform fine-tuning optimization with local fidelity, manufacturability constraints and edge continuity as loss terms under the boundary transition zone constraint to obtain the repaired local mask and write it back to the global mask.

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