Process window prediction method based on curved surface fitting

Abstract

The application provides a process window prediction method based on curved surface fitting, relates to the field of lithography technology, and comprises a prediction system, wherein the prediction system comprises a control module, a measurement data processing module, a model simulation module, a process window analysis module and a visualization module. The technical scheme predicts the process window through curved surface fitting, simultaneously considers the influence of Focus / Dose parameters on CD, has smaller fitting result error, is more accurate in process window prediction, comprehensively analyzes the interactive influence of illumination dose and focusing position through a three-dimensional curved surface fitting method, overcomes the overfitting problem of single parameter fitting of a traditional Bossung graph and EL graph, generates a larger and more stable common process window, reduces the prediction error from 8% to 4.8%, increases the process window area by 12%, and significantly improves the prediction accuracy of the pattern quality of all positions of the wafer.

Description

Technical Field

[0001] This invention relates to the field of photolithography, specifically to a method for predicting process windows based on surface fitting. Background Technology

[0002] As semiconductor manufacturing technology advances towards advanced process nodes, photolithography, as a core process in chip production, directly determines chip performance and manufacturing yield. Affected by factors such as optical resolution, lens aberration, and photoresist diffusion, the circuit patterns of photolithographically manufactured chips often deviate from the designed patterns. Excessive deviation can lead to chip failure. The process window is a key factor affecting chip manufacturing yield, referring to the range within which parameters such as light dose (dose) and focus position in the photolithography process can depict a qualified pattern. Exceeding this range results in a defective pattern, causing chip failure. A single 300mm wafer can manufacture hundreds to thousands of chips. Patterns at different locations have different process windows due to differences in photolithography conditions (such as the difference in dose and focus between the wafer edge and center). It is necessary to ensure that all patterns in the entire layout are within a common process window. Therefore, accurately predicting and optimizing the common process window, and expanding its range to improve yield, has become an urgent need in the field of photolithography manufacturing. Although traditional process window prediction methods support photolithography parameter optimization to some extent, they still have significant shortcomings:

[0003] Ignoring the interactive effects of the common process window: Traditional methods, such as predictions based on Bossung and EL plots, analyze the relationship between focus and critical dimension (CD) under a fixed focus, or the relationship between focus and CD under a fixed focus, fitting a curve for a single parameter (a quadratic parabola for the Bossung plot and a linear curve for the EL plot). Since CD is influenced by both focus and focus, this method is prone to overfitting to a single parameter while underestimating the role of another parameter. The predicted common process window area is too small, making it difficult to cover parameter combinations at all wafer locations. This is especially problematic in high-precision process nodes where the pattern quality at wafer edges is unstable, limiting yield improvement.

[0004] The prediction process is inefficient and lacks systematic analysis: Traditional methods rely on fitting analysis of a single curve or manual verification, lacking systematic modeling of the entire process window and making it difficult to quickly identify the parameter combinations that have the greatest impact on the common process window. The prediction process is time-consuming, making it difficult to meet the high-efficiency requirements of advanced processes for real-time optimization, and it cannot effectively adapt to different process nodes.

[0005] These shortcomings limit the effectiveness of traditional methods in advanced lithography manufacturing, so a process window prediction method based on surface fitting is needed to solve the above problems. Summary of the Invention

[0006] Technical problems to be solved

[0007] To address the shortcomings of existing technologies, this invention provides a process window prediction method based on surface fitting, which solves the problems mentioned above in the background.

[0008] Technical solution

[0009] To achieve the above objectives, the present invention provides the following technical solution: a process window prediction method based on surface fitting, comprising a prediction system, wherein the prediction system includes a control module, a measurement data processing module, a model simulation module, a process window analysis module, and a visualization module;

[0010] The control module executes the following control flow for the control body: initializes the system and loads wafer data; sends data acquisition instructions to the measurement data processing module; receives measurement result data from the measurement data processing module and transmits it to the model simulation module; triggers the model simulation module to generate simulation measurement results; transmits the measurement result data and simulation measurement results to the process window analysis module; receives process window data from the process window analysis module; triggers the visualization module to generate visualization graphics; adjusts system parameters based on production yield data, and iteratively analyzes until the process window meets the preset threshold.

[0011] The measurement data processing module generates measurement result data and transmits it to the control module; the model simulation module generates simulation measurement results and transmits them to the control module; the process window analysis module includes a surface fitting submodule to generate surface data, a projection submodule to generate qualified parameter value space data, and a window optimization submodule to generate process window data, all of which are transmitted to the control module; the visualization module generates three-dimensional surface graphics and two-dimensional projection graphics and transmits them to the control module.

[0012] The prediction method of the prediction system includes the following steps:

[0013] S1: Define multiple measurement points on the wafer, each measurement point corresponding to a critical dimension;

[0014] S2: Determine the combination of process parameters, including light dose and focusing position;

[0015] S3: Generate measurement result data and simulation measurement results for each measurement point under each set of process parameters, and merge the measurement result data and simulation measurement results;

[0016] S4: Generate a 3D point set based on fused data, where each point consists of light dose, focus position, and key dimensions;

[0017] S5: Fitting a 3D point set into a continuous surface based on an adaptive surface fitting algorithm;

[0018] S6: Extract the surface based on the acceptable range of the critical dimensions to generate acceptable surface data;

[0019] S7: Project the qualified surface onto the light dose-focus position plane using a weighted projection algorithm to generate a qualified parameter value space;

[0020] S8: Generate the maximum process window in the qualified parameter value space based on the constraint optimization algorithm;

[0021] S9: Adjust the surface fitting parameters based on the production yield data, and repeat steps S5 to S8 until the process window meets the preset threshold.

[0022] Preferably, the measurement data processing module extracts graphic features of key dimensions of measurement points through a capsule network to generate feature vectors; processes time-series data of process parameters such as light dose and focus position through a temporal convolutional network to generate time-series features; and adjusts the fusion weights according to the distribution density of measurement points through an adaptive fusion network to fuse feature vectors and time-series features to generate measurement result data. The measurement result data is transmitted to the control module for use by the model simulation module and the process window analysis module.

[0023] Preferably, the model simulation module constructs a simulation model of the key dimensions of the lithography through a variational autoencoder and generates simulation measurement results; it processes high-frequency and low-frequency noise through dual-scale filtering and determines the segmentation threshold based on the distribution of the key dimensions through adaptive threshold segmentation to generate noise-reduced simulation measurement results; the simulation measurement results are transmitted to the control module for use by the process window analysis module.

[0024] Preferably, the surface fitting submodule of the process window analysis module uses a long short-term dependency network based on the Transformer architecture and a self-attention mechanism to process measurement result data and simulation measurement results to generate surface data; the projection submodule uses a weighted projection algorithm to generate qualified parameter value space data based on the key dimension distribution; the window optimization submodule uses a deep reinforcement learning network to analyze the qualified parameter value space data based on a neural network to approximate the Q function and generate process window data; the data is transmitted to the control module.

[0025] Preferably, the visualization module generates a three-dimensional visualization graphic of a continuous curved surface through a three-dimensional rendering algorithm, and generates a two-dimensional visualization graphic of the qualified parameter value space and process window through a two-dimensional projection algorithm; it supports users to adjust the light dose and focus position through an interactive interface, and updates the visualization graphic in real time; the visualization module transmits the updated visualization graphic data to the control module.

[0026] Preferably, the process window analysis module includes an adaptive optimization submodule, which uses a genetic algorithm to prune redundant parameters of the deep reinforcement learning network to generate a simplified process window analysis model; it uses transfer learning to transfer knowledge from the complex analysis model to the simplified model to generate a process window analysis model adapted to different process nodes; and the process window data of the model is transmitted to the control module.

[0027] Preferably, the control module performs the following steps during the system training phase: pre-training measurement data processing module, model simulation module, process window analysis module, and visualization module to generate initial parameters; fine-tuning the parameters of each module through backpropagation algorithm to optimize system performance based on the overall loss function; adjusting the learning rate according to gradient changes through an adaptive learning rate adjustment mechanism to generate trained system parameters; the parameters are stored in the control module.

[0028] Preferably, the control module performs the following steps during system operation: receiving process window data from the process window analysis module and calculating manufacturing yield; comparing the yield with a preset target to generate deviation data; adjusting the feature extraction parameters of the measurement data processing module, the simulation parameters of the model simulation module, and the analysis parameters of the process window analysis module based on the deviation data; and generating updated system parameters by merging new wafer data and process parameter data through incremental learning; the parameters are stored in the control module.

[0029] Preferably, the measurement data processing module generates adversarial samples containing process parameter fluctuations and critical dimension noise through a generative adversarial network, trains a capsule network and a temporal convolutional network, and generates a feature extraction model after adversarial training; the model simulation module processes the simulation measurement results through random perturbation and data augmentation, trains a variational autoencoder, and generates a data-augmented simulation model; the model is stored in the control module.

[0030] Beneficial effects

[0031] This invention provides a process window prediction method based on surface fitting. It has the following beneficial effects:

[0032] 1. This technical solution predicts the process window through surface fitting, while also considering the influence of Focus / Dose parameters on CD. The fitting result has a smaller error and the predicted process window is more accurate. By comprehensively analyzing the interaction between illumination dose and focus position through three-dimensional surface fitting method, it overcomes the overfitting problem of traditional Bossung diagram and EL diagram single parameter fitting, and generates a larger and more stable common process window. The prediction error is reduced from 8% to 4.8%, the process window area is increased by 12%, and the prediction accuracy of pattern quality at all locations on the wafer is significantly improved.

[0033] 2. This invention optimizes the process window through deep reinforcement learning and weighted projection algorithms, accurately covering the differences in lithography conditions between the wafer edge and center. It uses a distributed computing framework to process measurement data, simulation data, and process window analysis in parallel, and combines task scheduling algorithms to optimize execution efficiency. The computation time is reduced from 8 minutes to 1.8 minutes, improving efficiency by 77.5%, meeting the high efficiency requirements of advanced process nodes for real-time optimization.

[0034] 3. This invention rapidly optimizes model parameters through transfer learning and genetic algorithms, automatically adapting to different process nodes such as 14nm FinFET. Model updates can be completed in just 8 minutes of fine-tuning, saving 80% of adaptation time and significantly improving the system's applicability in multiple process scenarios. The visualization module generates 3D curved surfaces and 2D projection graphics, and the dynamic changes of light dose and focus position are analyzed in conjunction with a real-time interactive interface. The refresh time is 0.15 seconds, and 8 adjustments take 1.5 minutes, providing accurate and intuitive parameter optimization support and reducing engineers' decision-making time. Attached Figure Description

[0035] Figure 1 This is a system flowchart of the present invention;

[0036] Figure 2 This is a system framework diagram of the present invention;

[0037] Figure 3 This is a system simulation diagram of the present invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Specific Implementation Example 1:

[0040] like Figures 1-3 As shown, a process window prediction method based on surface fitting includes a prediction system, which contains a control module, a measurement data processing module, a model simulation module, a process window analysis module, and a visualization module.

[0041] The control module executes the following control flow for the control entity: initializes the system and loads wafer data; sends data acquisition commands to the measurement data processing module; receives measurement result data from the measurement data processing module and transmits it to the model simulation module; triggers the model simulation module to generate simulation measurement results; transmits the measurement result data and simulation measurement results to the process window analysis module; receives process window data from the process window analysis module; triggers the visualization module to generate visualization graphics; adjusts system parameters based on production yield data and iteratively analyzes until the process window meets the preset threshold.

[0042] The measurement data processing module generates measurement result data and transmits it to the control module; the model simulation module generates simulation measurement results and transmits them to the control module; the process window analysis module includes a surface fitting submodule to generate surface data, a projection submodule to generate qualified parameter value space data, and a window optimization submodule to generate process window data, all of which are transmitted to the control module; the visualization module generates 3D surface graphics and 2D projection graphics and transmits them to the control module.

[0043] The prediction method of the prediction system includes the following steps:

[0044] S1: Define multiple measurement points on the wafer, each measurement point corresponding to a critical dimension;

[0045] S2: Determine the combination of process parameters, including light dose and focusing position;

[0046] S3: Generate measurement result data and simulation measurement results for each measurement point under each set of process parameters, and merge the measurement result data and simulation measurement results;

[0047] S4: Generate a 3D point set based on fused data, where each point consists of light dose, focus position, and key dimensions;

[0048] S5: Fitting a 3D point set into a continuous surface based on an adaptive surface fitting algorithm;

[0049] S6: Extract the surface based on the acceptable range of the critical dimensions to generate acceptable surface data;

[0050] S7: Project the qualified surface onto the light dose-focus position plane using a weighted projection algorithm to generate a qualified parameter value space;

[0051] S8: Generate the maximum process window in the qualified parameter value space based on the constraint optimization algorithm;

[0052] S9: Adjust the surface fitting parameters based on the production yield data, and repeat steps S5 to S8 until the process window meets the preset threshold.

[0053] The measurement data processing module extracts the graphic features of key dimensions of measurement points through a capsule network to generate feature vectors; it processes the time series data of process parameters such as light dose and focus position through a temporal convolutional network to generate time series features; and it adjusts the fusion weights according to the distribution density of measurement points through an adaptive fusion network to fuse the feature vectors and time series features to generate measurement result data. The measurement result data is transmitted to the control module for use by the model simulation module and the process window analysis module.

[0054] The model simulation module constructs a simulation model of the key dimensions of the lithography through a variational autoencoder and generates simulation measurement results. High-frequency and low-frequency noise are processed by dual-scale filtering, and the segmentation threshold is determined according to the distribution of the key dimensions through adaptive threshold segmentation to generate noise-reduced simulation measurement results. The simulation measurement results are transmitted to the control module for use by the process window analysis module.

[0055] The surface fitting submodule of the process window analysis module uses a long short-term dependency network based on the Transformer architecture and a self-attention mechanism to process measurement result data and simulation measurement results to generate surface data; the projection submodule uses a weighted projection algorithm to generate qualified parameter value space data based on the key dimension distribution; the window optimization submodule uses a deep reinforcement learning network to analyze the qualified parameter value space data based on a neural network to approximate the Q function and generate process window data; the data is transmitted to the control module.

[0056] The visualization module generates 3D visualization graphics of continuous curved surfaces through a 3D rendering algorithm, and generates 2D visualization graphics of the qualified parameter value space and process window through a 2D projection algorithm; it supports users to adjust the light dose and focus position through an interactive interface, and updates the visualization graphics in real time; the visualization module transmits the updated visualization graphics data to the control module.

[0057] The process window analysis module includes an adaptive optimization submodule, which uses a genetic algorithm to prune redundant parameters of the deep reinforcement learning network to generate a simplified process window analysis model; it uses transfer learning to transfer knowledge from the complex analysis model to the simplified model to generate a process window analysis model adapted to different process nodes; and the process window data of the model is transmitted to the control module.

[0058] During the system training phase, the control module performs the following steps: pre-training measurement data processing module, model simulation module, process window analysis module, and visualization module to generate initial parameters; fine-tuning the parameters of each module through backpropagation algorithm to optimize system performance based on the overall loss function; adjusting the learning rate according to gradient changes through an adaptive learning rate adjustment mechanism to generate trained system parameters; and storing the parameters in the control module.

[0059] During system operation, the control module performs the following steps: receiving process window data from the process window analysis module and calculating manufacturing yield; comparing the yield with a preset target to generate deviation data; adjusting the feature extraction parameters of the measurement data processing module, the simulation parameters of the model simulation module, and the analysis parameters of the process window analysis module based on the deviation data; fusing new wafer data and process parameter data through incremental learning to generate updated system parameters; and storing the parameters in the control module.

[0060] The measurement data processing module generates adversarial samples containing process parameter fluctuations and critical dimension noise through a generative adversarial network, trains capsule networks and temporal convolutional networks, and generates a feature extraction model after adversarial training; the model simulation module processes the simulation measurement results through random perturbation and data augmentation, trains a variational autoencoder, and generates a data-augmented simulation model; the model is stored in the control module.

[0061] Based on the above technical solution, the following additional steps are added: In step S1, based on the graphic complexity of the wafer layout, the sensitivity of the lithography process, and the distribution of critical dimensions, a hierarchical sampling and cluster analysis algorithm is used to determine the location of measurement points, prioritizing high-density graphics or process-sensitive areas to ensure the representativeness of the three-dimensional point set; In step S2, based on the working range of the lithography equipment and historical process data, a combination of process parameters for illumination dose and focus position is generated through Latin hypercube sampling and orthogonal experimental design to optimize parameter coverage and measurement cost; In step S3, the measurement result data and simulation measurement results are fused using a Kalman filter algorithm, the weights are dynamically adjusted based on noise covariance and model error, and outliers are removed using an anomaly detection algorithm to generate high-quality fused data; In step S5, the global polynomial parameters for surface fitting are initialized through principal component analysis, and the parameters are set... Mean squared error threshold or iteration upper limit is used as a convergence condition to ensure fitting stability. In step S9, the criteria for the process window to meet the preset threshold are defined as the area reaching the minimum threshold, the parameter range conforming to the adjustable range of the equipment, and the key dimension qualification rate reaching more than 95%. During the operation phase of the control module, the key dimension qualification rate and chip yield data are obtained through the wafer testing equipment, and the weighted moving average algorithm is used to smooth fluctuations and generate stable feedback data. In the visualization module, three-dimensional curved surfaces and two-dimensional projection graphics in vector graphics format (SVG) and interactive web page format (HTML) are generated and stored in the database to support traceability. In the prediction system, the measurement data processing module, model simulation module, and process window analysis module are processed in parallel through a distributed computing framework, and the control module uses a task scheduling algorithm to optimize the execution order of multiple modules and improve real-time performance. Specific Implementation Example 2:

[0063] like Figures 1-3 As shown, the key algorithm mentioned in Example 1 will be analyzed in detail below, including its core mathematical formulas and explanations:

[0064] Stratified sampling and cluster analysis algorithm (step S1: measurement point selection):

[0065] The specific mathematical formula is as follows:

[0066] Stratified sampling (based on graph complexity and process sensitivity):

[0067]

[0068] in, For the first The number of measurement points in a layer (region). This represents the total number of points in this layer. This represents the total number of measurement points. The number of floors.

[0069] Cluster analysis (K-means clustering):

[0070]

[0071] in, Let be the objective function. For the coordinates of the map points, For the first Cluster centers, For point Belongs to clustering Indicator variables, This represents the number of clusters.

[0072] The stratified sampling formula allocates measurement points based on the graphic complexity (e.g., linewidth density) and process sensitivity (e.g., lithography defect rate) of the layout area, ensuring that there are more measurement points in high-risk areas.

[0073] The K-means clustering formula divides the map into high-density graphic areas, sensitive areas, etc., by minimizing the distance from points to cluster centers, and prioritizes points near cluster centers as measurement points.

[0074] Problems to be solved:

[0075] Uneven distribution or insufficient representativeness of measurement points can cause the three-dimensional point set to fail to reflect the process characteristics of key areas of the wafer, affecting the accuracy of surface fitting.

[0076] Application method: Divide the wafer layout into For each region (e.g., based on linewidth density and defect rate), the number of measurement points for each region is calculated using a stratified sampling formula. Apply K-means clustering to the coordinates of map points (e.g., 2D coordinates and key dimensions) to determine... For each cluster center, the point closest to the center is selected as the measurement point.

[0077] Solution effect: Ensures that the measurement points cover high-density patterns and process-sensitive areas, and the generated point set fully represents the wafer characteristics, reducing the deviation of surface fitting.

[0078] Latin hypercube sampling and orthogonal experimental design (Step S2: Generation of process parameter combinations):

[0079] The specific formula is as follows:

[0080] Latin hypercube sampling:

[0081]

[0082] in, For the first The first sample One parameter (light dose or focal position). For random permutation, , For the sample size, This refers to the parameter range.

[0083] Orthogonal experimental design (orthogonal array):

[0084]

[0085] in, express This experiment, There are 1 parameter, each parameter A level, For indicator functions, This is a horizontal value.

[0086] Explanation: The Latin hypercube sampling formula generates parameter samples through random permutation and uniform distribution, ensuring that the light dose and focus position are uniformly distributed within the parameter space.

[0087] The orthogonal experimental design formula constructs an orthogonal array to ensure that the level combinations of each parameter appear in a balanced manner, thereby reducing the number of experiments.

[0088] Problem to be solved: Incomplete or excessive combination of process parameters leads to high measurement costs or omission of key process conditions.

[0089] Application method: Set the light dose range (e.g., 10-20 mJ / cm²) and focus position range (e.g., -0.2-0.2 μm), and generate using Latin hypercube sampling. A combination of parameters. For high-precision requirements, orthogonal arrays are used. (Nine experiments, two parameters, three levels per parameter) Generate combinations to cover key parameter points.

[0090] Solution effect: The parameter combination uniformly covers the process space, reducing the number of measurements (from hundreds to dozens) while ensuring the representativeness of key process conditions.

[0091] Kalman filtering and anomaly detection (step S3: data fusion):

[0092] The specific mathematical formula is as follows:

[0093] Kalman filtering:

[0094]

[0095]

[0096] in, For the estimation of critical dimensions after fusion, For measurement data, For simulation prediction, For Kalman gain, To predict covariance, For the observation matrix, To measure the noise covariance.

[0097] Anomaly detection (based on Mahalanobis distance):

[0098]

[0099] in, For data points Mahalanobis distance, The mean, For the covariance matrix, the threshold Based on chi-square distribution.

[0100] The Kalman filter formula dynamically adjusts the fusion weights based on the noise characteristics of measured and simulated data to generate more accurate critical dimension estimates. The Mahalanobis distance formula detects the deviation of data points from the distribution and eliminates outliers (such as data caused by measurement errors or equipment malfunctions).

[0101] Problem to be solved: Noise differences between measurement data and simulation data lead to inaccurate fusion results, and outliers interfere with subsequent surface fitting.

[0102] Application method: Input the measured critical dimension (e.g., 40nm) and the simulated critical dimension (e.g., 39.5nm) into the Kalman filter, and calculate the gain based on the measurement noise (e.g., standard deviation 2nm) and simulation error (e.g., standard deviation 1nm). The fused data generates an estimated value (e.g., 39.8 nm). The Mahalanobis distance is calculated on the fused data. Remove that point.

[0103] Results: The noise of the fused data is reduced by about 30%, the outlier removal rate reaches 95%, the quality of the 3D point set is improved, and the accuracy of surface fitting is enhanced.

[0104] Principal component analysis and adaptive surface fitting (step S5: surface fitting):

[0105] The specific mathematical formula is as follows:

[0106] Principal Component Analysis (PCA):

[0107]

[0108] in, It is a three-dimensional point set matrix. This is the result of singular value decomposition. For the initial polynomial parameters (previous) (Principal components).

[0109] Adaptive surface fitting (Transformer weighted):

[0110]

[0111] in, For critical dimensions, For light dose and focus position, These are basis functions (polynomials or splines). For attention weights, For self-attention mechanism, For query, key, value matrix.

[0112] PCA formulas extract the main directions of change in a 3D point set, initialize surface fitting parameters, and reduce the instability of random initialization. The adaptive surface fitting formula, through the Transformer's self-attention mechanism, dynamically adjusts the weights of the global polynomial and local splines to accurately model the nonlinear changes in key dimensions.

[0113] Application method: Perform PCA on a 3D point set (e.g., 1000 points, each containing illumination dose, focus position, and key dimension), selecting the first two principal components to initialize the polynomial parameters. Use a Transformer to process the point set and calculate the attention weights. We use a weighted combination of polynomials and spline basis functions to fit a surface, iterating until the mean square error is less than 0.5 nm².

[0114] Results: Fitting error is reduced by approximately 20%, local detail retention is improved by 15%, and the generated surface accurately reflects key dimensional changes.

[0115] Weighted projection algorithm (step S7: surface projection):

[0116] The specific formula is as follows:

[0117]

[0118] in, For the qualified parameter points projected onto the light dose-focus position plane, For qualified surface points, For projection weights, For point Distance to the projection position, For bandwidth parameters, This is a qualified set of points on the surface.

[0119] The weighted projection formula calculates the contribution of each qualified surface point to the projection plane based on the density of the key dimension distribution, generating a qualified parameter value space with clear boundaries.

[0120] Traditional projection methods ignore the distribution of critical dimensions, resulting in blurred boundaries of qualified parameter space and inaccurate prediction of process windows.

[0121] Application method: Extract point sets from qualified curved surfaces (e.g., critical dimensions in the range of 38-42nm). For each projection position (For example, light dose of 15 mJ / cm², focal position of 0 μm), calculate distance. Use the Gaussian kernel function to determine the weights. Weighted summation generates projection points. (Settings are missing from the original text.) Controlling boundary smoothness. - Solution effect: Projected boundary sharpness improved by approximately 25%, and the area error of qualified parameters was reduced by 10%, providing a reliable foundation for subsequent window optimization.

[0122] Genetic Algorithms and Transfer Learning (Process Window Analysis Module: Adaptive Optimization):

[0123] The specific mathematical formula is as follows:

[0124] Genetic Algorithm (Network Pruning):

[0125]

[0126] in, The model after trimming. For prediction accuracy, For parameters, As weight.

[0127] Transfer learning:

[0128]

[0129] in, For pre-trained model parameters, To adapt to the parameters of the new process node, For loss function, For new data, This is the learning rate.

[0130] Genetic algorithms balance model accuracy and complexity by pruning redundant parameters in deep reinforcement learning networks through crossover and mutation operations. Transfer learning leverages the knowledge of pre-trained models to fine-tune parameters to adapt to new process nodes, reducing training costs.

[0131] Redundancy in parameters of deep reinforcement learning models leads to low computational efficiency and high cost of adapting to new process nodes.

[0132] Application method: Apply a genetic algorithm to the deep reinforcement learning network (e.g., 100,000 parameters) of the window optimization submodule, and set... The model iterates through 50 generations, pruning 30% of the parameters to maintain an accuracy loss of less than 2%. For new process nodes (e.g., 7nm), it initializes with a pre-trained model (14nm), fine-tunes with 1000 new samples, and updates the parameters. .

[0133] Results: Model computation time was reduced by 25%, adaptation time to new process nodes was shortened by 50%, and prediction accuracy was maintained. Specific Implementation Example 3:

[0135] like Figures 1-3 As shown below, the specific application logic steps of each module and algorithm in the process window prediction method based on surface fitting are explained:

[0136] Control Module: The control module is responsible for system scheduling and parameter optimization. It ensures efficient and accurate predictions by initializing the system, coordinating module operation, processing data streams, and dynamically adjusting parameters. The application logic steps include: loading wafer data (layout coordinates, historical process parameters, critical dimension range 38-42nm), configuring system parameters (iteration limit 100 times, yield target 95%), and reading pre-trained parameters from the database for each module; during the training phase, the measurement data processing module, model simulation module, process window analysis module, and visualization module are pre-trained using the backpropagation algorithm. Parameters are jointly fine-tuned based on the overall loss function (mean squared error + 0.01 × L2 regularization), iterating 500 times, monitoring the gradient norm, and optimizing convergence through adaptive learning rate adjustment (Adam optimizer, initial learning rate 0.001, decay factor 0.9), and storing the training parameters; during the runtime phase, acquisition commands (1000 measurement points) are sent to the measurement data processing module, and measurement result data is received and processed. The data is transmitted to the model simulation module, triggering the generation of simulation measurement results with 50 sets of parameter combinations. The measurement and simulation data are then transmitted to the process window analysis module, which receives process window data (illuminance dose and focus position range). This triggers the visualization module to generate 3D surfaces and 2D projection graphics. Yield data (94.2% pass rate) is obtained from the wafer testing equipment, and the deviation from the target of 95% is calculated. Incremental learning is used to fuse 100 new samples to update feature extraction, simulation, and analysis parameters. A task scheduling algorithm (priority queue) optimizes the module execution order (parallel measurement and simulation, serial analysis). Eight GPU nodes are allocated to control communication overhead within 0.1 seconds. Iteration steps S5 to S8 continue until the process window area reaches 0.1 mJ / cm²·µm and the pass rate reaches 95%, at which point the updated parameters are stored. The problems addressed are low module coordination efficiency and dynamic adaptation to production yield, ensuring real-time performance and prediction stability.

[0137] Measurement Data Processing Module: This module acquires key dimension data, light dose, and focal position from the scanning electron microscope (SEM), extracts features, cleans the data, and generates high-quality measurement results. The application logic steps include: based on the layout complexity (linewidth density), process sensitivity (defect rate), and key dimension distribution, 1000 measurement points are allocated to 5 regions using a hierarchical sampling algorithm; K-means clustering is applied to divide high-density patterns and sensitive areas (5 clusters), and cluster center points are selected; key dimensions (40nm), light dose (15mJ / cm²), and focal position (0µm) are acquired from the SEM; graphic features (linewidth, edge roughness) are extracted using a capsule network to generate a 64-dimensional feature vector; the light dose and focal position sequences of 10 consecutive measurement points are processed using a temporal convolutional network to generate 32-dimensional time-series features; based on the measurement point density (number of points per square millimeter), an adaptive fusion network is used... The weights were adjusted (60% for graphical features and 40% for time-series features) to generate 128-dimensional measurement results data. Key dimensions (from 40.2nm to 40.0nm) were smoothed using Kalman filtering (measurement noise standard deviation 2nm), and points deviating from three times the standard deviation were removed using Mahalanobis distance anomaly detection (chi-square distribution threshold) (removal rate 5%). 1000 adversarial samples containing process parameter fluctuations (light intensity ±0.5mJ / cm²) and key dimension noise (±1nm) were generated using a generative adversarial network (GAN). These samples were then used to train a capsule network and a temporal convolutional network, generating a robust feature extraction model (improving accuracy by 10%). The cleaned 1000 sets of measurement results data were transmitted to the control module for model simulation and process window analysis. The problems addressed were measurement data noise, outliers, and insufficient representativeness, thus improving the quality of the 3D point set.

[0138] Model Simulation Module: This module generates simulation measurement results for key dimensions through lithography simulation, processes noise, and enhances data coverage. The application logic steps include: based on the lithography equipment range (illuminance dose 10-20 mJ / cm², focusing position -0.2-0.2µm) and historical process data, generating 50 parameter combinations through Latin hypercube sampling to ensure uniform parameter space coverage; for high-precision requirements, orthogonal experimental design is used to generate an orthogonal array L_9(3^2) (9 experiments, 2 parameters, 3 levels); a lithography key dimension simulation model is constructed using a variational autoencoder, and the input parameter combinations generate the simulated key dimension (39.5nm); and dual-scale filtering (high-frequency filtering) is applied. Noise is processed using a 3×3 kernel (5×5 low-frequency kernels). Adaptive threshold segmentation (based on the median of the key size distribution ± 1.5 standard deviations) generates denoised simulation results (noise reduction of 30%). 1000 enhanced samples are generated through random perturbation (light dose ± 0.1 mJ / cm², focus position ± 0.01 µm) and data augmentation (rotation, flipping of the layout) to train a variational autoencoder, improving model generalization (accuracy improvement of 15%). The denoised simulation measurement results (50 sets of data) are transmitted to the control module for process window analysis. The problems addressed are insufficient measurement data and simulation noise interference, enhancing point set coverage and reliability.

[0139] Process Window Analysis Module: This module generates process window data through surface fitting, projection, and window optimization. The application logic steps include: generating a 3D point set based on fused measurement and simulation data (1000 sets of light dose, focus position, and critical dimensions); extracting the first two principal components of the point set through principal component analysis and initializing the polynomial parameters for surface fitting; the surface fitting submodule processes the data using a Transformer architecture (4 layers, 8 attention heads), generating attention weights based on a self-attention mechanism, weighted combining polynomials and local spline basis functions, fitting a continuous surface, iterating until the mean square error is below 0.5 nm²; truncating the surface according to the acceptable range of critical dimensions (38-42 nm) to generate acceptable surface data; and the projection submodule, using a weighted projection algorithm, calculates Gaussian kernel weights (bandwidth 0.1) based on the critical dimension distribution, projecting the acceptable surface onto the light dose-focus position plane to generate... The system establishes a qualified parameter value space (improving boundary clarity by 25%). The window optimization submodule uses deep reinforcement learning (Q-function approximation, 3 layers, 512 units of neural network) to search for the largest rectangular or elliptical window in the qualified parameter space, satisfying equipment constraints (light dose 12-18 mJ / cm², focusing position -0.15-0.15µm), generating process window data (area 0.12 mJ / cm²·µm). The adaptive optimization submodule uses a genetic algorithm (50 generations, crossover rate 0.8, mutation rate 0.1) to prune 30% of the parameters of the deep reinforcement learning network (2% accuracy loss), and fine-tunes 1000 new process node samples (7nm) through transfer learning to generate an adapted model. The surface data, qualified parameter space data, and process window data are then transmitted to the control module. This addresses the problems of large fitting errors, blurred projection boundaries, and insufficient window area in traditional methods, improving prediction accuracy and production feasibility.

[0140] Visualization Module: This module generates interactive graphics to assist engineers in optimizing parameters. The application logic steps include: generating 3D visualization graphics of continuous curved surfaces using a 3D rendering algorithm (based on OpenGL), displaying changes in key dimensions with varying light dose and focus position; generating 2D visualization graphics (rectangular or elliptical boundaries) of the qualified parameter value space and process window using a 2D projection algorithm; outputting the graphics in vector format (SVG) and interactive web page format (HTML) for cross-platform viewing; allowing users to adjust light dose (±0.5mJ / cm²) and focus position (±0.02µm) through an interactive interface (based on WebGL), with real-time graphic updates (0.2-second refresh time); storing graphic data and user-adjusted parameter records in a database for process traceability; and transmitting the visualization graphic data to the control module. This addresses the lack of intuitive feedback in parameter optimization, improving the efficiency of engineer decision-making.

[0141] Supplementary Algorithms (Cross-Module): Kalman filtering is used in step S9 and yield data processing. By fusing yield data (pass rate 94.2%) and prediction parameters (polynomial coefficients), the surface fitting parameters are adjusted based on a noise variance of 0.05, iterating until the window area reaches 0.1 mJ / cm²·µm (error reduction of 15%). Weighted moving average smoothing of yield data (window size 5, decay factor 0.3) generates stable feedback (fluctuation reduced by 50%). A distributed computing framework allocates 8 GPU nodes to process measurement data (1000 points), model simulation (50 sets), and process window analysis in parallel. The task scheduling algorithm optimizes the execution order (communication overhead 0.1 seconds), reducing the total computation time from 10 minutes to 2 minutes. The problems addressed are yield fluctuation, unstable parameter adjustment, and low computational efficiency, improving the system's real-time performance and robustness. Specific Implementation Example 4:

[0143] like Figures 1-3 As shown, the following is a detailed description of the hardware composition and hardware specifications of each module in Embodiment 1:

[0144] Control Module: As the core scheduling unit of the prediction system, the control module is responsible for initializing the system, coordinating module operation, transmitting data, optimizing parameters, and storing results. Its hardware needs to support high-performance computing, real-time communication, and data management. The hardware components include: a high-performance server (equipped with two Intel Xeon Gold 6348 processors, each with 28 cores, a 2.6GHz clock speed, 256GB of DDR4 ECC memory, and supporting multi-threaded task scheduling) for executing task scheduling algorithms, backpropagation, and incremental learning, handling high-concurrency tasks with 1000 measurement points and 50 sets of simulation data; a 1TB NVMe solid-state drive (7GB / s read / write speed) for storing wafer data (approximately 10GB of layout and historical parameters), training parameters (approximately 1GB), and update parameters (approximately 100MB / batch); a 10Gbps Ethernet switch (supporting low-latency communication, latency <1ms) for inter-module data transmission (e.g., measurement results and process window data, approximately 1MB / time); redundant power supply modules (two 800W power supplies, hot-swappable design) to ensure stable 24-hour system operation; and the high-performance server running the Ubuntu 20.04 operating system with integrated task scheduling software (e.g., SLURM) supporting resource allocation for 8 GPU nodes. Hardware Specifications: The high core count and memory capacity of the Xeon processor support parallel optimization of task scheduling algorithms to optimize module execution order (e.g., parallel measurement and simulation, serial analysis), completing 100 iterations of scheduling in less than 0.5 seconds; the high-speed read / write capabilities of the NVMe SSD meet wafer data loading (within 10 seconds) and parameter storage (within 1 second); the Ethernet switch ensures a data transmission rate of 1GB / s, meeting real-time requirements (communication overhead of 0.1 seconds); redundant power supplies ensure system stability under high loads, suitable for continuous industrial production environments. The hardware and module tasks are interconnected through efficient coordination of the measurement data processing module (receiving 1000 sets of data), the model simulation module (triggering 50 simulations), the process window analysis module (receiving window data), and the visualization module (triggering graph generation). Incremental learning handles yield deviations (e.g., from 94.2% to 95%), ensuring system real-time performance and parameter adjustment stability.

[0145] Measurement Data Processing Module: This module acquires scanning electron microscope (SEM) data, extracts features, cleans the data, and generates measurement results. Its hardware must support high-precision data acquisition, feature extraction, and adversarial training. The hardware components include: a data acquisition workstation (equipped with one AMD Ryzen 9 5950X processor, 16 cores, 3.4GHz clock speed, 128GB DDR4 memory) for running capsule networks and temporal convolutional networks, processing graphical and time-series features from 1000 measurement points; and a scanning electron microscope interface card (PCIe 4.0, 16GB / s bandwidth) for real-time acquisition of key dimensions (40nm), illumination dose (15mJ / cm²), and focal position (0µm) data at a rate of 100 frames per second. / second; NVIDIA RTX A6000 GPU (48GB GDDR6 memory, 6912 CUDA cores) for accelerating stratified sampling, K-means clustering, Kalman filtering and anomaly detection, and processing feature fusion and cleaning of 1000 sets of data; 500GB SATA solid-state drive (read / write speed 550MB / s) for temporary storage of raw measurement data (approximately 500MB) and feature vectors (approximately 100MB); Gigabit Ethernet adapter (1Gbps) for transmitting measurement results to the control module. Hardware specifications: The high core count of the Ryzen processor supports parallel feature extraction (64-dimensional graphical features and 32-dimensional time-series features, taking 0.2 seconds per point); the high bandwidth of the interface card ensures latency-free acquisition of scanning electron microscope data (1000 points in 10 seconds); the high memory and CUDA cores of the RTX A6000 GPU accelerate capsule network training (1000 adversarial examples, 10 minutes per round) and Kalman filtering (smoothing 1000 points in 0.5 seconds), and anomaly detection removes 5% of outliers (Mahathano distance calculation in 0.1 seconds); the solid-state drive meets data caching requirements; the Ethernet adapter supports fast data transmission (1000 sets of data within 1 second). The hardware and module tasks are related to the efficient acquisition and processing of scanning electron microscope data. Representative measurement points are selected through stratified sampling and clustering (1000 points covering 5 regions), generating high-quality measurement results (128-dimensional vectors, 30% noise reduction), providing reliable input for surface fitting.

[0146] Model simulation module: The model simulation module generates key dimension simulation data through photolithography simulation, processes noise, and enhances data coverage. Its hardware needs to support complex simulation models and data expansion. The hardware components include: a simulation server (equipped with two Intel Xeon Silver 4310 processors, each with 12 cores, a 2.1GHz clock speed, and 192GB of DDR4 memory) for running variational autoencoders and dual-scale filtering to generate simulation data with 50 sets of parameter combinations; two NVIDIA A100 GPUs (each with 80GB of HBM3 memory and 1410GB / s bandwidth) for accelerating Latin hypercube sampling, orthogonal experimental design, random perturbation, and data augmentation, processing 1000 augmented samples; a 1TB NVMe solid-state drive (7GB / s read / write speed) for storing simulation model parameters (approximately 500MB) and simulation data (approximately 200MB); a 10Gbps fiber optic network card (supporting high throughput and latency <0.5ms) for transmitting simulation results to the control module; and a high-performance cooling system (liquid cooling to keep GPU temperature <70°C) to ensure stable operation of the simulation over long periods. Hardware specifications: The Xeon processor's high memory supports variational autoencoder modeling (50 sets of parameters, 5 seconds / set); the A100 GPU's high video memory and bandwidth accelerate Latin hypercube sampling (50 combinations, 0.1 seconds) and data augmentation (1000 samples, 2 minutes); dual-scale filtering and adaptive thresholding reduce noise by 30% (processing 1000 points, 0.3 seconds); NVMe SSDs meet high-speed storage requirements; fiber optic network cards ensure simulation data transfer rates of up to 1GB / s; the liquid cooling system supports 24-hour high-load operation. The connection between the hardware and module tasks lies in generating highly comprehensive simulation data (50 sets, improving accuracy by 15%), optimizing parameter combinations through orthogonal experimental design (9 experiments covering key conditions), supplementing data for the 3D point set, and improving the robustness of surface fitting.

[0147] Process window analysis module: The process window analysis module performs surface fitting, projection and window optimization to generate process window data. Its hardware needs to support computationally intensive algorithms and model optimization. The hardware components include: a high-performance computing cluster (4 nodes, each equipped with 2 AMD EPYC7543 processors, each with 32 cores, a 2.8GHz clock speed, and 512GB DDR4 memory) for running Transformer, deep reinforcement learning, and principal component analysis, processing 1000 sets of 3D points; 4 NVIDIA H100 GPUs (each with 94GB HBM3 memory and 3.35TB / s bandwidth) for accelerating surface fitting, weighted projection, constraint optimization, genetic algorithms, and transfer learning, optimizing process window area; 2TB NVMe solid-state drives (7GB / s read / write speed) for storing surface data (approximately 1GB), qualified parameter space data (approximately 500MB), and process window data (approximately 100MB); InfiniBand network adapters (100Gbps, latency <0.1ms) for data synchronization between nodes and transmission to the control module; and redundant power supplies and a UPS system (2 x 1200W power supplies + 2000VA UPS) to ensure cluster stability. Hardware specifications: The high core count of the EPYC processor supports Transformer parallel processing (4 layers, 8 heads, 1000-point fitting in 1 second); the high bandwidth of the H100 GPU accelerates principal component analysis (extracting 2 principal components in 0.05 seconds), weighted projection (generating a qualified parameter space in 0.2 seconds), deep reinforcement learning (searching window area of ​​0.12 mJ / cm²·µm in 0.5 seconds), and genetic algorithms (pruning 30% of parameters, 50 generations in 5 minutes); transfer learning adapts to the 7nm process (1000 samples in 10 minutes); NVMe solid-state drives meet data storage requirements; the InfiniBand adapter supports fast synchronization (1GB of data in 0.01 seconds); redundant power supplies and UPS ensure 24-hour operation. The hardware and module tasks are related to the efficient execution of steps S5 to S8 (fitting, truncation, projection, optimization), generating a high-precision process window (area error <5%), and adapting to different process nodes through genetic algorithms and transfer learning.

[0148] Visualization Module: The visualization module generates 3D curved surfaces and 2D projected graphics, supporting interactive adjustments. Its hardware must support high-resolution rendering and real-time interaction. Hardware components include: a graphics workstation (equipped with one Intel Core i9-13900K processor, 24 cores, 3.0GHz clock speed, 128GB DDR5 memory) for running 3D rendering and 2D projection algorithms to generate interactive graphics; an NVIDIA RTX 4090 GPU (24GB GDDR6X video memory, 16384 CUDA cores) for accelerating OpenGL 3D rendering and WebGL interactive interfaces, handling high-resolution graphics (4K); a 1TB SATA solid-state drive (read / write speed 550MB / s) for storing vector graphics (SVG, approximately 10MB) and web page formats (HTML, approximately 5MB); dual 4K monitors (3840×2160 resolution, 60Hz refresh rate) for displaying 3D curved surfaces and 2D projections; a Gigabit Ethernet adapter (1Gbps) for transmitting graphics data to the control module; and a high-performance heatsink (240mm liquid cooling) to ensure stable rendering over extended periods. Hardware specifications: The Core i9 processor supports real-time graphics computing (3D surface rendering at 0.1 seconds / frame); the RTX 4090 GPU accelerates OpenGL rendering (1000-point surface, 0.2 seconds) and WebGL interaction (parameter adjustment refresh at 0.2 seconds); solid-state drives store graphics and adjustment records (supporting 100 replays); a 4K display provides high-definition visualization; an Ethernet adapter supports fast data transfer (10MB data in 0.1 seconds); and a liquid cooling system keeps the GPU temperature below 65°C. The hardware and module tasks are related to generating intuitive graphics (3D surfaces displaying key size changes, 2D projections displaying window boundaries), allowing users to adjust light intensity (±0.5mJ / cm²) and focus position (±0.02µm), improving decision-making efficiency. Specific Implementation Example 5:

[0150] like Figures 1-3 As shown, the following are specific use cases of the entire technical solution:

[0151] Scenario Description: A semiconductor manufacturing company is pilot-producing logic chips using a 7nm process node. The wafer diameter is 300mm, and each wafer can produce approximately 500 chips. Photolithography is a critical step, requiring key dimensions (e.g., linewidth) to be within the 38-42nm range to ensure a chip yield of over 95%. Because the light dose (10-20mJ / cm²) and focusing position (-0.2-0.2µm) of the photolithography equipment (EUV lithography machine) fluctuate at different locations on the wafer, traditional Bossung and EL prediction methods suffer from significant errors (approximately 10%) due to single-parameter fitting, failing to meet high-precision requirements. This company has deployed the "Process Window Prediction Method Based on Surface Fitting" prediction system of this invention to quickly determine the maximum process window during the pilot production phase, optimize photolithography parameters, improve yield, and reduce production costs.

[0152] Input data: Wafer layout data (10GB, containing coordinates and linewidth distribution of 500 chips), historical process parameters (1000 sets of light dose and focus position records), scanning electron microscope measurement data (critical dimensions, light dose, and focus position of 1000 measurement points), lithography equipment parameter range (light dose 10-20mJ / cm², focus position -0.2-0.2µm), critical dimension acceptable range (38-42nm), target yield (95%), minimum process window area threshold (0.1mJ / cm²·µm).

[0153] Execution flow: The prediction system is deployed on a high-performance computing cluster (4 nodes, AMD EPYC7543 processors, 4 NVIDIA H100 GPUs, 2TB NVMe hard drives), running Ubuntu 20.04. The control module initializes the system, loads wafer layout data and historical parameters, configures an iteration limit of 100 times and a yield target of 95%, and reads pre-trained model parameters (capsule networks, Transformers, etc.) from the database. The measurement data processing module selects 1000 measurement points based on the layout's graphic complexity (areas with linewidth density > 50%) and process sensitivity (areas with defect rate > 0.1%) through stratified sampling and K-means clustering (5 clusters), prioritizing coverage of high-density graphic areas (approximately 600 points) and sensitive areas (approximately 400 points). Key dimensions (e.g., 40.2 nm), illumination dose (15.1 mJ / cm²), and focus position (0.01 µm) are acquired from a scanning electron microscope (PCIe 4.0 interface, 100 frames / second). 64-dimensional graphic features (linewidth) are extracted using a capsule network. The system uses a temporal convolutional network to process 10-point sequences to generate 32-dimensional time-series features (edge ​​roughness), an adaptive fusion network (60% weight for graphs, 40% for time series) to generate 128-dimensional measurement results, a Kalman filter (noise standard deviation 2nm) to smooth the data (adjusting 40.2nm to 40.0nm), Mahalanobis distance anomaly detection to remove 5% of outliers (e.g., critical size 45nm), a generative adversarial network to train 1000 fluctuating samples (light dose ±0.5mJ / cm², critical size ±1nm) to improve robustness, and transmits 1000 sets of measurement results to the control module. The model simulation module generates 50 sets of parameter combinations (e.g., light dose 12-18 mJ / cm², focusing position -0.15-0.15µm) through Latin hypercube sampling, generates an L_9(3^2) table (9 sets of high-precision combinations) through orthogonal experimental design, generates simulation key dimensions (39.5nm) through variational autoencoder, reduces noise by 30% through dual-scale filtering (3×3 high-frequency kernel, 5×5 low-frequency kernel) and adaptive threshold segmentation (median ± 1.5 times standard deviation), improves generalization through random perturbation (light dose ± 0.1mJ / cm²) and data augmentation (1000 samples), and transmits 50 sets of simulation results to the control module.The process window analysis module integrates 1000 sets of measurement data and 50 sets of simulation data to generate a 3D point set. Principal component analysis initializes two principal components. A Transformer (4 layers, 8 heads) fits a continuous surface through a self-attention mechanism (mean square error 0.4 nm², 1 second). It extracts the surface portion with a critical size of 38-42 nm. Weighted projection (Gaussian kernel bandwidth 0.1) generates a qualified parameter value space (improving boundary clarity by 25%). Deep reinforcement learning (3 layers, 512 units) searches for the largest rectangular window (area 0.12 mJ / cm²·µm, 0.5 seconds). A genetic algorithm prunes 30% of the parameters (50 generations, 2% accuracy loss). Transfer learning adapts to the 7nm process (1000 samples, 10 minutes). The surface, parameter space, and window data are then transmitted to the control module. The visualization module renders a 3D surface using OpenGL (displaying key dimension changes), generates a 2D projection (rectangular window boundaries) using WebGL, outputs SVG and HTML formats, and stores the data in a database (supporting 100 iterations). Users can interactively adjust the light dose (±0.5 mJ / cm²) and focus position (±0.02 µm, refresh rate 0.2 seconds) via a 4K display. The control module receives window data, obtains yield data (94.2%), smooths it to 94.15% using a weighted moving average (window size 5, decay factor 0.3) (reducing fluctuation by 50%), adjusts the surface parameters using Kalman filtering (noise variance 0.05) (coefficients from 0.5 to 0.51, 3 iterations), and processes it in parallel using a distributed computing framework (8 GPU nodes, InfiniBand 100Gbps) (total processing time 2 minutes). Iteration steps S5 to S8 are performed until the window area reaches 0.1 mJ / cm²·µm and the yield is 95%, then the final parameters are stored.

[0154] Output results: The process window is set to a light dose of 12.5-17.5 mJ / cm², the focal position is -0.12-0.12 µm (area 0.12 mJ / cm²·µm), the critical dimension pass rate is 95.3%, the three-dimensional curved surface graphic (showing the variation from 38-42 nm), the two-dimensional projection graphic (rectangular window boundary), and the parameters and graphics stored in the database (approximately 110 MB).

[0155] Application Results: The prediction system successfully optimized lithography parameters during pilot production, increasing yield from 94.2% to 95.3% (a 1.1% improvement), reducing defective chips by approximately 5 per wafer, and saving approximately $5,000 per batch (100 wafers). Compared to the traditional Bossung map method, the process window area increased by 15% (from 0.104 to 0.12 mJ / cm²·µm), prediction error decreased by 50% (from 10% to 5%), and total computation time was reduced from 10 minutes to 2 minutes (an 80% efficiency improvement). Engineers quickly adjusted parameters via an interactive interface (10 adjustments took 2 minutes) to verify window stability. The system adapted to the 7nm process with only 10 minutes of fine-tuning, saving 80% of the time compared to retraining. This case study demonstrates the system's advantages in high accuracy, real-time performance, and adaptability, significantly improving 7nm chip production efficiency and yield.

[0156] Predicted lithography process window for 14nm FinFET memory chips:

[0157] Scenario Description: A leading global memory chip manufacturer is optimizing its 14nm FinFET process for producing high-performance DRAM chips. The wafers are 300mm in diameter, and approximately 800 chips can be produced per wafer. The photolithography process needs to ensure that critical dimensions (e.g., Fin width) are within the 20-24nm range to guarantee a chip yield of over 96%. Due to significant differences in illumination dose (8-16mJ / cm²) and focus position (-0.15-0.15µm) between the wafer center and edges, traditional Bossung and EL plot methods suffer from large process window prediction errors (approximately 8%) due to single-parameter fitting, making it difficult to meet the high consistency requirements of memory chips. This manufacturer has deployed the "Process Window Prediction Method Based on Surface Fitting" prediction system of this invention to quickly determine the maximum process window during the mass production optimization phase, adjust photolithography parameters, reduce wafer edge defects, improve yield, and lower production costs.

[0158] Input data: Wafer layout data (8GB, containing coordinates and Fin width distribution of 800 chips), historical process parameters (500 sets of light dose and focus position records), scanning electron microscope measurement data (critical dimensions, light dose, and focus position of 800 measurement points), lithography equipment parameter range (light dose 8-16mJ / cm², focus position -0.15-0.15µm), critical dimension acceptable range (20-24nm), target yield (96%), minimum process window area threshold (0.08mJ / cm²·µm).

[0159] Execution flow: The prediction system is deployed on a high-performance computing cluster (4 nodes, AMD EPYC7543 processors, 4 NVIDIA H100 GPUs, 2TB NVMe hard drives), running Ubuntu 20.04. The control module initializes the system, loads wafer layout data and historical parameters, configures an iteration limit of 80 times and a yield target of 96%, and reads pre-trained model parameters (capsule networks, Transformers, etc.) from the database. The measurement data processing module, based on the layout's graphic complexity (fin density > 40% of the area) and process sensitivity (defect rate in edge areas > 0.2%), selects 800 measurement points through hierarchical sampling and K-means clustering (4 clusters), prioritizing coverage of wafer edges (approximately 500 points) and the central high-density area (approximately 300 points). Key dimensions (e.g., 22.1 nm), illumination dose (12.2 mJ / cm²), and focus position (-0.02 µm) are acquired from a scanning electron microscope (PCIe 4.0 interface, 100 frames / second). 64-dimensional graphic features are extracted using a capsule network. (n width, surface roughness), a temporal convolutional network processes 8-point sequences to generate 32-dimensional time series features, an adaptive fusion network (weights 55% graph, 45% time series) generates 128-dimensional measurement results, Kalman filtering (noise standard deviation 1.5nm) smooths the data (adjusting 22.1nm to 22.0nm), Mahalanobis distance anomaly detection removes 4% of outliers (e.g., critical size 26nm), a generative adversarial network trains 800 fluctuating samples (light dose ±0.4mJ / cm², critical size ±0.8nm) to improve robustness, and 800 sets of measurement results are transmitted to the control module. The model simulation module generates 40 sets of parameter combinations (e.g., light dose 9-15 mJ / cm², focusing position -0.12-0.12µm) through Latin hypercube sampling, generates an L_9(3^2) table (9 sets of high-precision combinations) through orthogonal experimental design, generates the simulation critical size (21.8nm) through variational autoencoder, reduces noise by 25% through dual-scale filtering (3×3 high-frequency kernel, 5×5 low-frequency kernel) and adaptive threshold segmentation (median ± 1.2 times standard deviation), improves generalization through random perturbation (light dose ± 0.08 mJ / cm²) and data augmentation (800 samples), and transmits 40 sets of simulation results to the control module.The process window analysis module integrates 800 sets of measurement data and 40 sets of simulation data to generate a 3D point set. Principal component analysis initializes two principal components. A Transformer (4 layers, 8 heads) fits a continuous surface through a self-attention mechanism (mean square error 0.3nm², time 0.8 seconds), extracts the surface portion with a critical size of 20-24nm, and generates a qualified parameter value space through weighted projection (Gaussian kernel bandwidth 0.08) (improving boundary clarity by 20%). Deep reinforcement learning (3 layers, 512 units) searches for the largest elliptical window (area 0.09mJ / cm²·µm, time 0.4 seconds). A genetic algorithm prunes 25% of the parameters (40 generations, accuracy loss 1.5%). Transfer learning adapts to the 14nm FinFET process (800 samples, 8 minutes). The surface, parameter space, and window data are then transmitted to the control module. The visualization module renders a 3D surface (displaying variations from 20-24nm) using OpenGL, generates a 2D projection (elliptical window boundaries) using WebGL, outputs SVG and HTML formats, and stores the data in a database (supporting 80 iterations). Users can interactively adjust the light dose (±0.4mJ / cm²) and focus position (±0.015µm, refresh rate 0.15 seconds) via a 4K display. The control module receives window data, obtains yield data (95.4%), smooths it to 95.5% using a weighted moving average (window size 4, decay factor 0.25) (reducing fluctuation by 45%), adjusts the surface parameters using Kalman filtering (noise variance 0.04) (coefficients from 0.4 to 0.41, 2 iterations), and processes it in parallel using a distributed computing framework (8 GPU nodes, InfiniBand 100Gbps) (total processing time 1.8 minutes). Iteration steps S5 to S8 are performed until the window area reaches 0.08mJ / cm²·µm and the yield reaches 96%, then the final parameters are stored.

[0160] Output results: The process window has an illumination dose of 9.5-14.5 mJ / cm², a focusing position of -0.1-0.1 µm (area of ​​0.09 mJ / cm²·µm), a critical dimension pass rate of 96.2%, a 3D curved surface graphic (showing a 20-24 nm change), a 2D projection graphic (elliptical window boundary), and parameters and graphics stored in the database (approximately 90 MB).

[0161] Application Results: The prediction system successfully adjusted lithography parameters during mass production optimization, improving yield from 95.4% to 96.2% (an increase of 0.8%), reducing approximately 6 defective chips per wafer, and saving approximately $4,000 per batch (100 wafers). Compared to traditional EL map methods, the process window area increased by 12% (from 0.08 to 0.09 mJ / cm²·µm), prediction error decreased by 40% (from 8% to 4.8%), and total computation time was reduced from 8 minutes to 1.8 minutes (an efficiency improvement of 77.5%). Engineers verified window stability through an interactive interface (8 adjustments took 1.5 minutes). The system adaptation to the 14nm FinFET process requires only 8 minutes of fine-tuning, saving 75% of time compared to retraining. In particular, the defect rate in the wafer edge region decreased by 20% (from 0.25% to 0.2%), significantly improving DRAM chip consistency. Case studies demonstrate the system's advantages in high consistency, rapid optimization, and edge defect control, contributing to improved mass production efficiency and yield of 14nm memory chips.

[0162] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising a reference structure" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0163] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A process window prediction method based on surface fitting, comprising a prediction system, characterized in that: The prediction system includes a control module, a measurement data processing module, a model simulation module, a process window analysis module, and a visualization module; The control module executes the following control flow for the control body: system initialization, loading wafer data; Send data acquisition commands to the measurement data processing module; receive measurement result data from the measurement data processing module and transmit it to the model simulation module; The model simulation module is triggered to generate simulation measurement results; the measurement result data and simulation measurement results are then transmitted to the process window analysis module. Receive process window data from the process window analysis module; Trigger the visualization module to generate visual graphics; Adjust system parameters based on production yield data, and iterate until the process window meets the preset threshold. The measurement data processing module generates measurement result data and transmits it to the control module; the model simulation module generates simulation measurement results and transmits them to the control module. The process window analysis module includes a surface fitting submodule to generate surface data, a projection submodule to generate qualified parameter value space data, and a window optimization submodule to generate process window data, which are then transmitted to the control module; the visualization module generates 3D surface graphics and 2D projection graphics, which are then transmitted to the control module. The prediction method of the prediction system includes the following steps: S1: Define multiple measurement points on the wafer, each measurement point corresponding to a critical dimension; S2: Determine the combination of process parameters, including light dose and focusing position; S3: Generate measurement result data and simulation measurement results for each measurement point under each set of process parameters, and merge the measurement result data and simulation measurement results; S4: Generate a 3D point set based on fused data, where each point consists of light dose, focus position, and key dimensions; S5: Fitting a 3D point set into a continuous surface based on an adaptive surface fitting algorithm; S6: Extract the surface based on the acceptable range of the critical dimensions to generate acceptable surface data; S7: Project the qualified surface onto the light dose-focus position plane using a weighted projection algorithm to generate a qualified parameter value space; S8: Generate the maximum process window in the qualified parameter value space based on the constraint optimization algorithm; S9: Adjust the surface fitting parameters based on the production yield data, and repeat steps S5 to S8 until the process window meets the preset threshold.

2. The process window prediction method based on surface fitting according to claim 1, characterized in that: The measurement data processing module extracts graphic features of key dimensions of measurement points through a capsule network to generate feature vectors; it processes time-series data of process parameters such as light dose and focus position through a temporal convolutional network to generate time-series features; and it adjusts the fusion weights according to the distribution density of measurement points through an adaptive fusion network to fuse feature vectors and time-series features to generate measurement result data. The measurement result data is transmitted to the control module for use by the model simulation module and the process window analysis module.

3. The process window prediction method based on surface fitting according to claim 2, characterized in that: The model simulation module constructs a simulation model of the key dimensions of the lithography through a variational autoencoder and generates simulation measurement results; it processes high-frequency and low-frequency noise through dual-scale filtering and determines the segmentation threshold based on the distribution of the key dimensions through adaptive threshold segmentation to generate noise-reduced simulation measurement results; the simulation measurement results are transmitted to the control module for use by the process window analysis module.

4. The process window prediction method based on surface fitting according to claim 3, characterized in that: The surface fitting submodule of the process window analysis module uses a long short-term dependency network of the Transformer architecture and a self-attention mechanism to process measurement result data and simulation measurement results to generate surface data; the projection submodule uses a weighted projection algorithm to generate qualified parameter value space data based on the key dimension distribution. The window optimization submodule uses a deep reinforcement learning network to approximate the Q-function based on a neural network, analyzes the qualified parameter value space data, and generates process window data; the data is then transmitted to the control module.

5. The process window prediction method based on surface fitting according to claim 4, characterized in that: The visualization module generates three-dimensional visualization graphics of continuous curved surfaces through a three-dimensional rendering algorithm, and generates two-dimensional visualization graphics of the qualified parameter value space and process window through a two-dimensional projection algorithm; it supports users to adjust the light dose and focus position through an interactive interface, and updates the visualization graphics in real time. The visualization module transmits the updated visualization graphic data to the control module.

6. The process window prediction method based on surface fitting according to claim 5, characterized in that: The process window analysis module includes an adaptive optimization submodule, which uses a genetic algorithm to prune redundant parameters of the deep reinforcement learning network to generate a simplified process window analysis model; it uses transfer learning to transfer knowledge from the complex analysis model to the simplified model to generate a process window analysis model adapted to different process nodes; the process window data of the model is transmitted to the control module.

7. The process window prediction method based on surface fitting according to claim 6, characterized in that: The control module performs the following steps during the system training phase: pre-training measurement data processing module, model simulation module, process window analysis module, and visualization module to generate initial parameters; fine-tuning the parameters of each module through backpropagation algorithm to optimize system performance based on the overall loss function; adjusting the learning rate according to gradient changes through an adaptive learning rate adjustment mechanism to generate trained system parameters; the parameters are stored in the control module.

8. The process window prediction method based on surface fitting according to claim 7, characterized in that: The control module performs the following steps during system operation: receiving process window data from the process window analysis module and calculating manufacturing yield; comparing the yield with a preset target to generate deviation data; adjusting the feature extraction parameters of the measurement data processing module, the simulation parameters of the model simulation module, and the analysis parameters of the process window analysis module based on the deviation data; and generating updated system parameters by merging new wafer data and process parameter data through incremental learning. The parameters are stored in the control module.

9. The process window prediction method based on surface fitting according to claim 8, characterized in that: The measurement data processing module generates adversarial samples containing process parameter fluctuations and critical dimension noise through a generative adversarial network, trains a capsule network and a temporal convolutional network, and generates a feature extraction model after adversarial training. The model simulation module processes the simulation measurement results through random perturbation and data augmentation, trains the variational autoencoder, and generates a data-augmented simulation model; the model is stored in the control module.

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