Wafer map defect knowledge graph evolution reasoning method based on structural causal intervention
By constructing a three-layer directed weighted knowledge graph and a graph convolutional evolutionary reasoning model based on structural causal intervention, the problem of insufficient samples in wafer image defect detection methods under OEM production mode is solved. It realizes a unified expression of the hierarchical correlation and causal propagation relationship between preparation process, grain defects and wafer image defects, and improves the accuracy and stability of wafer image defect prediction and detection.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DONGHUA UNIV
- Filing Date
- 2026-04-02
- Publication Date
- 2026-06-09
AI Technical Summary
Existing wafer pattern defect detection methods lack sufficient historical samples in OEM production models, making it difficult to accurately obtain prior distribution information of potential wafer pattern defects. Furthermore, they lack a unified way of expressing the hierarchical relationship and causal propagation relationship between fabrication processes, grain defects, and wafer pattern defects, and cannot effectively cope with process disturbances and equipment status changes.
A three-layer directed weighted knowledge graph based on structural causal intervention is constructed. The causal propagation strength is represented by the causal propagation matrix and the causal purification matrix. Combined with the graph convolutional evolutionary reasoning model, the hierarchical association and causal propagation relationship between the fabrication process, grain defects and wafer image defects are realized, and the prior distribution information of potential wafer image defects is generated.
It improves the accuracy and stability of wafer pattern defect prediction and detection, and is applicable to the generation of prediction and detection models and quality analysis of wafer pattern defects in semiconductor manufacturing processes.
Smart Images
Figure CN121960799B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a wafer defect knowledge graph evolution reasoning method based on structural causal intervention, belonging to the field of semiconductor manufacturing defect analysis and knowledge reasoning technology. Background Technology
[0002] In wafer manufacturing, multiple fabrication processes such as diffusion, thin film deposition, photolithography, etching, and ion implantation can lead to defects at the grain level, such as breakdown, short circuits, and threshold voltage deviations, due to equipment conditions, batch variations, and process disturbances. Grain defects further manifest as wafer pattern defects in the wafer spatial layout, such as central ring defects, scratch defects, and edge-local defects.
[0003] Existing wafer image defect detection methods primarily employ data-driven approaches based on historical samples, particularly machine learning and deep learning methods, to identify and classify wafer image defect patterns. While these methods can achieve a certain level of defect detection effectiveness under known sample distribution conditions, they are highly dependent on the number of training samples, the stability of the sample distribution, and known defect patterns. In OEM production, due to significant differences in structural design, fabrication process paths, and process parameter settings among different wafer products, and the lack of sufficient historical defect samples in the early stages of new product production, existing methods struggle to accurately obtain prior distribution information on potential wafer image defects. This makes it difficult to provide stable and effective prior constraints for subsequent defect prediction or detection model construction. Furthermore, existing wafer image defect detection technologies mainly focus on the identification and classification of the defect image itself, lacking a unified structured representation of the hierarchical relationships between fabrication processes, grain defects, and wafer image defects. They also lack path purification mechanisms based on structural causal intervention for defect propagation relationships caused by process disturbances, equipment status changes, and batch fluctuations; and they lack corresponding dynamic evolutionary reasoning capabilities for knowledge changes brought about by new processes, edge weight changes, or structural updates.
[0004] Therefore, there is an urgent need to propose a wafer image defect knowledge graph evolution reasoning method based on structural causal intervention, in order to construct the hierarchical association and causal propagation relationship between manufacturing process, grain defects and wafer image defects in the OEM scenario, generate prior distribution information of potential wafer image defects, and provide knowledge constraints for the generation of subsequent defect prediction or detection models. Summary of the Invention
[0005] The technical problem to be solved by this invention is that existing wafer image defect detection methods suffer from insufficient defect samples and a lack of knowledge about wafer image defects.
[0006] To address the aforementioned technical problems, the present invention discloses a wafer image defect knowledge graph evolution reasoning method based on structural causal intervention, comprising the following steps:
[0007] Step 1: Collect historical structured production data of multi-wafer products under the OEM production mode. After associating the historical structured production data based on wafer ID, batch ID and / or process path ID, a unified dataset is formed for subsequent knowledge graph construction and evolutionary reasoning.
[0008] Step 2: Construct a three-layer directed weighted knowledge graph based on a unified dataset Three-layer directed weighted knowledge graph It includes first-type causal edges from fabrication process nodes to grain defect nodes, second-type causal edges from grain defect nodes to wafer image defect nodes, and cross-layer causal edges from fabrication process nodes to wafer image defect nodes.
[0009] Step 3: Calculate a three-layer directed weighted knowledge graph based on historical statistical data. The conditional probability weights of the first and second type causal edges are used to construct the causal propagation matrix. Through the causal propagation matrix Representation of a three-layer directed weighted knowledge graph The strength of causal propagation in the middle;
[0010] Step 4: Based on a three-layer directed weighted knowledge graph and causal propagation matrix Constructing a structural causal model Based on the aforementioned structural causal model Identifying three-layer directed weighted knowledge graphs Causal propagation paths and confusion paths between fabrication process nodes and wafer defect nodes, for a three-layer directed weighted knowledge graph. The set of manufacturing process nodes in Perform causal intervention to obtain the post-intervention path propagation relationship, and then apply the aforementioned structural causal model. Construct a causal intervention matrix based on the intervention results obtained from the path propagation causal relationships after intervention. Using causal propagation matrix and causal intervention matrix Constructing a causal purification propagation matrix ;
[0011] Step 5: Based on the causal purification propagation matrix and causal propagation matrix Construct a graph convolutional evolutionary reasoning model for the three-layer directed weighted knowledge graph. Perform multi-layer propagation computation to obtain the three-layer directed weighted knowledge graph. Node embedding representation;
[0012] Step 6: Utilize the results obtained from steps 1 to 5 The node embedding representation at time is denoted as Obtain the incremental change of the propagation matrix at the current moment, resulting from the addition of new nodes, edges, or edge weight updates. Then, the incremental change of the propagation matrix is utilized. Node embedding representation Perform evolutionary updates to obtain the final node embedding representation after evolutionary reasoning;
[0013] Step 7: Embed the set of wafer map defect nodes in the final node embedding representation obtained in Step 6. The corresponding embedding results are normalized to obtain the prior probability distribution vector of the wafer image defect type. ,in, Represents a random variable indicating the type of defect in the wafer plot. This represents the prior probability of each defect type.
[0014] Preferably, in step 1, the historical structured production data includes manufacturing process record data, equipment status data, grain defect detection data, grain layout data, and wafer image defect statistics. Then, for each wafer sample, a unified index key is established based on the wafer ID, batch ID, and / or process path ID. The process segment sequence, process order, and process parameter summary are extracted from the manufacturing process record data; equipment health indicators, maintenance information, and aging indicators are extracted from the equipment status data; grain-level defect types and defect indicators are extracted from the grain defect detection data; the spatial coordinates and effective region boundaries of the grains are extracted from the grain layout data; and wafer image defect type labels or statistical distributions are extracted from the wafer image defect statistics. These are then associated according to the unified index key to form a unified dataset for subsequent knowledge graph construction and evolutionary reasoning.
[0015] Preferably, in step 2, the constructed three-layer directed weighted knowledge graph Represented as:
[0016]
[0017] in: Let be a set of nodes, and , For the preparation of a set of process nodes, It is a set of grain defect nodes. This is the set of defect nodes in the wafer diagram;
[0018] The set of edges includes: first-type causal edges from fabrication process nodes to grain defect nodes, second-type causal edges from grain defect nodes to wafer map defect nodes, and cross-layer causal edges from fabrication process nodes to wafer map defect nodes.
[0019] Let be the set of edge weights.
[0020] Preferably, in step 3, the causal propagation matrix is constructed using the following steps. :
[0021] Statistical analysis of historical data on manufacturing process nodes Grain defect nodes appear under certain conditions The occurrence ratio is used to obtain the conditional probability weights of the first type of causal edge. ,in, Represents conditional probability;
[0022] Statistical analysis of grain defect nodes in historical data Wafer pattern defect nodes under certain conditions The occurrence ratio is used to obtain the conditional probability weights of the second type of causal edge. ,in;
[0023] Weight the conditional probability of the first type of causal edge and the conditional probability weights of the second type of causal edge Write into the causal propagation matrix middle.
[0024] Preferably, in step 4, the structural causal model Represented as:
[0025]
[0026] in: It is a set of exogenous variables used to characterize external influencing factors;
[0027] The set of endogenous variables is the three-layer directed weighted knowledge graph. The set of nodes, including the set of manufacturing process nodes. Grain defect node set Wafer image defect node set ;
[0028] This is a set of structural equations used to characterize fabrication process nodes, grain defect nodes, and wafer map defect nodes. , , The structural causal relationship between them includes at least:
[0029]
[0030]
[0031] in: Represents the set of grain defect variables. Represents the set of defect variables in the wafer diagram;
[0032] and For the set of exogenous variables A subset of;
[0033] and This is the structural equation mapping function.
[0034] Preferably, in step 4, the causal intervention matrix Based on causal path contribution The construction, wherein the causal path is based on the three-layer directed weighted knowledge graph. edge set in and the causal propagation matrix The extracted propagation path from the fabrication process node to the wafer defect node, and the contribution of the causal path. satisfy:
[0035]
[0036] in, For the first causal path The edge weights corresponding to each edge, This represents the product of the weights of all edges along the path;
[0037] The causal purification propagation matrix Calculated by the following formula:
[0038]
[0039] in, This indicates element-wise multiplication.
[0040] Preferably, step 5 includes the following steps:
[0041] Step 501: Construct the graph convolutional evolutionary inference model using a dual-channel structure of observation and intervention channels, wherein: the observation channel is based on the original causal propagation matrix. Graph convolution propagation is represented as:
[0042]
[0043] in, For the observation channel in the first The node feature matrix of the layer For the observation channel in the first The node feature matrix of the layer For the observation channel in the first The trainable parameter matrix of the layer, For the causal propagation matrix The calculated degree matrix, It is a non-linear activation function. For network layer indexing;
[0044] Intervention channels are based on causal purification propagation matrices Graph convolution propagation is represented as:
[0045]
[0046] in, For the intervention channel in the first The node feature matrix of the layer For the intervention channel in the first The node feature matrix of the layer For the intervention channel in the first The trainable parameter matrix of the layer, For the causal purification propagation matrix The calculated degree matrix;
[0047] Step 502: Weightedly fuse the outputs of the observation channel and the intervention channel to obtain the fused node feature matrix. ,in, Indicates the preset final propagation layer number;
[0048] Step 503: Convert the node feature matrix The distributed embedding vector of each node is fused with the rule semantic representation vector to obtain the three-layer directed weighted knowledge graph. The node embedding representation.
[0049] Preferably, in step 503, the first The regular semantic representation vector of each node The following method was used to obtain it:
[0050] Based on the fabrication process record data, equipment status data, grain defect detection data obtained in step 1, and the structural causal model established in step 4. By combining a pre-built expert rule base, rule matching and semantic encoding are performed on the process attributes, defect attributes, and causal relationships of nodes, thereby obtaining the rule semantic representation vector of the corresponding node. .
[0051] Preferably, step 6 includes the following steps:
[0052] Step 601 、 get The incremental changes in the propagation matrix at any given moment are caused by the addition of new nodes, edges, or edge weights. , Momentary, Causal propagation matrix at time step ,as well as Node embedding representation at time ;
[0053] Step 602, Update Causal propagation matrix at time step , ;
[0054] Step 603, based on Causal propagation matrix at time step Calculation obtained Causal intervention matrix at time and further obtained Momentary Causal Purification Propagation Matrix ;
[0055] Step 604: Based on the updated causal propagation matrix and causal purification propagation matrix The method in step 5 is used to calculate and obtain Node embedding representation at time As the final node embedding representation after evolutionary reasoning.
[0056] Preferably, in step 7, the prior probability distribution vector Used for defect prediction in newly commissioned wafers or for generating constraints for defect detection models.
[0057] This invention proposes a wafer image defect knowledge graph evolution reasoning method based on structural causal intervention. It constructs a defect prior distribution generation framework integrating unified representation of multi-source production data, three-layer knowledge graph modeling of fabrication process, grain defects, and wafer image defects, structural causal intervention purification, graph convolutional evolution reasoning, and spatial aggregation constraints. By introducing a hierarchical knowledge representation structure among fabrication process, grain defects, and wafer image defects, unified modeling of multi-layer defect relationships in wafer manufacturing is achieved. Combining the structural causal model and intervention mechanism, the method suppresses obfuscation propagation paths and enhances credible causal paths. Furthermore, through graph convolutional propagation and time-increment update strategies, dynamic evolution reasoning of the knowledge graph is achieved under conditions of new processes, edge weight changes, and structural updates. Finally, through grain spatial aggregation constraints, the method realizes the mapping and prior distribution generation from grain-level defect information to wafer image-level defect patterns. This method can effectively alleviate the reasoning difficulties caused by insufficient samples, frequent process changes, and difficulty in explicitly utilizing defect knowledge in the early stages of new product production under the OEM production model. It improves the accuracy and stability of wafer image potential defect distribution prediction and is applicable to tasks such as wafer image defect prediction, detection model generation, and quality analysis in the semiconductor manufacturing process. Attached Figure Description
[0058] Figure 1 This is a flowchart of a wafer image defect knowledge graph evolution reasoning method based on structural causal intervention according to the present invention. Detailed Implementation
[0059] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.
[0060] like Figure 1 As shown in the figure, the wafer image defect knowledge graph evolution reasoning method based on structural causal intervention disclosed in this embodiment of the invention specifically includes the following steps:
[0061] Step 1: Data collection and unified representation of wafer production data.
[0062] Structured production data for multi-wafer products under OEM production mode is collected. The structured production data includes fabrication process record data, equipment status data, grain defect detection data, grain layout data, and wafer pattern defect statistics.
[0063] In this embodiment, a unified index key is established for each wafer sample, including wafer ID, batch ID, and process path ID. Process segment sequences, process order, and process parameter summaries are extracted from the fabrication process record data. Equipment health indicators, maintenance information, and aging indicators are extracted from equipment status data. Grain-level defect types and defect indicators are extracted from grain defect detection data. Spatial coordinates and effective region boundaries of the grains are extracted from the grain layout data. Wafer map defect type labels or statistical distributions are extracted from wafer map defect statistics.
[0064] The above data are linked together using a unified index key to form a unified dataset for subsequent knowledge graph construction and evolutionary reasoning.
[0065] Step 2: Wafer process - Defect knowledge graph construction.
[0066] Based on the unified dataset formed in step 1, a three-layer directed weighted knowledge graph is constructed. ,in:
[0067] Let be a set of nodes, and , This is a set of process nodes used to represent process path nodes such as diffusion, thin film deposition, photolithography, etching, ion implantation, or combinations thereof. This is a set of grain defect nodes used to represent grain-level defect types such as breakdown, short circuit, and threshold shift. It is a set of wafer map defect nodes used to represent wafer map-level defect modes such as central ring type, scratch type, and edge local type;
[0068] Let the set of edges contain: first-kind causal edges from fabrication process nodes to grain defect nodes. (Process-induced grain defects), second-type causal edges from grain defect nodes to wafer map defect nodes. (Grain defect-induced wafer map defect modes) and cross-layer causal edges from fabrication process nodes to wafer map defect nodes (The cross-layer effect of process on wafer pattern defects);
[0069] Let be the set of edge weights.
[0070] Step 3: Calculate conditional probability edge weights and construct the causal propagation matrix.
[0071] Calculate the conditional probability weights of causal edges in the knowledge graph based on historical statistical data, and construct the causal propagation matrix. ,satisfy.
[0072] In this embodiment, a certain manufacturing process node is statistically analyzed from historical data. Grain defect nodes appear under certain conditions The proportion of occurrence is obtained as follows: ;
[0073] Similarly, statistical grain defect nodes Wafer pattern defect nodes under certain conditions The proportion of occurrence is obtained as follows: ,in:
[0074] Indicates the first Each manufacturing process node Indicates the first Each grain defect node Indicates the first One wafer image defect node;
[0075] Represents conditional probability;
[0076] For the first type of causal edge point to The right to the side;
[0077] For the second type of causal edge point to The right to the side;
[0078] Write the above edge weights into the propagation matrix. In the middle, make the propagation matrix Used to characterize the strength of causal propagation in knowledge graphs.
[0079] Step 4: Construction of structural causal model and causal intervention and purification.
[0080] Characterizing the strength of causal propagation in knowledge graphs and the causal propagation matrix formed in step 3 Construct a structural causal model:
[0081]
[0082] in:
[0083] It is a set of exogenous variables used to characterize external influencing factors such as equipment status, batch disturbances, or process disturbances;
[0084] The set of endogenous variables, i.e., the set of knowledge graph nodes, contains , , ;
[0085] This is a set of structural equations used to characterize fabrication process nodes, grain defect nodes, and wafer map defect nodes. , , The structural causal relationship between them includes at least:
[0086]
[0087]
[0088] in:
[0089] Represents the set of grain defect variables. Represents the set of defect variables in the wafer diagram;
[0090] and For the set of exogenous variables A subset of;
[0091] and This is the structural equation mapping function.
[0092] Based on this, a structural causal model is used to identify the causal propagation paths and obfuscated paths between fabrication process nodes and wafer map defect nodes, and to analyze the set of fabrication process variables. Perform causal intervention:
[0093]
[0094] in, Represents the set of variables related to the preparation process. Apply intervention and fix it as the intervention value. , This represents the intervention value applied to the preparation process variables. It is used to fix a specific process segment or process condition to simulate the causal reasoning process under specific process conditions and obtain the path propagation relationship after intervention.
[0095] Based on the aforementioned structural causal model and the causal intervention results, a causal intervention matrix C is constructed. Matrix C is used to suppress or adjust the weights related to the obfuscated paths in the propagation matrix according to the path propagation relationships after intervention. Then, a causal purification propagation matrix is constructed based on matrix A and matrix C. ,satisfy:
[0096]
[0097] in:
[0098] This represents element-wise multiplication.
[0099] The propagation matrix after causal purification;
[0100] This is a causal intervention matrix, used to suppress or adjust the weights related to confusing paths in the propagation matrix based on the path propagation relationships after intervention. Causal intervention matrix Based on causal path contribution The causal path is constructed based on the knowledge graph built in step 2. edge set in and the causal propagation matrix formed in step 3 The extracted propagation paths from fabrication process nodes to wafer defect nodes show that the causal path contribution satisfies the following:
[0101]
[0102] in:
[0103] For the first causal path The edge weights corresponding to each edge;
[0104] This represents the product of the weights of all edges along the path;
[0105] This is used to characterize the overall contribution strength of the causal path to defect propagation.
[0106] Step 5: Construction of the graph convolutional evolutionary inference model and multi-layer propagation.
[0107] Based on the causal purification propagation matrix obtained in step 4 Construct a graph convolutional evolutionary reasoning model to perform multi-layer propagation computation on the knowledge graph.
[0108] In this embodiment, the graph convolutional evolutionary inference model adopts a dual-channel structure of observation channel and intervention channel, wherein:
[0109] (1) Propagation through the observation channel
[0110] The observation channel is based on the original causal propagation matrix. Graph convolution propagation is performed, satisfying:
[0111]
[0112] in:
[0113] For the observation channel in the first The node feature matrix of the layer;
[0114] For the observation channel in the first The node feature matrix of the layer;
[0115] For the observation channel in the first The trainable parameter matrix of the layer;
[0116] For the causal propagation matrix The calculated degree matrix;
[0117] It is a non-linear activation function;
[0118] For network layer indexes.
[0119] (2) Intervention channel transmission
[0120] Intervention channels are based on causal purification propagation matrices Graph convolution propagation is performed, satisfying:
[0121]
[0122] in:
[0123] For the intervention channel in the first The node feature matrix of the layer;
[0124] For the intervention channel in the first The node feature matrix of the layer;
[0125] For the intervention channel in the first The trainable parameter matrix of the layer;
[0126] For the causal purification propagation matrix The calculated degree matrix;
[0127] (3) Dual-channel fusion
[0128] After completing multi-layer propagation, the outputs of the observation channel and the intervention channel are weighted and fused to obtain the node embedding representation:
[0129]
[0130] in:
[0131] For the fusion of the first Layer node feature matrix;
[0132] To integrate the weighting coefficients, and satisfy the following conditions: .
[0133] Through the aforementioned dual-channel propagation and fusion, a distributed embedded representation of each node in the knowledge graph is obtained.
[0134] Furthermore, after completing the final layer of propagation, the fused node feature matrix is... The corresponding number in the middle The feature vector of each node is denoted as . ,in, This indicates the preset final propagation layer number, therefore, This represents the first layer obtained through multi-layer propagation of graph convolution. Distributed embedding vectors of nodes.
[0135] (4) Fusion of rule-based semantic representation and distributed embedding representation
[0136] In this embodiment, the node features are further obtained by fusing rule-based semantic representation and distributed embedding representation:
[0137]
[0138] in:
[0139] For the first The fusion feature representation of each node;
[0140] The first layer obtained through multi-layer propagation of the above graph convolution is... Distributed embedding vectors of nodes;
[0141] For the first The rule semantic representation vector of each node;
[0142] To integrate the weighting coefficients, and satisfy the following conditions: .
[0143] In this embodiment of the invention, The construction method is as follows:
[0144] Based on the fabrication process record data, equipment status data, grain defect detection data obtained in step 1, and the structural causal model established in step 4. By combining a pre-built expert rule base, rule matching and semantic encoding are performed on the process attributes, defect attributes, and causal relationships of nodes, thereby obtaining the rule semantic representation vector of the corresponding node. .
[0145] After the above fusion, a fused embedding representation of each node is obtained, which is used for subsequent evolution updates and defect prior distribution reasoning.
[0146] Step 6: Introduce an evolutionary update mechanism for time variables.
[0147] To accommodate situations such as new wafer data, process changes, or edge weight updates in OEM production models, a time variable is introduced. The historical statistical data and causal propagation matrix in step 3 are incrementally updated based on the structured production data at the new time point.
[0148] In this embodiment, time is set Causal propagation matrix at time step According to time The matrix increment change is obtained by re-statistically analyzing the newly added structured production data. And update the causal propagation matrix as follows:
[0149]
[0150] in:
[0151] For time The causal propagation matrix is updated in real time;
[0152] For time The causal propagation matrix at any given moment;
[0153] Indicates time The propagation matrix changes incrementally at all times due to the addition of new nodes, edges, or edge weights.
[0154] After obtaining the updated causal propagation matrix Then, by further combining the causal intervention mechanism in step 4, the causal purification propagation matrix at the current moment is reconstructed. ,satisfy:
[0155]
[0156] in:
[0157] For time A causal intervention matrix is constructed based on the current knowledge graph structure, causal paths, and intervention results at every moment;
[0158] For time The causal purification propagation matrix of time.
[0159] Then, based on time Node embedding representation at time and time The propagation matrix updated at each time step The node embedding representation is then evolved and updated. In this embodiment, the evolution update can be expressed as:
[0160]
[0161] For time Node embedding representation at time;
[0162] For time The node embedding representation updated in real time;
[0163] This is an incremental update function used to update... Update the node embedding representation under constraints;
[0164] The The final node is embedded in the representation after evolutionary reasoning.
[0165] Furthermore, in this embodiment, the incremental update function The implementation method is as follows:
[0166] In time Node embedding representation at time As initial input, based on the updated causal propagation matrix and causal purification propagation matrix Re-execute the graph convolution propagation and dual-channel fusion calculation in step 5 to obtain the time. Node embedding representation at time .
[0167] Therefore, the knowledge graph evolution reasoning process in this embodiment can be understood as follows:
[0168] First, the propagation matrix increment is obtained from the structured production data at the new time step. Then update the causal propagation matrix. Furthermore, by combining causal intervention, a causal purification and propagation matrix can be constructed for the current moment. Finally, graph convolutional propagation is re-executed to obtain the evolved and updated node embedding representation. .
[0169] The The final node is embedded in the representation after evolutionary reasoning.
[0170] Step 7: Defect prior distribution output and spatial aggregation constraints.
[0171] The final node embedding representation obtained in step 6 Set of defect nodes in the wafer diagram The corresponding embedding results are normalized to obtain the initial prior probability distribution vector of wafer image defects based on graph evolution reasoning. ,in Represents a random variable indicating the type of defect in the wafer plot. Representation based on final node embedding The initial prior probabilities of each wafer pattern defect type are calculated.
[0172] Furthermore, to ensure that the prior distribution of defects is consistent with the grain spatial layout information, a set of grain layout spatial coordinates is introduced in this embodiment:
[0173]
[0174] Wherein, the set of space coordinates of the grain layout It is directly derived from the grain layout data in step 1.
[0175] Meanwhile, the grain defect detection data in step 1 includes the defect type, defect intensity, or defect indication value corresponding to each grain. After aligning with the grain spatial coordinates, the grain defect response or defect indication value corresponding to each spatial coordinate position can be obtained:
[0176]
[0177] in:
[0178] For the first The spatial coordinates of each grain;
[0179] This represents the grain defect response or defect indication quantity corresponding to the spatial coordinates.
[0180] Based on the set of grain space coordinates and grain defect response Construct a spatial aggregation function from grain defects to wafer map defects. ,satisfy:
[0181]
[0182] in:
[0183] This represents the aggregate summation over all grain coordinate positions;
[0184] Used to map the spatial aggregation results of grain defects to wafer map defect types.
[0185] In this embodiment, based on the spatial aggregation function Further, auxiliary distribution results of wafer map defects under spatial aggregation constraints can be obtained. Then, the initial prior probability distribution obtained based on the final node embedding representation is... Compared with the auxiliary distribution results obtained based on spatial aggregation functions By applying joint constraints, the final wafer image defect prior probability distribution vector is obtained. .
[0186] In this embodiment of the invention, the joint constraint can be represented by a weighted fusion method as follows:
[0187]
[0188] in:
[0189] To integrate the weighting coefficients, and satisfy the following conditions: ;
[0190] This represents the prior probability distribution vector of defects in the final wafer image.
[0191] In this embodiment, the prior probability distribution vector It can be used for defect prediction in newly commissioned wafers, or for prior constraints in the defect detection model generation process, including model structure selection, initial weight adjustment, and sample enhancement strategy control.
Claims
1. A method for evolutionary reasoning of wafer image defect knowledge graph based on structural causal intervention, characterized in that, Includes the following steps: Step 1: Collect historical structured production data of multi-wafer products under the OEM production mode. After associating the historical structured production data based on wafer ID, batch ID and / or process path ID, a unified dataset is formed for subsequent knowledge graph construction and evolutionary reasoning. Step 2: Construct a three-layer directed weighted knowledge graph based on a unified dataset Three-layer directed weighted knowledge graph It includes first-type causal edges from fabrication process nodes to grain defect nodes, second-type causal edges from grain defect nodes to wafer image defect nodes, and cross-layer causal edges from fabrication process nodes to wafer image defect nodes. Step 3: Calculate a three-layer directed weighted knowledge graph based on historical statistical data. The conditional probability weights of the first and second type causal edges are used to construct the causal propagation matrix. Through the causal propagation matrix Representation of a three-layer directed weighted knowledge graph The intensity of causal propagation in; Step 4: Based on a three-layer directed weighted knowledge graph and causal propagation matrix Constructing a structural causal model Based on the aforementioned structural causal model Identifying three-layer directed weighted knowledge graphs Causal propagation paths and confusion paths between fabrication process nodes and wafer defect nodes, for a three-layer directed weighted knowledge graph. The set of manufacturing process nodes in Perform causal intervention to obtain the post-intervention path propagation relationship, and then apply the aforementioned structural causal model. Construct a causal intervention matrix based on the intervention results obtained from the path propagation causal relationships after intervention. Using causal propagation matrix and causal intervention matrix Constructing a causal purification propagation matrix ; Step 5: Based on the causal purification propagation matrix and causal propagation matrix Construct a graph convolutional evolutionary reasoning model for the three-layer directed weighted knowledge graph. Perform multi-layer propagation computation to obtain the three-layer directed weighted knowledge graph. The node embedding representation includes the following steps: Step 501: Construct the graph convolutional evolutionary inference model using a dual-channel structure of observation and intervention channels, wherein: the observation channel is based on the original causal propagation matrix. Graph convolution propagation is represented as: in, For the observation channel in the first The node feature matrix of the layer For the observation channel in the first The node feature matrix of the layer, For the observation channel in the first The trainable parameter matrix of the layer, For the causal propagation matrix The calculated degree matrix, It is a non-linear activation function. For network layer indexing; Intervention channels are based on causal purification propagation matrices Graph convolution propagation is represented as: in, For the intervention channel in the first The node feature matrix of the layer, For the intervention channel in the first The node feature matrix of the layer, For the intervention channel in the first The trainable parameter matrix of the layer, For the causal purification propagation matrix The calculated degree matrix; Step 502: Weightedly fuse the outputs of the observation channel and the intervention channel to obtain the fused node feature matrix. ,in, Indicates the preset final propagation layer number; Step 503: Convert the node feature matrix The distributed embedding vector of each node is fused with the rule semantic representation vector to obtain the three-layer directed weighted knowledge graph. Node embedding representation; Step 6: Utilize the results obtained from steps 1 to 5 The node embedding representation at time is denoted as Obtain the incremental change of the propagation matrix at the current moment, resulting from the addition of new nodes, edges, or edge weight updates. Then, the incremental change of the propagation matrix is utilized. Node embedding representation Perform evolutionary updates to obtain the final node embedding representation after evolutionary reasoning; Step 7: Embed the set of wafer map defect nodes in the final node embedding representation obtained in Step 6. The corresponding embedding results are normalized to obtain the prior probability distribution vector of wafer image defect types. ,in, Represents a random variable indicating the type of defect in the wafer plot. This represents the prior probability of each defect type.
2. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, In step 1, the historical structured production data includes fabrication process record data, equipment status data, grain defect detection data, grain layout data, and wafer image defect statistics. For each wafer sample, a unified index key is established based on the wafer ID, batch ID, and / or process path ID. Then, process segment sequences, process order, and process parameter summaries are extracted from the fabrication process record data; equipment health indicators, maintenance information, and aging indicators are extracted from the equipment status data; grain-level defect types and defect indicators are extracted from the grain defect detection data; the spatial coordinates and effective region boundaries of the grains are extracted from the grain layout data; and wafer image defect type labels or statistical distributions are extracted from the wafer image defect statistics. These are then associated according to the unified index key to form a unified dataset for subsequent knowledge graph construction and evolutionary reasoning.
3. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, In step 2, the constructed three-layer directed weighted knowledge graph Represented as: in: Let be a set of nodes, and , For the preparation of a set of process nodes, It is a set of grain defect nodes. This is the set of defect nodes in the wafer diagram; The set of edges includes: first-type causal edges from fabrication process nodes to grain defect nodes, second-type causal edges from grain defect nodes to wafer map defect nodes, and cross-layer causal edges from fabrication process nodes to wafer map defect nodes. Let be the set of edge weights.
4. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, In step 3, the causal propagation matrix is constructed using the following steps. : Statistical analysis of historical data on manufacturing process nodes Grain defect nodes appear under certain conditions The occurrence ratio is used to obtain the conditional probability weights of the first type of causal edge. ,in, Represents conditional probability; Statistical analysis of grain defect nodes in historical data Wafer pattern defect nodes under certain conditions The occurrence ratio is used to obtain the conditional probability weights of the second type of causal edge. ,in; Weight the conditional probability of the first type of causal edge and the conditional probability weights of the second type of causal edge Write into the causal propagation matrix middle.
5. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, In step 4, the structural causal model Represented as: in: It is a set of exogenous variables used to characterize external influencing factors; The set of endogenous variables is the three-layer directed weighted knowledge graph. The set of nodes, including the set of manufacturing process nodes. Grain defect node set Wafer image defect node set ; This is a set of structural equations used to characterize fabrication process nodes, grain defect nodes, and wafer map defect nodes. , , The structural causal relationship between them includes at least: in: Represents the set of grain defect variables. Represents the set of defect variables in the wafer diagram; and For the set of exogenous variables A subset of; and This is the structural equation mapping function.
6. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, In step 4, the causal intervention matrix Based on causal path contribution The construction, wherein the causal path is based on the three-layer directed weighted knowledge graph. edge set in and the causal propagation matrix The extracted propagation path from the fabrication process node to the wafer defect node, and the contribution of the causal path. satisfy: in, For the first causal path The edge weights corresponding to each edge, This represents the product of the weights of all edges along the path; The causal purification propagation matrix Calculated by the following formula: in, This indicates element-wise multiplication.
7. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, In step 503, the first The regular semantic representation vector of each node The following method was used to obtain it: Based on the fabrication process record data, equipment status data, grain defect detection data obtained in step 1, and the structural causal model established in step 4. By combining a pre-built expert rule base, rule matching and semantic encoding are performed on the process attributes, defect attributes, and causal relationships of nodes, thereby obtaining the rule semantic representation vector of the corresponding node. .
8. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, Step 6 includes the following steps: Step 601 、 get The incremental changes in the propagation matrix at any given moment are caused by the addition of new nodes, edges, or edge weights. , Momentary, Causal propagation matrix at time step ,as well as Node embedding representation at time ; Step 602, Update Causal propagation matrix at time step , ; Step 603, based on Causal propagation matrix at time step Calculation obtained Causal intervention matrix at time and further obtained Momentary Causal Purification Propagation Matrix ; Step 604: Based on the updated causal propagation matrix and causal purification propagation matrix The method in step 5 is used to calculate and obtain Node embedding representation at time As the final node embedding representation after evolutionary reasoning.
9. The wafer image defect knowledge graph evolution reasoning method based on structural causal intervention as described in claim 1, characterized in that, In step 7, the prior probability distribution vector Used for defect prediction in newly commissioned wafers or for generating constraints for defect detection models.