Wafer warpage adaptive probe station pressure closed-loop control method and system

Abstract

The present application relates to the technical field of semiconductor testing, and particularly relates to a probe station pressure closed-loop control method and system adaptive to wafer warping, which comprises the following steps: obtaining wafer warping characteristic data and performing space-time correlation analysis to obtain a warping dynamic characteristic map; constructing a pressure matching prediction model based on the map and generating a partition pressure regulation strategy; driving a multi-point pressure execution unit to apply differential pressure and collecting response data according to the strategy; performing tensor projection operation based on the response data and the map; and reconstructing model parameters according to a projection component offset vector to realize continuous evolution of the model. The method can adaptively adjust the pressure distribution of the probe station, effectively compensate for local deformation of the wafer, and significantly improve the testing stability and precision.

Description

Technical Field

[0001] This invention relates to the field of semiconductor testing technology, and in particular to a probe station pressure closed-loop control method and system for wafer warpage adaptive control. Background Technology

[0002] In the field of probe station testing, wafer warpage is a core issue affecting testing accuracy and yield. Current conventional practices typically employ global mechanical leveling devices or uniform pressure application schemes, using pneumatic or piezoelectric actuators on a support platform to apply constant pressure to the entire wafer to compensate for flatness deviations caused by warpage. Some improved solutions introduce static warpage measurement, such as using laser interferometers or capacitive sensors to acquire macroscopic deformation data of the wafer surface, and adjusting the height or tilt angle of the support platform accordingly to achieve a fixed pressure distribution after a single calibration. These methods rely on pre-set rigid correction strategies and lack the ability to capture and respond to the dynamic characteristics of wafer microscopic deformation in real time.

[0003] Current methods have significant drawbacks. Wafer warpage exhibits highly spatiotemporal evolution characteristics, especially in multilayer thin-film stacking or thermal cycling tests, where local deformation dynamically migrates with changes in process parameters. Traditional correction methods based on static or low-frequency sampling cannot identify this evolutionary trend, leading to a mismatch between applied pressure and the actual deformation state. When certain areas of the wafer experience nonlinear buckling due to stress concentration, uniform pressure can exacerbate local contact unevenness, causing probe slippage or overpressure damage, directly reducing the reliability of the test signal.

[0004] Existing control mechanisms are mostly open-loop structures, where the compensation amount of the pressure actuation unit depends only on the initial measurement results, lacking systematic feedback and self-optimization capabilities regarding the applied effect. Even when closed-loop regulation is introduced, it typically only applies PID control to the overall pressure value, ignoring the differentiated requirements of deformation sensitivity in different regions. This coarse-grained strategy cannot handle the significant differences in warpage modes between the wafer edge and center regions, resulting in insufficient robustness of pressure control. As wafer size increases and process nodes shrink, these shortcomings become increasingly severe, necessitating a closed-loop control scheme that can adaptively adapt to dynamic changes in wafer warpage and continuously optimize pressure distribution. Summary of the Invention

[0005] The present invention provides a probe station pressure closed-loop control method and system for wafer warpage adaptive control, which can solve the problems in the prior art.

[0006] A first aspect of the present invention provides a wafer warpage adaptive probe station pressure closed-loop control method, comprising: Multidimensional microscopic warping feature data of the wafer on the carrier platform is obtained, and spatiotemporal correlation analysis is performed on the multidimensional microscopic warping feature data to identify feature patterns that characterize the local deformation evolution trend of the wafer and obtain a warping dynamic feature map. Based on the warp dynamic feature map, a pressure matching prediction model is constructed. The deformation sensitivity of different regions on the wafer surface is quantitatively evaluated through the pressure matching prediction model, and a partitioned pressure control strategy adapted to the warp feature mode of each region is generated. Based on the partitioned pressure control strategy, the multi-point pressure execution unit of the drive platform applies differentiated pressure to the wafer and collects the wafer micro-warpage response data after pressure application. Based on the wafer micro-warping response data, a response feature matrix characterizing the actual deformation state is constructed. The response feature matrix and the warping dynamic feature map are subjected to tensor projection operation. Based on the component offset vector in the projection operation result, the regional sensitivity evaluation weight and coupling effect parameters in the pressure matching prediction model are vectorized and reconstructed to realize the continuous evolution of the model.

[0007] Spatiotemporal correlation analysis was performed on the multidimensional microscopic warping feature data to identify characteristic patterns representing the evolution trend of local deformation in the wafer, resulting in a warping dynamic feature map including: Multidimensional micro-warping feature data are used to construct a multidimensional feature tensor according to the spatial coordinates of the wafer surface and the time series dimension. The multidimensional feature tensor is then analyzed along the spatial dimension to identify the deformation coupling relationship between adjacent regions. The evolution trajectory of the multidimensional feature tensor is tracked along the time dimension to capture the change law of warping features at each spatial location with the process progress, and a temporal evolution feature sequence is obtained. Based on the deformation coupling relationship and the temporal evolution feature sequence, a feature pattern representation system integrating spatial coupling topology and temporal evolution dynamics is constructed. By jointly quantifying the spatial coupling strength and temporal evolution rate, a warping dynamic feature map representing the local deformation evolution trend of the wafer is generated.

[0008] Multidimensional microscopic warping feature data are used to construct a multidimensional feature tensor based on the spatial coordinates of the wafer surface and the time series dimension. Neighborhood correlation analysis is then performed on this multidimensional feature tensor along the spatial dimension to identify the deformation coupling relationship between adjacent regions, including: Multidimensional microscopic warping feature data are spatially gridded according to the radial and angular coordinates of the wafer surface. The warping amplitude and curvature change of the corresponding time series are embedded at each grid node to construct a multidimensional feature tensor that integrates spatial topology and temporal dynamics. A spatial adjacency graph is established for each grid node in the multidimensional feature tensor along the radial and angular directions. The deformation correlation strength between each node and its neighboring nodes is quantified by calculating the warping gradient vector field distribution between adjacent nodes. Based on the deformation correlation strength, a coupled topology network reflecting the mechanical transmission path between neighboring nodes is constructed. Based on the connection weight distribution characteristics and the directionality of the transmission path between nodes in the coupled topology network, the deformation coupling relationship between adjacent regions on the wafer surface is identified.

[0009] Based on the aforementioned warpage dynamic feature map, a pressure matching prediction model is constructed. This model is then used to quantitatively evaluate the deformation sensitivity of different regions on the wafer surface, generating a zoned pressure control strategy adapted to the warpage feature patterns of each region. Feature pattern vectors characterizing the local deformation evolution trend of the wafer are extracted from the warp dynamic feature map. The feature pattern vectors are correlated and mapped with the mechanical response mechanism of the wafer material and the coupling effect of the process environment to construct a pressure matching prediction model with the feature pattern vectors as input and the pressure response prediction result as output. Using the pressure matching prediction model, virtual pressure perturbation is applied to the feature mode vector of each region on the wafer surface, and the rate of change of the warping feature response of the region relative to the pressure perturbation is calculated to obtain the sensitivity coefficient characterizing the deformation sensitivity of each region. Based on the spatial distribution differences of the sensitivity coefficients, the wafer surface is divided into multiple pressure control zones with similar deformation sensitivity. For the characteristic mode vectors and sensitivity coefficients of each pressure control zone, the pressure application parameters required to achieve the target warp control state are deduced in reverse through the pressure matching prediction model, generating a zone pressure regulation strategy that includes the pressure amplitude and application sequence of each pressure control zone.

[0010] Based on the aforementioned partitioned pressure control strategy, the multi-point pressure execution unit of the drive platform applies differentiated pressure to the wafer, and collects wafer micro-warpage response data after pressure application, including: The pressure amplitude and application sequence of each pressure control zone in the partitioned pressure control strategy are analyzed. The spatial boundary coordinates of each pressure control zone are matched and located with the physical distribution of multiple pressure execution units on the bearing platform. A spatial mapping relationship between the pressure control zone and the corresponding pressure execution unit group is established, and a partitioned execution instruction set containing the driving amplitude and action timing of each pressure execution unit group is generated. According to the partition execution instruction set, each pressure execution unit group is driven to apply differentiated pressure to the wafer surface according to the pressure amplitude and application sequence of the corresponding pressure control partition, which has spatial differences and temporal coordination. During the application of differentiated pressure, the deformation displacement response and curvature change response of each measurement point on the wafer surface are synchronously collected by a micro-warping sensor array deployed on the support platform. The deformation displacement response and the curvature change response are associated and bound with the driving state and acquisition time of the corresponding pressure execution unit group to generate wafer micro-warping response data containing the execution unit driving state identifier and timing identifier.

[0011] Based on the wafer micro-warping response data, a response feature matrix characterizing the actual deformation state is constructed. Tensor projection operations are then performed between the response feature matrix and the warping dynamic feature map. Based on the component offset vectors in the projection operation results, the regional sensitivity evaluation weights and coupling effect parameters in the pressure matching prediction model are vectorized and reconstructed, including: The deformation displacement response and curvature change response of each measurement point in the wafer micro warping response data under pressure are arranged in a multi-level matrix according to the spatial position of the measurement point and the timing of pressure application, and a response feature matrix characterizing the actual deformation state is constructed. The response feature matrix and the warped dynamic feature map are subjected to tensor projection operation in a unified high-dimensional tensor space. By calculating the projection component of the response feature matrix on the dominant feature basis vector of the warped dynamic feature map, the component offset vector representing the deviation of the actual deformation state from the expected feature pattern is obtained. The component offset vector is orthogonally deconstructed along the spatial direction corresponding to each pressure control zone. Based on the difference in distribution characteristics of the deconstructed orthogonal components in the spatial position dimension and coupling correlation dimension, a dual-path separation mechanism for the sensitivity deviation component and the coupling deviation component is established. The sensitivity deviation component and the coupling deviation component are applied to the regional sensitivity assessment weight and coupling effect parameter respectively through gradient backpropagation calculation, thereby completing the vectorization reconstruction of the pressure matching prediction model.

[0012] The component offset vector is orthogonally deconstructed along the spatial direction corresponding to each pressure control zone. Based on the difference in distribution characteristics of the deconstructed orthogonal components in the spatial position dimension and coupling correlation dimension, a dual-path separation mechanism for the sensitivity deviation component and the coupling deviation component is established, including: For the component offset vector, a local orthogonal coordinate system is established with the spatial center position of each pressure control zone as the origin. The component offset vector is decomposed and projected in the coordinate axis direction of the local orthogonal coordinate system to obtain the orthogonal component group representing the component offset vector in the corresponding spatial direction of each pressure control zone. For each orthogonal component in the orthogonal component group, calculate the gradient change rate of the orthogonal component in the spatial position dimension of the wafer surface and the transmission strength in the coupling correlation dimension of adjacent pressure control intervals. Based on the numerical difference characteristics of the gradient change rate and the transmission strength, determine the dominant classification type of each orthogonal component. Orthogonal components whose dominant dimension is spatial location are aggregated to form sensitivity deviation components, and orthogonal components whose dominant dimension is coupling correlation are aggregated to form coupling deviation components, thus establishing a dual-path separation mechanism for sensitivity deviation components and coupling deviation components.

[0013] A second aspect of the present invention provides a wafer warpage adaptive probe station pressure closed-loop control system, comprising: The warpage analysis unit is used to acquire multi-dimensional micro-warpage feature data of the wafer on the carrier platform, perform spatiotemporal correlation analysis on the multi-dimensional micro-warpage feature data, identify feature patterns that characterize the local deformation evolution trend of the wafer, and obtain a warpage dynamic feature map. The pressure control unit is used to construct a pressure matching prediction model based on the warp dynamic feature map, and to quantitatively evaluate the deformation sensitivity of different regions on the wafer surface through the pressure matching prediction model, and generate a partitioned pressure control strategy that is adapted to the warp feature mode of each region. The pressure execution unit is used to drive the multi-point pressure execution unit of the carrier platform to apply differentiated pressure to the wafer according to the partitioned pressure control strategy, and to collect the wafer micro-warpage response data after the pressure is applied. The model evolution unit is used to construct a response feature matrix representing the actual deformation state based on the wafer micro-warping response data, perform tensor projection operation on the response feature matrix and the warping dynamic feature map, and vectorize and reconstruct the regional sensitivity evaluation weights and coupling effect parameters in the pressure matching prediction model according to the component offset vector in the projection operation result, so as to realize the continuous evolution of the model.

[0014] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0015] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0016] Significant improvements have been made in the pressure control accuracy and wafer warpage adaptation capability of the direct probe station. By acquiring multi-dimensional microscopic warpage feature data of the wafer and performing spatiotemporal correlation analysis, local deformation evolution trends are effectively identified, forming a dynamic feature map that provides a real-time and accurate deformation basis for pressure regulation. Based on this map, a pressure matching prediction model can quantitatively assess the deformation sensitivity of different regions, generating differentiated pressure strategies for each region. This avoids the local overpressure or underpressure problems caused by traditional uniform pressure application, significantly reducing the risk of wafer damage during probe contact and improving the contact consistency between probes and pads in each region.

[0017] After differential pressure is applied, the response feature matrix constructed from the collected microscopic warpage response data is used to perform tensor projection operations with the warpage dynamic feature map, achieving an accurate comparison between the actual deformation and the prediction model. Based on the component offset vectors in the projection results, the regional sensitivity evaluation weights and coupling effect parameters of the pressure matching prediction model are vectorized and reconstructed, enabling the model to automatically correct for changes in deformation characteristics introduced by wafer batch differences, process drift, or aging. This closed-loop feedback mechanism allows the pressure control strategy to continuously evolve, ensuring high adaptability from the first test to subsequent batches without requiring manual intervention to reset parameters.

[0018] This closed-loop control method significantly improves the robustness of the probe station to varying degrees of wafer warpage, making it particularly suitable for pressure-sensitive processes such as ultra-thin wafers or advanced packaging. Model self-optimization reduces trial-and-error iterations, shortens wafer test calibration time, and improves overall test efficiency and yield. Simultaneously, precise zoned pressure application extends the lifespan of the probes and the platform, reduces maintenance costs, and provides stable and reliable technical support for high-precision semiconductor testing. Attached Figure Description

[0019] Figure 1 This is a schematic flowchart of the wafer warpage adaptive probe station pressure closed-loop control method according to an embodiment of the present invention; Figure 2 The flowchart for establishing the dual-path separation mechanism based on orthogonal component dominant dimension determination in the embodiments of the present invention is shown below. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0022] Figure 1 This is a schematic flowchart of the wafer warpage adaptive probe station pressure closed-loop control method according to an embodiment of the present invention.

[0023] The wafer warpage adaptive probe station pressure closed-loop control method includes: Multidimensional microscopic warping feature data of the wafer on the carrier platform is obtained, and spatiotemporal correlation analysis is performed on the multidimensional microscopic warping feature data to identify feature patterns that characterize the local deformation evolution trend of the wafer and obtain a warping dynamic feature map. Based on the warp dynamic feature map, a pressure matching prediction model is constructed. The deformation sensitivity of different regions on the wafer surface is quantitatively evaluated through the pressure matching prediction model, and a partitioned pressure control strategy adapted to the warp feature mode of each region is generated. Based on the partitioned pressure control strategy, the multi-point pressure execution unit of the drive platform applies differentiated pressure to the wafer and collects the wafer micro-warpage response data after pressure application. Based on the wafer micro-warping response data, a response feature matrix characterizing the actual deformation state is constructed. The response feature matrix and the warping dynamic feature map are subjected to tensor projection operation. Based on the component offset vector in the projection operation result, the regional sensitivity evaluation weight and coupling effect parameters in the pressure matching prediction model are vectorized and reconstructed to realize the continuous evolution of the model.

[0024] In one optional implementation, spatiotemporal correlation analysis is performed on the multidimensional microscopic warping feature data to identify characteristic patterns representing the evolution trend of local deformation in the wafer, resulting in a warping dynamic feature map including: Multidimensional micro-warping feature data are used to construct a multidimensional feature tensor according to the spatial coordinates of the wafer surface and the time series dimension. The multidimensional feature tensor is then analyzed along the spatial dimension to identify the deformation coupling relationship between adjacent regions. The evolution trajectory of the multidimensional feature tensor is tracked along the time dimension to capture the change law of warping features at each spatial location with the process progress, and a temporal evolution feature sequence is obtained. Based on the deformation coupling relationship and the temporal evolution feature sequence, a feature pattern representation system integrating spatial coupling topology and temporal evolution dynamics is constructed. By jointly quantifying the spatial coupling strength and temporal evolution rate, a warping dynamic feature map representing the local deformation evolution trend of the wafer is generated.

[0025] After acquiring multi-dimensional microscopic warpage feature data of the wafer on the carrier platform, in-depth spatiotemporal correlation analysis is required to identify the evolution law of local deformation of the wafer. Multi-dimensional microscopic warpage feature data typically includes information such as height offset values, curvature changes, stress distribution parameters, and temperature field distribution at various measurement points on the wafer surface. These data spatially correspond to different coordinates on the wafer surface, and temporally reflect the dynamic changes in the deformation state from wafer placement to testing.

[0026] To effectively process this multidimensional heterogeneous data, the multidimensional microscopic warping feature data is organized into a structured data representation based on the spatial coordinates of the wafer surface and the time series dimension. Specifically, the wafer surface is divided into several measurement regions, each corresponding to a spatial coordinate. ,in Indicates the first One horizontal coordinate position, Indicates the first Each vertical coordinate position. For each spatial position, at different time points. Multiple physical quantity measurements are collected to form feature vectors. These feature vectors are then organized according to spatial coordinates and time series to construct a multidimensional feature tensor. The dimension of this tensor is ,in and These represent the number of spatial grid divisions in each of the two directions. Indicates the number of time sampling points. This indicates the number of feature dimensions collected at each spatiotemporal location.

[0027] After constructing the multidimensional feature tensor, its neighborhood correlation needs to be analyzed along the spatial dimension. As a continuous physical entity, the deformation states of adjacent regions of a wafer are not independent but exhibit significant mechanical coupling. Warping deformation in one region can affect the deformation state of surrounding regions through stress transmission within the wafer. To identify this spatial coupling, spatial neighborhood analysis is performed on the multidimensional feature tensor at each time slice. This analysis considers spatial location... For a given measurement point, extract the feature values ​​of all measurement points in its surrounding neighborhood. The neighborhood is defined as a radius extending radially from the given node, where the distance does not exceed a certain threshold. The angle difference in the angular direction does not exceed All measurement points. In the neighborhood definition, and These represent the threshold constraints for radial distance and angular difference, respectively. Generally speaking, It should be less than 15-20% of the wafer radius to ensure locality; These angles are typically set between 15° and 30° to capture sufficient angular variation. These parameters need to be adjusted based on the wafer mesh density: a typical 300mm wafer meshed at 5×5 to 9×9 grids... It is advisable to set it to 20-30mm. For denser divisions, the value can be reduced accordingly to ensure a balance between the accuracy of neighborhood analysis and computational efficiency.

[0028] The correlation of eigenvalues ​​between the central measurement point and its neighboring measurement points is calculated. This correlation can be quantified by calculating the cosine similarity, Pearson correlation coefficient, or mutual information between eigenvectors. When the warping eigenvalues ​​of adjacent measurement points exhibit a highly synchronous trend, it indicates a strong coupling relationship between these regions; conversely, if the eigenvalue changes of adjacent measurement points are relatively independent, the coupling strength is weak. By calculating the neighborhood correlation of all measurement points on the wafer surface, the spatial coupling strength matrix is ​​obtained. Elements in the matrix Indicates position With position The deformation coupling strength between them.

[0029] Furthermore, by analyzing the topological structure of spatial coupling relationships, measurement points are treated as nodes, and connecting edges are established between pairs of measurement points with significant coupling relationships, forming a spatial coupling topological network. Within this network, by identifying connected regions with high coupling strength, sub-regions of deformation co-evolution can be delineated. The deformation states of measurement points within these sub-regions are highly correlated, typically corresponding to areas on the wafer with similar material properties and consistent stress states. Through topological network analysis, the boundaries of regions with abnormal coupling strength can also be identified. These boundaries often correspond to locations of stress concentration or abrupt changes in material properties within the wafer, and are key areas with high deformation sensitivity.

[0030] After completing the spatial correlation analysis, the evolution trajectory of the multidimensional feature tensor along the time dimension is traced. The warpage state of the wafer is not static during testing, but continuously evolves with factors such as the applied contact pressure of the test probe, changes in the temperature field, and stress relaxation. By tracing the change trajectory of the warpage features at each spatial location over time, the dynamic evolution law of deformation can be revealed. This is particularly relevant at the spatial center of each pressure control zone. Extract the feature value sequence of this position at all time points to form a time-series feature vector. .

[0031] Temporal pattern mining is performed on temporal feature vectors using a sliding time window method, where a window length is set on the temporal feature vectors. Feature subsequences within adjacent time periods are extracted sequentially. For each subsequence, its trend characteristics are calculated, including the average rate of change, maximum amplitude of change, stability of the direction of change, and periodic oscillation characteristics. The average rate of change reflects the average evolution speed of deformation within that time period and is obtained by calculating the mean of the differences between feature values ​​at adjacent time points in the subsequence. The maximum amplitude of change characterizes the maximum fluctuation of deformation and is obtained by calculating the range or standard deviation of feature values ​​in the subsequence. The stability of the direction of change is assessed by analyzing the consistency of the sign of the difference sequence. If the sign of the difference sequence remains unchanged, it indicates that the deformation exhibits a monotonically increasing or decreasing trend; if the sign changes frequently, it indicates that the deformation state fluctuates repeatedly within that time period.

[0032] For measurement points exhibiting periodic variations, the oscillation period is identified using frequency domain analysis. Fourier transform or wavelet transform is performed on the time-series eigenvectors to convert the time-domain signal to the frequency domain. The main oscillation period is determined by identifying the peak frequency in the spectrum. Periodic warping variations are typically associated with mechanical vibrations of the testing equipment, periodic fluctuations in the temperature field, or periodic release of internal stress within the wafer.

[0033] By tracing the evolution trajectory of the temporal feature vectors of all measurement points on the wafer surface, a set of temporal evolution feature sequences is obtained. This set contains detailed information on the deformation evolution over time at each spatial location, reflecting the dynamic changes in the overall wafer warpage state. Furthermore, cluster analysis is performed on the temporal evolution feature sequences to group measurement points with similar evolution patterns into the same category. Measurement points with the same evolution pattern are usually dominated by the same physical mechanism, and effective control can be achieved by employing similar pressure regulation strategies.

[0034] After obtaining the spatial deformation coupling relationship and the temporal evolution feature sequence, it is necessary to construct a feature pattern representation system that integrates these two aspects of information. The spatial coupling relationship reflects the mutual influence between different regions on the wafer surface, while the temporal evolution feature sequence describes the dynamic changes in the deformation state of each region. By organically combining these two aspects of information, the spatiotemporal evolution characteristics of wafer warpage can be comprehensively characterized.

[0035] Construct a spatiotemporal fusion feature representation model. For each spatial location... It not only records its own temporal evolution characteristics, but also the temporal evolution characteristics of related measurement points in its neighborhood. By weighting and aggregating the evolution characteristics of neighborhood measurement points, the weights are determined by the spatial coupling strength matrix. By determining the corresponding elements, we obtain enhanced temporal features that incorporate the influence of the surrounding area. These enhanced features include both the evolutionary information of the location itself and the influence transmitted from the surrounding area through coupling relationships, enabling us to more accurately predict the future deformation trend of that location.

[0036] Furthermore, analyzing the correlation between spatial coupling strength and temporal evolution rate reveals that regions with high coupling strength often exhibit synchronous deformation evolution rates, meaning that the deformation of adjacent regions increases or decreases at similar rates over time. Conversely, regions with low coupling strength show relatively independent deformation evolution, with significant differences in evolution rates. By calculating the joint distribution characteristics of spatial coupling strength and temporal evolution rate, the co-evolutionary deformation patterns of different regions on the wafer surface can be identified.

[0037] The spatial coupling strength and temporal evolution rate are jointly quantified to define a spatiotemporal evolution synergy index. This indicator takes into account location. The mean spatial coupling strength and temporal evolution rate at a given location were calculated using a weighted combination. High spatiotemporal coordination indicates that the location and its neighborhood exhibit strong spatial and temporal correlation, with deformation evolution significantly influenced by the surrounding environment, necessitating a coordinated control strategy. Low spatiotemporal coordination, on the other hand, indicates that deformation evolution at this location is relatively independent, allowing for localized pressure control.

[0038] Based on the spatiotemporal evolution synergy index, measurement points on the wafer surface are partitioned and clustered. Hierarchical clustering or density clustering algorithms are used to group measurement points with similar spatiotemporal synergy into the same region. Each region corresponds to a spatiotemporal evolution pattern with a specific characteristic. Measurement points within a region are spatially coupled and temporally co-evolve, and can be considered as a whole for pressure regulation. This partitioning method transforms the complex spatiotemporal evolution characteristics of the wafer surface into a finite number of typical characteristic patterns.

[0039] Representative spatiotemporal evolution features are extracted for each partition, including the average spatial coupling strength of measurement points within the region, the statistical characteristics of the temporal evolution rate, the stability of the evolution trend, and the coupling relationship with other regions. These feature parameters collectively constitute the feature pattern label for that region. The feature pattern labels of all partitions are organized with their corresponding spatial location information to generate a warpage dynamic feature map. This map visually presents the warpage evolution characteristics of different regions on the wafer surface, providing structured input data for subsequent pressure matching prediction model construction. The warpage dynamic feature map not only contains static spatial distribution information but also integrates dynamic temporal evolution patterns, comprehensively reflecting the complex spatiotemporal characteristics of wafer warpage and laying the foundation for achieving precise adaptive pressure control.

[0040] In one optional implementation, a multidimensional feature tensor is constructed from the multidimensional microscopic warping feature data according to the spatial coordinates of the wafer surface and the time series dimension. Neighborhood correlation analysis is performed on the multidimensional feature tensor along the spatial dimension to identify the deformation coupling relationship between adjacent regions, including: Multidimensional microscopic warping feature data are spatially gridded according to the radial and angular coordinates of the wafer surface. The warping amplitude and curvature change of the corresponding time series are embedded at each grid node to construct a multidimensional feature tensor that integrates spatial topology and temporal dynamics. A spatial adjacency graph is established for each grid node in the multidimensional feature tensor along the radial and angular directions. The deformation correlation strength between each node and its neighboring nodes is quantified by calculating the warping gradient vector field distribution between adjacent nodes. Based on the deformation correlation strength, a coupled topology network reflecting the mechanical transmission path between neighboring nodes is constructed. Based on the connection weight distribution characteristics and the directionality of the transmission path between nodes in the coupled topology network, the deformation coupling relationship between adjacent regions on the wafer surface is identified.

[0041] The acquired multidimensional microscopic warping feature data includes information on various physical quantities such as height offset, local curvature, strain rate, and temperature distribution at each measurement point on the wafer surface. To construct a data representation structure that reflects both spatial distribution and temporal evolution, the wafer surface is spatially divided using a radial-angular coordinate system. Specifically, with the wafer center as the origin, the surface is divided radially from the center to the edge using equal or logarithmic spacing. A radial hierarchical region is divided along the angular direction at uniform angular intervals. A sector-shaped partition, forming Each spatial grid cell. Each grid node A local measurement area corresponding to the wafer surface, wherein Representing the The radius value of each radial level, Representing the Angles from the center of the sector.

[0042] At each grid node At this location, the warped physical quantity acquired over a continuous time series is embedded. For the time dimension, a fixed sampling period is used. During the test cycle Internal Acquisition Each snapshot records the warp amplitude at that point in time. With curvature change superscript Indicates the first Each time-series sampling point. The warping amplitude reflects the degree of vertical deviation of that location relative to the ideal plane, while the curvature change is obtained by approximating the height data of neighboring nodes using a second-order difference, characterizing the degree of bending of the local deformation. These time-series physical quantities are arranged into a vector in chronological order. and This forms the temporal characteristics at each node. Furthermore, the warp amplitude, curvature change, and other physical characteristics are stacked into a multi-channel feature vector. ,in The number of feature channels covers multi-physics information such as height, curvature, and strain gradient.

[0043] The fourth-order tensor representation is constructed using the above method. This tensor integrates radial, angular, feature channel, and temporal dimensions, comprehensively depicting the spatiotemporal evolution of wafer surface warping. Elements in the tensor... Indicates radial hierarchy Angular sector Feature types At the point of time The physical quantity measurements at the location. This tensor structure not only preserves the spatial topological properties of the wafer's circular geometry, but also captures the continuous change trajectory of the warp parameters of each region over time.

[0044] To analyze the deformation coupling mechanism between adjacent regions, a neighborhood correlation analysis is performed on the multidimensional feature tensor along the spatial dimension. For each grid node... Define its spatial neighborhood set, including radially adjacent nodes and angularly adjacent nodes. Radially adjacent nodes refer to sectors with the same angular orientation. Nodes of the next adjacent radial level and Angular adjacent nodes refer to nodes at the same radial level. Nodes of the next adjacent angle sector and In polar coordinates, due to the periodicity of angular coordinates, angular indices are processed using modulo operations to handle boundary conditions, ensuring... Equivalent to For radial boundary nodes, the innermost node Only has outer radial neighbors, outermost node It has only inner radial neighbors.

[0045] Based on the defined neighborhood structure, construct a spatial adjacency graph. Where the node set V corresponds to all grid nodes, and the edge set This represents the topological connections between adjacent nodes. Each edge in the graph... Connecting nodes Its neighboring nodes The weights of the edges are determined by calculating the warping gradient vector field characteristics between the two nodes. The warping gradient vector is defined radially and angularly: the radial gradient component... Using the central difference approximation ,in Radial grid spacing; angular gradient components Considering the effects of the curvilinear coordinate system, the calculation is as follows: ,in The angular grid spacing is used. This yields the gradient vector at each node. The direction of this vector indicates the direction of the steepest change in local deformation, and the magnitude reflects the severity of the deformation.

[0046] When quantifying the deformation correlation strength between adjacent nodes, not only the difference in gradient vector magnitudes is considered, but also the consistency of vector directions. For nodes... and its neighboring nodes Calculate the cosine similarity between gradient vectors. This similarity measure assesses the degree of coordination between the deformation directions of two nodes. When adjacent regions have consistent gradient directions and similar amplitudes, it indicates that the deformation exhibits continuous spatial transmission characteristics; when the gradient directions are opposite or the amplitudes differ significantly, it suggests that the deformation mechanisms of the two regions are decoupled or that there is a deformation concentration zone. Combining gradient amplitude and direction information, the deformation correlation strength is defined. ,in The attenuation coefficient controls the sensitivity of amplitude differences to the correlation strength. This expression takes a larger value when the gradient amplitudes are close and in the same direction, indicating a strong coupling relationship; conversely, it takes a smaller value, indicating a weak coupling or decoupling state.

[0047] In the time series dimension, the evolution trajectory of deformation correlation strength also contains important information for each time point. Calculate the correlation strength separately Forming a time series By analyzing the trend characteristics of this sequence, the dynamic change pattern of deformation coupling can be identified: a continuous increase in the correlation intensity indicates an increase in the synergistic deformation of adjacent regions, due to the spatial redistribution of stress; fluctuations or decreases in the correlation intensity suggest local deformation concentration or the emergence of new stress concentration areas. A first-order time difference is performed on the correlation intensity sequence to obtain the rate of change index. Positive values ​​indicate enhanced coupling, while negative values ​​indicate weakened coupling.

[0048] Based on the spatial distribution and temporal evolution characteristics of the aforementioned deformation correlation strength, a coupled topological network is constructed. ,in To form a weighted edge set, it is obtained by traversing all adjacent node pairs. If the deformation correlation strength between two nodes Greater than the preset threshold Then in the edge set Establish connection edges The weight value of this edge is set to , This is a weight matrix, with elements... storage nodes With nodes The strength of deformation correlation between nodes. This network not only includes direct adjacency relationships but also identifies indirect coupling effects through multi-hop path analysis. For example, when nodes... With nodes ,node With nodes Both have strong coupling, even and Even if they are not directly adjacent, deformation information can still be obtained through... The deformation is transmitted. The degree centrality and betweenness centrality of nodes in the network reveal the pivotal role of a specific region in the deformation transmission network: highly central nodes connect multiple neighborhoods, and local deformation can affect multiple directions simultaneously; highly betweenness central nodes are located at the intersection of multiple deformation transmission paths and become key nodes for stress redistribution.

[0049] To identify the directional characteristics of deformation coupling relationships, the gradient vector field is decomposed into divergence and curl. Divergence The divergence field reflects the divergence or convergence characteristics of deformation at the node: a positive divergence region indicates that deformation diffuses outward from the point, while a negative divergence region indicates that deformation concentrates towards the point. The curl component reveals the rotational nature of the deformation field, although in two-dimensional plane warping, curl primarily manifests as torsional deformation. The divergence field distribution can be used to delineate deformation source and sink regions on the wafer surface. Source regions typically correspond to stress release areas or initial deformation induction points, while sink regions correspond to stress concentration or deformation accumulation areas. These regions are represented in the coupled topology network as nodes with larger out-degree and larger in-degree, respectively.

[0050] By combining the characteristics of the inter-node connection weight distribution and the directionality analysis of the transmission path, three typical deformation coupling relationships between adjacent regions on the wafer surface were identified: cooperative coupling, characterized by adjacent regions having consistent gradient directions and similar amplitudes, resulting in a smooth spatial transition of deformation; antagonistic coupling, characterized by adjacent regions having opposite gradient directions, with abrupt deformation bands or stress concentration lines; and transmission coupling, characterized by deformation propagating from the source region to the sink region through intermediate regions, forming a chain-like coupling path. The identification of these coupling relationships provides spatially dependent constraints for the formulation of subsequent pressure control strategies: cooperative coupling regions require synchronous adjustment of pressure distribution to maintain deformation continuity; antagonistic coupling regions require differentiated pressure to alleviate stress concentration; and key nodes on the transmission coupling path need to be prioritized for control to cut off or guide the deformation transmission direction.

[0051] In practical implementation, when the wafer radius is 150 mm, the radial direction can be divided into: Layers, each with a radial spacing of approximately 5 millimeters; angularly divided into Each sector corresponds to a 10-degree angle range, forming 1080 spatial grid nodes. The time sampling period is set to 0.1 seconds, and data is acquired within a 10-second test period. A snapshot at time. Number of feature channels. This includes height offset, curvature, radial strain, angular strain, and local temperature. Attenuation coefficient. An empirical value of 0.5 is chosen to ensure that gradient magnitude differences within the range of 0 to 2 standard deviations significantly impact correlation strength. By configuring these parameters, high-resolution spatiotemporal analysis of wafer surface warping can be achieved with reasonable computational resource consumption, laying a data foundation for the subsequent construction of pressure matching prediction models and the implementation of closed-loop control.

[0052] In one optional implementation, a pressure matching prediction model is constructed based on the warp dynamic feature map. This model is used to quantitatively evaluate the deformation sensitivity of different regions on the wafer surface, generating a zoned pressure control strategy adapted to the warp feature patterns of each region. Feature pattern vectors characterizing the local deformation evolution trend of the wafer are extracted from the warp dynamic feature map. The feature pattern vectors are correlated and mapped with the mechanical response mechanism of the wafer material and the coupling effect of the process environment to construct a pressure matching prediction model with the feature pattern vectors as input and the pressure response prediction result as output. Using the pressure matching prediction model, virtual pressure perturbation is applied to the feature mode vector of each region on the wafer surface, and the rate of change of the warping feature response of the region relative to the pressure perturbation is calculated to obtain the sensitivity coefficient characterizing the deformation sensitivity of each region. Based on the spatial distribution differences of the sensitivity coefficients, the wafer surface is divided into multiple pressure control zones with similar deformation sensitivity. For the characteristic mode vectors and sensitivity coefficients of each pressure control zone, the pressure application parameters required to achieve the target warp control state are deduced in reverse through the pressure matching prediction model, generating a zone pressure regulation strategy that includes the pressure amplitude and application sequence of each pressure control zone.

[0053] From the warp dynamic feature map, feature pattern vectors characterizing the local deformation evolution trend of the wafer are extracted. Let be an η-dimensional vector, where the first to the second... The first component represents the warping amplitude principal component coefficient on the time series, and the second component represents the warping amplitude principal component coefficient. To the The first component represents the Fourier coefficient representing the trend of curvature change. The nth component represents the spatial coupling response intensity, requiring normalization and dimensionality reduction mapping of multi-dimensional feature information such as spatiotemporal evolution coordination index, curvature change, and warpage amplitude. For each sampling node on the wafer surface, features such as the warpage amplitude evolution trajectory, curvature change trend, and spatial coupling response intensity in the time series are extracted, and a weighted principal component analysis method is used to project the high-dimensional feature space onto a low-dimensional feature pattern vector representation space. The dimension of the feature pattern vector is set to... This vector, denoted by dimensionality, comprehensively reflects the dynamic laws governing the deformation evolution of the corresponding region. Let the characteristic mode vector of a certain region on the wafer surface be denoted as . It contains Each of the 10 characteristic components represents a different dimension of deformation and evolution characteristics.

[0054] When mapping characteristic pattern vectors to the mechanical response mechanism of wafer materials, a constitutive model reflecting the elastoplastic behavior of the crystalline material needs to be established. The deformation response of wafer materials under external pressure depends not only on the magnitude of the pressure but also on mechanical parameters such as the material's elastic modulus, Poisson's ratio, and yield strength. Therefore, a material mechanical response tensor is introduced. This tensor describes the deformation behavior of the wafer material under different stress states. Simultaneously, it considers the coupling effects of the process environment, including the influence of environmental factors such as temperature field distribution, humidity changes, and air pressure fluctuations on wafer deformation. An environmental coupling effect matrix is ​​then established. This matrix quantifies the coupling strength of various environmental factors on wafer warpage behavior. The feature pattern vector is then processed using tensor multiplication. Material mechanical response tensor Coupling effect matrix with environment Perform multidimensional correlation to obtain the comprehensive response feature vector. This comprehensive response feature vector, used as input to the pressure matching prediction model, can fully reflect the deformation response characteristics of the wafer under specific material properties and process environments.

[0055] The stress matching prediction model employs a deep neural network architecture, which includes an input layer, multiple hidden layers, and an output layer. The input layer receives the comprehensive response feature vector. The hidden layer employs a residual connection structure and an attention mechanism, enabling it to adaptively learn the complex nonlinear mapping relationship between feature patterns and stress response. The output layer generates stress response prediction results, including the predicted change in warpage amplitude. (Unit: micrometers); Curvature evolution trend coefficient (unit: Stress distribution uniformity index (Dimensionless, value range 0-1). The network training process employs a loss function based on physical constraints. This loss function not only includes the deviation term between predicted and measured values ​​but also incorporates physical laws such as the conservation laws of materials mechanics and boundary condition constraints as regularization terms, ensuring that the model's predictions conform to the actual physical processes. The training data comes from a historical test database, which records the correspondence between warpage characteristics and pressure responses under various wafer batches and process conditions.

[0056] Before unified calculation, the response indicators of each dimension are normalized: the change in warpage amplitude is divided by the wafer diameter to obtain the relative warpage rate; the curvature evolution trend coefficient is multiplied by the test cycle duration to obtain the dimensionless curvature change; and the stress distribution uniformity indicator is now dimensionless. The normalized indicators are then uniformly calculated using a weighted summation method, with the weighting coefficients as follows: , , .

[0057] When quantitatively evaluating the deformation sensitivity of different regions on the wafer surface, a virtual pressure perturbation method is used. This method yields a comprehensive response characteristic vector for a specific region. A small perturbation is superimposed on its corresponding pressure application parameter. The disturbance amount is much smaller than the actual applied pressure range, but sufficient to trigger a change in the model's response. The warping characteristic response before and after the disturbance is calculated using a pressure-matched prediction model. The warping characteristic response before the disturbance is denoted as... The warping characteristic response after perturbation is Calculate the rate of change of the warping characteristic response relative to the pressure disturbance, and define the deformation sensitivity coefficient for this region. This is the ratio of the amplitude of the change in response quantity to the amount of disturbance. If the sensitivity coefficient of a certain region is large, it indicates that the deformation in that region is highly sensitive to pressure changes, and fine-tuning is required when actual pressure is applied; if the sensitivity coefficient is small, the deformation in that region is not sensitive to pressure changes, and a more coarse pressure control strategy can be adopted.

[0058] When calculating the sensitivity coefficient, the combined influence of multi-dimensional warp characteristic responses needs to be considered. Multiple response dimensions, such as warp amplitude variation, curvature variation, and stress distribution variation, are weighted and summed to obtain the comprehensive response change. The weights of each response dimension are allocated according to their impact on the wafer probe testing accuracy. For example, curvature variation has a significant impact on probe contact stability and can be assigned a higher weight. By traversing all sampling nodes on the wafer surface and performing virtual pressure perturbation calculations at each node, a global sensitivity coefficient spatial distribution matrix is ​​obtained. The row and column indices of this matrix correspond to the spatial coordinates of the wafer surface, and the matrix element values ​​represent the deformation sensitivity coefficients at the corresponding locations.

[0059] When dividing pressure control zones based on the spatial distribution differences of sensitivity coefficients, a two-stage clustering method is employed. The first stage uses a hierarchical clustering algorithm combined with a silhouette coefficient evaluation criterion to adaptively determine the optimal number of zones. The numerical values ​​in the sensitivity coefficient matrix are used as clustering features, while spatial coordinates are introduced as auxiliary clustering features to ensure spatial continuity of the partitions. By calculating the silhouette coefficient values ​​under different numbers of clusters, the cluster number that maximizes the silhouette coefficient is selected as the optimal number of zones. The second phase is defined. As input for the number of clusters, the fuzzy C-means method is used for fine-grained partitioning. The fuzzy C-means method allows boundary nodes to belong to multiple partitions simultaneously, and a membership function describes the degree to which a node belongs to different partitions. This clustering quantity... Based on factors such as wafer size, number of pressure actuation units, and computational resource constraints, the contour coefficient is automatically determined during the hierarchical clustering stage using an optimization criterion. The clustering results divide the wafer surface into... There are three pressure control partitions. Nodes within each partition have similar deformation sensitivity characteristics, but the sensitivity differences between partitions are significant. Each pressure control partition is assigned a unique identifier, and attribute information such as the set of node coordinates, average sensitivity coefficient, and statistical characteristics of feature pattern vectors within each partition are recorded.

[0060] When generating pressure control strategies for each pressure control zone, it is necessary to inversely deduce the required pressure application parameters using a pressure matching prediction model. The target warpage control state is set as follows: overall wafer surface flatness reaches a preset threshold, local curvature variation is controlled within allowable limits, and stress distribution uniformity meets process requirements. The target warpage control state is represented as a target response feature vector. This vector describes the desired combination of warping feature parameters. For the , Each pressure control zone is analyzed, and its feature pattern vector is extracted. With sensitivity coefficient The following optimization problem is constructed: the objective function is... ,in The pressure matching prediction model is based on the pressure amplitude. The predicted first The response feature vector of each partition, This represents the target response feature vector for this partition. Constraints include: upper and lower limits of pressure amplitude. Smoothness constraint of pressure gradient between adjacent partitions ,in for Adjacent partitions; total energy consumption constraints ,in For the first The area of ​​each partition is calculated. The gradient descent algorithm is used to solve this optimization problem, iteratively updating the pressure application parameters until the objective function converges. The optimized pressure application parameters include the pressure magnitude. This amplitude indicates the effect on the first The static pressure of each partition.

[0061] Considering the temporal effects during pressure application, a dynamic pressure control strategy incorporating the application sequence is generated. The wafer's warp response exhibits time lag and hysteresis, and the pressure application sequence affects the final warp control effect. A pressure application timing optimization model is established, using the pressure application sequence of each partition as the optimization variable, and a genetic algorithm is employed to search for the optimal application sequence. The fitness function comprehensively considers multiple objective optimization indicators such as warp control accuracy, pressure adjustment time, and energy consumption. The optimization results provide the pressure application sequence for each partition, denoted as the application sequence vector. Each element of this vector corresponds to a partition number, and the order of the elements indicates the temporal sequence of pressure application. For partitions requiring dynamic pressure regulation, a pressure-time trajectory function is further designed to describe the change curve of pressure amplitude over time, achieving gradual pressure control to reduce shock response.

[0062] The pressure amplitude parameters and application sequence information of each pressure control zone are integrated to form a complete zoned pressure control strategy. This strategy is stored in the form of a data structure, including zone division information, pressure amplitude parameters of each zone, application sequence vectors, and pressure time trajectory function parameters. The control strategy is transmitted to the pressure execution unit control system of the host platform, driving each execution unit to implement differentiated pressure application according to the strategy instructions. The control system adopts a distributed architecture, with each execution unit equipped with an independent pressure sensor and servo driver, enabling real-time monitoring of the actual applied pressure and closed-loop feedback adjustment. During pressure application, microscopic warpage response data of the wafer surface is continuously collected, providing feedback information for subsequent model updates and strategy optimization.

[0063] The generation process of the partitioned pressure control strategy fully integrates the prior knowledge of the warp dynamic feature map, the intelligent reasoning ability of the pressure matching prediction model, the physical constraints of the material mechanics mechanism, and the global search capability of the multi-objective optimization algorithm. It realizes a closed-loop mapping from feature recognition to pressure control, providing a precise and reliable execution basis for warp adaptive control in wafer probe testing.

[0064] In one optional implementation, according to the partitioned pressure control strategy, the multi-point pressure execution unit of the support platform applies differentiated pressure to the wafer, and collects wafer micro-warpage response data after pressure application, including: The pressure amplitude and application sequence of each pressure control zone in the partitioned pressure control strategy are analyzed. The spatial boundary coordinates of each pressure control zone are matched and located with the physical distribution of multiple pressure execution units on the bearing platform. A spatial mapping relationship between the pressure control zone and the corresponding pressure execution unit group is established, and a partitioned execution instruction set containing the driving amplitude and action timing of each pressure execution unit group is generated. According to the partition execution instruction set, each pressure execution unit group is driven to apply differentiated pressure to the wafer surface according to the pressure amplitude and application sequence of the corresponding pressure control partition, which has spatial differences and temporal coordination. During the application of differentiated pressure, the deformation displacement response and curvature change response of each measurement point on the wafer surface are synchronously collected by a micro-warping sensor array deployed on the support platform. The deformation displacement response and the curvature change response are associated and bound with the driving state and acquisition time of the corresponding pressure execution unit group to generate wafer micro-warping response data containing the execution unit driving state identifier and timing identifier.

[0065] After obtaining the partitioned pressure control strategy, the abstract control instructions in the strategy need to be transformed into specific driving parameters for each pressure execution unit on the platform. First, the partitioned pressure control strategy is structured and parsed to extract the core parameters of each pressure control partition from the strategy data structure. For each pressure control partition... (This index has been defined in the previous steps), parse its corresponding pressure amplitude. and applying sequence These parameters define the pressure intensity and timing pattern to be applied within the partition, respectively.

[0066] The multi-point pressure actuators on the platform are distributed in a grid or ring array, and each pressure actuator has a unique physical coordinate system, denoted as... subscript The sequence number of the execution unit ( For row index, (for column indexes), This indicates the lateral position coordinates (in millimeters) of the execution unit in the Cartesian coordinate system of the platform. Indicates longitudinal position coordinates (unit: millimeters). Pressure control zone. In the wafer coordinate system, there is a well-defined spatial boundary, which is a sequence of vertex coordinates. Description. During matching and positioning, the physical coordinates of each pressure actuator are determined. Whether a location falls within the boundary of a certain pressure control zone is determined using a point-polygon geometric inclusion detection algorithm. This applies to the execution unit location. If it satisfies the partitioning requirement Boundary conditions are then used to establish a mapping relationship. This indicates that the execution unit belongs to the partition. Pressure execution unit group.

[0067] In some implementations, when the execution unit is located When the execution unit falls within the boundary range of multiple partitions, calculate the distance to each candidate partition. Euclidean distance of the centroid The contribution ratio is obtained by normalizing based on the reciprocal of the distance. ,in This is the set of candidate partitions containing this execution unit. The total pressure output of this execution unit is set to... That is, the pressure amplitude of each zone is required to be weighted and summed according to its contribution ratio. The actual drive parameters of the execution unit are: .

[0068] After completing the space mapping, a partition execution instruction set is generated for each partition. The execution unit group extracts the pressure amplitude of the partition. As the target driving force, the applied sequence will be This is converted into timing parameters for the actions of each execution unit. The application sequence is typically represented as a time-indexed sequence. ,in Indicates the first The timestamp of each action node. Total number of action nodes. Partition execution instruction set. It contains the following structured information: Execution unit group identifier Drive amplitude mapping Action timing sequence and synchronous trigger signal identifier The instruction set is transmitted in the form of data packets to the distributed drive controller of the hosting platform.

[0069] When applying differentiated pressure, each pressure execution unit receives the corresponding drive command and then, based on the drive amplitude... Adjust the internal pneumatic or electromagnetic drive mechanism. For pneumatic actuators, control the air chamber pressure by adjusting the proportional valve opening to achieve the target drive strength; for electromagnetic actuators, adjust the drive current of the electromagnetic coil. There is an electromagnetic conversion relationship between this current and the output pressure. The execution of the action timing depends on a global synchronization clock, and each execution unit executes according to the action node timestamp. The drive state is initiated or adjusted at specified times to ensure that the pressure application in different partitions is time-coordinated. During the application process, certain partitions... Some areas require constant pressure, while others need to be dynamically adjusted according to a preset waveform. This combination of spatial variability and temporal synergy enables precise control over the complex warpage of the wafer.

[0070] To monitor the impact of applied pressure on wafer deformation in real time, a micro-warp sensing array is deployed on the support platform. This array comprises multiple displacement sensing units and curvature sensing units, used to measure deformation displacement response and curvature change response, respectively. The displacement sensing units employ laser interferometry or capacitance measurement principles to detect the vertical displacement of the wafer surface relative to a reference plane. ,in This is the spatial index for the sensing unit. The curvature sensing unit calculates the local curvature change by measuring the displacement gradient of multiple adjacent points. .

[0071] The synchronous acquisition mechanism relies on clock synchronization between the sensor data acquisition system and the pressure execution control system. The acquisition system uses a fixed sampling period. Data is read, and the current global clock time is recorded at each sampling. ,in This is the sampling sequence number. At each sampling time, the displacement measurement value of each sensing unit is acquired. and curvature measurement value Simultaneously query the current drive status of each pressure execution unit. The drive status information includes the current drive amplitude, the partition number to which it belongs, and the action stage identifier in the application sequence.

[0072] When performing association binding, for sampling points Based on the spatial location of the response data, determine which pressure execution units influence it. Establish an influence weight matrix between the response data and the execution unit group. Its elements The calculation method is as follows: First, calculate the sensing points. With execution unit Euclidean distance between Then, the weights are calculated based on the Gaussian decay function. ,in The influence range parameter is set to 15% of the wafer diameter. Each row of the weight matrix is ​​normalized to ensure... .

[0073] Action Phase Index This indicates the time node number in the pressure application sequence, and the action types include: Initially at rest. to For the phase of gradually increasing pressure, to During the pressure maintenance phase, to This is the pressure release phase. The time intervals corresponding to each phase are determined by the applied sequence vector. timestamps definition.

[0074] The generated wafer micro-warpage response data structure is in tuple form: ; in This represents the set of drive states of the group of execution units that affect the sensing point.

[0075] This associated data structure allows subsequent analysis to trace the causal relationship between the response at each measurement point and the specific pressure application action. During data storage, the execution unit drive status identifier includes a partition number. Action Phase Index And the driving amplitude value, while the timing identifier records the global clock time. and the relative time with respect to the start of pressure application This dual time stamping mechanism ensures both the temporal consistency of data across partitions and facilitates the analysis of dynamic response processes within a single partition.

[0076] In some application scenarios, the differential pressure application process can last from several seconds to tens of seconds, resulting in a massive amount of sampled data. To improve data processing efficiency, the raw sampled data is preprocessed, including removing sensor noise, identifying outlier data points, and performing spatiotemporal interpolation to fill in missing data. Noise denoising employs a filtering algorithm based on local temporal smoothing, anomaly detection is based on statistical deviation thresholds, and the interpolation method uses tensor completion technology that considers spatial gradient constraints. The preprocessed data retains the physical characteristics of the original data while reducing the computational burden of subsequent model updates.

[0077] In one optional implementation, a response feature matrix characterizing the actual deformation state is constructed based on the wafer micro-warping response data. Tensor projection operations are then performed between the response feature matrix and the warping dynamic feature map. Vectorization reconstruction of the region sensitivity evaluation weights and coupling effect parameters in the pressure matching prediction model is performed based on the component offset vectors in the projection operation result. The deformation displacement response and curvature change response of each measurement point in the wafer micro warping response data under pressure are arranged in a multi-level matrix according to the spatial position of the measurement point and the timing of pressure application, and a response feature matrix characterizing the actual deformation state is constructed. The response feature matrix and the warped dynamic feature map are subjected to tensor projection operation in a unified high-dimensional tensor space. By calculating the projection component of the response feature matrix on the dominant feature basis vector of the warped dynamic feature map, the component offset vector representing the deviation of the actual deformation state from the expected feature pattern is obtained. The component offset vector is orthogonally deconstructed along the spatial direction corresponding to each pressure control zone. Based on the difference in distribution characteristics of the deconstructed orthogonal components in the spatial position dimension and coupling correlation dimension, a dual-path separation mechanism for the sensitivity deviation component and the coupling deviation component is established. The sensitivity deviation component and the coupling deviation component are applied to the regional sensitivity assessment weight and coupling effect parameter respectively through gradient backpropagation calculation, thereby completing the vectorization reconstruction of the pressure matching prediction model.

[0078] The microscopic warpage response data of the wafer after pressure application is acquired. This response data includes the deformation displacement response and curvature change response of multiple measurement points distributed on the wafer surface under pressure. The response data of each measurement point are arranged into a multi-level matrix according to spatial location and pressure application sequence. Specifically, the response data of the first measurement point is... The vertical displacement of each measuring point after pressure is applied is denoted as . The local curvature change at the measurement point is denoted as For the total Each measurement point is used to organize its displacement response into a displacement response vector. Organize the curvature change response of all measurement points into a curvature response vector. .

[0079] Considering the temporal dynamic characteristics of the pressure application process, the pressure application period is divided into... Each of the 10 response sampling times corresponds to a complete set of measurement point response data. At the 10th... At each response sampling time, the displacement response vector of all measurement points is denoted as... Let the curvature response vector be denoted as The response vectors at different sampling times are stacked in chronological order to form a displacement response time series matrix. curvature response time series matrix Furthermore, the displacement response time series matrix and the curvature response time series matrix are concatenated along the feature dimension to construct a comprehensive response feature matrix. The row vectors of this response feature matrix correspond to different response types at different measurement points, and the column vectors correspond to different response sampling times, comprehensively characterizing the actual deformation state of the wafer under pressure.

[0080] The constructed response feature matrix Tensor projection operations are performed on the warped dynamic feature map obtained previously in a unified high-dimensional tensor space. The warped dynamic feature map has already yielded a set of dominant feature basis vectors during feature extraction using tensor decomposition or dimensionality reduction techniques. ,in This represents the number of dominant eigenvalue basis vectors. These eigenvalue basis vectors span a eigenspace in a high-dimensional eigenspace, representing the typical warping modes of the wafer. Each column of the response eigenvalue matrix is ​​projected onto the eigenspace, and the projection components of each response vector onto the dominant eigenvalue basis vectors are calculated. For the ... The response vector at each sampling time point In its first eigenbase vectors The projection coefficient on is .

[0081] Calculate the projection reconstruction vector of the response vector in the feature subspace. The projected reconstruction vector represents the best approximation of the actual response vector in the expected feature pattern subspace. By calculating the difference between the actual response vector and the projected reconstruction vector, we obtain the component offset vector representing the deviation of the actual deformation state from the expected feature pattern. The values ​​of each component of this offset vector reflect the degree and direction of deviation of the actual deformation state from the expected pattern at different spatial locations and in different dimensions of deformation characteristics. By aggregating and statistically analyzing the component offset vectors at all response sampling times, a comprehensive offset vector characterizing the overall deviation is obtained. .

[0082] The resulting composite offset vector Orthogonal basis decomposition is performed along the spatial directions corresponding to each pressure control zone. The pressure matching prediction model has been determined during the construction process. Each pressure control partition corresponds to a specific spatial region on the wafer surface. A spatial orientation basis vector is defined for each pressure control partition. The non-zero elements of this basis vector correspond to the indexes of the measurement points within the coverage area of ​​that partition. For the integrated offset vector... After spatial direction projection decomposition, the first The spatial projection components corresponding to each pressure control zone are denoted as follows: ,all The spatial projection components of each partition constitute the projection component vector. .

[0083] Simultaneously, a set of orthogonal basis vectors for the coupling correlation dimension is defined to characterize the mutual influence relationships between different pressure control zones. For the coupling correlation between zones, coupling direction basis vectors are defined. The construction method is as follows: in partitions With partitions Measurement points near the boundary are assigned non-zero weights, with the weight value inversely proportional to the distance from the measurement point to the boundary between the two partitions. All other positions have a weight of zero. The specific calculation steps are as follows: Identify the partitions. With partitions The common boundary line segment; for each measurement point Calculate the shortest distance from it to the boundary segment. ;like (Boundary influence range threshold, set to 10% of the partition feature size), then the basis vector element corresponding to this measurement point is set to Perform basic vector processing Normalization. Project the synthesized offset vector onto the basis vectors in the coupling direction, and calculate the projection components in the coupling direction. This projection component characterizes the deviation component in the actual deformation deviation caused by the inter-regional coupling effect. The projection components of the coupling directions of all inter-regional pairs constitute the coupling component vector. ,in This represents the total number of adjacent partition pairs.

[0084] Based on the difference in distribution characteristics between the spatial direction projection components and the coupling direction projection components after orthogonal basis deconstruction, a dual-path separation mechanism for the sensitivity deviation component and the coupling deviation component is established. The spatial projection components corresponding to each pressure control zone are denoted as follows: ,all The spatial projection components of each partition constitute the sensitivity deviation component set. . No. The coupling direction projection components between the partition pairs are denoted as follows: ,all The coupling direction projection components of adjacent partition pairs constitute the set of coupling deviation components. .

[0085] Spatial direction projection components Mainly reflects the first Deviation between the deformation response within each pressure control zone and the expected sensitivity assessment; coupling direction projection components Mainly reflects the first The actual effect of the interaction between partition pairs deviates from the predicted coupling effect.

[0086] Define the total loss function This function, used to evaluate the prediction accuracy of the pressure matching prediction model, consists of a prediction error term and a regularization term. ; The prediction error term is: ; For the first The actual response vector at each time step This is the response vector predicted by the model.

[0087] The regularization term is: ; The parameter reconstruction process minimizes the total loss function through gradient descent, specifically the gradient calculation is as follows: Gradient of sensitivity evaluation weights: ; in (Based on linear approximation).

[0088] Gradient of the coupling effect parameter: ; in (Based on linear approximation).

[0089] The convergence criterion for model evolution is: the change in the total loss function over three consecutive iterations is less than a threshold, i.e. ,in Set it to 0.1% of the initial loss value.

[0090] Using a gradient backpropagation mechanism, the sensitivity bias component and coupling bias component are applied to the corresponding parameters in the pressure matching prediction model. The regional sensitivity assessment weights for each pressure control zone in the pressure matching prediction model are denoted as... The interval coupling effect parameter is denoted as The updated gradient for calculating the sensitivity evaluation weights is: ,in Update the learning rate based on sensitivity. Adjust the sensitivity evaluation weights according to the gradient update rule: This update process adjusts the sensitivity assessment weights of each partition in the model in a direction that reduces deviations from actual deformation, thereby improving the accuracy of subsequent pressure control strategies.

[0091] The update gradient for calculating the coupling effect parameters is as follows: ,in Update the learning rate for the coupling parameters. Adjust the coupling effect parameters according to the gradient update rule: This update process adjusts the parameters of the inter-regional coupling effects in the model to more accurately represent the mutual influence between regions, correcting the prediction bias of the coupling effect.

[0092] To enhance the stability and convergence of model reconstruction, a regularization constraint term is introduced. This is added during the sensitivity evaluation weight update process. Norm regularization term ,in This is the sensitivity regularization coefficient. A sparsity regularization term is added during the coupling effect parameter update process. ,in These are the regularization coefficients for the coupling parameters. Regularization constraints prevent overfitting or numerical instability during parameter updates.

[0093] After the vectorized reconstruction of the pressure matching prediction model, the updated region sensitivity evaluation weights and coupling effect parameters can more accurately reflect the deformation response characteristics of the wafer during actual pressure control. The reconstructed model parameters are applied to the next round of pressure control strategy generation, enabling continuous model evolution and gradual improvement in control accuracy. Through multiple iterations of response data acquisition, offset vector calculation, parameter gradient updates, and model reconstruction, the pressure matching prediction model gradually adapts to the actual warpage characteristics and pressure response patterns of the wafer, forming a closed-loop adaptive control mechanism. This effectively improves the probe station pressure control system's adaptability and control accuracy to wafer warpage.

[0094] In one optional implementation, the component offset vector is orthogonally deconstructed along the spatial direction corresponding to each pressure control zone. Based on the difference in distribution characteristics of the deconstructed orthogonal components in the spatial position dimension and coupling correlation dimension, a dual-path separation mechanism for the sensitivity deviation component and the coupling deviation component is established, including: For the component offset vector, a local orthogonal coordinate system is established with the spatial center position of each pressure control zone as the origin. The component offset vector is decomposed and projected in the coordinate axis direction of the local orthogonal coordinate system to obtain the orthogonal component group representing the component offset vector in the corresponding spatial direction of each pressure control zone. For each orthogonal component in the orthogonal component group, calculate the gradient change rate of the orthogonal component in the spatial position dimension of the wafer surface and the transmission strength in the coupling correlation dimension of adjacent pressure control intervals. Based on the numerical difference characteristics of the gradient change rate and the transmission strength, determine the dominant classification type of each orthogonal component. Orthogonal components whose dominant dimension is spatial location are aggregated to form sensitivity deviation components, and orthogonal components whose dominant dimension is coupling correlation are aggregated to form coupling deviation components, thus establishing a dual-path separation mechanism for sensitivity deviation components and coupling deviation components.

[0095] like Figure 2 As shown, the method includes: Obtain the composite offset vector Next, the deformation response deviation contained in this vector needs to be further decomposed into components originating from regional sensitivity estimation errors and components originating from cross-regional pressure coupling effect errors. This separation process is achieved through a locally orthogonal coordinate framework established in each pressure control zone. For the first... For each pressure control zone, first determine the coordinates of its geometric center point. The center point serves as the origin of the local coordinate system. Based on the boundary shape characteristics of the partition, two orthogonal basis vectors aligned with the dominant direction of the partition are constructed. and When the partition is a regular rectangular region, the two basis vectors point to the long and short sides of the rectangle, respectively; when the partition is a sector-shaped region, one basis vector points radially towards the wafer center, and the other basis vector is tangentially perpendicular to the radial direction. (Synthetic offset vector) The former Each element corresponds to the displacement deviation of each measurement point, and then... Each element corresponds to the curvature deviation at each measurement point. For the ... Each pressure control partition is defined, and its extended basis vector is defined. and The non-zero elements of these two basis vectors appear only at the index positions corresponding to the measurement points of that partition, while the zero elements appear at the index positions of measurement points in other partitions. This is achieved by synthesizing the offset vector. Projection operations are performed on these two orthogonal basis vectors to obtain the orthogonal components corresponding to the partition. and The calculation method is as follows as well as Traverse all After dividing the pressure control zones, the data is summarized to form a system containing... orthogonal component group of elements .

[0096] Gradient analysis of the spatial location dimension is performed on each component in the orthogonal component group, specifically for the _th_ component. The first orthogonal component of each partition Along the direction corresponding to this component on the wafer surface Select multiple sampling points, and denote the positions of these sampling points as follows: ,in The displacement distance parameter is defined along the basis vector direction, with values ​​covering a spatial scale from the partition center to the boundary. Response feature matrices are extracted at each sampling point. The corresponding number in The eigenvectors formed by the warp amplitude evolution trajectory, curvature change trend, and spatial coupling response intensity of each pressure control zone over time series are as follows: Calculate these eigenvectors along the direction The numerical trend of gradient change is observed. The spatial gradient rate of change is estimated using the difference method. Specifically, the difference in characteristic values ​​between adjacent sampling points is divided by the spatial distance increment to obtain the change per unit distance. The gradient values ​​of all sampling points are averaged or the maximum value is taken, denoted as... This measure reflects the first The degree of spatial variation of the deformation characteristics of each partition in the first orthogonal direction is calculated similarly. Corresponding spatial gradient rate of change .

[0097] At the coupling and correlation dimension level, the transmission strength of each orthogonal component between adjacent partitions is analyzed. The first orthogonal component of each partition The material continuity of a wafer affects the deformation state of adjacent partitions. Identification and... Let the set of indexes of all adjacent partitions in a given partition space be denoted as . For neighboring partitions Extract the orthogonal components of the partition. and Calculate the original partition components A measure of correlation between components and neighboring partitions. The difference in component values ​​is used as an indicator of transmission strength. ,in Choosing 1 or 2 depends on which neighboring partition component is spatially closer to the original partition component. The first... The first orthogonal component of each partition is summed or its maximum value is taken from the transmission strength of all neighboring partitions to obtain the coupling transmission strength. This index quantifies the ability of this component to diffuse to surrounding areas through cross-regional coupling effects. The second orthogonal component is calculated similarly. Coupling transfer strength .

[0098] Based on a numerical comparison of the spatial gradient change rate and coupling transmission strength, the dominant affiliation type of each orthogonal component is determined. A determination threshold scaling factor is introduced. When a certain orthogonal component satisfies When this condition is met, the dominant dimension of the component is determined to be the spatial location dimension, meaning that the component primarily reflects the bias in deformation sensitivity estimation within a region, rather than the coupling and propagation error between regions. All orthogonal components satisfying this condition are then grouped into the sensitivity bias component set. Conversely, if an orthogonal component satisfies... This indicates that the numerical change of this component mainly stems from the influence transmission between adjacent partitions, and its dominant dimension is the coupling correlation dimension, thus it should be classified into the coupling deviation component set. For cases where the values ​​of the two are close, i.e. ,in To determine the tolerance parameter in a fuzzy manner, weights can be assigned based on the numerical values ​​of the two indicators, and the component can be proportionally included in both the sensitivity deviation and coupling deviation sets. Alternatively, further analysis of the physical contact between the partition and its neighboring partitions, boundary length, and other geometric features can be used to assist in the determination.

[0099] After determining the attribution of all orthogonal components, construct the sensitivity bias component vector. and coupling deviation component vector The sensitivity bias component vector is constructed as follows: traverse all orthogonal components determined to be dominated by the spatial location dimension, and reorganize them into vector form according to the partition index and component number. Assume there are a total of... Each partition If each orthogonal component is classified into the sensitivity bias category, then... The dimension is Each element in the vector corresponds to a specific orthogonal component value. Similarly, the coupling bias component vector... It consists of orthogonal components that are determined to be dominated by the coupling correlation dimension, and its dimension is This separation mechanism enables a dual-path deconstruction of the integrated offset vector: one path focuses on the error sources of the regional sensitivity assessment weights in the pressure matching prediction model, while the other path targets the error sources of the coupling effect parameters in the model, providing a clear direction for subsequent vectorization reconstruction of these two types of parameters.

[0100] In practice, the establishment of the local orthogonal coordinate system needs to be dynamically adjusted according to the wafer geometry and partitioning strategy. For circular wafers, a radial-tangential orthogonal basis derived from polar coordinates is used; for square or rectangular wafers, a transverse-vertical orthogonal basis from Cartesian coordinates is used. The selection of orthogonal basis vectors follows the principle of alignment with partition boundaries, ensuring that the projected orthogonal components reflect the dominant deformation direction within the partition to the greatest extent. The calculation of the spatial gradient rate of change depends on data from multiple spatial locations in the response feature matrix; the number and spacing of sampling points directly affect the accuracy of gradient estimation. Typically, 5 to 10 sampling points are evenly distributed along the orthogonal direction within the partition, with the sampling point spacing set to 10% to 20% of the partition feature size. The calculation of coupling transfer strength needs to consider the contact area and distance factors of the partition boundaries. For adjacent partition pairs with longer boundary contact lengths, the weight of their coupling transfer strength should be increased accordingly, which can be achieved by introducing a boundary length normalization factor. (The text then abruptly shifts to a different topic:) Threshold scaling factor. The typical value range is between 1.5 and 3.0. A smaller threshold assigns more components to the sensitivity deviation category, while a larger threshold increases the proportion of coupling deviation components. In practical applications, the value is adjusted based on the rigidity of the wafer material and the density of the partitioning. Fuzzy decision tolerance parameter It is usually set to 0.2 to 0.3 to handle the assignment of components with ambiguous boundaries.

[0101] The establishment of the dual-path separation mechanism lays the foundation for parameter reconstruction of the pressure matching prediction model, and the sensitivity deviation component vector The elements in the model will be used to correct the deformation sensitivity coefficients of each pressure control zone. By superimposing or proportionally adjusting the values ​​of the deviation components on the original sensitivity coefficient, the sensitivity assessment weights are updated in a vectorized manner. This involves coupling the deviation component vector. This is used to correct the coupling matrix parameters in the model that describe the cross-regional pressure transmission effect. By adjusting the coupling weight coefficients between adjacent regions, the model can more accurately predict the impact of applying pressure to one region on the deformation state of other regions. This physical mechanism-based parameter separation and targeted correction strategy avoids the parameter coupling confusion problem caused by traditional global parameter adjustment methods, and improves the convergence speed of model evolution and the final prediction accuracy.

[0102] A second aspect of the present invention provides a wafer warpage adaptive probe station pressure closed-loop control system, comprising: The warpage analysis unit is used to acquire multi-dimensional micro-warpage feature data of the wafer on the carrier platform, perform spatiotemporal correlation analysis on the multi-dimensional micro-warpage feature data, identify feature patterns that characterize the local deformation evolution trend of the wafer, and obtain a warpage dynamic feature map. The pressure control unit is used to construct a pressure matching prediction model based on the warp dynamic feature map, and to quantitatively evaluate the deformation sensitivity of different regions on the wafer surface through the pressure matching prediction model, and generate a partitioned pressure control strategy that is adapted to the warp feature mode of each region. The pressure execution unit is used to drive the multi-point pressure execution unit of the carrier platform to apply differentiated pressure to the wafer according to the partitioned pressure control strategy, and to collect the wafer micro-warpage response data after the pressure is applied. The model evolution unit is used to construct a response feature matrix representing the actual deformation state based on the wafer micro-warping response data, perform tensor projection operation on the response feature matrix and the warping dynamic feature map, and vectorize and reconstruct the regional sensitivity evaluation weights and coupling effect parameters in the pressure matching prediction model according to the component offset vector in the projection operation result, so as to realize the continuous evolution of the model.

[0103] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0104] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0105] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A probe station pressure closed-loop control method for wafer warpage adaptive control, characterized in that, include: Multidimensional microscopic warping feature data of the wafer on the carrier platform is obtained, and spatiotemporal correlation analysis is performed on the multidimensional microscopic warping feature data to identify feature patterns that characterize the local deformation evolution trend of the wafer and obtain a warping dynamic feature map. Based on the warp dynamic feature map, a pressure matching prediction model is constructed. The deformation sensitivity of different regions on the wafer surface is quantitatively evaluated through the pressure matching prediction model, and a partitioned pressure control strategy adapted to the warp feature mode of each region is generated. Based on the partitioned pressure control strategy, the multi-point pressure execution unit of the drive platform applies differentiated pressure to the wafer and collects the wafer micro-warpage response data after pressure application. Based on the wafer micro-warping response data, a response feature matrix characterizing the actual deformation state is constructed. The response feature matrix and the warping dynamic feature map are subjected to tensor projection operation. Based on the component offset vector in the projection operation result, the regional sensitivity evaluation weight and coupling effect parameters in the pressure matching prediction model are vectorized and reconstructed to realize the continuous evolution of the model.

2. The method according to claim 1, characterized in that, Spatiotemporal correlation analysis was performed on the multidimensional microscopic warping feature data to identify characteristic patterns representing the evolution trend of local deformation in the wafer, resulting in a warping dynamic feature map including: Multidimensional micro-warping feature data are used to construct a multidimensional feature tensor according to the spatial coordinates of the wafer surface and the time series dimension. The multidimensional feature tensor is then analyzed along the spatial dimension to identify the deformation coupling relationship between adjacent regions. The evolution trajectory of the multidimensional feature tensor is tracked along the time dimension to capture the change law of warping features at each spatial location with the process progress, and a temporal evolution feature sequence is obtained. Based on the deformation coupling relationship and the temporal evolution feature sequence, a feature pattern representation system integrating spatial coupling topology and temporal evolution dynamics is constructed. By jointly quantifying the spatial coupling strength and temporal evolution rate, a warping dynamic feature map representing the local deformation evolution trend of the wafer is generated.

3. The method according to claim 2, characterized in that, Multidimensional microscopic warping feature data are used to construct a multidimensional feature tensor based on the spatial coordinates of the wafer surface and the time series dimension. Neighborhood correlation analysis is then performed on this multidimensional feature tensor along the spatial dimension to identify the deformation coupling relationship between adjacent regions, including: Multidimensional microscopic warping feature data are spatially gridded according to the radial and angular coordinates of the wafer surface. The warping amplitude and curvature change of the corresponding time series are embedded at each grid node to construct a multidimensional feature tensor that integrates spatial topology and temporal dynamics. A spatial adjacency graph is established for each grid node in the multidimensional feature tensor along the radial and angular directions. The deformation correlation strength between each node and its neighboring nodes is quantified by calculating the warping gradient vector field distribution between adjacent nodes. Based on the deformation correlation strength, a coupled topology network reflecting the mechanical transmission path between neighboring nodes is constructed. Based on the connection weight distribution characteristics and the directionality of the transmission path between nodes in the coupled topology network, the deformation coupling relationship between adjacent regions on the wafer surface is identified.

4. The method according to claim 1, characterized in that, Based on the aforementioned warpage dynamic feature map, a pressure matching prediction model is constructed. This model is then used to quantitatively evaluate the deformation sensitivity of different regions on the wafer surface, generating a zoned pressure control strategy adapted to the warpage feature patterns of each region. Feature pattern vectors characterizing the local deformation evolution trend of the wafer are extracted from the warp dynamic feature map. The feature pattern vectors are correlated and mapped with the mechanical response mechanism of the wafer material and the coupling effect of the process environment to construct a pressure matching prediction model with the feature pattern vectors as input and the pressure response prediction result as output. Using the pressure matching prediction model, virtual pressure perturbation is applied to the feature mode vector of each region on the wafer surface, and the rate of change of the warping feature response of the region relative to the pressure perturbation is calculated to obtain the sensitivity coefficient characterizing the deformation sensitivity of each region. Based on the spatial distribution differences of the sensitivity coefficients, the wafer surface is divided into multiple pressure control zones with similar deformation sensitivity. For the characteristic mode vectors and sensitivity coefficients of each pressure control zone, the pressure application parameters required to achieve the target warp control state are deduced in reverse through the pressure matching prediction model, generating a zone pressure regulation strategy that includes the pressure amplitude and application sequence of each pressure control zone.

5. The method according to claim 1, characterized in that, Based on the aforementioned partitioned pressure control strategy, the multi-point pressure execution unit of the drive platform applies differentiated pressure to the wafer, and collects wafer micro-warpage response data after pressure application, including: The pressure amplitude and application sequence of each pressure control zone in the partitioned pressure control strategy are analyzed. The spatial boundary coordinates of each pressure control zone are matched and located with the physical distribution of multiple pressure execution units on the bearing platform. A spatial mapping relationship between the pressure control zone and the corresponding pressure execution unit group is established, and a partitioned execution instruction set containing the driving amplitude and action timing of each pressure execution unit group is generated. According to the partition execution instruction set, each pressure execution unit group is driven to apply differentiated pressure to the wafer surface according to the pressure amplitude and application sequence of the corresponding pressure control partition, which has spatial differences and temporal coordination. During the application of differentiated pressure, the deformation displacement response and curvature change response of each measurement point on the wafer surface are synchronously collected by a micro-warping sensor array deployed on the support platform. The deformation displacement response and the curvature change response are associated and bound with the driving state and acquisition time of the corresponding pressure execution unit group to generate wafer micro-warping response data containing the execution unit driving state identifier and timing identifier.

6. The method according to claim 1, characterized in that, Based on the wafer micro-warping response data, a response feature matrix characterizing the actual deformation state is constructed. Tensor projection operations are then performed between the response feature matrix and the warping dynamic feature map. Based on the component offset vectors in the projection operation results, the regional sensitivity evaluation weights and coupling effect parameters in the pressure matching prediction model are vectorized and reconstructed, including: The deformation displacement response and curvature change response of each measurement point in the wafer micro warping response data under pressure are arranged in a multi-level matrix according to the spatial position of the measurement point and the timing of pressure application, and a response feature matrix characterizing the actual deformation state is constructed. The response feature matrix and the warped dynamic feature map are subjected to tensor projection operation in a unified high-dimensional tensor space. By calculating the projection component of the response feature matrix on the dominant feature basis vector of the warped dynamic feature map, the component offset vector representing the deviation of the actual deformation state from the expected feature pattern is obtained. The component offset vector is orthogonally deconstructed along the spatial direction corresponding to each pressure control zone. Based on the difference in distribution characteristics of the deconstructed orthogonal components in the spatial position dimension and coupling correlation dimension, a dual-path separation mechanism for the sensitivity deviation component and the coupling deviation component is established. The sensitivity deviation component and the coupling deviation component are applied to the regional sensitivity assessment weight and coupling effect parameter respectively through gradient backpropagation calculation, thereby completing the vectorization reconstruction of the pressure matching prediction model.

7. The method according to claim 6, characterized in that, The component offset vector is orthogonally deconstructed along the spatial direction corresponding to each pressure control zone. Based on the difference in distribution characteristics of the deconstructed orthogonal components in the spatial position dimension and coupling correlation dimension, a dual-path separation mechanism for the sensitivity deviation component and the coupling deviation component is established, including: For the component offset vector, a local orthogonal coordinate system is established with the spatial center position of each pressure control zone as the origin. The component offset vector is decomposed and projected in the coordinate axis direction of the local orthogonal coordinate system to obtain the orthogonal component group representing the component offset vector in the corresponding spatial direction of each pressure control zone. For each orthogonal component in the orthogonal component group, calculate the gradient change rate of the orthogonal component in the spatial position dimension of the wafer surface and the transmission strength in the coupling correlation dimension of adjacent pressure control intervals. Based on the numerical difference characteristics of the gradient change rate and the transmission strength, determine the dominant classification type of each orthogonal component. Orthogonal components whose dominant dimension is spatial location are aggregated to form sensitivity deviation components, and orthogonal components whose dominant dimension is coupling correlation are aggregated to form coupling deviation components, thus establishing a dual-path separation mechanism for sensitivity deviation components and coupling deviation components.

8. A wafer warpage adaptive probe station pressure closed-loop control system for implementing the method as described in any one of claims 1-7, characterized in that, include: The warpage analysis unit is used to acquire multi-dimensional micro-warpage feature data of the wafer on the carrier platform, perform spatiotemporal correlation analysis on the multi-dimensional micro-warpage feature data, identify feature patterns that characterize the local deformation evolution trend of the wafer, and obtain a warpage dynamic feature map. The pressure control unit is used to construct a pressure matching prediction model based on the warp dynamic feature map, and to quantitatively evaluate the deformation sensitivity of different regions on the wafer surface through the pressure matching prediction model, and generate a partitioned pressure control strategy that is adapted to the warp feature mode of each region. The pressure execution unit is used to drive the multi-point pressure execution unit of the carrier platform to apply differentiated pressure to the wafer according to the partitioned pressure control strategy, and to collect the wafer micro-warpage response data after the pressure is applied. The model evolution unit is used to construct a response feature matrix representing the actual deformation state based on the wafer micro-warping response data, perform tensor projection operation on the response feature matrix and the warping dynamic feature map, and vectorize and reconstruct the regional sensitivity evaluation weights and coupling effect parameters in the pressure matching prediction model according to the component offset vector in the projection operation result, so as to realize the continuous evolution of the model.

9. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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