A method for input data quality assessment for lithography process window analysis
Through the method of dynamic integration of multiple models, combined with robust regression, unsupervised detection and Gaussian process uncertainty model, the problem of inaccurate data quality assessment in lithography process window analysis is solved, and efficient and accurate data quality assessment and model fitting are achieved.
Patent Information
- Application Number
- CN202510228382.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-28
- Publication Date
- 2025-10-10
- Estimated Expiration
- 2045-02-28
AI Technical Summary
In the existing technology of lithography process window analysis, the quality of input data is evaluated based on the experience of engineers. This has problems such as inaccurate evaluation and high manpower investment, and it is difficult to quickly confirm the confidence of the data.
The RANSAC regression algorithm, isolation tree detection, and local outlier factor method are combined with the Gaussian regression algorithm. Through dynamic integration of multiple models, the input data quality of lithography process window analysis is comprehensively evaluated. Robust regression residual analysis, unsupervised detection, and Gaussian process uncertainty model are used to generate comprehensive confidence.
It improves the accuracy and efficiency of input data quality assessment, reduces manpower input, can quickly identify and eliminate unreliable data points, and improves the fitting accuracy of the process window analysis model.
Smart Images
Figure CN119828423B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of semiconductor photolithography process optimization, and in particular to an input data quality assessment method for photolithography process window analysis. Background Art
[0002] Existing technologies for input data used in lithography process window analysis rely heavily on experienced engineers to assess collected FEM table data and re-retrieve CD-SEM images for potentially problematic data points to confirm data validity. This approach relies heavily on engineer experience, requires additional manpower for data verification, and carries the risk of omissions. Alternatively, it relies on simple statistical indicators or linear regression models, which differ significantly from the actual process window distribution model. This makes it difficult to find a universally applicable method for quickly confirming data confidence.
[0003] In summary, the prior art for evaluating the quality of input data used for lithography process window analysis suffers from the problem of inaccurate data confidence assessment. Summary of the Invention
[0004] The purpose of the present invention is to improve the evaluation accuracy of the input data quality for lithography process window analysis and to propose an input data quality evaluation method for lithography process window analysis.
[0005] The purpose of the present invention can be achieved by the following technical solutions:
[0006] A method for evaluating input data quality for photolithography process window analysis comprises the following steps:
[0007] S1. Acquire original FEM data, pre-process the original FEM data, and obtain standardized data, wherein the standardized data includes exposure energy, focal length, and critical dimensions;
[0008] S2. Using the RANSAC regression algorithm, with exposure energy and focal length as input features and key dimension prediction values as output targets, a nonlinear relationship model is fitted. The standardized residual is calculated for each data point of the standardized data, and the confidence level of the robust regression residual analysis is obtained based on the residual.
[0009] S3: Exposure energy, focal length, and key dimensions form a standardized three-dimensional matrix. Isolation tree detection is then performed to randomly partition the feature space, identify outliers in low-density areas, and output an isolation tree anomaly score. Based on the isolation tree anomaly score, the isolation tree confidence is obtained.
[0010] S4. Using the local outlier factor method, calculate the local density difference of the three-dimensional matrix, identify the outliers in the sparse area, output the local outlier factor anomaly score, and obtain the local outlier factor confidence based on the local outlier factor anomaly score;
[0011] S5, integrating the isolation tree confidence and the local outlier factor confidence to obtain the unsupervised confidence;
[0012] S6. Using a Gaussian regression algorithm and a radial basis function, with exposure energy and focal length as input features and the key dimension prediction value as the output target, a Gaussian process regression model is trained to obtain the prediction variance, and Gaussian confidence is obtained based on the prediction variance;
[0013] S7. Comprehensive confidence is obtained by integrating robust regression residual analysis confidence, unsupervised confidence and Gaussian confidence. Based on the comprehensive confidence, the input data quality assessment result for lithography process window analysis is obtained.
[0014] Furthermore, the confidence level of the robust regression residual analysis is:
[0015]
[0016] where MAD(e) is the median absolute difference of the residuals;
[0017]
[0018] CD scaled represents the critical dimension, Represents the key size prediction value, i represents the data sequence number, e represents the residual, and ε is a constant.
[0019] Furthermore, the isolation tree confidence is:
[0020]
[0021] Among them, Score IF is the isolation tree anomaly score.
[0022] Furthermore, the local outlier factor confidence is:
[0023]
[0024] Among them, Score LOF is the local outlier factor anomaly score.
[0025] Furthermore, the unsupervised confidence is:
[0026] Confidence unsupervised =0.5×Confidence IF +0.5×ConfidenceLOF
[0027] Among them, Confidence unsupervised Confidence is the unsupervised confidence IF Confidence is the confidence of the isolation tree. LOF is the local outlier factor anomaly score.
[0028] Furthermore, the local density difference is calculated based on the Euclidean distance.
[0029] Furthermore, the Gaussian confidence is:
[0030]
[0031] Among them, λ is a constant, σ scaled is the prediction variance.
[0032] Furthermore, the comprehensive confidence is:
[0033] Confidence final =0.4×Confidence residual +0.3×Confidence unsupervised
[0034] +0.3×Confidence GPR
[0035] Among them, Confidence final Confidence is the comprehensive confidence residual Represents the confidence level of robust regression residual analysis, Confidence unsupervised Confidence is the unsupervised confidence GPR is the Gaussian confidence level.
[0036] Furthermore, the specific steps for obtaining the input data quality assessment results for lithography process window analysis based on the comprehensive confidence are: determining a suitable threshold, screening out suspicious data points from the standardized data based on the comprehensive confidence, visualizing the suspicious data points, and obtaining the quality assessment results.
[0037] Furthermore, the preprocessing includes deduplication and standardization.
[0038] Compared with the prior art, the present invention has the following beneficial effects:
[0039] The present invention combines robust regression, unsupervised detection and probabilistic models through dynamic integration of multiple models, comprehensively covers data anomaly patterns, and weightedly combines them into a more accurate comprehensive confidence level, thereby enhancing the tolerance of input data for process window analysis model fitting. While investing less labor cost, the quality of input data can be quickly improved, and unreliable data points caused by accidental random errors can be avoided from being directly used for model analysis, which helps to improve the accuracy of subsequent process fitting model results. BRIEF DESCRIPTION OF THE DRAWINGS
[0040] Figure 1 is a flow chart of the present invention;
[0041] Figure 2 FEM data to be fitted for process window;
[0042] Figure 3 is the experimental data graph, where Figure 3 (a) is the confidence heat map of the input FEM data, Figure 3 (b) is the warning information of low confidence data points, Figure 3 (c) is the complete data point confidence report;
[0043] Figure 4 Original FEM data table obtained for the experiment;
[0044] Figure 5 It is a FEM data table assuming that there are unreliable data points;
[0045] Figure 6 is the confidence heat map of FEM data processed by the proposed program, where Figure 6 (a) is the data confidence heat map obtained by processing normal data. Figure 6 (b) is the data confidence heat map obtained by program processing after artificially introducing erroneous data points. DETAILED DESCRIPTION
[0046] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.
[0047] Variable definition:
[0048] E: Exposure energy (unit: mJ / cm 2 )
[0049] F: Focal length (unit: μm)
[0050] CD: critical dimension (unit: nm)
[0051] IQR(X): Interquartile Range of variable X
[0052] MAD(X): Median Absolute Deviation of variable X
[0053] The present invention provides a method for evaluating the quality of input data for photolithography process window analysis, the method comprising the following steps:
[0054] S1. Acquire original FEM data, pre-process the original FEM data, and obtain standardized data, wherein the standardized data includes exposure energy, focal length, and critical dimensions;
[0055] S2. Using the RANSAC regression algorithm, with exposure energy and focal length as input features and key dimension prediction values as output targets, a nonlinear relationship model is fitted. The standardized residual is calculated for each data point of the standardized data, and the confidence level of the robust regression residual analysis is obtained based on the residual.
[0056] S3: Exposure energy, focal length, and key dimensions form a standardized three-dimensional matrix. Isolation tree detection is then performed to randomly partition the feature space, identify outliers in low-density areas, and output an isolation tree anomaly score. Based on the isolation tree anomaly score, the isolation tree confidence is obtained.
[0057] S4. Using the local outlier factor method, calculate the local density difference of the three-dimensional matrix, identify the outliers in the sparse area, output the local outlier factor anomaly score, and obtain the local outlier factor confidence based on the local outlier factor anomaly score;
[0058] S5, integrating the isolation tree confidence and the local outlier factor confidence to obtain the unsupervised confidence;
[0059] S6. Using a Gaussian regression algorithm and a radial basis function, with exposure energy and focal length as input features and the key dimension prediction value as the output target, a Gaussian process regression model is trained to obtain the prediction variance, and Gaussian confidence is obtained based on the prediction variance;
[0060] S7. Comprehensive confidence is obtained by integrating robust regression residual analysis confidence, unsupervised confidence and Gaussian confidence. Based on the comprehensive confidence, the input data quality assessment result for lithography process window analysis is obtained.
[0061] The flow chart of the method is as follows Figure 1 The present invention constructs a systematic data quality assessment system, as shown in Figure 1 As shown in the figure, it mainly consists of a data preprocessing module, a multi-model confidence calculation module and a dynamic confidence integration module.
[0062] Data Preprocessing Module: This module receives raw measurement data from the lithography process, including focal lengths (F), exposure energies (E), and critical dimensions (CD). This module performs preliminary data processing to provide a high-quality foundation for subsequent model calculations.
[0063] Multi-model confidence calculation module: This module includes three sub-models, each evaluating data credibility from different perspectives. These sub-models are a robust regression residual analysis model, an unsupervised anomaly detection model, and a Gaussian process uncertainty model. They process preprocessed data in parallel and each outputs a corresponding data confidence score.
[0064] Dynamic Confidence Integration Module: This module receives the confidence scores output by the three sub-models and generates a comprehensive confidence score through weighted fusion. It also dynamically adjusts the rejection threshold based on data distribution, ultimately outputting the data quality assessment results.
[0065] The specific steps of the present invention are:
[0066] Data preprocessing principle:
[0067] Data cleaning: remove duplicate (E,F) combination data;
[0068] Robust normalization: Normalize E, F, and CD:
[0069]
[0070] IQR is the range of the middle 50% of the data, which is insensitive to outliers. In this way, the influence of outliers on the standardized results can be effectively eliminated, making the data more stable and reliable in subsequent processing. scaled is the standardized data.
[0071] Multi-model confidence calculation principle:
[0072] (1) Robust regression residual analysis:
[0073] Input data: variable E after robust standardization scaled 、F scaled 、CD scaled
[0074] Operation process:
[0075] 1. Model fitting: RANSAC (random sampling consensus) regression algorithm is used to fit the model with the standardized E scaled 、F scaled is the input feature, For the output target, fit the nonlinear relationship model.
[0076] 2. Residual calculation: Calculate the standardized residual for each data point, and use the residual to determine whether the data point is an inlier (reasonable data point) or an outlier (abnormal data point). The residual is defined as the absolute value of the difference between the actual CD value and the predicted CD value, that is, The residuals are standardized based on the median absolute difference (MAD) to generate a confidence level that reflects the credibility of the data point. The calculation formula is: Where MAD(e) is the median absolute difference of the residuals, and ε is a very small constant used to avoid the denominator being zero.
[0077] (2) Unsupervised anomaly detection:
[0078] Isolation Forest (IF): Based on the concept of isolation trees, it isolates data points by continuously randomly partitioning the data space. Outliers are usually easier to isolate and their paths to the root node are shorter.
[0079] Local Outlier Factor (LOF): Determines whether a point is an outlier by comparing the density of a point with its neighboring points. If the local density of a point is much lower than the density of its neighboring points, the point is more likely to be an outlier.
[0080] Input data: Standardized three-dimensional matrix X = [E scaled ,F scaled ,CD scaled ]
[0081] Operation process:
[0082] 1.Isolation Forest (IF):
[0083] Input the standardized data matrix X and set the contamination parameter (contamination = 0.05);
[0084] IF randomly divides the feature space (E scaled ,F scaled ,CD scaled ), quickly identify outliers in low-density areas;
[0085] Output anomaly score Score IF ∈[-1,1], normalized to confidence:
[0086] (mapped to [0,1])
[0087] 2. Local Outlier Factor (LOF):
[0088] Input the standardized data matrix X and set the number of neighbors n_neighbors = 20;
[0089] After standardization, the weights of each dimension of the data are consistent. LOF identifies outliers in sparse areas by calculating local density differences (based on Euclidean distance);
[0090] Output anomaly score Score LOF ∈[-1,1], normalized to confidence:
[0091] (mapped to [0,1])
[0092] 3. Comprehensive unsupervised confidence:
[0093] Confidence unsupervised =0.5×Confidence IF +0.5×Confidence LOF
[0094] (3) Gaussian process uncertainty:
[0095] Input data: variable E after robust standardization scaled 、F scaled 、CD scaled
[0096] Operation process:
[0097] 1. Kernel function selection:
[0098] Use the radial basis function (RBF) kernel to capture nonlinear relationships in the normalized data:
[0099]
[0100] Superimpose a white noise kernel (WhiteKernel) to model the measurement noise:
[0101] k 总 =k RBF (l=1.0)+k White (noise_level=0.1)
[0102] 2. Model training and prediction:
[0103] The standardized E scaled 、F scaled For input, As the output, train a Gaussian process regression model.
[0104] Output variance during prediction
[0105] 3. Prediction Variance Mapping to confidence:
[0106] Convert prediction variance to confidence:
[0107]
[0108] (λ is the scaling factor, calibrated based on historical data)
[0109] Dynamic confidence integration principle:
[0110] To fully leverage the strengths of each model, the confidence scores output by the three sub-models are weighted and fused. Based on the characteristics of different models in capturing data anomaly patterns, different weights are assigned to the confidence scores calculated by the robust regression residual analysis, unsupervised anomaly detection, and Gaussian process uncertainty model (for example, 0.4, 0.3, and 0.3, determined based on actual conditions), resulting in a comprehensive confidence score. The weighted comprehensive confidence score is:
[0111] Confidence final =0.4×Confidence residual +0.3×Confidence unsupervised
[0112] +0.3×Confidence GPR
[0113] Adaptive threshold adjustment: The rejection threshold can be dynamically set based on historical data distribution (for example, it can be 0.6, determined according to actual conditions, that is, data points with a confidence level less than 0.6 will be marked as untrustworthy)
[0114] The following is a practical experiment:
[0115] Step 1: Data preparation:
[0116] Get the experimental FEM data of a certain lithography machine in the range of E = [13.5, 28.5] mJ and F = [-0.2, 0.2] um. Figure 2 As shown (71 data points in total).
[0117] Step 2: Data preprocessing:
[0118] The original E, F, and CD data in the FEM data table obtained in step 1 are cleaned to remove duplicate (E, F) combination data. The data are then normalized using the robust normalization formula to eliminate dimensional effects and provide standardized data for subsequent model calculations.
[0119] Step 3: Multi-model confidence calculation:
[0120] The data processed by step 2 are parallelized through robust regression residual analysis, unsupervised anomaly detection, and Gaussian process uncertainty model to calculate the corresponding confidence residualConfidence unsupervised Confidence GPR .
[0121] Step 4: Dynamic confidence integration:
[0122] According to the weighted formula, the confidence calculated by different modules in step 3 is integrated to obtain the final confidence final , and determine the appropriate threshold based on historical data and other information to filter out suspicious data points and generate heat maps and data reports to assist decision-making, such as Figure 3 shown.
[0123] Since most of the data points used in actual model fitting are from the middle area of the input FEM data table, in this example, 7 data points are randomly selected from the middle area (e.g. Figure 4 As shown in the red cells in the figure, a deviation of ±5 to 10% of the original value is applied to the seven data points (used to simulate the deviation between the measured value and the true value caused by various accidental factors during actual analysis). The specific changes are as follows Figure 5 shown).
[0124] The above data are input into the program proposed by the present invention (as described in steps 2 to 4), and the obtained thermal map is as follows: Figure 6 shown.
[0125] from Figure 6 As can be clearly seen in the figure, the program effectively identifies each data point with errors, with their confidence levels significantly lower than before. This demonstrates the effectiveness of this method in identifying low-confidence data points in the FEM data to be fitted, helping engineers focus on suspicious data points, improving the quality of the fitting model input data, and contributing to enhanced process window analysis accuracy. The program also processes artificially introduced erroneous data points with lower confidence levels, demonstrating the algorithm's ability to effectively identify anomalous data points.
[0126] The improvements of the present invention are:
[0127] Dynamic integration of multiple models: For the first time, robust regression, unsupervised detection, and probabilistic models are combined to comprehensively cover data anomaly patterns.
[0128] Adaptive threshold mechanism: Dynamically adjust the confidence threshold based on data distribution to adapt to different process conditions.
[0129] Efficient visual output: Intuitively display low-confidence areas through heat maps and output CSV files containing the E, F, CD and confidence values of low-confidence points to assist in quick decision-making.
[0130] The beneficial effects of the present invention are:
[0131] Improved accuracy and robustness: By pre-identifying suspicious data points, we support the use of high-quality data points for model fitting. This increases the tolerance of input data for process window analysis model fitting, preventing unreliable data points caused by random errors from being directly used in model analysis.
[0132] Efficiency optimization: Automated evaluation is achieved through simple procedures, which greatly saves engineers' time in data review, focuses their attention on a small number of low-confidence data points, and improves the efficiency of data review before model fitting.
[0133] The FEM data used in the examples of the present invention can be replaced with other indicators according to the actual process window analysis needs, such as replacing the critical dimension with the line width roughness, defect rate, etc. under the corresponding process conditions; or other applications that require data confidence evaluation of experimental input data;
[0134] The LOF model mentioned in the present invention can be flexibly changed according to the measurement data error probability hypothesis. For example, it can be changed to a DBSCAN model in the presence of high-density data anomalies.
[0135] The standardization method involved in the present invention takes robust normalization as an example but is not limited thereto and can be replaced by other appropriate standardization methods such as quantile normalization;
[0136] The data, images, formulas, etc. in the figures involved in the present invention are for explanation and illustration only and do not represent any limitation to the technical solution.
[0137] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.
Claims
1. A method for evaluating input data quality for photolithography process window analysis, characterized in that: The method comprises the following steps: S1. Acquire original FEM data, pre-process the original FEM data, and obtain standardized data, wherein the standardized data includes exposure energy, focal length, and critical dimensions; S2. Using the RANSAC regression algorithm, with exposure energy and focal length as input features and key dimension prediction values as output targets, a nonlinear relationship model is fitted. The standardized residual is calculated for each data point of the standardized data, and the confidence level of the robust regression residual analysis is obtained based on the residual. S3: Exposure energy, focal length, and key dimensions form a standardized three-dimensional matrix. Isolation tree detection is then performed to randomly partition the feature space, identify outliers in low-density areas, and output an isolation tree anomaly score. Based on the isolation tree anomaly score, the isolation tree confidence is obtained. S4. Using the local outlier factor method, calculate the local density difference of the three-dimensional matrix, identify the outliers in the sparse area, output the local outlier factor anomaly score, and obtain the local outlier factor confidence based on the local outlier factor anomaly score; S5, integrating the isolation tree confidence and the local outlier factor confidence to obtain the unsupervised confidence; S6. Using a Gaussian regression algorithm and a radial basis function, with exposure energy and focal length as input features and the key dimension prediction value as the output target, a Gaussian process regression model is trained to obtain the prediction variance, and Gaussian confidence is obtained based on the prediction variance; S7. Comprehensive confidence is obtained by integrating robust regression residual analysis confidence, unsupervised confidence and Gaussian confidence. Based on the comprehensive confidence, the input data quality assessment result for lithography process window analysis is obtained.
2. The input data quality assessment method for lithography process window analysis according to claim 1, characterized in that: The confidence level of the robust regression residual analysis is: where MAD(e) is the median absolute difference of the residuals; CD scaled Indicates critical dimension, CD scaled Represents the key size prediction value, i represents the data sequence number, e represents the residual, and ε is a constant.
3. The input data quality assessment method for lithography process window analysis according to claim 1, characterized in that: The isolation tree confidence is: Among them, Score IF is the isolation tree anomaly score.
4. The input data quality assessment method for lithography process window analysis according to claim 3, characterized in that: The local outlier factor confidence is: Among them, Score LOF is the local outlier factor anomaly score.
5. The method for evaluating input data quality for photolithography process window analysis according to claim 4, wherein: The unsupervised confidence is: Confidence unsupervised =0.5×Confidence IF +0.5×Confidence LOF Among them, Confidence unsupervised Confidence is the unsupervised confidence IF Confidence is the confidence of the isolation tree. LOF is the local outlier factor anomaly score.
6. The method for evaluating input data quality for photolithography process window analysis according to claim 5, wherein: The local density difference is calculated based on the Euclidean distance.
7. The input data quality assessment method for lithography process window analysis according to claim 1, characterized in that: The Gaussian confidence level is: Among them, λ is a constant, σ scaled is the prediction variance.
8. The input data quality assessment method for lithography process window analysis according to claim 1, characterized in that: The overall confidence level is: Confidence final =0.4×Confidence residual +0.3×Confidence unsupervised +0.3×Confidence GPR Among them, Confidence final Confidence is the comprehensive confidence residual Represents the confidence level of robust regression residual analysis, Confidence unsupervised Confidence is the unsupervised confidence GPR is the Gaussian confidence level.
9. The method for evaluating input data quality for photolithography process window analysis according to claim 1, wherein: The specific steps for obtaining the input data quality assessment results for lithography process window analysis based on the comprehensive confidence are: determining a suitable threshold, filtering out suspicious data points from the standardized data based on the comprehensive confidence, visualizing the suspicious data points, and obtaining the quality assessment results.
10. The input data quality assessment method for photolithography process window analysis according to claim 1, characterized in that: The preprocessing includes deduplication and standardization.
Citation Information
Patent Citations
Photoetching process quality evaluation method and feedback control system
CN111221225A
Method and apparatus for monitoring lithographic manufacturing process
CN113867109A