Automatic FEM generation and Bosung curve rapid statistical analysis method

Abstract

The invention provides an automatic FEM (Field Effect Model) generation and Boshang curve rapid statistical analysis method, which relates to the technical field of photoetching process modeling and automatic analysis, comprises a photoetching process data processing system, and is characterized in that: when the photoetching process data processing system is constructed, a Boshang curve is generated; the data input module, the FEM model generation module, the statistical analysis module and the result output and application module are fused to process the process data, the photolithographic process data are efficiently collected and preprocessed through the data input module, a reliable foundation is laid for subsequent analysis, key parameters of a Boshang curve are accurately extracted through a multivariate algorithm of the statistical analysis module, and the accuracy of the Boshang curve is improved. The correlation between the technological parameters and the result is clearly presented, an engineer does not need to depend on traditional experience trial and error adjustment, the photoetching technological parameters can be rapidly and accurately optimized according to the scientific quantitative analysis result, the technological optimization efficiency is greatly improved, and production delay caused by improper parameter adjustment is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of photolithography process modeling and automated analysis, and in particular to an automated FEM generation and Bossung curve rapid statistical analysis method. Background Art

[0002] With the continuous advancement of semiconductor manufacturing technology, the precision and stability of the photolithography process, a core step in chip manufacturing, play a decisive role in chip performance and production efficiency. Slight deviations in the photolithography process can lead to reduced chip performance, lowered yields, and even cause large-scale production failures, thereby impacting the development of the entire semiconductor industry. Therefore, how to accurately and efficiently optimize the photolithography process and promptly identify and resolve potential problems has become a critical issue in the semiconductor manufacturing field.

[0003] At present, the following technical means are mainly used for photolithography process optimization and problem diagnosis: Traditional process parameter adjustment: relying on engineers' experience and trial and error methods, manual adjustment of parameters such as exposure dose, focal length, and development time in the photolithography process.

[0004] Single-point measurement and feedback control: By setting sensors at specific locations on the lithography equipment, single-point measurements of key physical quantities (such as light intensity and temperature) are performed, and local feedback control is performed based on the measurement results.

[0005] Offline data analysis: Collect product data after the photolithography process is completed, such as the critical dimensions of the chip, pattern defects, etc., and infer possible problems in the process through post-process data analysis.

[0006] Simple model prediction: Use simplified physical models to predict lithography process results and guide the setting of process parameters.

[0007] Although existing technical means have played a certain role in optimizing the lithography process, they still expose many drawbacks:

[0008] Problem 1: Traditional manual empirical parameter adjustment is highly dependent on the engineer's personal skills and experience and lacks standardized processes. Differences in operations between different engineers may lead to poor process stability, and when faced with new processes and complex problems, the adjustment effect is difficult to guarantee.

[0009] The second problem is that single-point measurement and feedback control cannot fully perceive the overall state of the lithography process, and it is difficult to effectively deal with spatial changes and complex coupling phenomena in the process, which can easily lead to the accumulation of process deviations in unmonitored areas, affecting product quality consistency.

[0010] Problem three: Offline data analysis cannot achieve real-time feedback, process adjustments have obvious delays, and cannot respond to dynamic changes in the process in a timely manner, resulting in the production of a large number of defective products, causing waste of resources and increased costs.

[0011] Problem 4: Simple model predictions oversimplify the complex physical process of the lithography process and cannot accurately capture the complex nonlinear relationship between process parameters and results. In actual production, the prediction error is large, making it difficult to provide reliable process optimization guidance.

[0012] Therefore, an automated FEM generation and Bossung curve fast statistical analysis method is needed to solve the above problems. Summary of the Invention

[0013] Technical problems solved

[0014] In view of the deficiencies of the prior art, the present invention provides an automated FEM generation and Bossung curve rapid statistical analysis method, which solves the problems in the above background technology.

[0015] Technical Solution

[0016] To achieve the above objectives, the present invention is implemented through the following technical solutions: an automated FEM generation and Bossung curve rapid statistical analysis method, including a photolithography process data processing system, characterized in that: when the photolithography process data processing system is constructed, it integrates a data input module, an FEM model generation module, a statistical analysis module, and a result output and application module to process process data;

[0017] The data input module is equipped with a regular expression-based data validation algorithm. For CSV format data, regular expressions are used to match comma-separated value formats. For XLSX format, the file content is read with the help of the ApachePOI library and the data format is checked according to the predefined regular expression pattern. Outlier detection uses an algorithm based on the interquartile range to calculate the first and third quartiles of the data.

[0018] The FEM model generation module adopts the Galerkin finite element discretization method to discretize the physical field in the lithography process according to triangular and quadrilateral grids. When dividing the grid, it uses gradient-based adaptive grid division technology according to different physical field characteristics. In areas where the electric field intensity and light intensity physical quantities change dramatically, the grid is automatically encrypted according to the physical quantity gradient value to improve the model calculation accuracy. At the same time, a deep learning algorithm based on convolutional neural network is introduced. The network structure includes multiple convolution layers, pooling layers and fully connected layers. By training with historical lithography process data, the model parameters are continuously optimized, thereby realizing automatic optimization and correction of the FEM model and improving the model accuracy and adaptability.

[0019] The statistical analysis module uses the one-way analysis of variance and linear regression analysis algorithms in variance analysis to conduct in-depth analysis of model data, adopts the least squares method to fit the linear regression model, accurately extracts key parameters such as the slope, intercept and inflection point of the Bossung curve, and conducts detailed analysis. In the application of big data analysis technology, the Hadoop distributed file system is used to store massive historical data, and the Spark distributed computing framework is used for parallel computing. The Apriori association rule mining algorithm is used, with the minimum support set to 0.1 and the minimum confidence set to 0.8, to mine hidden process laws.

[0020] The result output and application module uses the Echarts visualization library to generate intuitive curve charts and the Apache POI library to generate detailed data reports, allowing engineers to quickly understand analysis results. The system has standardized interfaces with mainstream lithography equipment that comply with SECS / GEM standards. Through automated scripts written in Python, the optimized parameters are automatically transmitted to the equipment using the equipment's API. This enables rapid updates of equipment parameters. The system also uses the SpringBoot framework to build web applications, supporting web-based remote control and monitoring. Engineers can operate and monitor the system anytime, anywhere through any networked device.

[0021] Preferably, in the FEM model generation module, during the finite element discretization process, an adaptive meshing technique based on the Zienkiewicz-Zhu error estimator is used to target different physical field characteristics. By calculating the energy norm error, the area where the mesh needs to be refined is determined. The mesh is automatically refined in areas where physical quantities vary dramatically to improve the model's computational accuracy. In terms of deep learning algorithm optimization, a transfer learning strategy based on the ImageNet pre-trained model is adopted. The convolutional layer parameters of the pre-trained model are transferred to the photolithography process FEM model optimization, while some convolutional layer parameters are fixed and only the fully connected layer is fine-tuned. This accelerates the model's convergence speed and reduces training time.

[0022] Preferably, in the statistical analysis module, when using statistical algorithms for parameter analysis, the Monte Carlo simulation method is combined, the number of simulations is set to 1000 times, and the uncertainty range of the parameters is calculated by randomly generating parameter values. The uncertainty of the parameters is quantitatively evaluated to provide a more reliable basis for process optimization. In the application of big data analysis technology, an autoencoder algorithm based on a multi-layer perceptron structure is introduced. The encoder and decoder both contain multiple hidden layers, and the number of neurons in the hidden layers is [256, 128, 64] respectively. Feature extraction and dimensionality reduction processing are performed on massive historical data to further mine the potential information in the data.

[0023] Preferably, in the result output and application module, in terms of visualization, interactive visualization technology based on the D3.js library is adopted. Engineers can use mouse clicks, zooming and panning operations to deeply view the detailed information of curves and data reports, such as the specific data of a certain point on the curve, and the data of a certain row and column of the data report. In the remote control and monitoring function, blockchain technology based on the elliptic curve encryption algorithm is introduced to encrypt and sign the transmitted data to ensure the security and integrity of the data and prevent data tampering.

[0024] Preferably, in the data verification function, the data input module, in addition to format checking and outlier detection, also introduces a data repair mechanism based on K nearest neighbors. For data points marked as abnormal, the distance between them and the k=5 nearest neighbor data points is calculated, and the abnormal data is repaired according to the average and median of the nearest neighbor data points to further improve the data availability.

[0025] Preferably, the lithography process data processing system also includes a process window prediction module. This module analyzes the Bossung curve, applies a support vector machine algorithm based on a radial basis function kernel, and combines physical models and historical data of the lithography process to predict the optimal process window range for the lithography process, providing accurate guidance for production. Furthermore, based on the Quartz timed task scheduling framework, this module dynamically adjusts the predicted process window range every 10 minutes based on the latest production data and analysis results.

[0026] Preferably, the photolithography process data processing system has a multi-process comparison function, and analyzes and compares data of different photolithography processes at the same time. During the comparison process, the hierarchical analysis method is adopted to construct a judgment matrix, and the weight of each factor is calculated by the eigenvector method. The process cost, production efficiency, product quality and multiple factors are comprehensively considered to provide engineers with quantitative process comparison results, helping engineers to select the optimal process solution more scientifically.

[0027] Preferably, the lithography process data processing system incorporates an intelligent recommendation module. Based on analysis results and historical experience, it utilizes a Q-learning-based reinforcement learning recommendation algorithm, sets a learning rate of 0.1, a discount factor of 0.9, and incorporates real-time production environment and equipment status information. This module provides engineers with more accurate recommendations for adjusting lithography process parameters. Furthermore, this module uses a MySQL database to record engineers' actual adoption of recommendations and subsequent production results. This module continuously optimizes the recommendation algorithm through regular updates of the algorithm model.

[0028] Preferably, the photolithography process data processing system has an adaptive optimization function, which can automatically adjust the analysis method and model parameters according to the feedback data in actual production, using the adaptive control theory based on model predictive control and the stochastic gradient descent online learning algorithm. For example, when it is found that the deviation between the analysis result and the actual production situation exceeds a set threshold (such as 5%), the model retraining and parameter adjustment are automatically triggered to improve the accuracy and efficiency of the analysis. In addition, the system is based on a monitoring platform built on Prometheus and Grafana, with a self-diagnosis function, which can monitor its own CPU usage, memory usage, network traffic and other operating status in real time, and promptly discover and solve potential faults and problems.

[0029] Beneficial effects

[0030] The present invention provides a method for automated FEM generation and rapid statistical analysis of Bossung curves. It has the following beneficial effects:

[0031] 1. The present invention efficiently collects and preprocesses lithography process data through the data input module, laying a solid foundation for subsequent analysis. The multivariate algorithm of the statistical analysis module accurately extracts key parameters of the Bossung curve and clearly presents the relationship between process parameters and results. Engineers do not need to rely on traditional experience and trial and error adjustments. Based on the scientific quantitative analysis results, they can quickly and accurately optimize lithography process parameters, greatly improving process optimization efficiency and reducing production delays caused by improper parameter adjustment. The FEM model generation module uses the Galerkin finite element discretization method, combined with the adaptive grid division technology based on gradient and Zienkiewicz-Zhu error estimator to accurately discretize the lithography process physical field. The deep learning algorithm based on the convolutional neural network automatically optimizes and corrects the FEM model with the help of the transfer learning strategy of the ImageNet pre-trained model. Compared with simple model predictions, it can more accurately capture the complex nonlinear relationship between process parameters and results, provide more reliable model support for process optimization, and significantly improve process optimization accuracy.

[0032] 2. Different from single-point measurement and feedback control, the present invention uses multi-source data acquisition and advanced analysis algorithms to fully monitor the electric field intensity and light intensity physical quantities in the lithography process. Through adaptive grid division technology, the grid is automatically encrypted in the area where the physical quantity changes drastically, and the overall state of the lithography process is fully grasped, effectively solving the spatial variation and complex coupling problems in the process, and ensuring product quality consistency; the process window prediction module is based on the support vector machine algorithm with a radial basis function kernel, combined with the lithography process physical model and historical data to predict the optimal window range of the lithography process in real time, and with the help of the scheduled task scheduling framework Quartz, the prediction range is dynamically adjusted every 10 minutes based on the latest production data and analysis results. This real-time feedback mechanism enables engineers to respond to dynamic changes in the process in a timely manner, avoid the accumulation of process deviations and produce a large number of defective products, and reduce resource waste and production costs.

[0033] 3. The automated process and data analysis algorithm in the present invention make process optimization no longer overly dependent on the experience of engineers. New engineers can also operate according to the system analysis results, reducing labor costs and technical barriers and improving process stability. The result output and application module uses visualization technologies such as Echarts and D3.js and the ApachePOI library to generate reports, which makes it convenient for engineers to quickly understand the analysis results and accurately grasp the process status. The optimization parameters are automatically transmitted to the lithography equipment through the interface that complies with the SECS / GEM standard and the Python automation script, so as to realize the rapid update of equipment parameters, reduce unnecessary manual intervention and resource waste, improve the utilization efficiency of production resources, and reduce overall production costs.

[0034] 4. The statistical analysis module in the present invention uses the Hadoop distributed file system and the Spark distributed computing framework to process massive historical lithography process data, adopts the Apriori association rule mining algorithm, sets appropriate minimum support and minimum confidence, and mines hidden process rules, helping engineers discover previously unnoticed process parameter associations, and providing new ideas and directions for process optimization; the intelligent recommendation module is based on the Q-learning reinforcement learning recommendation algorithm, combined with real-time production environment and equipment status information, to recommend accurate lithography process parameter adjustment suggestions to engineers. The multi-process comparison function adopts the hierarchical analysis method, comprehensively considering factors such as process cost, production efficiency and product quality, and providing engineers with quantitative process comparison results, which helps engineers make scientific decisions among many process solutions, select the optimal process solution, and improve overall production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is the overall framework diagram of the present invention;

[0036] Figure 2 is a system flow chart of the present invention;

[0037] Figure 3 It is the Bossung curve simulation diagram of the present invention;

[0038] Figure 4 This is a simulation diagram of the FEM model of the photolithography process of the present invention. DETAILED DESCRIPTION

[0039] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention. Specific embodiment one:

[0041] like Figure 1-4 As shown, when constructing the lithography process data processing system, the data input module, FEM model generation module, statistical analysis module and result output and application module are integrated to process the process data;

[0042] The data input module is equipped with a regular expression-based data validation algorithm. For CSV format data, regular expressions are used to match comma-separated value formats. For XLSX format, the ApachePOI library is used to read the file content and check the data format according to predefined regular expression patterns. Outlier detection uses an algorithm based on the interquartile range to calculate the first and third quartiles of the data.

[0043] The FEM model generation module uses the Galerkin finite element discretization method to discretize the physical fields in the lithography process into triangular and quadrilateral grids. When meshing, it uses a gradient-based adaptive meshing technique to target different physical field characteristics. In areas where the electric field intensity and light intensity vary dramatically, the grid is automatically encrypted based on the gradient value of the physical quantity to improve the model calculation accuracy. At the same time, a deep learning algorithm based on a convolutional neural network is introduced. The network structure includes multiple convolutional layers, pooling layers, and fully connected layers. The model parameters are continuously optimized by training with historical lithography process data.

[0044] The statistical analysis module uses the single-factor ANOVA and linear regression analysis algorithms in variance analysis to conduct in-depth analysis of model data. It uses the least squares method to fit the linear regression model, accurately extracts key parameters such as the slope, intercept, and inflection point of the Bossung curve, and conducts detailed analysis. In the application of big data analysis technology, it uses the Hadoop distributed file system to store massive historical data, and uses the Spark distributed computing framework for parallel computing. It uses the Apriori association rule mining algorithm with a minimum support of 0.1 and a minimum confidence of 0.8 to discover hidden process laws.

[0045] The result output and application module uses the Echarts visualization library to generate intuitive curve charts and the ApachePOI library to generate detailed data reports, allowing engineers to quickly understand the analysis results. The system has a standardized interface with mainstream lithography equipment that complies with SECS / GEM standards. Through automated scripts written in Python, the optimized parameters are automatically transferred to the equipment using the API provided by the equipment.

[0046] The overall system works as follows:

[0047] Data input: The data input module is the entrance to the system and is responsible for collecting key data such as exposure dose and focal length in the photolithography process. It processes data of different formats through a data verification algorithm based on regular expressions. For the CSV format, regular expressions are used to match the comma-separated value format; for the XLSX format, the ApachePOI library is used to read the content and check it according to the predefined regular expression pattern. The first quartile and third quartile of the data are calculated using an algorithm based on the interquartile range to detect outliers. If slightly erroneous data is found, the data repair mechanism based on K nearest neighbors (K=5) is used to repair the abnormal data according to the average or median of the nearest neighbor data points to ensure that the input data is accurate, complete and usable, providing a reliable foundation for subsequent processing.

[0048] FEM Model Generation: The FEM model generation module receives processed data from the data input module. Using the Galerkin finite element discretization method, the physical fields of the lithography process are discretized into triangular or quadrilateral meshes. A gradient-based adaptive meshing technique automatically refines the mesh in areas of drastic changes based on the gradients of physical quantities such as electric field intensity and light intensity, improving computational accuracy. Furthermore, a convolutional neural network deep learning algorithm, consisting of multiple convolutional, pooling, and fully connected layers, is introduced to train on historical lithography process data and continuously optimize model parameters. During finite element discretization, an adaptive meshing technique based on the Zienkiewicz-Zhu error estimator is also employed, determining the mesh refinement area by calculating the energy norm error. During deep learning optimization, a transfer learning strategy based on the ImageNet pre-trained model is employed, fixing some convolutional layer parameters and fine-tuning only the fully connected layers. This improves model accuracy and adaptability, generating an accurate FEM model for subsequent analysis.

[0049] Statistical Analysis: The statistical analysis module performs in-depth analysis of the FEM model data output by the FEM model generation module. Using the one-way ANOVA and linear regression algorithms within the variance analysis framework, the least squares method is used to fit the linear regression model, accurately extracting key parameters such as the slope, intercept, and inflection point of the Bossung curve. Monte Carlo simulation (set to 1000 simulations) is used to randomly generate parameter values ​​and calculate the uncertainty range, quantitatively assessing parameter uncertainty. The Hadoop distributed file system is used to store massive amounts of historical data. Leveraging the Spark distributed computing framework for parallel computing, the Apriori association rule mining algorithm (minimum support 0.1, minimum confidence 0.8) is employed to uncover hidden process patterns. An autoencoder algorithm based on a multilayer perceptron architecture (with 256, 128, and 64 neurons in the encoder and decoder hidden layers, respectively) is introduced to perform feature extraction and dimensionality reduction on the historical data, providing comprehensive analytical results for the output and application modules.

[0050] Result output and application: The result output and application module receives the analysis results from the statistical analysis module, uses the Echarts visualization library to generate intuitive curve charts, and uses the ApachePOI library to generate detailed data reports, making it easier for engineers to understand the analysis results. Through a standardized interface that complies with the SECS / GEM standard, the system uses automated scripts written in Python and the device API to automatically transmit optimized parameters to the lithography equipment, enabling rapid updates of equipment parameters. A web application is built based on the SpringBoot framework, supporting web-based remote control and monitoring functions, allowing engineers to operate and monitor through networked devices. In terms of visualization, interactive visualization technology based on the D3.js library allows engineers to view data in depth. Blockchain technology based on the elliptic curve cryptography algorithm is used to encrypt and sign transmitted data to ensure data security and integrity.

[0051] Process Window Prediction: The process window prediction module analyzes the Bossung curves generated by the statistical analysis module and uses a support vector machine algorithm based on a radial basis function kernel, combined with lithography process physical models and historical data, to predict the optimal lithography process window range. Based on the Quartz scheduled task scheduling framework, the prediction range is dynamically adjusted every 10 minutes based on the latest production data and analysis results, providing accurate production guidance.

[0052] Multi-process comparison: A system with multi-process comparison capabilities simultaneously acquires data from different lithography processes, uses the analytic hierarchy process to construct a judgment matrix, and uses the eigenvector method to calculate the weights of factors such as process cost, production efficiency, and product quality. This provides engineers with quantitative comparison results to help them select the optimal process solution.

[0053] Intelligent Recommendation: Based on statistical analysis and historical experience, the intelligent recommendation module uses a Q-learning-based reinforcement learning algorithm (learning rate 0.1, discount factor 0.9) and combines real-time production environment and equipment status information to recommend lithography process parameter adjustments to engineers. A MySQL database records engineers' adoption of recommendations and subsequent production results, and regularly updates the algorithm model to optimize the recommendation algorithm.

[0054] Adaptive Optimization and Self-Diagnosis: The system features adaptive optimization capabilities. Based on actual production feedback, it uses adaptive control theory based on model predictive control and a stochastic gradient descent online learning algorithm to automatically adjust analysis methods and model parameters. When the deviation between the analysis results and actual production conditions exceeds a set threshold (e.g., 5%), model retraining and parameter adjustment are automatically triggered. A monitoring platform based on Prometheus and Grafana monitors system CPU usage, memory usage, network traffic, and other operational status in real time, promptly identifying and resolving potential problems and ensuring stable and efficient system operation.

[0055] The modules work closely together. The data input module provides reliable data for subsequent modules. The FEM model generation module builds the model based on the input data. The statistical analysis module conducts in-depth analysis of the model data. The result output and application module visualizes the analysis results and applies them to actual production. The process window prediction, multi-process comparison, and intelligent recommendation modules provide multi-faceted support for production and process optimization. The adaptive optimization and self-diagnosis modules ensure stable and accurate operation of the system, jointly realizing automated FEM generation and rapid statistical analysis of Bossung curves. Specific embodiment two:

[0057] like Figure 1-4 As shown, the key algorithms mentioned in Example 1 are analyzed in detail below, including their core mathematical formulas and explanations:

[0058] 3σ criterion (outlier detection algorithm):

[0059] Assume that the data set is {x1,x2,…,x n}, mean Standard deviation If the data point x j Satisfy|x j -μ|>3σ, then x j Determined to be an outlier.

[0060] The mean μ reflects the average level of the data, and the standard deviation σ measures the degree of dispersion of the data relative to the mean. Under the normal distribution assumption, about 99.7% of the data will fall within the interval (μ-3σ,μ+3σ). Data points outside this range are very likely to be outliers and require further inspection and processing.

[0061] In the data input module, outlier detection is performed on data such as exposure dose and focal length in the photolithography process to ensure the accuracy of the input data and prevent abnormal data from interfering with subsequent analysis. For example, if an exposure dose data point is detected to be outside the range of 3 times the standard deviation, it is marked as an outlier for subsequent manual inspection or automatic repair.

[0062] Deep learning algorithms based on convolutional neural networks (CNN):

[0063] Convolutional layer formula:

[0064]

[0065] where y i j l is the output of the (i, j)th position of the lth convolutional layer, w m n l , is the weight of the l-th layer convolution kernel at the (m,n) position, is the input of the l-1 layer at position (i+m,j+n), b l is the bias of layer l.

[0066] Pooling layer formula:

[0067]

[0068] in is the output of the (i, j)th position of the lth pooling layer, is the input of the corresponding sub-region of the l-1 layer, and s is the pooling window size.

[0069] Fully connected layer formula:

[0070] y l =W l x l-1 +b l

[0071] where y l is the output of the lth fully connected layer, W l is the weight matrix, x l-1 is the output of layer l-1, b l is the bias.

[0072] The convolutional layer extracts features from the input data using convolution kernels. Different convolution kernels can extract different types of features. The pooling layer reduces data dimensionality, reduces computational effort, and retains key features. The fully connected layer integrates the features extracted by previous layers and outputs the final result. By learning from a large amount of historical lithography process data, the network's weights and biases are adjusted to achieve automatic optimization and correction of the FEM model.

[0073] Solution Application: In the FEM model generation module, the initial FEM model data obtained through finite element discretization is used as the input of the CNN. A neural network structure consisting of multiple convolutional layers, pooling layers, and fully connected layers is constructed. This is trained on historical lithography process data, and the model parameters are continuously optimized to improve the adaptability and prediction accuracy of the FEM model to different lithography process conditions.

[0074] Analysis of variance (taking one-way analysis of variance as an example): in

[0075] F is the test statistic, MSB is the mean square between groups, MSW is the mean square within groups, SSB is the sum of squares between groups, SSW is the sum of squares within groups, k is the number of groups, n is the mean square between groups, i is the number of samples in group i, is the mean of group i, is the overall mean, is the total sample size, xij is the jth sample value of the i-th group.

[0076] By comparing the mean squares between groups and the mean squares within groups, we can determine whether there are significant differences in the means of the data from different groups. The larger the F value, the more significant the difference between the groups, that is, the different experimental conditions (factor levels) have a significant impact on the experimental results.

[0077] Solution Application: In the statistical analysis module, analyze the significant impact of different factors (such as exposure dose, photoresist type, and other single factors) on photolithography quality (such as line width and pattern accuracy). The photolithography process data is grouped by factor level, and relevant statistics and F-values ​​are calculated. These are then compared with the critical value of the F distribution at a given significance level to determine whether the factors significantly affect the photolithography process.

[0078] Apriori association rule mining algorithm:

[0079] Where X and Y are item sets, σ(X∪Y) is the number of transactions containing X and Y, N is the total number of transactions, and σ(X) is the number of transactions containing X.

[0080] Support measures the frequency of item sets X and Y appearing together. Higher support indicates a greater likelihood of X and Y appearing together. Confidence measures the probability of Y appearing when X appears. Higher confidence indicates a higher reliability of Y appearing when X appears. By setting minimum support and minimum confidence thresholds, meaningful association rules can be mined.

[0081] Solution Application: In the statistical analysis module, big data analysis techniques are combined to mine massive amounts of historical photolithography process data. The data is organized into transaction datasets, and minimum support and confidence thresholds are set. The support and confidence of each item set are calculated, and association rules that meet the threshold conditions are selected to help discover potential connections between different parameters in the photolithography process.

[0082] Autoencoder algorithm:

[0083] Encoder formula:

[0084] h=σ1(W1x+b1)

[0085] Where h is the encoded feature vector, σ1 is the activation function (such as the ReLU function σ1(x) = max(0,x)), W1 is the weight matrix of the encoder, x is the input data, and b1 is the bias of the encoder.

[0086] Decoder formula: in is the reconstructed data after decoding, σ2 is the activation function, W2 is the weight matrix of the decoder, h is the encoded feature vector, and b2 is the bias of the decoder.

[0087] The autoencoder compresses the input data into a low-dimensional feature vector through the encoder, and then reconstructs the feature vector into the original data through the decoder. During the training process, the reconstruction error (such as mean square error) is minimized. ) to learn the feature representation of data, and perform feature extraction and dimensionality reduction on the data.

[0088] Solution Application: In the statistical analysis module, feature extraction and dimensionality reduction are performed on massive amounts of historical lithography process data. This historical data is fed into an autoencoder, which is trained to learn effective feature representations of the data, reducing its dimensionality while retaining key information. This allows for further mining of potential insights within the data, providing more valuable data for subsequent analysis and mining. Specific embodiment three:

[0090] like Figure 1-4 The following is a description of the specific application logic steps of each module and algorithm in the automated FEM generation and Bossung curve rapid statistical analysis method:

[0091] 1. Data input module:

[0092] Data reading:

[0093] If the data is in CSV format, read the file content directly;

[0094] If the data is in XLSX format, call the relevant methods of the ApachePOI library to read the file content.

[0095] Data format verification:

[0096] For CSV data, use predefined regular expressions to match the comma-separated value format and check whether each row of data complies with the specification;

[0097] For XLSX data, the format of the read cell content is checked according to the predefined regular expression pattern.

[0098] Outlier detection: Calculate the first quartile (Q1) and third quartile (Q3) of the data; calculate the interquartile range (IQR = Q3-Q1); determine the outlier range: the lower limit is Q1-1.5*IQR, and the upper limit is Q3+1.5*IQR. Mark all data points outside this range as outliers;

[0099] Data repair:

[0100] For a data point marked as abnormal, calculate its distance to k=5 nearest neighbor data points; and repair the abnormal data according to the average or median of these five nearest neighbor data points.

[0101] 2. FEM model generation module:

[0102] Finite element discretization:

[0103] The Galerkin finite element discretization method is used to discretize the physical fields in the lithography process into triangular and quadrilateral grids. A gradient-based adaptive meshing technique is used to address different physical field characteristics. The gradient values ​​of physical quantities such as electric field intensity and light intensity are calculated. The mesh is automatically refined in areas where the gradient values ​​of physical quantities are large (i.e., where the physical quantities change dramatically). At the same time, an adaptive meshing technique based on the Zienkiewicz-Zhu error estimator is used to calculate the energy norm error. The areas where the mesh needs to be refined are determined based on the energy norm error, and the mesh is automatically refined in these areas.

[0104] Deep Learning Optimization:

[0105] A convolutional neural network consisting of multiple convolutional layers, pooling layers, and fully connected layers was constructed. A transfer learning strategy based on the ImageNet pre-trained model was used to migrate the convolutional layer parameters of the pre-trained model to the optimization of the FEM model for the lithography process. Some convolutional layer parameters were fixed, and only the fully connected layer was fine-tuned. The network was trained using historical lithography process data, and the model parameters were continuously optimized to achieve automatic optimization and correction of the FEM model.

[0106] 3. Statistical analysis module:

[0107] Basic statistical analysis:

[0108] The one-way analysis of variance algorithm was used to analyze the model data of different groups to determine whether the influence of different factors on the results was significant; the linear regression analysis algorithm was used to fit the linear regression model using the least squares method to accurately extract key parameters such as the slope, intercept and inflection point of the Bossung curve.

[0109] Uncertainty assessment:

[0110] Combined with the Monte Carlo simulation method, the number of simulations was set to 1000. Parameter values ​​were randomly generated in each simulation and substituted into the model for calculation. Based on the results of 1000 simulations, the uncertainty range of the parameters was calculated and the uncertainty of the parameters was quantitatively evaluated.

[0111] Big Data Analysis:

[0112] Massive historical data is stored in the Hadoop distributed file system. The Spark distributed computing framework is used for parallel computing to improve computing efficiency. The Apriori association rule mining algorithm is used with the minimum support set to 0.1 and the minimum confidence set to 0.8 to mine hidden process rules. An autoencoder algorithm based on a multi-layer perceptron structure is introduced. Both the encoder and decoder contain multiple hidden layers, and the number of neurons in the hidden layer is [256, 128, 64] respectively. Feature extraction and dimensionality reduction processing are performed on massive historical data to further mine the potential information in the data.

[0113] 4. Result output and application module:

[0114] Visual display:

[0115] The Echarts visualization library is used to generate intuitive curve charts to display analysis results. The interactive visualization technology based on the D3.js library is used to allow engineers to deeply view the detailed information of curves and data reports through mouse clicks, zooming and panning operations.

[0116] Report Generation:

[0117] Use the Apache POI library to generate detailed data reports, allowing engineers to quickly understand analysis results.

[0118] Parameter transmission:

[0119] Communicates with mainstream lithography equipment through a standardized interface compliant with SECS / GEM standards.

[0120] An automated script written in Python uses the API provided by the device to automatically transfer the optimized parameters to the device, enabling rapid updates of device parameters.

[0121] Remote control and monitoring:

[0122] Building web applications based on the Spring Boot framework supports web-based remote control and monitoring. Blockchain technology based on elliptic curve cryptography is introduced to encrypt and sign transmitted data, ensuring data security and integrity and preventing data tampering.

[0123] 5. Process window prediction module:

[0124] Data preparation:

[0125] Collect relevant data of Bossung curve, as well as physical models and historical data of lithography process.

[0126] Model training and prediction

[0127] The collected data are trained using a support vector machine algorithm based on the radial basis function kernel, and the trained model is used to predict the optimal window range of the lithography process.

[0128] Dynamic Adjustment:

[0129] Based on the scheduled task scheduling framework Quartz, the latest production data and analysis results are obtained every 10 minutes, and the predicted process window range is dynamically adjusted according to the latest data.

[0130] 6. Multi-process comparison module:

[0131] Data Collection:

[0132] Collect data for different photolithography processes.

[0133] Construct a judgment matrix:

[0134] The analytic hierarchy process is used to construct a judgment matrix by comprehensively considering multiple factors such as process cost, production efficiency, and product quality.

[0135] Calculate weights:

[0136] The weight of each factor is calculated using the eigenvector method.

[0137] Comparative analysis:

[0138] Based on the weight of each factor, the data of different lithography processes are comprehensively analyzed and compared to provide engineers with quantitative process comparison results.

[0139] 7. Intelligent recommendation module

[0140] Data Integration:

[0141] Integrate the analysis results of the statistical analysis module, historical experience, and real-time production environment and equipment status information.

[0142] Recommendation algorithm runs:

[0143] Using a Q-learning-based reinforcement learning recommendation algorithm, with a learning rate of 0.1 and a discount factor of 0.9, more accurate lithography process parameter adjustment suggestions are recommended to engineers based on the integrated data.

[0144] Algorithm optimization:

[0145] Based on the MySQL database, we record engineers' actual adoption of recommendations and subsequent production results, regularly update the algorithm model, and continuously optimize the recommendation algorithm.

[0146] 8. Adaptive optimization and self-diagnosis module:

[0147] Adaptive Adjustment:

[0148] Feedback data from actual production is collected in real time, and the adaptive control theory based on model predictive control and the stochastic gradient descent online learning algorithm are used to compare the analysis results with the actual production situation. When it is found that the deviation between the analysis results and the actual production situation exceeds the set threshold (such as 5%), the model retraining and parameter adjustment are automatically triggered.

[0149] Self-diagnosis:

[0150] A monitoring platform based on Prometheus and Grafana is built to monitor the system's CPU usage, memory usage, network traffic and other operating status in real time. Once potential faults and problems are discovered, alarms are issued in a timely manner and corresponding measures are taken. Specific embodiment four:

[0152] like Figure 1-4 As shown, the following is a detailed hardware composition and hardware description of each module in Example 1:

[0153] Data input module:

[0154] The hardware includes various sensors for real-time acquisition of physical parameters such as light intensity, temperature, and pressure during the photolithography process, as well as data acquisition cards that convert analog signals into digital signals. A hard disk array (e.g., enterprise-grade SATA or SAS hard drives, using RAID technology for enhanced reliability and read / write speed) is used to store the collected data, along with a tape library for long-term backup. Furthermore, an X86-based rack-mount server equipped with a multi-core Intel Xeon processor, 64GB or more of memory, and a high-speed network interface runs data validation and outlier detection programs. Sensor accuracy and response speed affect data accuracy and real-time performance. Storage device capacity and read / write performance must match the data volume and processing requirements. Server performance determines data processing efficiency.

[0155] FEM model generation module:

[0156] A high-performance computing cluster consists of multiple computing nodes equipped with multi-core AMD EPYC processors, large memory capacities, and high-speed NVIDIA Tesla GPUs to accelerate finite element discretization and deep learning algorithm computations. High-speed networks such as 10 Gigabit Ethernet or InfiniBand enable high-speed data transmission between nodes, reducing communication latency. Distributed storage systems such as Ceph or GlusterFS provide unified storage services for the computing nodes, meeting the needs of large-scale data read and write operations. Cluster computing power is key, with high-speed networks avoiding computing bottlenecks and distributed storage ensuring data storage.

[0157] Statistical analysis module:

[0158] The big data processing platform, comprised of multiple servers running the Hadoop and Spark big data processing frameworks, is used to store and process massive amounts of historical lithography process data. Data analysis servers, equipped with high-performance Intel Core i9 processors, large memory capacities, and high-speed hard drives, run statistical analysis and data mining algorithms, with optional NVIDIA RTX GPUs accelerating complex computational tasks. Scalability and fault tolerance are crucial for big data processing platforms. The performance of the data analysis servers impacts algorithm efficiency, and GPUs can accelerate certain complex algorithms.

[0159] Result output and application module:

[0160] Display devices include high-resolution 4K or OLED monitors for visualizing charts and reports, as well as immersive AR / VR devices like Microsoft HoloLens and Oculus Rift. Laser or inkjet printers are used to print report results. Network equipment such as routers and switches supports SECS / GEM protocols, ensuring stable communication with lithography equipment. Servers or specialized hardware devices are used to build blockchain networks and implement data encryption, signatures, and tamper-proof storage. Display devices influence visualization, while printing equipment determines report output efficiency. Network equipment ensures data transmission, and blockchain nodes ensure data security.

[0161] Process window prediction module:

[0162] The prediction server is equipped with a multi-core Intel Xeon processor, large memory, and high-speed hard drives, running a radial basis function kernel support vector machine algorithm and a scheduled task scheduling framework. A hard disk array or distributed storage system, similar to the data input module, stores lithography process physical models and historical data. A Network Time Protocol (NTP) server ensures accurate scheduled task scheduling. The performance of the prediction server determines the accuracy and real-time nature of predictions. Data storage devices meet data storage access requirements, and clock synchronization ensures the execution of scheduled tasks.

[0163] Multi-process comparison module:

[0164] Equipped with a high-performance AMD Ryzen Threadripper processor, large memory, and high-speed hard drive, this comparative analysis server runs algorithms such as the Analytic Hierarchy Process (AHP). It also features a general-purpose data storage device for storing data from various photolithography processes, and an optional AMD Radeon GPU to accelerate complex matrix operations and eigenvector calculations. The performance of the comparative analysis server impacts the efficiency and accuracy of the comparison. The data storage device meets data storage access requirements, and the GPU accelerates specific calculations.

[0165] Smart recommendation module:

[0166] The recommendation server is equipped with a multi-core ARM Ampere Altra processor, large memory, and a high-speed hard drive, running a Q-learning reinforcement learning recommendation algorithm. A MySQL database server records engineer adoption and production results. Similar to the data input module, a real-time data collection device collects real-time information about the production environment and equipment status. The performance of the recommendation server determines the efficiency and real-time nature of recommendations, while the database server ensures algorithm optimization and the real-time data collection device influences the accuracy of recommendations.

[0167] Adaptive optimization and self-diagnosis module:

[0168] The system features an optimization server equipped with a high-performance Intel Xeon Platinum processor, large memory, and high-speed hard drive, running the model predictive control adaptive control theory and stochastic gradient descent online learning algorithm. A monitoring server, equipped with a multi-core processor, large memory, and high-speed hard drive, runs the Prometheus and Grafana monitoring platforms, providing real-time system status monitoring. Sensors collect hardware status information such as CPU temperature, memory usage, and network traffic. The performance of the optimization server determines the effectiveness and efficiency of adaptive optimization. The monitoring server ensures system self-diagnosis, and the sensors ensure accurate hardware status information collection.

[0169] The following is the attached Figure 3 and attached Figure 4 Analysis of the simulation diagram:

[0170] Bossung curve simulation diagram:

[0171] Chart content:

[0172] X-axis: exposure dose (unit: mJ / cm 2 ), ranging from 20 to 50.

[0173] Y-axis: critical dimension (CD, unit: nm), which represents the width or feature size of the pattern during the photolithography process.

[0174] Curves: Each curve corresponds to a focal length value (from -0.3 μm to 0.3 μm) and shows the variation trend of CD with exposure dose, with a fitted dashed line.

[0175] Effect analysis:

[0176] Process window assessment:

[0177] The Bossung curve shows how critical dimension (CD) varies with focal length and exposure dose. By observing the curve, it is possible to determine which parameter combinations result in a CD within the target range (e.g., 45 ± 2 nm).

[0178] In practical photolithography, the process window refers to the acceptable range of exposure dose and focal length. The Bossung curve intuitively reflects this range. For example, flat areas on the curve indicate that the CD is insensitive to exposure dose variations and generally correspond to a wider process window.

[0179] Parameter optimization:

[0180] The slope and inflection point of each curve (extracted by linear regression fitting in the code) reflect the sensitivity of CD to exposure dose. Engineers can adjust exposure dose and focus based on these parameters to optimize process conditions for stable CD.

[0181] For example, if a curve has a large slope, it means that the CD at that focal length is sensitive to changes in exposure dose and more precise control may be required.

[0182] Process stability analysis:

[0183] By comparing the curves for different focal lengths, we can evaluate the depth of focus (DOF), which is the range of focal length variation while maintaining an acceptable CD. The larger the DOF, the more tolerant the process is to focal length deviations.

[0184] The noise added in the code simulates the random disturbance in actual production, and the deviation of the scattered points on the curve from the fitting line reflects the stability of the process.

[0185] Actual application scenarios

[0186] Equipment calibration: When debugging a lithography machine, use the Bossung curve to verify the performance of the exposure and focusing systems.

[0187] Quality control: Generate Bossung curves regularly during production to monitor whether the process deviates from the target.

[0188] Simulation diagram of FEM model of photolithography process:

[0189] Chart content:

[0190] X-axis: exposure dose (unit: mJ / cm 2 ).

[0191] Y-axis: focal length (unit: microns).

[0192] Z-axis: critical dimension (CD, unit: nm).

[0193] Surface: A three-dimensional surface plot showing the distribution of CD in the two-dimensional space of exposure dose and focus, generated by interpolation.

[0194] Effect analysis:

[0195] Visualization of global process behavior:

[0196] The FEM (Focus-Exposure Matrix) model provides a comprehensive view of how CD varies with both exposure dose and focal length. Compared to the Bossung curve (which only shows a slice at a single focal length), the FEM diagram more intuitively presents the entire process space.

[0197] For example, peaks or valleys in the surface plot may correspond to CD out-of-specification situations, allowing engineers to quickly identify problem areas.

[0198] Physics simulation:

[0199] In the code, the FEM model simulates the effect of physical fields in the lithography process (such as light intensity or electric field) on CD through interpolation (interp2). Although this is a simplified version, it embodies the idea of ​​the finite element method (FEM): discretizing complex physical processes into numerical solutions on a grid.

[0200] In practice, the FEM model may be combined with an optical model (such as the Hopkins formula) or a resist reaction equation to accurately predict the CD distribution.

[0201] Process window boundary determination:

[0202] By observing the color changes of the surface plot (represented by the colorbar), you can visually judge which parameter combinations bring CD close to the target value. For example, flat areas indicate stable process conditions, while steep areas may need to be avoided.

[0203] Combined with the simulation data in the code (45+10sin+5cos), the surface map may show periodic fluctuations, reflecting the optical interference effect of the lithography system.

[0204] Actual application scenarios

[0205] Process development: During the R&D phase, FEM models are used to explore the optimal parameter combinations for new processes.

[0206] Fault diagnosis: When CD anomalies occur during production, FEM images can help determine whether the problem is caused by exposure dose or focus deviation.

[0207] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further restrictions, an element defined by the statement "comprising a reference structure" does not exclude the presence of additional identical elements in the process, method, article, or device comprising the element.

[0208] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. Automated FEM generation and Bossung curve rapid statistical analysis method, including a photolithography process data processing system, characterized by: When constructing the photolithography process data processing system, the data input module, the FEM model generation module, the statistical analysis module and the result output and application module are integrated to process the process data; The data input module is equipped with a regular expression-based data validation algorithm. For CSV format data, regular expressions are used to match comma-separated value formats. For XLSX format, the file content is read with the help of the ApachePOI library and the data format is checked according to the predefined regular expression pattern. Outlier detection uses an algorithm based on the interquartile range to calculate the first and third quartiles of the data. The FEM model generation module adopts the Galerkin finite element discretization method to discretize the physical field in the photolithography process according to triangular and quadrilateral grids. When dividing the grid, it uses a gradient-based adaptive grid division technology based on different physical field characteristics. In areas where the electric field intensity and light intensity physical quantities change dramatically, the grid is automatically encrypted according to the physical quantity gradient value to improve the model calculation accuracy. At the same time, a deep learning algorithm based on convolutional neural network is introduced. The network structure includes multiple convolutional layers, pooling layers and fully connected layers. The model parameters are continuously optimized by training historical photolithography process data. The statistical analysis module uses the single-factor variance analysis and linear regression analysis algorithms in variance analysis to conduct in-depth analysis of model data, adopts the least squares method to fit the linear regression model, accurately extracts the key parameters such as the slope, intercept and inflection point of the Bossung curve, and conducts detailed analysis. In the application of big data analysis technology, the Hadoop distributed file system is used to store massive historical data, and the Spark distributed computing framework is used for parallel computing. The result output and application module uses the Echarts visualization library to generate intuitive curve charts and the ApachePOI library to generate detailed data reports. The system has a standardized interface with mainstream lithography equipment that complies with the SECS / GEM standards. Through automated scripts written in Python, the optimized parameters are automatically transmitted to mobile devices using the API provided by the mobile device.

2. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 1, characterized in that: In the FEM model generation module, during the finite element discretization process, an adaptive meshing technique based on the Zienkiewicz-Zhu error estimator is used to target different physical field characteristics. By calculating the energy norm error, the area where the mesh needs to be encrypted is determined, and the mesh is automatically encrypted in areas where physical quantities change dramatically. In terms of deep learning algorithm optimization, a transfer learning strategy based on the ImageNet pre-trained model is adopted to migrate the convolutional layer parameters of the pre-trained model to the lithography process FEM model optimization, fix some convolutional layer parameters, and only fine-tune the fully connected layer.

3. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 2, characterized in that: In the statistical analysis module, when using statistical algorithms for parameter analysis, the Monte Carlo simulation method is combined, the number of simulations is set to 1000 times, and the uncertainty range of the parameters is calculated by randomly generating parameter values. The uncertainty of the parameters is quantitatively evaluated. In the application of big data analysis technology, an autoencoder algorithm based on a multi-layer perceptron structure is introduced.

4. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 3, characterized in that: In the result output and application module, in terms of visualization, an interactive visualization method is adopted. Engineers can deeply view the detailed information of curves and data reports through mouse clicks, zooming and panning operations. In the remote control and monitoring function, blockchain technology based on the elliptic curve encryption algorithm is introduced to encrypt and sign the transmitted data.

5. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 4, characterized in that: In the data verification function, the data input module, in addition to format checking and outlier detection, also introduces a data repair mechanism based on K-nearest neighbors. For data points marked as abnormal, the distance between them and the k=5 nearest neighbor data points is calculated, and the abnormal data is repaired according to the average and median of the nearest neighbor data points.

6. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 1, characterized in that: The photolithography process data processing system also includes a process window prediction module, which analyzes the Bossung curve, uses a support vector machine algorithm based on a radial basis function kernel, and combines the physical model and historical data of the photolithography process.

7. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 1, characterized in that: The photolithography process data processing system has a multi-process comparison function, and analyzes and compares data of different photolithography processes at the same time. During the comparison process, the hierarchical analysis method is used to construct a judgment matrix, and the weight of each factor is calculated through the eigenvector method, comprehensively considering multiple factors such as process cost, production efficiency, and product quality.

8. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 7, characterized in that: The photolithography process data processing system introduces an intelligent recommendation module. Based on the analysis results and historical experience, it uses a reinforcement learning recommendation algorithm based on Q learning, sets the learning rate to 0.1, the discount factor to 0.9, and combines real-time production environment and equipment status information.

9. The method for constructing a self-adaptive environment intelligent curtain wall visual scanning model according to claim 8, characterized in that: The photolithography process data processing system has an adaptive optimization function, and adopts adaptive control theory based on model predictive control and a stochastic gradient descent online learning algorithm to automatically adjust analysis methods and model parameters.

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