Intelligent Optimization Methods and Systems for High-Density Interconnect Board Manufacturing

Abstract

This invention relates to the field of high-density interconnect board (HDB) manufacturing technology, and more particularly to an intelligent optimization method and system for HDB manufacturing. The HDB to be manufactured is divided into spatial grid cells. The local energy deposition density distribution and material response gradient field are solved and encoded as process fingerprint vectors to obtain a process fingerprint tensor field. A multi-scale coupled computational framework is established, inputting the process fingerprint tensor field and outputting the board-level warpage deformation field, stress concentration region distribution, and micro-defect initiation probability distribution. Risk spatial grid cells are identified, and the target process fingerprint vector is determined through inverse iterative solving. The manufacturing optimization strategy is then decoded and generated. This invention achieves precise optimization of the HDB manufacturing process, improving product reliability and yield.

Description

Technical Field

[0001] This invention relates to the field of high-density interconnect board manufacturing technology, and in particular to a smart optimization method and system for high-density interconnect board manufacturing. Background Technology

[0002] In the manufacturing of high-density interconnect (HDI) boards, traditional process optimization methods typically rely on trial-and-error or offline simulation. Trial-and-error methods depend on the accumulated experience of operators, adjusting process parameters (such as temperature, pressure, and exposure time) and repeatedly prototyping to achieve product quality requirements. While intuitive, this approach is costly, time-consuming, and struggles to handle the complex thermal coupling effects of high-density wiring. Offline simulation methods, on the other hand, use tools such as finite element analysis or computational fluid dynamics to build physical models of single-layer or multi-layer boards, simulating deformation and stress distribution at specific process stages. These methods can predict macroscopic warpage and stress concentration, but they rely heavily on simplification assumptions, such as neglecting the inhomogeneity of the material's microstructure or dynamic responses during the process, thus limiting prediction accuracy.

[0003] Conventional methods fail to effectively couple multi-scale physical phenomena. HDI board manufacturing involves everything from micrometer-scale copper foil grains and resin molecular chains to millimeter-scale overall board deformation. Energy deposition, material response, and defect evolution at different scales are interconnected. Traditional methods often treat macroscopic or microscopic problems in isolation, such as focusing only on board-level warpage or analyzing stress in a localized area, making it difficult to establish a consistent correlation between local microscopic defects and global deformation. This scale fragmentation leads to inconsistent optimization objectives, where improving one defect may trigger a more serious problem elsewhere.

[0004] Existing technologies lack intelligent adaptive adjustment capabilities. Even if a set of optimal process parameters is obtained through simulation, these parameters are usually statically set for specific batches or product structures and cannot be dynamically adjusted according to real-time conditions during manufacturing. When local non-uniformities occur inside the board (such as abnormal resin flow or copper layer thickness deviation), the preset process parameters often cannot compensate for these variations, leading to an increased probability of defects. Furthermore, traditional optimization processes are mostly forward calculations—predicting outputs given inputs—lacking a mechanism for iteratively finding the optimal process path from the target quality. This makes optimization inefficient and difficult to achieve global optimization within short production cycles. Summary of the Invention

[0005] This invention provides a smart optimization method and system for manufacturing high-density interconnect boards, which can solve the problems in the prior art.

[0006] A first aspect of the present invention provides a smart optimization method for manufacturing high-density interconnect boards, comprising: The high-density interconnect board to be manufactured is divided into multiple spatial grid cells, and the local energy deposition density distribution and material response gradient field of each spatial grid cell are solved under the action of real-time operating status data. The local energy deposition density distribution and the material response gradient field are encoded into the process fingerprint vector of the spatial grid cell to obtain a process fingerprint tensor field covering the entire plate. A multi-scale coupled computational framework including plate-level computational units and unit-level computational units is established. The process fingerprint tensor field is taken as input. The plate-level warping deformation field and stress concentration region distribution are output through the plate-level computational unit. The micro-defect initiation probability distribution in each spatial grid cell is output through the unit-level computational unit. Based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution, a risk space grid cell set requiring process compensation is identified. Based on the risk space grid cell set, the multi-scale coupled computational framework is solved in reverse iteration to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate a manufacturing optimization strategy.

[0007] The high-density interconnect board to be manufactured is divided into multiple spatial grid cells. The local energy deposition density distribution and material response gradient field of each spatial grid cell under the influence of real-time operating data are solved as follows: Obtain the three-dimensional structural design data of the high-density interconnect board to be manufactured. The three-dimensional structural design data includes the spatial coordinate distribution of the micro-hole array, the material type identification and thickness distribution information of the conductive layer and the dielectric layer, and the geometric dimension parameters of the vias. Based on the spatial coordinate distribution of the microvia array and the geometric dimension parameters of the vias, an adaptive mesh generation algorithm is used to spatially discretize the high-density interconnect board to be manufactured, generating spatial mesh cells in the surrounding areas of the microvia array, the vias, the conductive layer, and the dielectric layer. The size distribution of the spatial mesh cells matches the geometric complexity in the three-dimensional structural design data. Acquire real-time operating status data of the manufacturing equipment, including laser energy output power curve, moving speed trajectory of the processing head, and temperature field distribution data within the process chamber; The material type identifier, thickness distribution information, laser energy output power curve, moving speed trajectory of the processing head, and temperature field distribution data at the corresponding positions of the spatial grid cell are coupled in a multi-physics field to perform heat conduction process calculation and stress-strain process calculation, thereby obtaining the local energy deposition density distribution and material response gradient field inside the spatial grid cell.

[0008] Encoding the local energy deposition density distribution and the material response gradient field into process fingerprint vectors of the spatial grid cells yields a process fingerprint tensor field covering the entire plate, including: Spatial sampling is performed on the local energy deposition density distribution. Sampling positions are set along the length, width, and thickness directions of the high-density interconnect board to be manufactured within the spatial grid cell. The energy deposition density values ​​corresponding to the sampling positions are obtained and organized into the energy distribution feature vector of the spatial grid cell. Gradient components are extracted from the material response gradient field to obtain the maximum gradient magnitude and direction angle of the temperature gradient field and the maximum gradient magnitude and direction angle of the stress gradient field within the spatial grid cell, and these are organized into the gradient response feature vector of the spatial grid cell. The geometric features of the spatial grid cell, the energy distribution feature vector, and the gradient response feature vector are concatenated in the order of geometric features first, energy distribution feature vector in the middle, and gradient response feature vector last to generate the process fingerprint vector of the spatial grid cell. The dimension of the process fingerprint vector is equal to the sum of the number of geometric features, the dimension of the energy distribution feature vector, and the dimension of the gradient response feature vector. Based on the spatial position index of the spatial grid cells in the high-density interconnect board to be manufactured, the process fingerprint vectors of all the spatial grid cells are organized into a three-dimensional tensor structure to generate a process fingerprint tensor field covering the entire board.

[0009] Using the process fingerprint tensor field as input, the plate-level warpage deformation field and stress concentration region distribution are output by the plate-level calculation unit, including: Spatial integration is performed on the process fingerprint tensor field along the length and width directions of the high-density interconnect board to be manufactured to extract the cumulative strain distribution at the whole board scale. Based on the strain accumulation distribution and the relationship between the plate deformation and strain accumulation of the high-density interconnect board to be manufactured, fixed constraints are applied to the boundary position of the high-density interconnect board to be manufactured, and the plate-level warping deformation field is calculated in the plate-level calculation unit. The curvature distribution is obtained by performing second derivative calculation on the deformation displacement along the spatial direction from the plate warping deformation field, and the curvature gradient distribution is obtained by performing gradient calculation on the curvature distribution along the spatial direction. The curvature gradient threshold is derived from the material fracture toughness parameter and geometric thickness parameter corresponding to the high-density interconnect board to be manufactured. Based on the curvature gradient distribution, spatial regions whose curvature gradient magnitude exceeds the curvature gradient threshold are identified and marked as stress concentration regions, and the stress concentration region distribution is generated.

[0010] The probability distribution of micro-defect germination within each spatial grid cell is output through the cell-level computing unit, including: The process fingerprint vector is analyzed to obtain the local stress tensor components and local strain tensor components of the spatial grid cell. The strain energy density of the spatial grid cell is calculated based on the local stress tensor components and the local strain tensor components. The ratio of the strain energy density to the critical strain energy density of the material type identifier of the spatial grid cell is calculated to obtain the defect initiation driving force index of the spatial grid cell. The number of temperature peaks and stress cycles of the spatial grid cells in the manufacturing process time series are extracted from the process fingerprint tensor field. The cumulative amount of process cycle damage of the spatial grid cells is calculated. The critical strain energy density of the corresponding material type identifier of the spatial grid cells is corrected according to the cumulative amount of process cycle damage to obtain the corrected critical strain energy density of the spatial grid cells. Substitute the defect initiation driving force index and the modified critical strain energy density into the Weibull distribution function to calculate the initial value of the micro-defect initiation probability of the spatial grid cell. Determine whether the spatial grid cell is located within the stress concentration region from the stress concentration region distribution, apply a stress concentration amplification factor to the initial value of the micro-defect initiation probability of the spatial grid cell located within the stress concentration region to obtain the micro-defect initiation probability of the spatial grid cell, and generate the micro-defect initiation probability distribution.

[0011] Based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution, the set of risky spatial mesh elements requiring process compensation is identified as follows: The warping displacement amplitude of each spatial grid cell is extracted from the plate-level warping deformation field. It is determined whether the warping displacement amplitude exceeds the deformation limit threshold of the material type identifier of the spatial grid cell. The spatial grid cell whose warping displacement amplitude exceeds the deformation limit threshold is marked as a deformation over-limit cell. The spatial grid cells located within the stress concentration region are extracted from the stress concentration region distribution and marked as stress concentration cells. The spatial grid cells whose micro-defect initiation probability exceeds a preset defect initiation probability threshold are extracted from the micro-defect initiation probability distribution and marked as high-risk defect cells. The deformation exceeding limit unit, the stress concentration unit and the defect high risk unit are combined and operated to obtain a preliminary risk spatial grid unit set. For each spatial grid unit in the preliminary risk spatial grid unit set, a comprehensive risk score is calculated by weighted summation based on the extent to which the warping deformation displacement amplitude exceeds the deformation limit threshold, the curvature gradient amplitude and the probability of micro-defect initiation. The spatial grid cells in the preliminary risk spatial grid cell set are sorted in descending order according to the comprehensive risk score, and the spatial grid cells with the comprehensive risk score ranking in the top preset position are selected to form the risk spatial grid cell set that requires process compensation.

[0012] Based on the risk space grid cell set, the multi-scale coupled computational framework is solved by inverse iteration to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is then decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate manufacturing optimization strategies, including: The spatial coordinates of each spatial grid cell in the risk spatial grid cell set are mapped to the plate-level and cell-level computing cells of the multi-scale coupled computing framework, and the plate-level risk region and cell-level risk grid are marked respectively. A bi-objective optimization function is constructed, which includes the weighted sum of the gradient magnitudes of the plate-level warping deformation field in the plate-level risk region and the variance of the micro-defect initiation probability distribution in the unit-level risk grid. A single-objective optimization function is obtained by weighting the gradient magnitudes and the variances by a preset weighting coefficient. The process fingerprint vector in the process fingerprint tensor field is used as the optimization variable to perform inverse iterative solution on the multi-scale coupled calculation framework. In each iteration, the process fingerprint vector is adjusted and the plate-level warping deformation field and the probability distribution of micro-defect initiation are recalculated. The single-objective optimization function value is calculated. When the single-objective optimization function value converges to the preset convergence threshold, the iteration is stopped to obtain the target process fingerprint vector. The temperature, stress, and strain components of the target process fingerprint vector are analyzed. Equipment energy output adjustment commands are generated based on the temperature components, and process chamber physical field control commands are generated based on the stress and strain components. A manufacturing optimization strategy is then generated by combining these components.

[0013] A second aspect of the present invention provides a smart optimization system for manufacturing high-density interconnect boards, comprising: The grid energy unit is used to divide the high-density interconnect board to be manufactured into multiple spatial grid units, and to solve the local energy deposition density distribution and material response gradient field of each spatial grid unit under the action of real-time operating status data. The fingerprint encoding unit is used to encode the local energy deposition density distribution and the material response gradient field into the process fingerprint vector of the spatial grid cell, so as to obtain a process fingerprint tensor field covering the entire plate. The multi-scale unit is used to establish a multi-scale coupled computational framework that includes plate-level computational units and unit-level computational units. The process fingerprint tensor field is taken as input, and the plate-level warping deformation field and stress concentration region distribution are output through the plate-level computational unit. The micro-defect initiation probability distribution in each of the spatial grid units is output through the unit-level computational unit. The optimization strategy unit is used to identify a set of risk space grid cells that require process compensation based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution. Based on the risk space grid cell set, iteratively solves the multi-scale coupled calculation framework to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is then decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate a manufacturing optimization strategy.

[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] The high-density interconnect board is divided into spatial grid cells, and the local energy deposition density distribution and material response gradient field are solved. These are encoded as process fingerprint vectors to form a full-plate process fingerprint tensor field, providing a highly accurate input foundation for subsequent multi-scale coupled analysis. The plate-level and cell-level computational frameworks simultaneously output the plate-level warping deformation field, stress concentration region distribution, and micro-defect initiation probability distribution, achieving full-dimensional quality prediction from macroscopic deformation to microscopic damage, overcoming the limitations of traditional single-scale analysis.

[0017] Based on the predicted risk grid cell set, the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the probability distribution of micro-defect initiation is determined through inverse iterative solution. This vector is then decoded into equipment energy output and chamber physical field control commands, generating a precise optimization strategy. This significantly reduces warpage deformation, effectively alleviates stress concentration, suppresses micro-defect initiation, and significantly improves the dimensional accuracy, structural integrity, and long-term reliability of the product.

[0018] Based on real-time operational data, the system automatically adapts to changes in material properties, process environment, and equipment status drift, dynamically adjusting process parameters to their optimal state. A reverse iteration mechanism ensures a globally optimal solution, avoiding local optima. The entire process requires no manual intervention, reducing trial-and-error costs and downtime, significantly improving manufacturing efficiency and product yield. It is particularly suitable for advanced printed circuit board manufacturing scenarios involving multilayer, high-density, fine-line circuitry. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a smart optimization method for manufacturing high-density interconnect boards; Figure 2 A schematic diagram illustrating the process of solving the local energy deposition density distribution and material response gradient field. 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 flowchart illustrating the intelligent optimization method for manufacturing high-density interconnect boards according to an embodiment of the present invention. Figure 1 As shown, the method includes: The high-density interconnect board to be manufactured is divided into multiple spatial grid cells, and the local energy deposition density distribution and material response gradient field of each spatial grid cell are solved under the action of real-time operating status data. The local energy deposition density distribution and the material response gradient field are encoded into the process fingerprint vector of the spatial grid cell to obtain a process fingerprint tensor field covering the entire plate. A multi-scale coupled computational framework including plate-level computational units and unit-level computational units is established. The process fingerprint tensor field is taken as input. The plate-level warping deformation field and stress concentration region distribution are output through the plate-level computational unit. The micro-defect initiation probability distribution in each spatial grid cell is output through the unit-level computational unit. Based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution, a risk space grid cell set requiring process compensation is identified. Based on the risk space grid cell set, the multi-scale coupled computational framework is solved in reverse iteration to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate a manufacturing optimization strategy.

[0023] In one optional implementation, the high-density interconnect board to be manufactured is divided into multiple spatial grid cells, and the local energy deposition density distribution and material response gradient field of each spatial grid cell under the action of real-time operating status data include: Obtain the three-dimensional structural design data of the high-density interconnect board to be manufactured. The three-dimensional structural design data includes the spatial coordinate distribution of the micro-hole array, the material type identification and thickness distribution information of the conductive layer and the dielectric layer, and the geometric dimension parameters of the vias. Based on the spatial coordinate distribution of the microvia array and the geometric dimension parameters of the vias, an adaptive mesh generation algorithm is used to spatially discretize the high-density interconnect board to be manufactured, generating spatial mesh cells in the surrounding areas of the microvia array, the vias, the conductive layer, and the dielectric layer. The size distribution of the spatial mesh cells matches the geometric complexity in the three-dimensional structural design data. Acquire real-time operating status data of the manufacturing equipment, including laser energy output power curve, moving speed trajectory of the processing head, and temperature field distribution data within the process chamber; The material type identifier, thickness distribution information, laser energy output power curve, moving speed trajectory of the processing head, and temperature field distribution data at the corresponding positions of the spatial grid cell are coupled in a multi-physics field to perform heat conduction process calculation and stress-strain process calculation, thereby obtaining the local energy deposition density distribution and material response gradient field inside the spatial grid cell.

[0024] like Figure 2 As shown, the method includes: Obtain the 3D structural design data of the high-density interconnect board to be manufactured. This 3D structural design data is typically generated by circuit design software and includes the precise spatial coordinate distribution of the microvia array within the board surface. The center coordinates and aperture size of each microvia are recorded in the data file. The design data also includes material type identifiers for each conductive and dielectric layer; for example, copper foil layers are identified as copper, and dielectric layers as epoxy resin-based composite materials. Each material type corresponds to a set of thermophysical and mechanical parameters. Thickness distribution information records the actual thickness values ​​of each layer at different locations. Considering the non-uniformity of the manufacturing process, the thickness of the same layer may vary slightly at different locations. The geometric parameters of vias include aperture, depth, and wall tilt angle; these parameters directly affect the local density requirements of subsequent mesh generation.

[0025] Based on the spatial coordinate distribution of the microvia array and the geometric dimensions of the vias, an adaptive mesh generation algorithm is used to spatially discretize the high-density interconnect board to be manufactured. The core idea of ​​the adaptive mesh generation algorithm is to generate smaller mesh cells in areas with high geometric complexity and larger mesh cells in areas with relatively uniform structures, thereby controlling the total number of mesh cells while ensuring computational accuracy. Specifically, in the region surrounding the microvia array, where the dense hole structure leads to steep local stress gradients, the spatial mesh cell size in this region is set to 1 / 10 to 1 / 5 of the hole diameter. In the region surrounding the vias, where the mismatch in thermal expansion coefficients between the hole walls and the substrate causes significant interfacial stress concentration, the mesh cell size in this region also needs to be refined to less than 1 / 8 of the via diameter. In the region surrounding the conductive and dielectric layers, especially at the interface between different material layers, the mesh cell size is adjusted according to the difference in elastic modulus between the two materials; the greater the difference in elastic modulus, the finer the mesh. In large, uniform areas far from the center of the board, away from the aforementioned characteristic structures, the mesh cell size can be appropriately enlarged to several times the characteristic size to reduce the computational burden. Through this adaptive strategy, the number and distribution of the generated spatial mesh cells are fully matched with the geometric complexity of the 3D structural design data, which ensures the computational resolution of key areas and avoids the waste of computational resources caused by global fine mesh.

[0026] After spatial mesh generation, real-time operational status data of the manufacturing equipment is acquired. This data originates from the sensor network installed on the equipment and the logs of the equipment control system. The laser energy output power curve records the output power value of the laser at various moments during processing, reflecting the dynamic change of energy input over time. The processing head's movement speed trajectory records the spatial coordinates of the processing head within the board surface and its corresponding velocity vector at any given moment. This trajectory allows for the calculation of the duration of laser irradiation and the cumulative energy at each spatial location. Temperature field distribution data within the process chamber is collected in real-time by multiple temperature sensors positioned at different locations within the chamber, recording the temperature values ​​at each location and their evolution over time. This comprehensive real-time operational status data reflects the actual operating status of the manufacturing equipment during the processing of this batch of high-density interconnect boards, providing boundary conditions and load inputs for subsequent physics coupling calculations.

[0027] The material type identification, thickness distribution information, laser energy output power curve, processing head movement velocity trajectory, and temperature field distribution data corresponding to the spatial grid cell are coupled using multiphysics to perform heat conduction and stress-strain calculations. For each spatial grid cell, the laser irradiation time and power level received by the cell during processing are first determined based on its spatial coordinates. Combined with the processing head movement velocity trajectory, the laser energy flux received by the cell per unit time is calculated and converted to the actual energy density deposited inside the material based on the absorptivity coefficient of the cell's material type. In the heat conduction calculation, the deposited energy is used as an internal heat source, and the chamber temperature field distribution is used as an external boundary condition to solve the transient temperature field evolution process inside the spatial grid cell. The calculation process must consider the nonlinear changes in thermophysical parameters such as thermal conductivity, specific heat capacity, and density with temperature to ensure that the temperature field calculation results accurately reflect the material's thermal response behavior at high temperatures. In the stress-strain calculation, the temperature gradient obtained from the temperature field calculation is used as the driving source of thermal strain, and the thermal strain distribution within each spatial grid cell is calculated using the material's thermal expansion coefficient. Simultaneously considering the changes in the elastic modulus and yield strength of the material under temperature, strain is converted into stress according to the material constitutive relation. For high-density interconnected plates with multilayer composite structures, the constraint effect of the interfaces between different layers also needs to be considered. The displacement continuity condition at the interface will cause the elements near the interface to bear additional constraint stress. Through coupled iterative calculations of the heat conduction process and the stress-strain process, the local energy deposition density distribution and material response gradient field inside each spatial grid element are finally obtained. The local energy deposition density distribution describes the spatial distribution of energy inside the element, while the material response gradient field describes the spatial distribution characteristics of the temperature gradient field and the stress gradient field. Together, they constitute a complete process state description of the spatial grid element under the action of real-time operating status data.

[0028] Through the above steps, the high-density interconnect board to be manufactured is decomposed from a macroscopic whole into a set of microscopic local spatial grid cells. Based on real-time manufacturing data and multi-physics field coupling calculations, detailed process status information of each cell is obtained, laying a solid data foundation for subsequent process fingerprint vector encoding and multi-scale coupling analysis.

[0029] In one optional implementation, encoding the local energy deposition density distribution and the material response gradient field into process fingerprint vectors of the spatial grid cells to obtain a process fingerprint tensor field covering the entire plate includes: Spatial sampling is performed on the local energy deposition density distribution. Sampling positions are set along the length, width, and thickness directions of the high-density interconnect board to be manufactured within the spatial grid cell. The energy deposition density values ​​corresponding to the sampling positions are obtained and organized into the energy distribution feature vector of the spatial grid cell. Gradient components are extracted from the material response gradient field to obtain the maximum gradient magnitude and direction angle of the temperature gradient field and the maximum gradient magnitude and direction angle of the stress gradient field within the spatial grid cell, and these are organized into the gradient response feature vector of the spatial grid cell. The geometric features of the spatial grid cell, the energy distribution feature vector, and the gradient response feature vector are concatenated in the order of geometric features first, energy distribution feature vector in the middle, and gradient response feature vector last to generate the process fingerprint vector of the spatial grid cell. The dimension of the process fingerprint vector is equal to the sum of the number of geometric features, the dimension of the energy distribution feature vector, and the dimension of the gradient response feature vector. Based on the spatial position index of the spatial grid cells in the high-density interconnect board to be manufactured, the process fingerprint vectors of all the spatial grid cells are organized into a three-dimensional tensor structure to generate a process fingerprint tensor field covering the entire board.

[0030] After obtaining the local energy deposition density distribution and material response gradient field of each spatial grid cell, these two types of physical field information need to be encoded in a structured manner into process fingerprint vectors that can be directly used by subsequent multi-scale coupled computational frameworks, and finally assembled into a process fingerprint tensor field covering the entire plate. The core of the encoding process is to preserve the spatial distribution characteristics of the physical field while unifying different physical quantities into the same vector space, so that the process states between different spatial grid cells are comparable.

[0031] For spatial sampling of localized energy deposition density distribution, sampling positions are set along the length, width, and thickness directions of the high-density interconnect board to be manufactured within each spatial grid cell. The selection of sampling positions follows the principle of uniform distribution, with sampling points set along the length direction. Each sampling point is set in the width direction. Each sampling point is set in the thickness direction. Each sampling point, formed by three directions, constitutes a total of [number] sampling points. A combination of sampling locations. For each sampling location, the corresponding energy deposition density value is read and denoted as . ,in , , These are the sampling location indices for the length, width, and thickness directions, respectively. The energy deposition density values ​​of all sampling locations are flattened and arranged in the order of length, then width, and finally thickness, forming a sequence with a length of... The energy distribution feature vector. This flattening method preserves the relative positional relationship of energy deposition density in three-dimensional space, ensuring that adjacent elements in the feature vector also have proximity relationships in physical space, which helps the subsequent computational framework capture the spatial continuity characteristics of energy deposition. In actual manufacturing scenarios, the thickness direction of high-density interconnect boards is usually much smaller than that in the length and width directions, therefore The value is usually less than and This is to avoid introducing redundant sampling points in the thickness direction, while ensuring effective characterization of the interlayer energy gradient.

[0032] To extract the gradient components of the material response gradient field, the temperature gradient field and stress gradient field are processed separately. For the temperature gradient field, the magnitude distribution of the temperature gradient vector is calculated within each spatial grid cell, and the maximum value of the temperature gradient magnitude within the cell is taken as the maximum gradient magnitude of the temperature gradient field of that cell, denoted as . Simultaneously determine the gradient direction corresponding to the maximum gradient magnitude, using the azimuth angle. and elevation angle Two angular parameters characterize, where Let be the angle between the projection of the gradient direction onto the length-width plane and the length direction. The angle between the gradient direction and the length-width plane is denoted as . For the stress gradient field, the concept of equivalent stress gradient is adopted, compressing the gradient information of the three-dimensional stress tensor into an equivalent scalar gradient field. The maximum value of the equivalent stress gradient magnitude within each spatial grid cell is taken as the maximum gradient magnitude of that cell, denoted as . The corresponding direction angle is also expressed as azimuth. and elevation angle Characterization. , , , , , Arranged in the order of temperature gradient first, then stress gradient, a gradient response feature vector of length 6 is formed. The maximum gradient magnitude and direction angle are selected as representative features, rather than recording all gradient field values, because in process optimization scenarios, the extreme values ​​and directions of the gradient field are key factors determining the risk of defect initiation. Recording the entire field would result in excessively high feature dimensionality, increasing the computational burden, while extreme value features can sufficiently characterize the degree of non-uniformity and dominant direction of the physical field within the cell.

[0033] After extracting the energy distribution feature vector and gradient response feature vector, it is also necessary to extract the geometric features of each spatial grid cell. Geometric features include the normalized spatial coordinates of the cell within the high-density interconnect board to be manufactured, the cell's length, width, and thickness, and the layer number of the cell (corresponding to the conductor or dielectric layer of the high-density interconnect board). Normalized spatial coordinates are obtained by dividing the actual coordinates of the cell's center point by the total board-level dimensions in the corresponding direction, normalizing the coordinate values ​​to the range of 0 to 1, thus eliminating the dimensional differences between boards of different sizes. The number of geometric features is denoted as... The dimension of the energy distribution feature vector is The gradient response feature vector has a dimension of 6. These three features are concatenated in the following order: geometric features first, energy distribution feature vector in the middle, and gradient response feature vector last, to generate the process fingerprint vector. The total dimension of the process fingerprint vector is... satisfy The design logic behind this splicing order is as follows: geometric features, as a priori description of spatial location, are placed at the forefront, making it easier for the computational framework to establish spatial awareness first; the energy distribution feature vector, as the main process excitation information, is placed in the middle; and the gradient response feature vector, as the material's response to the excitation, is placed at the end, forming a logical chain of "location-excitation-response," which is consistent with physical causal relationships.

[0034] After the process fingerprint vectors of all spatial mesh elements are generated, they are organized into a three-dimensional tensor structure according to the spatial position index of each spatial mesh element in the high-density interconnect board to be manufactured. Let the high-density interconnect board be divided into sections along its length, width, and thickness. , , If there are 1 spatial grid cell, then the shape of the process fingerprint tensor field is: The first three dimensions correspond to the three-dimensional position indices of the spatial grid cells, and the fourth dimension corresponds to the feature components of the process fingerprint vector. In actual organization, the arrangement order of the spatial position indices is consistent with the flattening order of the sampling points within the energy distribution feature vector, both following the rule of length first, then width, and finally thickness, ensuring a clear correspondence between the index semantics of the tensor field in spatial dimensions and the physical spatial coordinate system. This three-dimensional tensor structure naturally endows the process fingerprint tensor field with spatial topological information. Subsequent board-level computational units can directly utilize the spatial adjacency relationships between adjacent cells for local feature aggregation when processing this tensor field, without the need for an additional spatial position encoding mechanism. The process fingerprint tensor field covering the entire board completely preserves all process state information obtained from real-time operating status data through physical field solving and feature extraction, providing a unified and complete data foundation for the input of the multi-scale coupled computational framework.

[0035] In one optional implementation, the process fingerprint tensor field is used as input, and the plate-level warpage deformation field and stress concentration region distribution are output through the plate-level calculation unit, including: Spatial integration is performed on the process fingerprint tensor field along the length and width directions of the high-density interconnect board to be manufactured to extract the cumulative strain distribution at the whole board scale. Based on the strain accumulation distribution and the relationship between the plate deformation and strain accumulation of the high-density interconnect board to be manufactured, fixed constraints are applied to the boundary position of the high-density interconnect board to be manufactured, and the plate-level warping deformation field is calculated in the plate-level calculation unit. The curvature distribution is obtained by performing second derivative calculation on the deformation displacement along the spatial direction from the plate warping deformation field, and the curvature gradient distribution is obtained by performing gradient calculation on the curvature distribution along the spatial direction. The curvature gradient threshold is derived from the material fracture toughness parameter and geometric thickness parameter corresponding to the high-density interconnect board to be manufactured. Based on the curvature gradient distribution, spatial regions whose curvature gradient magnitude exceeds the curvature gradient threshold are identified and marked as stress concentration regions, and the stress concentration region distribution is generated.

[0036] After obtaining the process fingerprint tensor field covering the entire board, the board-level computational units need to extract macroscopic strain information that reflects the deformation trend at the board scale. Each spatial grid cell in the process fingerprint tensor field carries encoded information of the local energy deposition density distribution and the material response gradient field. The cumulative effect of these local information in space determines the macroscopic warping behavior of the entire high-density interconnect board. To this end, spatial integration operations are performed on the process fingerprint tensor field along the length and width directions of the high-density interconnect board to be manufactured, respectively. The local strain contributions of each grid cell are accumulated and superimposed within the board surface to obtain the cumulative strain distribution at the board scale. This integration operation essentially maps the discrete grid cell process fingerprint information into a continuous board surface strain field, eliminating the interference of local high-frequency fluctuations and retaining the low-frequency strain gradient components that play a dominant role in warping deformation. During the integration process, the geometric dimensions of each grid cell need to be weighted to ensure that the contribution of grid cells at different locations to the cumulative strain of the entire board is proportional to the actual spatial volume they occupy, avoiding systematic biases introduced due to uneven grid division.

[0037] A physical relationship between strain accumulation distribution and high-density interconnect (HDI) board deformation is established. During the manufacturing process of HDI boards, internal stresses generated due to factors such as material thermal expansion coefficient mismatch and interlayer curing shrinkage differences are ultimately released in the form of warping deformation. The board deformation and strain accumulation satisfy the compatibility equation in elasticity, i.e., there is a definite mathematical relationship between the spatial second derivative of the deformation displacement field and the strain field. In the board-level computational unit, the strain accumulation distribution is used as the equivalent load input, and fixed constraints are applied to the boundary positions of the HDI board to be manufactured. The application locations of the fixed constraints are usually selected from the clamping points or support points of the board in the actual production tooling. These locations are physically constrained during manufacturing, and their normal displacement and angular degrees of freedom are restricted to zero. The accurate setting of the fixed constraints has a decisive influence on the calculation results of the warping deformation field. If the constraint positions are not selected properly, the calculated warping deformation field will deviate significantly from the actual manufacturing results. After setting the boundary conditions, the plate-level calculation unit solves the governing equations of the plate and shell structure and outputs the plate-level warping deformation field covering the entire high-density interconnect plate. This deformation field uses the normal displacement components at each spatial location as the main characterizing quantity, reflecting the overall bending shape of the plate under the action of the manufacturing process.

[0038] Extracting stress concentration regions from a plate-level warping deformation field requires two differential operations. The deformation displacement field itself describes the absolute displacement at each location and cannot directly reflect the degree of local bending. Performing a second derivative operation on the deformation displacement field along the spatial direction yields the curvature distribution. Curvature is a geometric quantity describing the degree of bending of a surface; a larger amplitude indicates more severe bending at that location, and correspondingly higher bending stress. In plate-level analysis of high-density interconnect boards, the curvature distribution is typically described by curvature components along the length direction, curvature components along the width direction, and torsional curvature components, which together constitute a complete curvature tensor. After obtaining the curvature distribution, a gradient operation is further performed on the curvature distribution along the spatial direction to obtain the curvature gradient distribution. The curvature gradient reflects the rate of change of curvature in space, i.e., the degree of bending change from one location to an adjacent location. Regions with large curvature gradient amplitudes indicate abrupt changes in the bending state at that location, with the local material experiencing a rapid change in bending stress over a short distance—a typical characteristic of stress concentration. Therefore, the curvature gradient distribution is more accurate than the curvature distribution itself in locating the spatial location of stress concentration.

[0039] Determining the curvature gradient threshold requires deriving it from the fracture toughness parameters and geometric thickness parameters of the material corresponding to the high-density interconnect board to be manufactured. The fracture toughness parameter characterizes the material's ability to resist crack propagation, and is typically expressed as the critical stress intensity factor. To quantify, the unit is Geometric thickness parameters This describes the dimensions of the high-density interconnect board in the thickness direction. For multilayer boards, Take the equivalent thickness value corresponding to the equivalent bending stiffness. According to plate and shell theory, the maximum bending stress of a plate under bending load is... With curvature The relationship between them is satisfied ,in This represents the material's equivalent elastic modulus. When the additional stress caused by the local curvature gradient reaches the critical stress level corresponding to the material's fracture toughness, there is a potential risk of cracking at that location. Combining this with crack tip stress field analysis in fracture mechanics, the curvature gradient threshold can be derived. Its physical meaning is: when the magnitude of the curvature gradient at a certain location exceeds... At this time, the probability of microcrack initiation or interface delamination at this location increases significantly under manufacturing process loads, and it needs to be marked as a stress concentration area. The specific values ​​vary depending on the material system of the board. For multilayer interconnect boards with epoxy resin as the matrix, the typical range of values ​​is constrained by the thickness of the copper foil layer, the thickness of the dielectric layer, and the ratio of the elastic modulus of each layer.

[0040] The curvature gradient distribution is scanned point-by-point. For each spatial location within the plate surface, the scalar magnitude of the curvature gradient amplitude at that location is calculated by taking the square root of the sum of the squares of the curvature gradient components in the length direction, width direction, and torsional curvature direction. This yields the comprehensive curvature gradient amplitude. The comprehensive curvature gradient amplitude is then compared with the curvature gradient threshold. For comparison, any composite curvature gradient magnitude exceeding All spatial locations are marked as stress concentration regions. Spatial connectivity analysis is performed on the set of all marked locations, merging adjacent marked locations into connected stress concentration region patches, ultimately generating a stress concentration region distribution map. This distribution map is expressed as a binary spatial mask, where locations marked "1" indicate stress concentration risk, and locations marked "0" indicate within a safe range. The stress concentration region distribution, together with the plate-level warpage deformation field, constitutes the output of the plate-level computational unit, providing a quantitative basis for subsequent identification of risk spatial mesh unit sets and inverse iterative optimization of process fingerprint vectors. Through this complete computational process, the plate-level computational unit can transform the local process information contained in the process fingerprint tensor field into a macroscopic mechanical risk distribution that can directly guide process compensation decisions, achieving a positive mapping from the process parameter space to the structural response space.

[0041] In one optional implementation, outputting the probability distribution of micro-defect germination within each spatial grid cell via a cell-level computing unit includes: The process fingerprint vector is analyzed to obtain the local stress tensor components and local strain tensor components of the spatial grid cell. The strain energy density of the spatial grid cell is calculated based on the local stress tensor components and the local strain tensor components. The ratio of the strain energy density to the critical strain energy density of the material type identifier of the spatial grid cell is calculated to obtain the defect initiation driving force index of the spatial grid cell. The number of temperature peaks and stress cycles of the spatial grid cells in the manufacturing process time series are extracted from the process fingerprint tensor field. The cumulative amount of process cycle damage of the spatial grid cells is calculated. The critical strain energy density of the corresponding material type identifier of the spatial grid cells is corrected according to the cumulative amount of process cycle damage to obtain the corrected critical strain energy density of the spatial grid cells. Substitute the defect initiation driving force index and the modified critical strain energy density into the Weibull distribution function to calculate the initial value of the micro-defect initiation probability of the spatial grid cell. Determine whether the spatial grid cell is located within the stress concentration region from the stress concentration region distribution, apply a stress concentration amplification factor to the initial value of the micro-defect initiation probability of the spatial grid cell located within the stress concentration region to obtain the micro-defect initiation probability of the spatial grid cell, and generate the micro-defect initiation probability distribution.

[0042] Local stress and local strain tensor components are extracted from the data. During the manufacturing process of high-density interconnect boards, the thermo-mechanical coupling effects experienced by each spatial grid cell are encoded and recorded in the process fingerprint vector as tensor components. For any spatial grid cell, its local stress tensor contains six independent components, corresponding to normal stress and shear stress, respectively; the local strain tensor also contains six independent components, corresponding to normal strain and shear strain. Based on linear elastic or elastoplastic constitutive relations, these tensor components are decoupled from the energy deposition density distribution and material response gradient field information carried by the process fingerprint vector, providing basic data for subsequent strain energy density calculations.

[0043] After obtaining the local stress tensor components and local strain tensor components, the strain energy density of the spatial mesh element is calculated. (Strain energy density) Defined as the elastic strain energy stored in a material per unit volume, it is obtained by the double dot product of the stress tensor and the strain tensor. ,in These are the stress tensor components. For the corresponding strain tensor components, the subscripts are... , These are the row and column indices of the tensor components, respectively, and the summation is performed over all independent components. Strain energy density comprehensively reflects the degree of local energy accumulation in spatial grid cells under the combined action of thermal and mechanical loads, and is a core physical quantity for evaluating the driving force of material damage.

[0044] The calculated strain energy density Critical strain energy density corresponding to the material type identifier of this spatial grid cell By performing ratio calculations, the defect initiation driving force index is obtained. ,Right now Critical strain energy density This is the minimum energy density threshold required for the initiation of micro-defects in a material under monotonic loading conditions, retrieved from a material property database based on the material type of the spatial grid cell (e.g., copper foil, dielectric layer, solder alloy, etc.). When the value approaches 1, it indicates that the local energy accumulation of the spatial grid cell is close to the material's tolerance limit, and the risk of defect initiation increases significantly; when When the value is much less than 1, the unit is in a relatively safe state.

[0045] The frequency of temperature peaks and the number of stress cycles for a given spatial grid cell in the manufacturing process time series are extracted from the process fingerprint tensor field to calculate the cumulative amount of process cycle damage. (Number of temperature peaks) This reflects the frequency of thermal shocks the material experiences during manufacturing; for example, multiple reflow soldering or hot pressing processes can cause multiple temperature peaks in a short period of time; stress cycle count. This reflects the cumulative number of alternating stresses experienced by the material during the process. Based on Miner's linear damage superposition criterion, the cumulative damage from process cycles is... according to Calculation, where and The first The number of temperature peaks and the number of stress cycles under similar process steps. and These are the thermal fatigue life and mechanical fatigue life of the material corresponding to this process, respectively, both provided by the material fatigue database.

[0046] Based on the cumulative damage of process cycles The critical strain energy density is corrected to obtain the corrected critical strain energy density. The relationship is corrected to... ,in The damage degradation coefficient characterizes the rate of decay of the critical strain energy density of a material under cyclic loading. Its value is obtained from a material degradation database based on the material type and manufacturing process, and is typically in the range of 0.1 to 0.6. With... The increase, A gradual decrease means that material regions that have undergone multiple process cycles are more prone to developing microdefects at lower energy accumulation levels. The introduction of the modified critical strain energy density allows the assessment of the probability of microdefect initiation to reflect the cumulative impact of manufacturing history on material properties, rather than relying solely on the current instantaneous state.

[0047] Defect priming driving force indicators With the corrected critical strain energy density Substitute the Weibull distribution function to calculate the initial value of the micro-defect initiation probability for this spatial grid cell. The expression for the Weibull distribution function is: ,in The strain energy density of the current spatial grid cell. The Weibull scale parameter characterizes the statistically significant characteristic strain energy density of the material. is the Weibull shape parameter (also known as the Weibull modulus), which reflects the dispersion of defect initiation behavior in materials. When season This indicates that the current energy accumulation level has not yet reached the minimum driving force required for defect initiation. and All data were retrieved from a material statistics database based on material type identifiers. Significant differences exist in the Weibull parameters for different materials (such as copper foil and epoxy resin-based dielectric layers), requiring separate processing. The introduction of the Weibull distribution function makes the output of the micro-defect initiation probability statistically significant, enabling a quantitative description of the material's reliability level under manufacturing process loads.

[0048] From the stress concentration region distribution output by the plate-level computational unit, determine whether the current spatial mesh element is located within a stress concentration region. Stress concentration regions typically correspond to locations where the curvature gradient magnitude exceeds a threshold, as well as areas near geometric singularities such as hole edges and densely connected transition zones. For spatial mesh elements determined to be within stress concentration regions, initialize their micro-defect initiation probability. Apply stress concentration amplification factor on the basis Make corrections. The correction method is to... The strain energy density driving term in the middle is multiplied by This is equivalent to amplifying the local stress amplitude. After doubling the value, we resubstitute it into the Weibull function to obtain the corrected probability of microscopic defect initiation. . The value is determined based on the geometric characteristics and material properties of the stress concentration region. For a typical through-hole edge region, Typically within the range of 1.5 to 3.5; for the abrupt transition region of line width, Typically in the range of 1.2 to 2.0. For spatial mesh elements not located within stress concentration regions, directly set... No magnification correction is performed.

[0049] After traversing all spatial mesh elements across the entire plate and completing the complete process of calculating the driving force of defect initiation, correcting cyclic damage, evaluating Weibull probability, and amplifying stress concentration, the micro-defect initiation probability of each spatial mesh element is calculated. The results are summarized to generate a probability distribution of micro-defect initiation covering the entire board. This probability distribution is stored in the form of a three-dimensional tensor, corresponding one-to-one with the spatial grid index of the process fingerprint tensor field. This provides a quantitative probabilistic basis for subsequent identification of risk spatial grid cell sets and inverse iterative solution of the target process fingerprint vector. The spatial clustering characteristics of high-probability regions in the probability distribution can effectively reveal potential reliability weaknesses caused by improper manufacturing process parameter settings, thereby guiding the generation of manufacturing optimization strategies.

[0050] In one optional implementation, based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution, the set of risky spatial grid cells requiring process compensation is identified, including: The warping displacement amplitude of each spatial grid cell is extracted from the plate-level warping deformation field. It is determined whether the warping displacement amplitude exceeds the deformation limit threshold of the material type identifier of the spatial grid cell. The spatial grid cell whose warping displacement amplitude exceeds the deformation limit threshold is marked as a deformation over-limit cell. The spatial grid cells located within the stress concentration region are extracted from the stress concentration region distribution and marked as stress concentration cells. The spatial grid cells whose micro-defect initiation probability exceeds a preset defect initiation probability threshold are extracted from the micro-defect initiation probability distribution and marked as high-risk defect cells. The deformation exceeding limit unit, the stress concentration unit and the defect high risk unit are combined and operated to obtain a preliminary risk spatial grid unit set. For each spatial grid unit in the preliminary risk spatial grid unit set, a comprehensive risk score is calculated by weighted summation based on the extent to which the warping deformation displacement amplitude exceeds the deformation limit threshold, the curvature gradient amplitude and the probability of micro-defect initiation. The spatial grid cells in the preliminary risk spatial grid cell set are sorted in descending order according to the comprehensive risk score, and the spatial grid cells with the comprehensive risk score ranking in the top preset position are selected to form the risk spatial grid cell set that requires process compensation.

[0051] After calculating the plate-level warping deformation field, stress concentration region distribution, and micro-defect initiation probability distribution, risk information needs to be systematically extracted from these three types of fields to identify the set of spatial mesh elements requiring process compensation. This identification process is divided into multiple levels: first, abnormal elements are extracted independently from each type of field; then, the final screening is completed through set operations and quantitative scoring.

[0052] Starting from the plate-level warping deformation field, the warping deformation displacement amplitude is extracted for each spatial grid cell. This amplitude characterizes the normal offset of the element relative to its ideal planar position under current process conditions, comprehensively reflecting the degree of bending deformation at that location. Each spatial mesh element is assigned a material type identifier during the modeling phase; different material types correspond to different deformation thresholds. For example, the deformation threshold of a rigid medium-filled region is usually much lower than that of a flexible substrate region. This is because rigid media are more sensitive to local curvature, and even small deformations can cause interlayer cracking or solder joint failure. The judgment criterion is: if If so, the spatial mesh element is marked as a deformable over-limit element and included in subsequent set operations. Deformable over-limit threshold. The value is determined based on the process specifications of the corresponding material type in the material database. In the high-density interconnect board manufacturing scenario, this threshold is usually in the range of micrometers to sub-millimeters and needs to be given comprehensively based on the board thickness, stack-up structure and interconnect density.

[0053] The curvature gradient magnitude output by the multi-scale coupled computation framework exceeds the curvature gradient threshold. The area is designated as the spatial extent of the stress concentration region. Any spatial grid cell falling within this region is marked as a stress concentration cell. Stress concentration regions often appear at the edges and corners of plates, around through-holes, in areas with densely packed solder pads, and at interfaces between different materials. These locations experience localized high stress during the manufacturing process and are high-risk areas for crack initiation and delamination failure. These cells are recorded separately for later aggregation and merging with other risk cell categories.

[0054] The corrected micro-defect initiation probability of each spatial grid cell Compared with the preset defect occurrence probability threshold Compare them. It is the upper limit of probability calculated based on product reliability targets, when a certain unit's This means that, under the manufacturing conditions described by the current process fingerprint vector, the risk of micro-defects arising within the unit has exceeded the acceptable range, and it is marked as a high-risk defect unit. The setting needs to be combined with the failure rate index and reliability confidence level of the final product, and in actual engineering, it is usually taken as a value of... to The specific values ​​are determined by the quality engineer based on the product grade.

[0055] After completing the independent labeling of the three types of elements, the set of deformation-exceeding elements was... Stress concentration element set With high-risk defect unit set Perform a set union operation to obtain a preliminary risk space grid cell set. The reason for using union instead of intersection is that the three types of risk sources are physically independent of each other, and exceeding the limit of any one type of risk can lead to the failure of the final product. Therefore, units that meet any risk condition should be included in the scope of investigation to avoid omitting potential failure locations.

[0056] Preliminary risk spatial grid cell set Each spatial grid cell in the calculation of the comprehensive risk score . The magnitude of the warping deformation displacement exceeding the deformation limit threshold is obtained by weighted summation of the three risk dimensions. Characterizes the severity of deformation risk; curvature gradient magnitude The local intensity characterizing the risk of stress concentration; the corrected probability of microdefect initiation. This represents the level of risk of defect initiation. The three dimensions differ in size and magnitude, requiring normalization of each dimension before being assigned weights. , , The linear weighting is calculated using the following formula: ; in , , These represent the maximum values ​​of the corresponding indicators for all units within the initial risk set, used to normalize each dimension to... Interval. Weighting coefficients , , satisfy Its value reflects the relative importance of different failure modes to the overall reliability of the product. In high-density interconnect board manufacturing scenarios, if the product is most sensitive to warpage (such as the reliability of BGA package solder joint connections), then... Take the larger value; if the product is more sensitive to the initiation of micro-defects (such as the sensitivity of high-frequency signal integrity to microcracks), then Take the larger value. The weighting coefficient can be pre-configured by process engineers according to product type, or it can be automatically calibrated through statistical analysis of historical failure data.

[0057] Preliminary risk spatial grid cell set All units in Sort the data in descending order to form an ordered sequence, with the highest-risk units at the beginning and the lowest-risk units at the end. Select the units with the highest overall risk scores from this ordered sequence. The spatial grid cells of each position constitute the final set of risk spatial grid cells that require process compensation. . The preset bit length parameter determines the computational scale of subsequent reverse iterative optimization. Too small a value will cause some real risk units to be missed. If the value is too large, it will introduce a large number of low-risk units, increasing the redundancy burden of subsequent optimization calculations. In practical applications, The threshold can be set based on a combination of computational resource constraints and risk coverage targets, or a dynamic threshold strategy can be adopted, i.e., selecting... All units exceeding a certain absolute threshold, rather than a fixed number.

[0058] Through the above multi-level screening process, the final set of risk space grid cells is obtained. It takes into account three types of risk sources: deformation, stress, and defects, and achieves an orderly arrangement of risk priorities through quantitative scoring. This provides accurate spatial positioning information and priority basis for subsequent inverse iterative solution of multi-scale coupled calculation framework based on this set and determination of target process fingerprint vector.

[0059] In one optional implementation, the multi-scale coupled computational framework is solved iteratively based on the risk space grid cell set to determine a target process fingerprint vector that minimizes the gradient of the plate-level warping deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is then decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate a manufacturing optimization strategy, including: The spatial coordinates of each spatial grid cell in the risk spatial grid cell set are mapped to the plate-level and cell-level computing cells of the multi-scale coupled computing framework, and the plate-level risk region and cell-level risk grid are marked respectively. A bi-objective optimization function is constructed, which includes the weighted sum of the gradient magnitudes of the plate-level warping deformation field in the plate-level risk region and the variance of the micro-defect initiation probability distribution in the unit-level risk grid. A single-objective optimization function is obtained by weighting the gradient magnitudes and the variances by a preset weighting coefficient. The process fingerprint vector in the process fingerprint tensor field is used as the optimization variable to perform inverse iterative solution on the multi-scale coupled calculation framework. In each iteration, the process fingerprint vector is adjusted and the plate-level warping deformation field and the probability distribution of micro-defect initiation are recalculated. The single-objective optimization function value is calculated. When the single-objective optimization function value converges to the preset convergence threshold, the iteration is stopped to obtain the target process fingerprint vector. The temperature, stress, and strain components of the target process fingerprint vector are analyzed. Equipment energy output adjustment commands are generated based on the temperature components, and process chamber physical field control commands are generated based on the stress and strain components. A manufacturing optimization strategy is then generated by combining these components.

[0060] In obtaining the risk space grid cell set that ultimately requires process compensation. Subsequently, the 3D spatial coordinates of each spatial grid cell in the set are mapped to two computational levels of the multi-scale coupled computational framework. At the plate-level computational cell level, the planar coordinates of the risk cell are projected onto the plate-level grid, marking the corresponding plate-level risk region. At the element-level computational cell level, the complete 3D coordinates of the risk cell are directly mapped to the element-level grid nodes, marking the element-level risk grid. This two-layer mapping ensures that the subsequent optimization process can simultaneously perceive the risk distribution at two scales, avoiding the omission of risk regions due to scale transformation. The plate-level risk region is used to constrain the gradient calculation range of the warping deformation field, and the element-level risk grid is used to constrain the statistical range of the probability distribution of micro-defect initiation. Together, they constitute the spatial support domain for subsequent bi-objective optimization.

[0061] Mathematical expressions are provided for two types of optimization objectives: plate-level and element-level. The plate-level objective function is the weighted sum of the curvature gradient magnitudes of the plate-level warping deformation field at all nodes within the plate-level risk region. The weight of each node is determined by the comprehensive risk score of the spatial grid element to which that node belongs. After normalization, nodes with higher risk scores have a larger weight in the gradient weighted sum, thus driving the optimization process to prioritize eliminating warped gradient anomalies in high-risk regions. The unit-level objective function takes the variance of the micro-defect initiation probability distribution within the unit-level risk grid. A larger variance means a higher degree of dispersion in the defect initiation probability among risk units. Minimizing this variance can make the defect initiation probability of each risk unit tend to be uniform and decrease overall. To transform the bi-objective problem into a single-objective problem that is easier to solve iteratively, a preset weight coefficient is introduced. and By performing a linear weighted sum of the gradient magnitude and variance values ​​respectively, the single-objective optimization function is obtained. , expressed as: ; in This is a weighted sum of the curvature gradient magnitudes of the warping deformation field within the plate-level risk region. This represents the variance of the probability distribution of micro-defect initiation within a single-cell-level risk grid. and Preset weighting coefficients and satisfying The weighting coefficients are configured based on the relative importance of warpage control and defect suppression in the actual manufacturing scenario. When board-level warpage has a more significant impact on product functionality, the weighting coefficients can be appropriately increased. When the impact of microscopic defects on reliability becomes more prominent, the value can be appropriately increased. .

[0062] Using the process fingerprint vector corresponding to the risk space grid cell in the process fingerprint tensor field as the optimization variable, a reverse iterative solution is performed on the multi-scale coupled computational framework. Each iteration starts with the current process fingerprint vector as the initial point, and a single-objective optimization function is calculated using gradient estimation. The partial derivatives of each process fingerprint vector component are used to determine the adjustment direction and magnitude of the process fingerprint vector. The adjusted process fingerprint vector is then re-input into the multi-scale coupled computational framework. The plate-level computational units recalculate the plate-level warping deformation field and stress concentration region distribution, while the element-level computational units recalculate the micro-defect initiation probability distribution within each risk mesh element, thereby updating the process fingerprint vector. and The value, and recalculate. The iterative process continues until the interval between two adjacent iterations. The change was less than the preset convergence threshold. At this point, the iteration stops, and the current process fingerprint vector is determined as the target process fingerprint vector. During the iteration process, physical constraints are imposed on the adjustment range of the process fingerprint vector to ensure that the adjusted energy deposition density distribution and material response gradient field parameters are within the range achievable by the actual process equipment, thus avoiding the optimization results from exceeding the equipment capability boundary and causing the instructions to fail to execute.

[0063] Obtain the target process fingerprint vector Subsequently, its components are analyzed. The temperature component in the target process fingerprint vector includes the target energy deposition density value of each risk space grid cell and the target maximum gradient magnitude and orientation angle parameters of the temperature gradient field. Based on the difference between these temperature components and the current actual energy deposition state, the required energy compensation for each risk area is calculated, thereby generating equipment energy output adjustment commands. The equipment energy output adjustment commands specifically include the power adjustment values ​​of each heating area or laser scanning area, the time offset of the heating sequence, and the correction parameters of the energy distribution profile. The command format matches the control interface of the actual manufacturing equipment and can be directly sent to the equipment controller for execution.

[0064] The stress and strain components in the target process fingerprint vector include the maximum gradient magnitude and orientation angle parameters of the target stress gradient field for each risk space grid cell, as well as the target state of material deformation response reflected by the strain components. Based on the deviation between the target values ​​and the current state of the stress and strain components, the physical field parameters that need to be adjusted within the process chamber are calculated, including the chamber's air pressure distribution, cooling airflow velocity and direction, the magnitude and distribution of the prestress applied by the clamping mechanism, and chamber temperature uniformity adjustment parameters. These parameters together constitute the physical field control commands for the process chamber, used to change the thermo-mechanical coupling boundary conditions within the chamber, thereby causing the stress and strain states in each risk cell during the actual manufacturing process to converge to the state described by the target process fingerprint vector.

[0065] The energy output adjustment commands and process chamber physical field control commands are combined and arranged according to the temporal relationship of the manufacturing process to form a complete manufacturing optimization strategy. This strategy includes the execution time node, execution order, command parameter values, and corresponding spatial grid cell identifiers for each command, ensuring that energy output adjustment and chamber physical field control are synchronously applied to the corresponding spatial locations according to the correct timing during actual manufacturing. The strategy also includes expected evaluation data of the optimization effect, namely, the expected improvement amount of the weighted sum of the gradient amplitude of the board-level warpage deformation field predicted by the multi-scale coupled calculation framework under the target process fingerprint vector, and the variance of the probability distribution of micro-defect initiation. This data is provided for manufacturing engineers to verify the rationality of the strategy before execution. Through this complete reverse iterative optimization and command generation process, end-to-end intelligent optimization from risk identification to closed-loop control of manufacturing parameters is achieved, effectively improving the manufacturing quality and process consistency of high-density interconnect boards.

[0066] A second aspect of the present invention provides a smart optimization system for manufacturing high-density interconnect boards, comprising: The grid energy unit is used to divide the high-density interconnect board to be manufactured into multiple spatial grid units, and to solve the local energy deposition density distribution and material response gradient field of each spatial grid unit under the action of real-time operating status data. The fingerprint encoding unit is used to encode the local energy deposition density distribution and the material response gradient field into the process fingerprint vector of the spatial grid cell, so as to obtain a process fingerprint tensor field covering the entire plate. The multi-scale unit is used to establish a multi-scale coupled computational framework that includes plate-level computational units and unit-level computational units. The process fingerprint tensor field is taken as input, and the plate-level warping deformation field and stress concentration region distribution are output through the plate-level computational unit. The micro-defect initiation probability distribution in each of the spatial grid units is output through the unit-level computational unit. The optimization strategy unit is used to identify a set of risk space grid cells that require process compensation based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution. Based on the risk space grid cell set, iteratively solves the multi-scale coupled calculation framework to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is then decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate a manufacturing optimization strategy.

[0067] 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.

[0068] 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.

[0069] 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.

[0070] 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 smart optimization method for manufacturing high-density interconnect boards, characterized in that, include: The high-density interconnect board to be manufactured is divided into multiple spatial grid cells, and the local energy deposition density distribution and material response gradient field of each spatial grid cell are solved under the action of real-time operating status data. The local energy deposition density distribution and the material response gradient field are encoded into the process fingerprint vector of the spatial grid cell to obtain a process fingerprint tensor field covering the entire plate. A multi-scale coupled computational framework including plate-level computational units and unit-level computational units is established. The process fingerprint tensor field is taken as input. The plate-level warping deformation field and stress concentration region distribution are output through the plate-level computational unit. The micro-defect initiation probability distribution in each spatial grid cell is output through the unit-level computational unit. Based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution, a risk space grid cell set requiring process compensation is identified. Based on the risk space grid cell set, the multi-scale coupled computational framework is solved in reverse iteration to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate a manufacturing optimization strategy.

2. The method according to claim 1, characterized in that, The high-density interconnect board to be manufactured is divided into multiple spatial grid cells. The local energy deposition density distribution and material response gradient field of each spatial grid cell under the influence of real-time operating data are solved as follows: Obtain the three-dimensional structural design data of the high-density interconnect board to be manufactured. The three-dimensional structural design data includes the spatial coordinate distribution of the micro-hole array, the material type identification and thickness distribution information of the conductive layer and the dielectric layer, and the geometric dimension parameters of the vias. Based on the spatial coordinate distribution of the microvia array and the geometric dimension parameters of the vias, an adaptive mesh generation algorithm is used to spatially discretize the high-density interconnect board to be manufactured, generating spatial mesh cells in the surrounding areas of the microvia array, the vias, the conductive layer, and the dielectric layer. The size distribution of the spatial mesh cells matches the geometric complexity in the three-dimensional structural design data. Acquire real-time operating status data of the manufacturing equipment, including laser energy output power curve, moving speed trajectory of the processing head, and temperature field distribution data within the process chamber; The material type identifier, thickness distribution information, laser energy output power curve, moving speed trajectory of the processing head, and temperature field distribution data at the corresponding positions of the spatial grid cell are coupled in a multi-physics field to perform heat conduction process calculation and stress-strain process calculation, thereby obtaining the local energy deposition density distribution and material response gradient field inside the spatial grid cell.

3. The method according to claim 1, characterized in that, Encoding the local energy deposition density distribution and the material response gradient field into process fingerprint vectors of the spatial grid cells yields a process fingerprint tensor field covering the entire plate, including: Spatial sampling is performed on the local energy deposition density distribution. Sampling positions are set along the length, width, and thickness directions of the high-density interconnect board to be manufactured within the spatial grid cell. The energy deposition density values ​​corresponding to the sampling positions are obtained and organized into the energy distribution feature vector of the spatial grid cell. Gradient components are extracted from the material response gradient field to obtain the maximum gradient magnitude and direction angle of the temperature gradient field and the maximum gradient magnitude and direction angle of the stress gradient field within the spatial grid cell, and these are organized into the gradient response feature vector of the spatial grid cell. The geometric features of the spatial grid cell, the energy distribution feature vector, and the gradient response feature vector are concatenated in the order of geometric features first, energy distribution feature vector in the middle, and gradient response feature vector last to generate the process fingerprint vector of the spatial grid cell. The dimension of the process fingerprint vector is equal to the sum of the number of geometric features, the dimension of the energy distribution feature vector, and the dimension of the gradient response feature vector. Based on the spatial position index of the spatial grid cells in the high-density interconnect board to be manufactured, the process fingerprint vectors of all the spatial grid cells are organized into a three-dimensional tensor structure to generate a process fingerprint tensor field covering the entire board.

4. The method according to claim 1, characterized in that, Using the process fingerprint tensor field as input, the plate-level warpage deformation field and stress concentration region distribution are output by the plate-level calculation unit, including: Spatial integration is performed on the process fingerprint tensor field along the length and width directions of the high-density interconnect board to be manufactured to extract the cumulative strain distribution at the whole board scale. Based on the strain accumulation distribution and the relationship between the plate deformation and strain accumulation of the high-density interconnect board to be manufactured, fixed constraints are applied to the boundary position of the high-density interconnect board to be manufactured, and the plate-level warping deformation field is calculated in the plate-level calculation unit. The curvature distribution is obtained by performing second derivative calculation on the deformation displacement along the spatial direction from the plate warping deformation field, and the curvature gradient distribution is obtained by performing gradient calculation on the curvature distribution along the spatial direction. The curvature gradient threshold is derived from the material fracture toughness parameters and geometric thickness parameters corresponding to the high-density interconnect board to be manufactured. Based on the curvature gradient distribution, spatial regions whose curvature gradient magnitude exceeds the curvature gradient threshold are identified and marked as stress concentration regions, and the stress concentration region distribution is generated.

5. The method according to claim 1, characterized in that, The probability distribution of micro-defect germination within each spatial grid cell is output through the cell-level computing unit, including: The process fingerprint vector is analyzed to obtain the local stress tensor components and local strain tensor components of the spatial grid cell. The strain energy density of the spatial grid cell is calculated based on the local stress tensor components and the local strain tensor components. The ratio of the strain energy density to the critical strain energy density of the material type identifier of the spatial grid cell is calculated to obtain the defect initiation driving force index of the spatial grid cell. The number of temperature peaks and stress cycles of the spatial grid cells in the manufacturing process time series are extracted from the process fingerprint tensor field. The cumulative amount of process cycle damage of the spatial grid cells is calculated. The critical strain energy density of the corresponding material type identifier of the spatial grid cells is corrected according to the cumulative amount of process cycle damage to obtain the corrected critical strain energy density of the spatial grid cells. Substitute the defect initiation driving force index and the modified critical strain energy density into the Weibull distribution function to calculate the initial value of the micro-defect initiation probability of the spatial grid cell. Determine whether the spatial grid cell is located within the stress concentration region from the stress concentration region distribution, apply a stress concentration amplification factor to the initial value of the micro-defect initiation probability of the spatial grid cell located within the stress concentration region to obtain the micro-defect initiation probability of the spatial grid cell, and generate the micro-defect initiation probability distribution.

6. The method according to claim 1, characterized in that, Based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution, the set of risky spatial mesh elements requiring process compensation is identified as follows: The warping displacement amplitude of each spatial grid cell is extracted from the plate-level warping deformation field. It is determined whether the warping displacement amplitude exceeds the deformation limit threshold of the material type identifier of the spatial grid cell. The spatial grid cell whose warping displacement amplitude exceeds the deformation limit threshold is marked as a deformation over-limit cell. The spatial grid cells located within the stress concentration region are extracted from the stress concentration region distribution and marked as stress concentration cells. The spatial grid cells whose micro-defect initiation probability exceeds a preset defect initiation probability threshold are extracted from the micro-defect initiation probability distribution and marked as high-risk defect cells. The deformation exceeding limit unit, the stress concentration unit and the defect high risk unit are combined and operated to obtain a preliminary risk spatial grid unit set. For each spatial grid unit in the preliminary risk spatial grid unit set, a comprehensive risk score is calculated by weighted summation based on the extent to which the warping deformation displacement amplitude exceeds the deformation limit threshold, the curvature gradient amplitude and the probability of micro-defect initiation. The spatial grid cells in the preliminary risk spatial grid cell set are sorted in descending order according to the comprehensive risk score, and the spatial grid cells with the comprehensive risk score ranking in the top preset position are selected to form the risk spatial grid cell set that requires process compensation.

7. The method according to claim 1, characterized in that, Based on the risk space grid cell set, the multi-scale coupled computational framework is solved by inverse iteration to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is then decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate manufacturing optimization strategies, including: The spatial coordinates of each spatial grid cell in the risk spatial grid cell set are mapped to the plate-level and cell-level computing cells of the multi-scale coupled computing framework, and the plate-level risk region and cell-level risk grid are marked respectively. A bi-objective optimization function is constructed, which includes the weighted sum of the gradient magnitudes of the plate-level warping deformation field in the plate-level risk region and the variance of the micro-defect initiation probability distribution in the unit-level risk grid. A single-objective optimization function is obtained by weighting the gradient magnitudes and the variances by a preset weighting coefficient. The process fingerprint vector in the process fingerprint tensor field is used as the optimization variable to perform inverse iterative solution on the multi-scale coupled calculation framework. In each iteration, the process fingerprint vector is adjusted and the plate-level warping deformation field and the probability distribution of micro-defect initiation are recalculated. The single-objective optimization function value is calculated. When the single-objective optimization function value converges to the preset convergence threshold, the iteration is stopped to obtain the target process fingerprint vector. The temperature, stress, and strain components of the target process fingerprint vector are analyzed. Equipment energy output adjustment commands are generated based on the temperature components, and process chamber physical field control commands are generated based on the stress and strain components. A manufacturing optimization strategy is then generated by combining these components.

8. A high-density interconnect board manufacturing intelligent optimization system for implementing the method as described in any one of claims 1-7, characterized in that, include: The grid energy unit is used to divide the high-density interconnect board to be manufactured into multiple spatial grid units, and to solve the local energy deposition density distribution and material response gradient field of each spatial grid unit under the action of real-time operating status data. The fingerprint encoding unit is used to encode the local energy deposition density distribution and the material response gradient field into the process fingerprint vector of the spatial grid cell, so as to obtain a process fingerprint tensor field covering the entire plate. The multi-scale unit is used to establish a multi-scale coupled computational framework that includes plate-level computational units and unit-level computational units. The process fingerprint tensor field is taken as input, and the plate-level warping deformation field and stress concentration region distribution are output through the plate-level computational unit. The micro-defect initiation probability distribution in each of the spatial grid units is output through the unit-level computational unit. The optimization strategy unit is used to identify a set of risk space grid cells that require process compensation based on the plate-level warpage deformation field, the stress concentration region distribution, and the micro-defect initiation probability distribution. Based on the risk space grid cell set, iteratively solves the multi-scale coupled calculation framework to determine the target process fingerprint vector that minimizes the gradient of the plate-level warpage deformation field and the variance of the micro-defect initiation probability distribution. The target process fingerprint vector is then decoded into corresponding equipment energy output adjustment commands and process chamber physical field control commands to generate a manufacturing optimization strategy.

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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