Semiconductor anomaly detection method and system based on physical causal relationship modeling

Abstract

The application relates to the technical field of semiconductor manufacturing quality control, in particular to a semiconductor anomaly detection method and system based on physical causal relationship modeling, which comprises the following steps executed in sequence: S1: acquiring multi-dimensional sensor data of a semiconductor production line, and establishing a sensor causal relationship model based on etching process physical mechanism; S2: performing time sequence alignment, anomaly propagation modeling and root cause positioning along a causal relationship path; and S3: adaptive intelligent decision based on a graph attention network. Through the establishment of the physical causal relationship model between sensors, time sequence alignment and anomaly detection driven by the causal relationship are realized, and adaptive intelligent decision and predictive feedback optimization of the graph attention network are combined, so that the technical problems of low time sequence alignment accuracy, lack of root cause analysis in anomaly detection and insufficient intelligence of system decision in the prior art are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor manufacturing quality control, and particularly relates to a semiconductor anomaly detection method and system based on physical causal relationship modeling. BACKGROUND

[0002] In the semiconductor manufacturing process, a large number of different types of sensors are equipped on the equipment for real-time monitoring, including radio frequency power sensors, chamber pressure sensors, gas flow sensors, temperature sensors, etc. There are clear physical causal relationships among these sensors, such as radio frequency power directly exciting plasma generation, plasma density determining etching rate, gas flow affecting chamber pressure change, etc. However, the existing anomaly detection methods have significant technical limitations in dealing with the correlation between multiple sensors.

[0003] Firstly, the time series alignment method lacks physical mechanism guidance. Traditional methods mainly use DTW, i.e. dynamic time warping algorithm and cross-correlation analysis for time series alignment. The DTW algorithm is based on distance similarity for dynamic programming matching, which has high computational complexity and cannot reflect the physical correlation between sensors. Cross-correlation analysis is simple to calculate, but only considers statistical correlation, ignoring the clear physical causal relationship between sensors in semiconductor processes. For example, in the etching process, the change of radio frequency power will cause the change of plasma density within microseconds, and then affect the etching rate within milliseconds, and finally cause the change of temperature distribution within seconds. This clear physical causal chain is completely ignored in traditional alignment methods, resulting in limited alignment accuracy and easy to make wrong judgments of cause and effect reversal.

[0004] Secondly, the anomaly detection lacks root cause analysis capability. Existing anomaly detection methods include statistical methods such as 3σ criterion and box plot detection, machine learning methods such as support vector machine and isolation forest, and deep learning methods such as autoencoder and LSTM network. Statistical methods can only identify numerical anomalies and cannot analyze the root cause of the anomaly; machine learning methods require a large amount of labeled data, which is difficult to obtain sufficient abnormal samples in the semiconductor manufacturing environment; deep learning methods have high detection accuracy, but belong to black box models and cannot provide explainable analysis of the mechanism and propagation path of anomalies. When an anomaly is detected, engineers still need to rely on experience to check possible fault sources one by one, which seriously affects the fault diagnosis efficiency.

[0005] Thirdly, the sensor fusion decision lacks adaptability. Existing multi-sensor fusion methods mainly adopt fixed weight allocation strategies, such as weight setting based on expert experience or weight calculation based on historical statistics. This fixed weight method cannot adapt to changes in different process conditions, equipment states and production demands. For example, during the aging process of equipment, the reliability of some sensors will decrease, but the fixed weight method cannot dynamically adjust the importance of these sensors; when different products are switched, the process parameters change, but the system still uses the same detection strategy, resulting in a decrease in detection accuracy.

[0006] In addition, the system optimization mechanism lacks foresight. Traditional system optimization mainly adopts a passive response mode, that is, adjustment is made only after the system performance decreases or a fault occurs. This passive optimization mode cannot predict the performance degradation trend of the system and is prone to cause sudden failures and production interruptions. At the same time, lacking a systematic performance prediction mechanism, preventive optimization cannot be actively performed before problems occur. SUMMARY

[0007] The purpose of the present application is to provide a semiconductor anomaly detection method and system based on physical causal relationship modeling, which realizes accurate time alignment and interpretable anomaly root cause analysis by establishing real physical causal relationships between sensors, and has adaptive decision and predictive optimization capabilities.

[0008] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0009] The semiconductor anomaly detection method based on physical causal relationship modeling comprises the following steps executed in sequence:

[0010] S1: Obtain multi-dimensional sensor data of a semiconductor production line, and establish a sensor causal relationship model based on the physical mechanism of the etching process:

[0011] The data support degree of the causal relationship in the sensor causal relationship model is verified using conditional mutual information:

[0012] ;

[0013] Wherein, is the mutual information between sensor and sensor , is the information entropy of sensor , is the conditional entropy of sensor under the condition of sensor data;

[0014] The sensor causal relationship model is constructed by combining physical prior knowledge and data verification results:

[0015] The semiconductor anomaly detection method based on physical causal relationship modeling has the advantages that: ;

[0016] in, For sensors To the sensor The strength of the causal relationship For causal prior probabilities based on physical laws, For time-series causality verification coefficients, , and This is the weighting balance coefficient;

[0017] S2: Perform time-series alignment, anomaly propagation modeling, and root cause localization along the causal path, incorporating causal constraints into the objective function of time-series alignment, and calculating the anomaly originating from the sensor. propagation to sensor Based on the probability, Bayesian inference methods are used to locate the root cause of the anomaly;

[0018] S3: Computational Sensor Average alignment quality and anomaly detection statistics of all involved causal relationships, fused sensors Based on causal relationships, average alignment quality, and anomaly detection statistics, sensor node feature vectors are constructed. A graph attention mechanism is employed to calculate dynamic attention weights among sensors. An attention score is calculated for each attention head, and LeakyReLU activation and softmax normalization are used to obtain the single-head attention weight and the average weight of multi-head attention. Based on the normalized average weight of multi-head attention, the sensor's attention weight is calculated. Importance weights are used to adaptively adjust the detection strategy based on the importance weights of the sensors.

[0019] Preferably, in step S1, the multidimensional sensor data includes the radio frequency power, chamber pressure, gas flow rate and temperature distribution of the etching equipment, the power matching, reaction gas flow rate and heating temperature of the PECVD equipment, and the multidimensional sensor data is preprocessed using a data quality assessment mechanism.

[0020] Preferably, step S2 specifically includes the following steps:

[0021] S2-1: Incorporating causal constraints into the time-aligned objective function:

[0022] ;

[0023] in, For causally driven alignment quality evaluation functions, For sensors To the sensor The importance weight of causal paths For the strength of causality, For the sensor to in time delay The cross-correlation function under the following conditions For physical constraint regularization terms, These are the physical constraint weighting coefficients;

[0024] S2-2: The anomaly from the sensor is calculated using the following formula. propagation to sensor probability :

[0025] ;

[0026] in, For sensors Abnormal intensity at the location, Spatial decay function along causal path, This is a time decay function, reflecting the time delay effect of anomaly propagation;

[0027] S2-3: Using Bayesian inference to locate the root cause of anomalies:

[0028] ;

[0029] in, For sensors It is the probability of the abnormal root cause. To from the sensor Starting from the causal relationship path, we can explain the probability of the observed anomalous sensor set. For sensors As the prior probability of an anomaly source, when When the value is greater than or equal to the preset root cause threshold, the sensor... As the root cause of the abnormality, The total number of sensors represents the total number of sensors in the system.

[0030] Preferably, S3: Adaptive intelligent decision-making based on graph attention networks, the specific steps of which are as follows:

[0031] S3-1: The sensor is calculated using the following formula. Average alignment quality of all involved causal relationships:

[0032] ;

[0033] in, , To be compatible with sensors A set of neighbors with a significant causal relationship, when the sensor To the sensor strength of causation Exceeding the significance threshold of causation At that time, the sensor Only then was it considered a sensor Only significant causal neighbors are included in the calculation of average quality. Indicates the significance threshold of causal relationship. For sensors and sensors The optimal alignment quality evaluation function value, middle Indicates sensor Neighbor sensor set Each sensor in the system;

[0034] S3-2: The historical false alarm rate is calculated using the following formula based on anomaly detection statistics within the sliding window:

[0035] ;

[0036] in, For sensors The number of false alarms within the historical window Total number of tests;

[0037] S3-3: Constructing sensor node feature vectors It integrates causal relationships, average alignment quality, and anomaly detection statistics:

[0038] ;

[0039] in, Indicates sensor The causal relationship vector;

[0040] S3-4: Calculate the dynamic attention weights between sensors using a graph attention mechanism, and calculate the attention score for each attention head:

[0041] ;

[0042] in, For the first The weight matrix of the science department for each attention head, For the first The parameter vector of each attention head, This indicates a feature concatenation operation. This is the vector transpose operator;

[0043] The single-head attention weights are obtained using LeakyReLU activation and softmax normalization:

[0044] ;

[0045] in, This represents an exponential function, i.e. , To leak the linear rectifier function, , middle Indicates sensor Neighbor sensor set Each sensor in the system;

[0046] Calculate the average weight of multi-head attention:

[0047] ;

[0048] in, For attention indexing, ,in, For the total number of attention heads;

[0049] The average weight of multi-head attention is normalized:

[0050] ;

[0051] in, These are the normalized attention weights;

[0052] S3-5: Sensor for calculating average weights based on normalized multi-head attention Importance weight:

[0053] ;

[0054] The detection strategy is adaptively adjusted based on the importance weight of the sensors: when When the weight is greater than or equal to the preset maximum importance weight, a precision detection mode is used. Lightweight detection mode is used when the weight is less than or equal to the preset minimum importance weight; otherwise, standard detection mode is used.

[0055] Preferably, the method further includes step S4: implementing active feedback optimization based on graph attention networks, the specific steps of which are as follows:

[0056] S4-1: In At any given time, the number of anomaly detections detected by the system is calculated as follows:

[0057] ;

[0058] in, This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise. The preset root cause threshold;

[0059] S4-2: System response time is the average time taken from an anomaly detection to root cause localization.

[0060] ;

[0061] in, and The first The time for detecting an anomaly and the time for completing root cause localization;

[0062] S4-3: Define the causal relationship state vector and fuse the multi-layer features of the graph attention network:

[0063] ;

[0064] in, To calculate the mean of the output features of the graph attention network, This is the updated feature vector after processing by the multi-head attention mechanism of the graph attention network. , For the total number of sensors, This represents the mean of the importance weights for each sensor.

[0065] S4-4: A time-series test model is established using a graph convolutional neural network to enhance prediction accuracy by leveraging graph structure information.

[0066] ;

[0067] in, From time At the time The historical causal relationship state vector sequence, The prediction time step represents the time interval for forward prediction. For graph convolutional prediction networks, For network parameters;

[0068] S4-5: Based on the prediction results, trigger a hierarchical feedback optimization mechanism and define the prediction bias:

[0069] ;

[0070] in, The system target state vector is set according to the optimal operating conditions; Given the L2 norm, calculate the Euclidean distance deviation between the predicted state and the target state;

[0071] Attention weight fine-tuning layer, when At the same time, fine-tune the attention parameters:

[0072] ;

[0073] in, These are the attention vector parameters of the current graph attention network. For the updated parameters, For learning rate, This represents the gradient of the system state loss function with respect to the attention parameters.

[0074] Graph structure reconstruction layer: when At that time, key causal edges are reconstructed based on attention weights:

[0075] ;

[0076] in, To reconstruct the weight coefficients for the graph structure, control the magnitude of the adjustment of causal relationship strength based on attention weights. For the first Sensors in a single attention head For sensors Attention weights;

[0077] Causal model reconstruction layer: when At that time, the causal modeling update in step S1 is triggered:

[0078] ;

[0079] in, , and Recalibrate based on the weight patterns learned by the graph attention network. For causal prior probabilities based on physical laws, For sensors and The temporal causal verification coefficient between them.

[0080] A semiconductor anomaly detection system based on physical causality modeling includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the semiconductor anomaly detection method based on physical causality modeling described above.

[0081] By adopting the aforementioned design scheme, the beneficial effects of the present invention are as follows: This application establishes a physical causal relationship model between sensors to achieve causal relationship-driven temporal alignment and anomaly detection, and combines the adaptive intelligent decision-making and predictive feedback optimization of graph attention networks to solve the technical problems in the prior art such as low temporal alignment accuracy, lack of root cause analysis in anomaly detection, and insufficient intelligence in system decision-making. Attached Figure Description

[0082] Figure 1 This is a flowchart of the semiconductor anomaly detection process of the present invention. Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0084] The terms "first," "second," "third," etc., used in the specification, claims, and accompanying drawings of this invention are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0085] Semiconductor anomaly detection methods based on physical causality modeling, such as Figure 1 As shown, the steps are executed sequentially as follows:

[0086] S1: Acquire multi-dimensional sensor data from the semiconductor production line. Based on the physical mechanism of the etching process, in this embodiment, the multi-dimensional sensor data includes the radio frequency power, chamber pressure, gas flow rate, and temperature distribution of the etching equipment, as well as the power matching, reaction gas flow rate, and heating temperature of the PECVD equipment. The multi-dimensional sensor data is preprocessed using a data quality assessment mechanism. In this embodiment, the data quality assessment mechanism includes data integrity checks, outlier handling, and noise filtering.

[0087] In this embodiment, by deeply analyzing the physical mechanisms of semiconductor processes, the true causal relationships between sensors are identified: radio frequency power is the direct driving force for plasma generation, and there is a clear causal relationship between the two; plasma density directly determines the activity of chemical reactions, thus affecting the etching rate; changes in gas flow rate directly affect chamber pressure, and changes in pressure cause a redistribution of the temperature field; radio frequency matching status affects power transmission efficiency, ultimately determining process stability. These physical causal relationships constitute a complete causal network from energy input to process results, with both dominant causal chains and complex cross-coupling relationships among the parameters.

[0088] Based on the physical mechanism of etching process, a complete causal relationship network is established: with radio frequency power Plasma density Etching rate, gas flow rate Chamber pressure Temperature distribution, radio frequency matching Power transfer efficiency Process stability is the main causal chain, and there are also cross-coupling relationships between various parameters, forming a complex physical causal relationship model.

[0089] Establish a causal relationship model for sensors:

[0090] In semiconductor manufacturing processes, the physical relationships between sensors are often nonlinear. For example, the relationship between radio frequency power and plasma density is influenced by multiple factors such as gas type, pressure, and temperature. Traditional Pearson correlation coefficients can only measure linear correlations, while mutual information can capture any form of statistical dependency. To quantify these physical causal relationships, conditional mutual information is used to verify the data support for the causal relationships in this sensor causal model:

[0091] ;

[0092] in, For sensors and sensors Inter-information For sensors Information entropy For in the sensor Under data conditions, sensors Conditional entropy;

[0093] A causal relationship model for sensors is constructed by integrating prior physical knowledge and data verification results:

[0094] ;

[0095] in, For sensors To the sensor The strength of the causal relationship This is based on the causal prior probability derived from physical laws, assessed according to the degree of determinism of the process's physical mechanism. For example, the physical relationship of RF power-excited plasma has extremely high determinism, with a value close to 1.0. The time-series causality verification coefficient is calculated using the F-statistic of the Granger causality test: ,in, This is the F-statistic value of the Granger causality test. The critical F value, The significance level; , and These are weighting balancing coefficients used to coordinate the contributions of physical priors, data validation, and temporal validation. This causal matrix provides a scientific physical constraint basis for subsequent temporal alignment and anomaly detection.

[0096] S2: Perform time-series alignment, anomaly propagation modeling, and root cause localization along the causal path, incorporating causal constraints into the objective function of time-series alignment, and calculating the anomaly originating from the sensor. propagation to sensor Based on the probability, Bayesian inference methods are used to locate the root cause of the anomaly;

[0097] Step S2 specifically includes the following steps:

[0098] S2-1: Incorporating causal constraints into the time-aligned objective function:

[0099] ;

[0100] in, This is a causal-driven alignment quality evaluation function used to find the optimal time alignment parameters. For sensors To the sensor The importance weight of the causal path reflects the priority of the causal relationship in time alignment optimization, and is determined based on process importance and physical constraint strength. For the strength of causality, For the sensor to in time delay The cross-correlation function under the following conditions The physical constraint regularization term ensures that the alignment result conforms to the time constraints of physical laws, such as plasma response time being on the order of microseconds and temperature response time being on the order of seconds. These are the physical constraint weighting coefficients, used to balance statistical fitting and physical rationality, with values ​​ranging from [0,1]. When the size is larger, more emphasis is placed on physical constraints, when When the value is small, it relies more on statistical correlation; this objective function organically incorporates physical causality into the alignment process, significantly improving alignment accuracy.

[0101] After completing the causal-driven time alignment, when the system detects an anomaly, it no longer stops at the simple anomaly labeling level, but analyzes the propagation mode of the anomaly based on the established sensor causal relationship model to achieve automatic location of the root cause of the anomaly.

[0102] S2-2: The anomaly from the sensor is calculated using the following formula. propagation to sensor probability :

[0103] ;

[0104] in, For sensors The anomaly intensity at time t is used to quantify the severity of the anomaly. Assuming a spatial decay function along the causal path, this simulates the attenuation of anomaly effects with propagation distance. The path distance for causal relationships between sensors. For spatial attenuation parameters; This is a time decay function, reflecting the time delay effect of anomaly propagation. To from the sensor propagation to sensor Abnormal propagation delay, The time decay constant; The moment of anomaly detection; through calculation Used to predict the path and scope of abnormal spread.

[0105] S2-3: Using Bayesian inference to locate the root cause of anomalies:

[0106] ;

[0107] in, For sensors It represents the probability of the root cause of the anomaly, used to locate the source of the anomaly. To from the sensor Starting from the causal relationship path, we can explain the probability of the observed anomalous sensor set. For sensors As the prior probability of an anomaly source, when When the value is greater than or equal to the preset root cause threshold, the sensor... The root cause is the abnormality; in this embodiment, the preset root cause threshold is... The root cause threshold can also be set according to actual needs. This method can automatically identify the root cause of anomalies, providing engineers with clear guidance for fault diagnosis. The total number of sensors represents the total number of sensors in the system.

[0108] S3: Adaptive intelligent decision-making based on Graph Attention Network (GAT), the specific steps are as follows:

[0109] S3-1: The sensor is calculated using the following formula. Average alignment quality of all involved causal relationships:

[0110] ;

[0111] in, , To be compatible with sensors A set of neighbors with a significant causal relationship, when the sensor To the sensor strength of causation Exceeding the significance threshold of causation At that time, the sensor Only then was it considered a sensor Only significant causal neighbors are included in the calculation of average quality. Indicates the significance threshold of causal relationship. For sensors and sensors The optimal alignment quality evaluation function value, middle Indicates sensor Neighbor sensor set Each sensor in the system;

[0112] S3-2: The historical false alarm rate is calculated using the following formula based on anomaly detection statistics within the sliding window:

[0113] ;

[0114] in, For sensors The number of false alarms within the historical window Total number of tests;

[0115] S3-3: Constructing sensor node feature vectors It integrates causal relationships, average alignment quality, and anomaly detection statistics:

[0116] ;

[0117] in, Indicates sensor The causal relationship vector, i.e., the causal relationship matrix. The A 9-dimensional vector of rows, For sensors Feature representation;

[0118] S3-4: Calculate the dynamic attention weights between sensors using a graph attention mechanism, and calculate the attention score for each attention head:

[0119] ;

[0120] in, For the first The weight matrix of the science department for each attention head, For the first The parameter vector of each attention head, This indicates a feature concatenation operation. This is the vector transpose operator;

[0121] The single-head attention weights are obtained using LeakyReLU activation and softmax normalization:

[0122] ;

[0123] in, This represents an exponential function, i.e. , To leak the linear rectifier function, , middle Indicates sensor Neighbor sensor set Each sensor in the setup; Each attention head learns different types of causal relationship patterns.

[0124] Softmax normalization is used to ensure the sensor The sum of attention weights for all its neighboring nodes is 1, ensuring the probabilistic constraints of weight allocation and the comparability of relative importance. This is the core requirement of the graph attention mechanism.

[0125] To capture different types of causal relationship patterns, a multi-head attention fusion mechanism is employed to calculate the average weight of multi-head attention:

[0126] ;

[0127] in, For attention indexing, ,in, For the total number of attention heads;

[0128] Because each head in the graph attention mechanism learns different causal relationship patterns, the attention weights of each head may have different numerical ranges and distribution characteristics. To ensure the effectiveness of multi-head attention fusion, the average weight of the multi-head attention needs to be normalized.

[0129] ;

[0130] in, For the normalized attention weights, ensure the sensor The sum of the attention weights for all its neighboring nodes is 1, thus ensuring the rationality of the weight allocation;

[0131] S3-5: Sensor for calculating average weights based on normalized multi-head attention Importance weight:

[0132] ;

[0133] The detection strategy is adaptively adjusted based on the importance weight of the sensors: when Greater than or equal to the preset maximum importance weight At that time, a precision detection mode is adopted. Less than or equal to the preset minimum importance weight Lightweight detection mode is used when necessary; otherwise, standard detection mode is used. and Based on the distribution characteristics of sensor importance weights and the requirements for detection resource allocation, in this embodiment, , To ensure that sensors with higher importance weights receive more detection resources, and sensors with lower weights employ a lightweight detection strategy, thereby optimizing the allocation of detection resources, the three detection modes are technically layered based on the sensor causal network weights as follows:

[0134] Precision detection mode: Suitable for key node sensors with high weight coefficients in causal relationship networks. It adopts enhanced sampling frequency, such as increasing it by 50%, and a multi-algorithm parallel verification mechanism, such as statistical detection and machine learning verification. It also lowers the detection threshold to improve anomaly sensitivity. The system response time is ≤0.1 seconds.

[0135] Standard detection mode: Suitable for conventional node sensors with moderate weight coefficients in causal networks, maintaining a standard sampling frequency, using a main detection algorithm in conjunction with an auxiliary verification mechanism, using default detection threshold parameters, and a system response time ≤ 0.5 seconds;

[0136] Lightweight detection mode: Suitable for edge node sensors with low weight coefficients in causal networks, it reduces the sampling frequency by 30%, adopts a fast statistical detection algorithm, and appropriately increases the detection threshold to reduce the false alarm rate. The system response time is ≤1.0 second.

[0137] As a preferred embodiment, the detection method further includes step S4: implementing active feedback optimization based on graph attention network, the specific steps of which are as follows:

[0138] S4-1: In At any given time, the number of anomaly detections detected by the system is calculated as follows:

[0139] ;

[0140] in, This is an indicator function that takes the value 1 when the condition within the parentheses is true, and 0 otherwise. It is used to count the number of sensors that meet the condition. For the preset root cause threshold; when When the value is greater than 0.8, the sensor is considered to be... As a reliable root cause of anomalies, this threshold setting ensures that only root cause localization results with high confidence are included in the anomaly statistics, avoiding misjudgments from interfering with system performance evaluation.

[0141] S4-2: System response time is the average time taken from an anomaly detection to root cause localization.

[0142] ;

[0143] in, and The first The time for detecting an anomaly and the time for completing root cause localization;

[0144] S4-3: Define the causal relationship state vector and fuse the multi-layer features of the graph attention network:

[0145] ;

[0146] in, To calculate the mean of the output features of the graph attention network, This is the updated feature vector after processing by the multi-head attention mechanism of the graph attention network. , For the total number of sensors, The mean of the sensor importance weights is used to evaluate the average importance level of the entire sensor network, where... Indicates sensor The overall importance in the causal relationship network, with a value range of [0,1];

[0147] S4-4: A time-series test model is established using a graph convolutional neural network to enhance prediction accuracy by leveraging graph structure information.

[0148] ;

[0149] in, From time At the time The historical causal relationship state vector sequence, The prediction time step represents the time interval for forward prediction. For graph convolutional prediction networks, For network parameters;

[0150] S4-5: Based on the prediction results, trigger a hierarchical feedback optimization mechanism and define the prediction bias:

[0151] ;

[0152] in, The system target state vector is set according to the optimal operating conditions; Given the L2 norm, calculate the Euclidean distance deviation between the predicted state and the target state;

[0153] Attention weight fine-tuning layer, when At the same time, fine-tune the attention parameters:

[0154] ;

[0155] in, These are the attention vector parameters of the current graph attention network. For the updated parameters, For learning rate, This represents the gradient of the system state loss function with respect to the attention parameters.

[0156] Graph structure reconstruction layer: when At that time, key causal edges are reconstructed based on attention weights:

[0157] ;

[0158] in, To reconstruct the weight coefficients for the graph structure, control the magnitude of the adjustment of causal relationship strength based on attention weights. For the first Sensors in a single attention head For sensors Attention weights;

[0159] Causal model reconstruction layer: when At that time, the causal modeling update in step S1 is triggered:

[0160] ;

[0161] in, , and Recalibrate based on the weight patterns learned by the graph attention network. For causal prior probabilities based on physical laws, For sensors and The temporal causal verification coefficient between them.

[0162] Through this hierarchical feedback mechanism based on graph attention networks, the system achieves comprehensive adaptive optimization from fine-tuning of attention parameters to reconstruction of causal models, ensuring that the anomaly detection system always maintains optimal causal relationship perception capabilities.

[0163] The adaptive decision-making method based on graph attention networks captures different types of physical causal relationship patterns through a multi-head attention mechanism, which significantly improves the accuracy of sensor importance assessment and the adaptability of decision-making strategies.

[0164] The feedback optimization method based on graph convolution prediction enhances the accuracy of time series prediction by utilizing graph structure information, and realizes intelligent feedback optimization from local parameter adjustment to global model reconstruction.

[0165] To better explain this semiconductor anomaly detection method, this embodiment evaluates a 12-inch wafer etching production line of a semiconductor manufacturing company and describes in detail the implementation process of the core algorithm.

[0166] S1: Acquire multi-dimensional sensor data from the semiconductor production line and establish a causal relationship model for the sensors based on the physical mechanism of the etching process;

[0167] Data was collected from 15 key sensors during etching: RF power sensor: sampling frequency 1kHz, response time 5μs; plasma density sensor: sampling frequency 500Hz, response time 10μs; chamber pressure sensor: sampling frequency 100Hz, response time 50ms; gas flow sensor: sampling frequency 50Hz, response time 100ms; temperature sensor: sampling frequency 10Hz, response time 2s; and mechanical position sensor: sampling frequency 20Hz, response time 10ms.

[0168] Data restoration includes outlier detection, missing value repair, and standardization, and establishes a sensor characteristic database to provide a high-quality data foundation for subsequent causal relationship modeling.

[0169] Based on the physical mechanism of etching process, a complete causal relationship network is established: taking radio frequency power ( ) Plasma density ( ) Etching rate ( ), gas flow rate ( ) Chamber pressure ( ) Temperature distribution ( ), RF matching ( ) Power transfer efficiency ( ) Process stability ( The main causal chain is , and there are cross-coupling relationships between the parameters, forming a complex physical causal relationship network.

[0170] In the specific calculations for conditional mutual information verification, the verification of RF power and plasma density in causal chain 1 is performed using conditional mutual information calculations:

[0171] ;

[0172] The specific calculation process involves discretizing the RF power data according to power levels. Using seven power levels {100W, 150W, 200W, 250W, 300W, 350W, 400W}, calculate the information entropy of the RF power data: ; Calculate the conditional entropy of RF power under a given plasma density condition: ; Obtain conditional mutual information: This result indicates a strong correlation between RF power and plasma density, verifying the data support for the physical causal relationship.

[0173] Similarly, calculations were performed on other sensors: plasma density versus etching rate: Gas flow rate and chamber pressure Chamber pressure and temperature distribution: .

[0174] Construction of the probability relationship strength matrix: Using the causal strength calculation formula, taking the relationship between radio frequency power and plasma density as an example:

[0175] ;

[0176] Specific parameter settings and calculations: Physical prior probability calculation: Expert scoring In this context, RF power-induced plasma excitation is a defined physical process, and the physical coupling strength coefficient is... The direct activation relationship was calculated to yield the following: Conditional mutual information (standardization): (2.27 bits normalized to the [0,1] interval);

[0177] Time-series causality verification: Granger causality test yields the F-statistic. Critical F value α=0.05 level ;

[0178] The calculation yielded: ;

[0179] Weight settings: ;

[0180] Comprehensive calculation verification: The result was consistent with expectations.

[0181]

[0182] in, Indicates RF power. Indicates plasma density, Indicates the etching rate. Indicates gas flow rate, Indicates chamber pressure, Indicates temperature distribution. Indicates RF matching, Indicates power transmission efficiency. This represents process stability. In the matrix... Indicates sensor To the sensor The strength of the causal relationship is indicated by the numerical value; a larger value indicates a stronger causal relationship.

[0183] S2: Time alignment, anomaly propagation modeling, and root cause localization along causal paths:

[0184] Causal-driven alignment objective function: Taking the key causal chain "RF power → plasma density → etching rate" as an example, the causal relationship formula driven by causality is adopted:

[0185] ;

[0186] Specific parameters and calculation process: Sensor weight settings: Based on process importance; causal relationship strength: , Step 1: Result of the relation matrix; Calculation of the cross-correlation function: calculated under different time delays. and Physical constraints: Physical response time; Physical constraint weights: Optimal latency was obtained through optimized calculation: , Alignment quality assessment: The improvement of 0.72 compared to the traditional cross-correlation method is significant.

[0187] Anomaly propagation analysis: When an abnormal etching rate (abnormal intensity) was detected at 456 seconds... At that time, the anomaly propagation formula is used to trace along the causal chain:

[0188] ;

[0189] Detailed calculation process: Spatial attenuation function: (Sensor physical distance 1 unit); Time decay function: (delay) decay time constant ); Probability of abnormal propagation: .

[0190] Continuing to trace back to the source, it was found that the RF power sensor began to show anomalies (anomaly intensity of 0.65) at 454.2 seconds, which propagated to the etching rate through the causal chain.

[0191] The specific calculation of Bayesian root cause localization: Observing the set of anomalies { abnormal, For anomalies, Bayesian inference is used to locate the root cause:

[0192] ;

[0193] Specific calculation: Likelihood probability: (Based on the causal chain propagation model); Prior probability: (Historical failure rate of RF power system); Marginal probability: (Historical occurrence rate of this anomalous pattern); Root cause probability: (After normalization); the system automatically identifies the RF power supply system as the root cause of the anomaly with a probability of 94%, providing engineers with clear guidance for fault location.

[0194] S3: Adaptive intelligent decision-making based on graph attention networks:

[0195] Based on the causal anomaly detection results obtained in step S2, a graph attention network is used to dynamically learn the importance of sensors and optimize the decision-making strategy.

[0196] First, the historical performance metrics of each sensor are calculated to provide feature input for the graph attention network. (Using sensors...) Taking (RF power) as an example, based on the statistics of operating data over the past 168 hours (7 days):

[0197] False alarm count statistics: Number of times (the number of times the RF power sensor triggered an abnormal alarm but was manually confirmed as a false alarm); Total number of detections: Count; Historical false alarm rate: .

[0198] Similar calculations are performed on other sensors: (Plasma density) (Etching rate) (Gas flow rate), etc.

[0199] The alignment quality score is based on the average alignment quality of the causal pairs involved by each sensor in step 3. For the sensor its neighbor set (Strength of causal relationship) (sensor)

[0200] ;

[0201] in The optimal alignment quality score for RF power and plasma density in step 3 is given.

[0202] Similar calculations: wait.

[0203] Construct sensor feature vectors, in order to For example:

[0204] ;

[0205] A graph attention mechanism is used to calculate the dynamic weight relationships between sensors. Graph attention network parameters are set as follows: feature dimension... The hidden layer has a dimension of 64 and a slope of Attention count .

[0206] To calculate ( right Taking attention weights as an example: the feature vector after linear transformation and Concatenate the data using attention vectors. The calculation yielded: Activated by LeakyReLU: ; Softmax normalization yields: .

[0207] Similarly, calculation Attention weights for other neighboring nodes, Attention weight calculation:

[0208] Eigenvectors after linear transformation and The concatenation is performed, and the result is calculated using the attention vector a:

[0209] ;

[0210] Activated by LeakyReLU: ;

[0211] Attention weights are obtained by normalization using the softmax function:

[0212] ;

[0213] right Attention weight calculation:

[0214] ;

[0215] Activated by LeakyReLU: ;

[0216] Softmax normalization yields: ;

[0217] A multi-head attention mechanism with four attention heads is used, and the calculation results for each head are as follows:

[0218] Head 1: , , ;

[0219] Second head: , , ;

[0220] The third head: , , ;

[0221] 4th head: , , ;

[0222] Calculate the average weight of multi-head attention:

[0223] ;

[0224] ;

[0225] ;

[0226] The complete attention matrix calculation results show that the RF power sensor primarily focuses on plasma density. Matching with RF .

[0227] To ensure the effectiveness of multi-head attention fusion, the attention weights are normalized based on the method in step S3:

[0228] ;

[0229] ;

[0230] Use the correct values ​​from the causality matrix:

[0231] , , ;

[0232] Calculate the sensor importance weights according to the formula in step S3:

[0233] ;

[0234] The importance weights of each sensor are calculated using the same normalization method:

[0235] , , , wait.

[0236] An adaptive detection strategy is adjusted based on sensor importance weights, and a threshold is set: , . Employing a precision detection mode, and Standard testing methods are adopted.

[0237] Step S4: Implement active feedback optimization based on graph attention network. The specific steps are as follows:

[0238] Define system performance monitoring metrics. The number of detected anomalies is based on root cause localization probability statistics: set anomaly judgment thresholds. At time 456, the root cause localization probability ,therefore This indicates that a specific abnormal root cause sensor has been detected, namely sensor X1 (RF power sensor), and the system automatically locates the RF power system as the source of the fault.

[0239] System response time is the time taken from an anomaly detection to root cause localization.

[0240] ;

[0241] Mean of graph attention feature: The mean of the feature vectors after updating the nine sensors is calculated to obtain a 4-dimensional vector. .

[0242] The mean sensor importance weight is derived by using all the sensor importance weights calculated above.

[0243] ;

[0244] This mean reflects the average importance level of the entire sensor network.

[0245] Constructing a causal state vector:

[0246] ;

[0247] Graph convolutional temporal prediction employs a 2-layer graph convolutional network with a hidden dimension of 32. The prediction time span is set to 8 hours. Based on the current timeframe of 456 seconds and historical 24-hour data, the causal relationship matrix C is used as the graph structure input to predict the system state 8 hours from now. .

[0248] A hierarchical feedback optimization mechanism is triggered based on the prediction results. The target state is set based on optimal operating conditions. These correspond to the expected values ​​of performance metrics such as the mean of graph attention features, the mean of importance weights, the number of anomalies, and response time.

[0249] L2 norm deviation calculation: Predicted state The deviation vector from the target state is , norm .

[0250] because If the deviation exceeds the moderate deviation threshold, the causal model reconstruction layer optimization is triggered, and the physical causal relationship modeling parameters are recalibrated. The causal relationship modeling parameters in step 2 are recalibrated based on the weight patterns learned by the graph attention network.

[0251] Analysis of the importance of weight patterns: The contribution of physical prior weights is Data validation weight contribution is The contribution of time-series verification weights is .

[0252] Recalibrate parameters: , , ;

[0253] Update the causal matrix: with For example, The value remained stable with the original value, verifying the convergence of the model.

[0254] Through this closed-loop feedback mechanism based on graph attention networks and graph convolutional prediction, the system achieves comprehensive adaptive optimization from sensor importance learning to dynamic updating of the causal model. After 30 days of validation, the accuracy of sensor importance assessment increased from 79% to 92.1%, the system response time was optimized from 0.15 seconds to 0.08 seconds, the accuracy of causal relationship state prediction reached 90.8%, and the system performance fluctuation was reduced by 67%.

[0255] This invention relates to the field of semiconductor manufacturing quality control technology, specifically to a semiconductor anomaly detection method and system based on physical causal relationship modeling, comprising the following steps executed sequentially: S1: acquiring multi-dimensional sensor data from the semiconductor production line, and establishing a sensor causal relationship model based on the physical mechanism of the etching process; S2: performing time-series alignment, anomaly propagation modeling, and root cause localization along the causal relationship path;

[0256] This embodiment also provides a system for implementing the above-described anomaly detection method.

[0257] A semiconductor anomaly detection system based on physical causality modeling includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the semiconductor anomaly detection method based on physical causality modeling described above.

[0258] In summary, this application establishes a physical causal relationship model between sensors to achieve causal relationship-driven temporal alignment and anomaly detection. By combining adaptive intelligent decision-making and predictive feedback optimization of graph attention networks, it solves the technical problems in the prior art, such as low temporal alignment accuracy, lack of root cause analysis in anomaly detection, and insufficient system decision-making intelligence.

[0259] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A semiconductor anomaly detection method based on physical causal relationship modeling, characterized in that... The steps are as follows, executed sequentially: S1: Acquire multi-dimensional sensor data from the semiconductor production line and establish a causal relationship model for the sensors based on the physical mechanism of the etching process. Conditional mutual information was used to verify the data support for the causal relationships in the sensor causal relationship model: ； in, For sensors and sensors Inter-information For sensors Information entropy For in the sensor Under data conditions, sensors Conditional entropy; A causal relationship model for sensors is constructed by integrating prior physical knowledge and data verification results: ； in, For sensors To the sensor The strength of the causal relationship For causal prior probabilities based on physical laws, For time-series causality verification coefficients, , and This is the weighting balance coefficient; S2: Perform time-series alignment, anomaly propagation modeling, and root cause localization along the causal path, incorporating causal constraints into the objective function of time-series alignment, and calculating the anomaly originating from the sensor. propagation to sensor Based on the probability, Bayesian inference methods are used to locate the root cause of the anomaly; S3: Computational Sensor Average alignment quality and anomaly detection statistics of all involved causal relationships, fused sensors Based on causal relationships, average alignment quality, and anomaly detection statistics, sensor node feature vectors are constructed. A graph attention mechanism is employed to calculate dynamic attention weights among sensors. An attention score is calculated for each attention head, and LeakyReLU activation and softmax normalization are used to obtain the single-head attention weight and the average weight of multi-head attention. Based on the normalized average weight of multi-head attention, the sensor's attention weight is calculated. Importance weights are used to adaptively adjust the detection strategy based on the importance weights of the sensors.

2. The semiconductor anomaly detection method based on physical causal relationship modeling as described in claim 1, characterized in that: In step S1, the multidimensional sensor data includes the radio frequency power, chamber pressure, gas flow rate and temperature distribution of the etching equipment, the power matching, reaction gas flow rate and heating temperature of the PECVD equipment, and the multidimensional sensor data is preprocessed using a data quality assessment mechanism.

3. The semiconductor anomaly detection method based on physical causal relationship modeling as described in claim 1, characterized in that: Step S2 specifically includes the following steps: S2-1: Incorporating causal constraints into the time-aligned objective function: ； in, For causally driven alignment quality evaluation functions, For sensors To the sensor The importance weight of causal paths For the strength of causality, For the sensor to in time delay The cross-correlation function under the following conditions For physical constraint regularization terms, These are the physical constraint weighting coefficients; S2-2: The anomaly from the sensor is calculated using the following formula. propagation to sensor probability : ； in, For sensors Abnormal intensity at the location, Spatial decay function along causal path, This is a time decay function, reflecting the time delay effect of anomaly propagation; S2-3: Using Bayesian inference to locate the root cause of anomalies: ； in, For sensors It is the probability of the abnormal root cause. To from the sensor Starting from the causal relationship path, we can explain the probability of the observed anomalous sensor set. For sensors As the prior probability of an anomaly source, when When the value is greater than or equal to the preset root cause threshold, the sensor... As the root cause of the abnormality, The total number of sensors represents the total number of sensors in the system.

4. The semiconductor anomaly detection method based on physical causal relationship modeling as described in claim 3, characterized in that: Step S3, the adaptive intelligent decision-making based on graph attention network, consists of the following steps: S3-1: The sensor is calculated using the following formula. Average alignment quality of all involved causal relationships: ； in, , To be compatible with sensors A set of neighbors with a significant causal relationship, when the sensor To the sensor strength of causation Exceeding the significance threshold of causation At that time, the sensor Only then was it considered a sensor Only significant causal neighbors are included in the calculation of average quality. Indicates the significance threshold of causal relationship. For sensors and sensors The optimal alignment quality evaluation function value, middle Indicates sensor Neighbor sensor set Each sensor in the system; S3-2: The historical false alarm rate is calculated using the following formula based on anomaly detection statistics within the sliding window: ； in, For sensors The number of false alarms within the historical window Total number of tests; S3-3: Constructing sensor node feature vectors It integrates causal relationships, average alignment quality, and anomaly detection statistics: ； in, Indicates sensor The causal relationship vector; S3-4: Calculate the dynamic attention weights between sensors using a graph attention mechanism, and calculate the attention score for each attention head: ； in, For the first The weight matrix of the science department for each attention head, For the first The parameter vector of each attention head, This indicates a feature concatenation operation. This is the vector transpose operator; The single-head attention weights are obtained using LeakyReLU activation and softmax normalization: ； in, This represents an exponential function, i.e. , To leak the linear rectifier function, , middle Indicates sensor Neighbor sensor set Each sensor in the system; Calculate the average weight of multi-head attention: ； in, For attention indexing, ,in, For the total number of attention heads; The average weight of multi-head attention is normalized: ； in, These are the normalized attention weights; S3-5: Sensor for calculating average weights based on normalized multi-head attention Importance weight: ； The detection strategy is adaptively adjusted based on the importance weight of the sensors: when When the weight is greater than or equal to the preset maximum importance weight, a precision detection mode is used. Lightweight detection mode is used when the weight is less than or equal to the preset minimum importance weight; otherwise, standard detection mode is used.

5. The semiconductor anomaly detection method based on physical causality modeling as described in claim 4, characterized in that: It also includes step S4: implementing active feedback optimization based on graph attention networks, the specific steps of which are as follows: S4-1: In At any given time, the number of anomaly detections detected by the system is calculated as follows: ； in, This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise. The preset root cause threshold; S4-2: System response time is the average time taken from an anomaly detection to root cause localization. ； in, and The first The time for detecting an anomaly and the time for completing root cause localization; S4-3: Define the causal relationship state vector and fuse the multi-layer features of the graph attention network: ； in, To calculate the mean of the output features of the graph attention network, This is the updated feature vector after processing by the multi-head attention mechanism of the graph attention network. , For the total number of sensors, This represents the mean of the importance weights of the sensors; S4-4: A time-series test model is established using a graph convolutional neural network to enhance prediction accuracy by leveraging graph structure information. ； in, From time At the time The historical causal relationship state vector sequence, The prediction time step represents the time interval for forward prediction. For graph convolutional prediction networks, For network parameters; S4-5: Based on the prediction results, trigger a hierarchical feedback optimization mechanism and define the prediction bias: ； in, The system target state vector is set according to the optimal operating conditions; Given the L2 norm, calculate the Euclidean distance deviation between the predicted state and the target state; Attention weight fine-tuning layer, when At the same time, fine-tune the attention parameters: ； in, These are the attention vector parameters of the current graph attention network. For the updated parameters, For learning rate, This represents the gradient of the system state loss function with respect to the attention parameters. Graph structure reconstruction layer: when At that time, key causal edges are reconstructed based on attention weights: ； in, To reconstruct the weight coefficients for the graph structure, control the magnitude of the adjustment of causal relationship strength based on attention weights. For the first Sensors in a single attention head For sensors Attention weights; Causal model reconstruction layer: when At that time, the causal modeling update in step S1 is triggered: ； in, , and Recalibrate based on the weight patterns learned by the graph attention network. For causal prior probabilities based on physical laws, For sensors and The temporal causal verification coefficient between them.

6. A semiconductor anomaly detection system based on physical causal relationship modeling, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the semiconductor anomaly detection method based on physical causal relationship modeling as described in any one of claims 1-5.

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