Input data quality evaluation method for photoetching process window analysis

Abstract

The invention relates to an input data quality evaluation method for photoetching process window analysis. The method comprises the following steps: S1, obtaining standardized data; s2, adopting an RANSAC regression algorithm to obtain a robust regression residual analysis confidence coefficient; s3, obtaining the confidence of the isolation tree based on the abnormal score of the isolation tree; s4, adopting a local outlier factor method to obtain local outlier factor confidence; s5, integrating the isolation tree confidence coefficient and the local outlier factor confidence coefficient to obtain an unsupervised confidence coefficient; s6, obtaining a Gaussian confidence coefficient; and S7, integrating the robust regression residual analysis confidence coefficient, the unsupervised confidence coefficient and the Gaussian confidence coefficient to obtain a comprehensive confidence coefficient, and obtaining an input data quality evaluation result for photoetching process window analysis. Compared with the prior art, the method has the advantages of improving the input data quality of photoetching process window analysis and the like.

Description

Technical Field

[0001] The invention relates to the field of semiconductor lithography process optimization, and in particular to an input data quality assessment method for lithography process window analysis. Background Art

[0002] For input data used for lithography process window analysis, existing technologies mostly rely on experienced engineers to judge the collected FEM table data and re-retrieve CD-SEM images for data points that may have problems to confirm whether the data is usable. This method is highly dependent on engineer experience, requires additional manpower for data confirmation, and has the risk of omissions. It is also based on simple statistical indicators or simple linear regression models, which are far from the actual process window distribution model. It is difficult to find a universal method for rapid confirmation of data confidence.

[0003] In summary, the prior art for evaluating the quality of input data for photolithography process window analysis has the problem of inaccurate data confidence evaluation. 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, the method comprising the following steps:

[0007] S1, obtaining original FEM data, preprocessing the original FEM data, and obtaining standardized data, wherein the standardized data includes exposure energy, focal length, and key dimensions;

[0008] S2. Using the RANSAC regression algorithm, taking the exposure energy and focal length as input features and the key dimension prediction value as the output target, fitting the nonlinear relationship model, calculating the standardized residual for each data point of the standardized data, and obtaining the confidence of the robust regression residual analysis based on the residual;

[0009] S3, exposure energy, focal length and key size form a standardized three-dimensional matrix, and then perform isolation tree detection, randomly divide the feature space, identify abnormal points in low-density areas, output isolation tree anomaly scores, and obtain isolation tree confidence based on the isolation tree anomaly scores;

[0010] S4, using the local outlier factor method, calculate the local density difference of the three-dimensional matrix, identify the abnormal points in the sparse area, output the local outlier factor abnormal score, and obtain the local outlier factor confidence based on the local outlier factor abnormal score;

[0011] S5, combining the isolation tree confidence and the local outlier factor confidence to obtain the unsupervised confidence;

[0012] S6. Gaussian regression algorithm is adopted, radial basis function is used, exposure energy and focal length are used as input features, key size prediction value is used as output target, Gaussian process regression model is trained, prediction variance is obtained, and Gaussian confidence is obtained based on the prediction variance;

[0013] S7. The comprehensive confidence is obtained by combining the 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 absolute median difference of the residuals;

[0017]

[0018] CD scaled represents the critical size, represents the predicted value of the key size, 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 is the unsupervised confidence, 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 is the comprehensive confidence, Confidence residual Represents the confidence of robust regression residual analysis, Confidence unsupervised is the unsupervised confidence, Confidence GPR is the Gaussian confidence level.

[0036] Furthermore, the specific steps for obtaining the input data quality assessment result 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 result.

[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 probability models through dynamic integration of multiple models, comprehensively covers data anomaly patterns, and weighted combinations into a more accurate comprehensive confidence level, thereby enhancing the tolerance of input data for process window analysis model fitting, quickly improving input data quality while investing less labor cost, avoiding unreliable data points caused by accidental random errors from being directly used for model analysis, and helping 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 for process window fitting;

[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 a complete data point confidence report;

[0043] Figure 4 The 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 thermogram 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 in conjunction with 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: um)

[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, obtaining original FEM data, preprocessing the original FEM data, and obtaining standardized data, wherein the standardized data includes exposure energy, focal length, and key dimensions;

[0055] S2. Using the RANSAC regression algorithm, taking the exposure energy and focal length as input features and the key dimension prediction value as the output target, fitting the nonlinear relationship model, calculating the standardized residual for each data point of the standardized data, and obtaining the confidence of the robust regression residual analysis based on the residual;

[0056] S3, exposure energy, focal length and key size form a standardized three-dimensional matrix, and then perform isolation tree detection, randomly divide the feature space, identify abnormal points in low-density areas, output isolation tree anomaly scores, and obtain isolation tree confidence based on the isolation tree anomaly scores;

[0057] S4, using the local outlier factor method, calculate the local density difference of the three-dimensional matrix, identify the abnormal points in the sparse area, output the local outlier factor abnormal score, and obtain the local outlier factor confidence based on the local outlier factor abnormal score;

[0058] S5, combining the isolation tree confidence and the local outlier factor confidence to obtain the unsupervised confidence;

[0059] S6. Gaussian regression algorithm is adopted, radial basis function is used, exposure energy and focal length are used as input features, key size prediction value is used as output target, Gaussian process regression model is trained, prediction variance is obtained, and Gaussian confidence is obtained based on the prediction variance;

[0060] S7. The comprehensive confidence is obtained by combining the 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, such as Figure 1 As shown, it is mainly composed of a data preprocessing module, a multi-model confidence calculation module and a dynamic confidence integration module.

[0062] Data preprocessing module: Receives raw measurement data of different focal lengths (F), exposure energies (E) and critical dimensions (CD) from the photolithography process. The function of this module is to perform preliminary processing on the data and provide a high-quality data foundation for subsequent model calculations.

[0063] Multi-model confidence calculation module: It contains three sub-models, which evaluate the credibility of data from different perspectives. These three sub-models are the robust regression residual analysis model, the unsupervised anomaly detection model, and the Gaussian process uncertainty model. They process the pre-processed data in parallel and output the corresponding data confidence.

[0064] Dynamic confidence integration module: receives the confidence output by the three sub-models and generates a comprehensive confidence by weighted fusion. At the same time, it dynamically adjusts the rejection threshold according to the data distribution and finally outputs 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, Fit a nonlinear relationship model to the output target.

[0076] 2. Residual calculation: Calculate the standardized residual for each data point, and determine whether the data point is an inlier (reasonable data point) or an outlier (abnormal data point) by calculating the residual. 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 deviation (MAD) to generate a confidence level that reflects the credibility of the data points. The calculation formula is: Where MAD(e) is the absolute median 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 idea of ​​isolation tree, it isolates data points by continuously and randomly dividing the data space. Outliers are usually easier to isolate and have a shorter path to the root node.

[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] In order to give full play to the advantages of each model, the confidence output by the three sub-models is weighted and fused. According to the characteristics of different models in capturing data abnormal patterns, different weights are assigned to the confidence calculated by robust regression residual analysis, unsupervised anomaly detection and Gaussian process uncertainty model (for example, 0.4, 0.3, 0.3, determined according to actual conditions), and the comprehensive confidence is obtained, the weighted comprehensive confidence:

[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 according to the historical data distribution (for example, it can be 0.6, determined according to the actual situation, that is, the confidence level less than 0.6 will be marked as unreliable data points)

[0114] The following is the actual experiment:

[0115] Step 1: Data preparation:

[0116] Get the experimental FEM data of a photolithography machine in the range of E = [13.5, 28.5] mJ, F = [-0.2, 0.2] um. Figure 2 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. Then the data is normalized according to the robust normalization formula to eliminate the dimension effect and provide standardized data for subsequent model calculations.

[0119] Step 3: Multi-model confidence calculation:

[0120] The data processed by step 2 are parallelly processed 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 the actual model fitting are the data in the middle area of ​​the input FEM data table, in this example, 7 data points are randomly selected in the middle area (such as Figure 4 The seven data points are subjected to a deviation of ±5 to 10% of the original value (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 diagram is as follows: Figure 6 shown.

[0125] from Figure 6 It can be clearly seen that the program has well identified each data point with errors, and its confidence has been significantly reduced compared to the original. This verifies that this method can effectively identify low-confidence data points in the FEM data to be fitted, assist engineers to focus on suspicious data points, improve the quality of fitting model input data, and help improve the accuracy of process window analysis. The confidence of the artificially introduced erroneous data points is low after being processed by the program, which verifies that the algorithm can effectively identify abnormal data points.

[0126] The improvement of the present invention is:

[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: The low-confidence area is intuitively displayed through a heat map, and a CSV file is output, which contains the E, F, CD and confidence values ​​of the 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, it provides support for model fitting using high-quality data points. It enhances the tolerance of input data for process window analysis model fitting and avoids the direct use of unreliable data points caused by accidental random errors in model analysis.

[0132] Efficiency optimization: Automated evaluation is achieved through simple procedures, which greatly saves engineers’ time in data checking, focuses their attention on a few low-confidence data points, and improves the efficiency of data checking 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 changing the critical dimensions to 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 standardization as an example but is not limited thereto, and can be replaced by other suitable standardization methods such as quantile normalization;

[0136] The data, images, formulas, etc. in the figures involved in the present invention are only used for explanation and illustration and do not represent any limitation on the technical solution.

[0137] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined 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, obtaining original FEM data, preprocessing the original FEM data, and obtaining standardized data, wherein the standardized data includes exposure energy, focal length, and key dimensions; S2. Using the RANSAC regression algorithm, taking the exposure energy and focal length as input features and the key dimension prediction value as the output target, fitting the nonlinear relationship model, calculating the standardized residual for each data point of the standardized data, and obtaining the confidence of the robust regression residual analysis based on the residual; S3, exposure energy, focal length and key size form a standardized three-dimensional matrix, and then perform isolation tree detection, randomly divide the feature space, identify abnormal points in low-density areas, output isolation tree anomaly scores, and obtain isolation tree confidence based on the isolation tree anomaly scores; S4, using the local outlier factor method, calculate the local density difference of the three-dimensional matrix, identify the abnormal points in the sparse area, output the local outlier factor abnormal score, and obtain the local outlier factor confidence based on the local outlier factor abnormal score; S5, combining the isolation tree confidence and the local outlier factor confidence to obtain the unsupervised confidence; S6. Gaussian regression algorithm is adopted, radial basis function is used, exposure energy and focal length are used as input features, key size prediction value is used as output target, Gaussian process regression model is trained, prediction variance is obtained, and Gaussian confidence is obtained based on the prediction variance; S7. The comprehensive confidence is obtained by combining the 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 method for evaluating input data quality for photolithography 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 absolute median difference of the residuals; CD scaled Denotes critical dimension, CD scaled represents the predicted value of the key size, 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 method for evaluating input data quality for photolithography 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, characterized in that: The unsupervised confidence is: Confidence unsupervised =0.5×Confidence IF +0.5×Confidence LOF Among them, Confidence unsupervised is the unsupervised confidence, 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, characterized in that: The local density difference is calculated based on the Euclidean distance.

7. The method for evaluating input data quality for photolithography 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 method for evaluating input data quality for photolithography process window analysis according to claim 1, characterized in that: The overall confidence is: Confidence final =0.4×Confidence residual +0.3×Confidence unsupervised +0.3×Confidence GPR Among them, Confidence final is the comprehensive confidence, Confidence residual Represents the confidence of robust regression residual analysis, Confidence unsupervised is the unsupervised confidence, Confidence GPR is the Gaussian confidence level.

9. The method for evaluating input data quality for photolithography process window analysis according to claim 1, characterized in that: The specific steps for obtaining the quality assessment results of input data for lithography process window analysis based on comprehensive confidence are: determining a suitable threshold, screening out suspicious data points from the standardized data based on 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.

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