An adaptive analysis method for glass via defect exclusion zones

Abstract

This invention discloses an adaptive analysis method for the defect elimination zone of a glass through-hole (TGV) structure, comprising: acquiring process parameters of the TGV structure, determining the material properties of the TGV structure, and constructing an input variable set; determining different levels of each process parameter in the input variable set to obtain the configuration of the TGV structure, calculating the maximum principal stress response of the TGV structure, and calculating the contribution rate of each process parameter in the input variable set; selecting the optimal configuration of the TGV structure corresponding to the maximum principal stress response, determining the morphological parameters, load type, and interface fracture behavior parameters of the pre-crack in the TGV structure, and calculating the fracture mechanical properties of the crack tip at various locations of the TGV structure using the contour integral method, thereby obtaining the defect elimination zone range of the TGV structure. This invention can effectively solve the problems of low process trial-and-error efficiency, poor collaborative design, and low product quality yield in glass through-hole structures.

Description

Technical Field

[0001] This invention relates to the field of semiconductor three-dimensional integrated circuit technology, and in particular to an adaptive analysis method for eliminating glass through-hole damage defects based on fracture mechanics indices. Background Technology

[0002] Moore's Law's continuous advancement in integrated circuit miniaturization has encountered fundamental physical limitations. The feature size of integrated circuits continues to shrink, while device interconnect density continues to increase, prompting a strategic shift towards three-dimensional heterogeneous integration technology for micro / nano systems. Therefore, vertical interconnect stacked packaging based on through-glass vias (TGVs), with its key technological advantages of short-distance interconnection and high-density integration, has gradually led the trend in packaging technology development. However, subcritical defects arising from non-uniform metallization during the manufacturing process of TGVs, including micron-sized holes / pores and interface discontinuities, persist despite rigorous non-destructive evaluation of the quality assurance protocols for electroplated TGVs. These initial defects introduced by manufacturing inevitably enter the product's lifespan, acting as stress concentration points under thermoelectric loads. Furthermore, due to the significant thermal stress generated by the high-temperature environment during processing and service of the glass through-hole (TGV) structure, delamination at the TGV-copper / glass interconnect interface will lead to a decrease in the hermeticity of the package structure and an increase in resistance, causing chip malfunction. In addition, radial cracks caused by cracking of the glass substrate will lead to catastrophic fracture of the substrate. Delamination and cracks generated by large-sized glass through-hole (TGV) affect the performance of semiconductor devices, thus hindering the large-scale commercialization of glass through-hole (TGV) technology.

[0003] Regarding existing quality inspection methods for interconnect structures in semiconductor devices, patent number CN 104064487 B discloses a method for inspecting the quality of through-silicon vias (TSVs). This method involves forming a test structure above the TSVs in a semiconductor device, performing heat treatment on the semiconductor device to cause the voids in the TSVs to expand, resulting in a bulge on the surface of the test structure. A defect inspection machine is then used to detect surface anomalies, thus achieving the detection of void defects within the TSVs. However, this method does not achieve initial control over TSV defects at the manufacturing stage; it only performs quality screening on the already fabricated TSV structures and does not address glass through-hole structures. Furthermore, due to the low correlation between process uncertainties and processing quality during manufacturing, it is easily affected by processing parameters. Therefore, this method suffers from low process trial-and-error efficiency, poor collaborative design, and low yield improvement in product quality. Summary of the Invention

[0004] To address the aforementioned deficiencies in existing technologies, the present invention aims to provide an adaptive analysis method for the damage exclusion zone of glass through-hole (TGV) structures in three-dimensional heterogeneous integration technology. This invention obtains the contribution rate of various process parameters, and based on the optimal configuration of the TGV structure, utilizes fracture mechanics indices and potential gradient values ​​corresponding to different crack states to determine the crack propagation trend and defect exclusion zone. This solves the problems of low process trial-and-error efficiency, poor collaborative design, and low product yield improvement in glass through-hole structures.

[0005] The present invention is achieved through the following technical solution.

[0006] This invention provides an adaptive analysis method for glass through-hole defect exclusion zone, comprising:

[0007] Obtain the process parameters of the glass through-hole TGV structure, determine the material properties of the glass through-hole TGV structure, and construct the input variable set.

[0008] The Taguchi orthogonal experimental method was used to determine the different levels of each process parameter factor in the input variable set, and the Taguchi OA table was constructed to obtain the glass through-hole TGV structure configuration.

[0009] Based on the TaguchiOA table, the thermal stress simulation of the glass through-hole TGV structure configuration was carried out using numerical analysis to calculate the maximum principal stress response of the glass through-hole TGV structure.

[0010] Based on the maximum principal stress response data of the glass through-hole TGV structure, the contribution rate of each process parameter factor in the input variable set was calculated using the analysis of variance method.

[0011] The contribution rate of each process parameter factor was determined by using the main effect analysis method to select the optimal value of the maximum principal stress response, thereby obtaining the optimal configuration of the corresponding glass through-hole TGV structure.

[0012] Based on the optimal configuration of the glass through-hole TGV structure, the morphological parameters of the pre-crack in the glass through-hole are determined, the load type of the optimal configuration of the glass through-hole TGV structure is obtained, and the interface fracture behavior parameters are determined.

[0013] Based on the interface fracture behavior parameters, the fracture mechanical properties of the crack tip at each part of the glass through-hole TGV structure are calculated using the contour integral method, and the potential gradient value corresponding to different crack states is calculated using the thermoelectric coupling method.

[0014] Based on the fracture mechanics parameters of the crack tip at each location and the potential gradient values ​​corresponding to different crack states, the defect exclusion zone range of the glass through-hole TGV structure is obtained, and the defect exclusion zone range is adaptively adjusted according to the glass through-hole TGV structure configuration.

[0015] As a preferred option, the factors for obtaining the process parameters of the glass through-hole TGV structure include the external dimensions of the through-holes, the morphological dimensions between the through-holes, and environmental factors during manufacturing and service.

[0016] Material properties include elastic modulus, Poisson's ratio, plastic stress-strain data, and temperature-dependent electrical conductivity.

[0017] As a preferred approach, different levels of each process parameter factor in the input variable set are determined, and a TaguchiOA table is constructed to obtain the glass through-hole TGV structure configuration, including:

[0018] Based on all process parameter factors whose upper and lower limits have been defined, set the level of each process parameter factor in the input variable set;

[0019] Convert the actual physical quantities of each process parameter factor level into standardized codes;

[0020] Based on the standardized coding of each process parameter factor and its level in the input variable set, the Taguchi OA table is constructed using the Taguchi orthogonal experimental method.

[0021] Based on different combinations of process parameter factors in the TaguchiOA table, various glass through-hole TGV structural configurations are generated, including trapezoidal, annular, hollow trapezoidal, and cylindrical configurations.

[0022] Preferably, at the taper angle At this time, a trapezoidal glass through-hole TGV structure configuration is generated;

[0023] In outer diameter ratio At this time, an annular glass through-hole TGV structure configuration is generated;

[0024] At taper angle And the ratio of inner to outer diameter At this time, a hollow trapezoidal glass through-hole TGV structure configuration is generated;

[0025] At taper angle And the ratio of inner to outer diameter At this time, a cylindrical glass through-hole TGV structure configuration is generated.

[0026] As a preferred method, the thermal stress simulation of the glass-through-hole TGV structure configuration is performed using numerical analysis to calculate the maximum principal stress response of the glass-through-hole TGV structure, including:

[0027] Numerical analysis and simulation were performed using the ABAQUS / Standard finite element solver to construct a simulation model assembly of the glass through-hole TGV structure.

[0028] An analysis step was established to calculate the output response values ​​under different glass through-hole TGV structural configurations, and the maximum principal stress response corresponding to all glass through-hole TGV configurations was obtained.

[0029] Preferably, the output response values ​​are calculated for different glass through-hole TGV structural configurations, including:

[0030] Solve for the displacement field of the nodes in the simulation model assembly;

[0031] The strain of the glass through-hole TGV configuration was calculated by the gradient of the displacement field at the nodes.

[0032] By utilizing the constitutive relations of the material, the strain of the glass through-hole TGV configuration is updated to the stress of the glass through-hole TGV configuration;

[0033] The maximum principal stress response of the glass through-hole TGV configuration is calculated based on the updated stress of the glass through-hole TGV configuration.

[0034] As a preferred method, analysis of variance is used to calculate the contribution rate of each process parameter factor in the input variable set, including:

[0035] Calculate the total sum of squares and the sum of squares of each process parameter factor;

[0036] Calculate the sum of squared deviations of the average values ​​corresponding to different levels of each process parameter factor;

[0037] Calculate the sum of squared errors to obtain the deviation between the total sum of squares and the sum of squared deviations;

[0038] Calculate the mean square and error mean square of each process parameter factor;

[0039] Calculate the contribution rate of each process parameter factor to obtain the ANOVA table.

[0040] As a preferred approach, the optimal value of the maximum principal stress response is selected using the main effect analysis method. The average value of the maximum principal stress response at all levels of each process parameter factor is calculated by selecting the minimum signal-to-noise ratio among four signal-to-noise ratios, including the minimum, maximum, and two minimum ratios.

[0041] All process parameter factors are sequentially screened from highest to lowest contribution rate, and the optimal combination of process parameter factors corresponding to the optimal value of the maximum principal stress response is selected to obtain the optimal configuration of the glass through-hole TGV structure.

[0042] As a preferred method, the morphological parameters of the pre-existing cracks in the glass through-hole are determined to obtain the load type of the optimal configuration of the glass through-hole TGV structure, and the interface fracture behavior parameters are determined, including:

[0043] Determine the morphological parameters of the glass through-hole, including the length, location, and orientation of the pre-fabricated single crack;

[0044] A multi-crack model was set up based on the single crack morphology, and load types including thermal cycling field and thermoelectric coupling field were applied to determine the behavioral parameters of single crack parameters, multi-crack mode and thermoelectric coupling load interface fracture.

[0045] Preferably, the fracture mechanical properties of the crack tips at various locations in the glass through-hole TGV structure are calculated using the contour integral method, and the potential gradient values ​​corresponding to different crack states are calculated using the thermoelectric coupling method, including:

[0046] Set the pre-fabricated crack parameters, including length, location, orientation, and number, and perform J-integral calculations;

[0047] The potential gradient values ​​corresponding to different crack states were calculated using the thermoelectric coupling method.

[0048] The present invention, by adopting the above technical solution, has the following beneficial effects:

[0049] 1. By introducing the Taguchi orthogonal experimental method to analyze the thermal stress response of multiple process parameters to the structure, the stress distribution law of multi-configuration glass through-hole TGV structure, especially under thermal load, is established. The evolution law of crack propagation driving force under cyclic loading is quantitatively characterized based on fracture dynamics, providing key variables for crack control. This effectively solves the problem of low correlation between process uncertainty and processing quality, i.e., low process trial and error efficiency.

[0050] 2. By obtaining the contribution rate of each process parameter factor, the optimal value of the maximum principal stress response is selected, and the problem of poor collaborative design of glass through-hole TGV structure is solved based on the optimal configuration of the glass through-hole structure.

[0051] 3. The morphological parameters of cracks appearing in glass through-holes during thermal cycling are preset. By using fracture mechanics indicators and potential gradient values ​​corresponding to different crack states, the crack propagation trend and defect elimination zone of the structure can be determined, thus solving the problem of low product yield in glass through-hole structures. Attached Figure Description

[0052] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, do not constitute an undue limitation of the invention. In the drawings:

[0053] Figure 1 This is a flowchart of the adaptive analysis method for the glass through-hole defect exclusion area in an embodiment of the present invention;

[0054] Figure 2 These are diagrams of various glass through-hole TGV structures formed under different combinations of process parameters, namely (a) cylindrical, (b) annular, (c) trapezoidal and (d) hollow trapezoidal glass through-hole TGV structures.

[0055] Figure 3 This is a diagram showing the principal effect analysis of the maximum principal stress in the output response corresponding to the six input variables during the heating stage, obtained based on the experimental design.

[0056] Figure 4 This is a principal effect analysis diagram of the mean signal-to-noise ratio of the maximum principal stress in the output response corresponding to the six input variables during the heating stage, obtained based on the experimental design.

[0057] Figure 5 This is a diagram showing the principal effect analysis of the maximum principal stress in the output response corresponding to the six input variables during the cooling stage, obtained based on the experimental design.

[0058] Figure 6 This is a principal effect analysis diagram of the mean signal-to-noise ratio of the maximum principal stress in the output response corresponding to the six input variables during the cooling stage, obtained based on the experimental design.

[0059] Figure 7 These are five crack pattern diagrams established based on experimental configurations;

[0060] Figure 8 This is a graph showing the integral results of the fracture mechanics index J, obtained from fracture mechanics experimental tables.

[0061] Figure 9 These are Von Mises stress contour maps and contour maps during heating;

[0062] Figure 10 This is a potential gradient distribution diagram of a multi-cracked glass through-hole TGV structure under thermal cycling and thermo-electric coupling loads.

[0063] Figure 11 This is a diagram illustrating the definition process of the crack exclusion zone. It includes (a) a diagram showing the normalization of crack locations to interface lengths, (b) the J-integral value of a single crack at the corresponding location, and (c) a diagram showing the distribution of thermal stress and potential gradients among multiple cracks. Detailed Implementation

[0064] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention.

[0065] like Figure 1 As shown, this embodiment of the invention provides an adaptive analysis method for glass through-hole defect exclusion zone, including the following steps:

[0066] Step 1: Based on the actual application requirements of the glass through-hole TGV structure, obtain the process parameter factors of the glass through-hole TGV structure, determine the material properties of the glass through-hole TGV structure, and construct the input variable set.

[0067] Based on the actual operating conditions of the glass through-hole (TGV) structure, this invention defines the types and ranges of various process parameters in its manufacturing process and constructs a set of input variables. Taking heterogeneous integration advanced packaging in the field of 3D integration as an example, this invention defines the glass through-hole (TGV) structure as a heterogeneous interconnect structure integrating copper-filled vias (TGV-Cu) and a glass substrate. Priority is given to the thermoelectric coupling analysis of the metal via structure and the interposer substrate assembly (TGV-Cu / glass).

[0068] The selection of core process parameters crucial to the performance and manufacturability of glass-through-hole TGV structures was based on a comprehensive consideration of application requirements, manufacturing constraints, and literature standards. The process parameters included in the input variables were determined as follows: the through-hole dimensions, the morphological dimensions between through-holes, and environmental factors during manufacturing and service (considering temperature loads caused by temperature variations). The material properties of the glass-through-hole TGV structure were also determined, including elastic modulus, Poisson's ratio, plastic stress-strain data, and temperature-dependent electrical conductivity.

[0069] Considering the coupling effect between parameters, a feasible boundary range for the initial process parameter factors of the input variable set is formed. The input variable set is constructed, including all process parameter factors, the boundary ranges of corresponding process parameter factors with defined upper and lower limits, and the material properties of the glass through-hole TGV structure, thus obtaining the input variable set.

[0070] Step 2: The Taguchi orthogonal experimental method is used to determine the different levels of each process parameter factor in the input variable set, and the Taguchi OA table is constructed to obtain the glass through-hole TGV structure configuration.

[0071] The Taguchi orthogonal experimental method reduces the number of experiments by leveraging orthogonality while maintaining statistical significance, minimizing the required number of trials while exploring the optimal parameter combination. The Taguchi OA table generates glass via TGV structural configurations, visually representing the structural configurations contained at different levels of each process parameter factor in the input variable set. It also provides a dataset for determining the optimal process parameter combination for the optimal structural configuration in the input variable set. The specific steps are as follows:

[0072] First, based on all process parameter factors whose upper and lower limits have been defined, set the level of each process parameter factor in the input variable set.

[0073] From step 1, we obtain the process parameter factors and their ranges in the input variable set, and then set the levels of all process parameters and the number of levels for each process parameter factor.

[0074] Based on the upper and lower limits of each process parameter factor, the actual physical quantity of each process parameter factor level is converted into a standardized code, thus obtaining the standardized code corresponding to the level of each process parameter factor.

[0075]

[0076] in and For the actual physical quantities and standardized codes of different input variables and These are the maximum and minimum values ​​of actual physical quantities. l The number of factor levels for each process parameter.

[0077] Furthermore, based on the standardized coding of each process parameter factor and its level in the input variable set, an orthogonal experimental design table (Taguchi OA table) was constructed using the Taguchi orthogonal experimental method.

[0078] This invention uses the Taguchi orthogonal experimental design method (DOE) as the experimental design method. By standardizing the coding of each process parameter factor and its level, the orthogonality of the levels of each process parameter factor is determined through orthogonality conditions. The orthogonal combination of the levels of each process parameter factor in the input variable set in step 1 is determined, and the experimental design orthogonal table (Taguchi OA table) is obtained.

[0079] The orthogonality condition in Taguchi's orthogonal experimental method is:

[0080]

[0081] in and For different process parameter factors, ensure that each input variable is independent and uniformly covers the design space; Due to process parameter factors, The total number of levels corresponding to each process parameter factor.

[0082] To effectively reduce the number of samples and improve experimental efficiency, the Taguchi method employed in this invention's Design of Experiments (DOE) has the advantage of reducing the number of experiments through orthogonality while maintaining statistical significance. The Taguchi method uses the OA table as a statistically efficient experimental design optimization framework, which can minimize the number of experiments required while exploring the optimal parameter combination, making it particularly suitable for analyzing optimization problems with multiple input parameters. Therefore, a brief explanation of the selection of the experimental design method is provided here.

[0083] Furthermore, various glass through-hole TGV structural configurations are generated based on different level combinations of process parameter factors in the Taguchi OA table.

[0084] The glass through-hole TGV structure configuration is generated by the horizontal combination of each input variable in the Taguchi OA table above. Different horizontal combinations of each input variable in the Taguchi OA table correspond to different combinations of process parameters, and the output forms a variety of glass through-hole TGV structure configurations, such as trapezoidal, annular, hollow trapezoidal and cylindrical.

[0085] At taper angle At this time, a trapezoidal glass through-hole TGV structure configuration is generated; at the outer diameter ratio At this time, a ring-shaped glass through-hole TGV structure configuration is generated; at the taper angle And the ratio of inner to outer diameter At this time, a hollow trapezoidal glass through-hole TGV structure configuration is generated; at the taper angle And the ratio of inner to outer diameter At this time, a cylindrical glass through-hole TGV structure configuration is generated.

[0086] Step 3: Based on the Taguchi OA table, perform thermal stress simulation on the glass through-hole TGV structure configuration using numerical analysis method, and calculate the maximum principal stress response of the glass through-hole TGV structure.

[0087] Based on the different combinations of process parameters obtained in the Taguchi OA table in step 2, thermal stress simulation experiments were performed on all generated glass through-hole TGV structural configurations using numerical analysis, with the maximum principal stress in the fracture mechanics index set as the output response. The specific steps are as follows:

[0088] First, numerical analysis and simulation experiments were conducted using the ABAQUS / Standard finite element solver to construct a simulation model assembly of the glass through-hole TGV structure.

[0089] Based on the process parameter factors in the Taguchi OA table regarding the configuration and morphology parameters of the glass through-hole TGV structure, different combinations of the external dimensions of the glass through-hole TGV structure and the morphology dimensions between the through holes are input. Simulation models of copper-filled through-hole TGV-Cu and glass substrate in the glass through-hole TGV structure are established respectively, and the assembly is completed to construct the glass through-hole TGV structure simulation model assembly.

[0090] Select the numerical element type for thermal stress analysis, input material properties, apply boundary conditions on both sides of the simulation model assembly to constrain the spatial displacement of the simulation model assembly, then apply temperature change conditions to the simulation model assembly in the form of a field, generate nodes of the simulation model assembly by meshing, and establish an analysis step, with the maximum principal stress as the output response result file.

[0091] Furthermore, by establishing the analysis steps, the output response values ​​under different glass through-hole TGV structural configurations are calculated, and the maximum principal stress response data corresponding to all glass through-hole TGV configurations are obtained.

[0092] a) First, solve for the displacement field of the nodes of the assembly in the simulation model. .

[0093]

[0094] The coordinates of one of the material points before and after deformation are respectively and In the Cartesian coordinate system, it can be written as .

[0095] b) Calculate the strain of the glass-through-hole TGV configuration by using the gradient of the displacement field at the nodes.

[0096] The strain equation for the glass through-hole TGV configuration is:

[0097]

[0098] in, , , It is a positive response. , , Represents the displacement of the node. , , These represent the orientations along the x, y, and z axes, respectively.

[0099] c) Using the constitutive relation of the material, the stress of the glass through-hole TGV configuration is updated from the calculated strain.

[0100] For the constitutive relation of linear elastic materials, i.e., the generalized Hooke's law, the stress tensor is obtained as follows:

[0101]

[0102] in, It is the Cauchy stress tensor. It is the elastic stiffness matrix. It is the strain tensor.

[0103] d) Calculate the maximum principal stress response corresponding to the glass through-hole TGV configuration.

[0104] The maximum principal stress response is obtained by the following equation:

[0105]

[0106] in, It is the eigenvalue, which is the required principal stress. ; It is an eigenvector, representing the principal direction; It is an identity matrix.

[0107] Step 4: Based on the obtained maximum principal stress response data, use the analysis of variance method to calculate the contribution rate of each process parameter factor in the input variable set.

[0108] Specifically, based on the maximum principal stress response data obtained in step 3, an analysis of variance (ANOVA) is performed. First, the total sum of squares and the sum of squares of each process parameter factor are calculated.

[0109] a) Calculate the total sum of squares Let represent the sum of squares of the deviations of all data from the overall mean:

[0110]

[0111] in, This is the total number of experiments in the Taguchi OA table. It is the first i The observed values ​​from this experiment, It is the average of all observations.

[0112] b) Calculate the sum of squared deviations of the average values ​​corresponding to different levels of each process parameter factor. .

[0113] Assume a process parameter factor A have l There are several levels, each level has m The experiment (i.e., the number of times each level of the process parameter factor appears in the orthogonal table, and) m × l = n Then process parameter factors A The sum of squares is:

[0114]

[0115] in, It is a factor of process parameters. A In the j The average of all observations at the given level.

[0116] Furthermore, the sum of squares of errors is calculated to obtain the deviation between the total sum of squares and the sum of squares of deviations, thereby determining whether there are statistically significant differences between different groups.

[0117] Sum of squared errors It can be obtained by subtracting the sum of squares of all process parameter factors from the total sum of squares (under the assumption of no interaction):

[0118]

[0119] Furthermore, the mean square and error mean square of each process parameter factor are calculated.

[0120] Mean square of process parameter factors:

[0121]

[0122] in, It refers to the degree of freedom of process parameter factors.

[0123] Mean square error:

[0124]

[0125] in, It is the degree of freedom of error.

[0126] Furthermore, the contribution rate of each process parameter factor was calculated to obtain the ANOVA table.

[0127] Contribution rate ( ρ The sum of squares for each process parameter factor represents the percentage of the total sum of squares, indicating the contribution of that process parameter factor to the total variation.

[0128]

[0129] ANOVA tables were obtained for each process parameter factor with the maximum principal stress as the output response. The ANOVA results were presented in a structured manner using the analysis of variance tables in ANOVA.

[0130] The ANOVA table includes the total square, the sum of squares of each process parameter factor, the sum of squares of deviations, the sum of squares of errors, the mean square of each process parameter factor, the mean square of errors, and the contribution rate. It also includes the F-value and the P-value, where the F-value is the ratio of the between-group mean square to the within-group mean square. F factor = MS factor / MS e The p-value is significance (Sig.), which is the probability of observing the current data or a more extreme case. If the p-value is less than the predetermined significance level (usually 0.05), the null hypothesis is rejected.

[0131] The ANOVA statistic described above can be used to effectively measure the dispersion of data.

[0132] Step 5: Based on the contribution rate obtained by the variance analysis method, the optimal value of the maximum principal stress response is selected by the main effect analysis method to obtain the optimal configuration of the corresponding glass through-hole TGV structure.

[0133] The specific steps are as follows:

[0134] First, the selected response characteristics are calculated for each combination of process parameter factors. For each process parameter factor, a signal-to-noise ratio (SNR) is provided, offering four SNR values: minimum, maximum, and two target values. Maximizing the SNR is desired in all cases; however, this invention targets the output response at the maximum principal stress of the structure, therefore, the minimum SNR is used. The minimum SNR is calculated for each combination of process parameter factors. The formula for minimizing the signal-to-noise ratio using the logarithm to base 10 is:

[0135]

[0136] in, The maximum principal stress response value for a given combination of process parameter levels. This represents the total number of responses in the combination of process parameter factor levels.

[0137] Furthermore, the mean responses of each process parameter level are connected by a line to form a main effect plot. When different levels of the process parameter have different effects on the response (i.e., the line is not horizontal), it indicates the existence of a main effect; when the line is horizontal (parallel to the x-axis), it indicates the absence of a main effect. Each level of the process parameter affects the response in the same way, and the mean response is the same across all process parameter levels; different levels of the process parameter have different effects on the response. The steeper the line, the larger the magnitude of the main effect.

[0138] Use a main effects plot to examine the difference between the average levels of one or more process parameter factors. In the main effects plot, select the maximum value of the vertical axis corresponding to the connecting line as the optimal level of that process parameter factor.

[0139] Similarly, by referring to the contribution rate of all process parameter factors obtained by the analysis of variance method, all process parameter factors are sequentially screened from high to low contribution rate, and the combination of process parameter factors corresponding to the optimal value of the maximum principal stress response is selected to obtain the optimal configuration of the glass through-hole TGV structure.

[0140] Step 6: Based on the optimal configuration of the glass-through-hole TGV structure, determine the morphological parameters (length, location, orientation, and number) of the pre-existing cracks in the glass-through-hole, obtain the load type for the optimal configuration of the glass-through-hole TGV structure, and determine the interface fracture behavior parameters. The specific steps are as follows:

[0141] First, determine the morphological parameters, including the length, location, and orientation of the pre-fabricated single crack in the glass through-hole.

[0142] Cracks in different regions are defined at the copper / glass interface of the optimal glass via TGV configuration obtained under the optimal parameter combination in step 5. That is, the first type of crack starts at the top of the TGV-Cu and glass substrate interface, the second type of crack starts at the upper middle part of the two, and the third type of crack starts at the middle part of the two.

[0143] Different length gradients for each crack were set based on the total interface length. Different experimental groups were set up to study the dependence of crack length on the discrete ratio, with the range based on the normalized ratio of half the interface length. The crack propagation direction was defined, and due to the influence of interface properties, the crack exhibited two propagation trends: upward and downward.

[0144] Furthermore, based on the single crack morphology, a multi-crack model was set up and load types including thermal cycling field and thermoelectric coupling field were applied to determine the behavioral parameters including single crack parameters, multi-crack mode and thermoelectric coupling load interface fracture.

[0145] The influence of crack parameters at the interface of a glass-through-hole TGV structure (composed of both TGV-Cu and glass) on crack propagation space characteristics was determined.

[0146] Step 7: Based on the interface fracture behavior parameters, the fracture mechanical properties of the crack tips at various parts of the glass through-hole TGV structure are calculated using the contour integral method, and the potential gradient values ​​corresponding to different crack states are calculated using the thermoelectric coupling method.

[0147] First, crack parameters in the interfacial fracture behavior parameters are sequentially set at the TGV-Cu / glass interface of the optimal configuration of the glass through-hole TGV structure. The mechanical characterization of the crack tip region is directly performed by bypassing the local singularity-dominant region of the crack through the two-dimensional elastoplastic fracture parameter J integral.

[0148] Multiple concentric contour lines are set around the crack tip. The J-integral value of different crack tips is calculated using the contour integration method of far-field stress and displacement, and the J-integral curve of its evolution with time under thermal cycling conditions is obtained. Based on this, the propagation trend of the crack tip in this location is determined. The specific steps are as follows:

[0149] First, set the crack parameters of the pre-fabricated crack, including length, location, orientation, and number, and then perform J-integral calculation.

[0150] J-integral is defined as follows:

[0151]

[0152] in, and For displacement components, This refers to the profile of the closed crack tip that spans from the bottom to the top crack surface. and These are the traction components along a unit length profile. These variables satisfy:

[0153]

[0154] in, and These are the outline paths. The outward pointing of the unit normal vector component, It is along The differential arc length. Strain energy density. Defined as:

[0155]

[0156] in, , , and represent stress, strain, and shear strain, respectively.

[0157] Numerical calculations of the J-integral require a reformulation of the standard expression. The adapted form for this two-dimensional configuration is:

[0158]

[0159] When length As it approaches zero, it converges to the crack tip. (Unit vector) The direction of crack propagation is defined, vector. express The external direction.

[0160]

[0161] in, For unit tensors, Indicates the equivalent displacement. This represents the elastic strain energy density.

[0162] Considering the pre-existing crack parameters, including length, location, orientation, and number, the J-integral is calculated as follows:

[0163]

[0164] in, It is a closed crack tip profile, and It is a unit vector on the profile, defining the direction of crack propagation.

[0165] Furthermore, the potential gradient values ​​corresponding to different crack states are calculated using the thermoelectric coupling method. The specific steps are as follows:

[0166] Thermoelectric simulation experiments were conducted based on the multi-crack mode set in step 6. The potential gradient values ​​corresponding to different crack states under thermoelectric load were calculated using the thermoelectric coupling method, and the potential coupling between cracks was obtained. Based on this, the Joule heat distribution at the crack tip was determined.

[0167] The potential gradient at the crack tip is calculated based on Maxwell's charge conservation equation. In a conductive medium, the electric field is controlled using Maxwell's charge conservation equation.

[0168]

[0169] in, Define the flow through the control surface The normal component of the current density.

[0170] Step 8: Based on the fracture mechanics parameters of the crack tip in each part and the potential gradient value corresponding to different crack states, the defect exclusion zone range of the glass through-hole TGV structure is obtained, and the defect exclusion zone range is adaptively adjusted according to the glass through-hole TGV structure configuration.

[0171] By combining the J integral values ​​under different crack parameters obtained in step 7 with the potential gradient values ​​corresponding to different crack states, the crack propagation trend at this location is comprehensively judged, and the defect exclusion zone range of the glass through-hole TGV structure is obtained. This range is adaptively adjusted based on the structural configuration obtained in step 4. The specific steps are as follows:

[0172] Since initial defects are inevitably introduced during the manufacturing process of the glass through-hole TGV structure, based on the J-integral results of multiple cracks under thermal load and the potential gradient coupling effect under thermoelectric coupling, the size and range of the defect removal zone are specifically determined by the crack length, the location of the defect removal zone is specifically determined by the crack position, and the distance limit between defects is determined according to the number of cracks. When the application scenario changes, the results of adaptive adjustment of the comprehensive process parameter range and adaptive optimization of the structural configuration are used to iteratively ensure that all input variables meet the fracture mechanics index, thereby realizing adaptive response analysis of the glass through-hole defect removal zone.

[0173] The following specific embodiment is provided to more clearly explain the adaptive analysis method for glass through-hole defect exclusion zone of the present invention.

[0174] 1) Obtain the structural process parameters of the TGV and construct a set of input variables.

[0175] This embodiment takes advanced heterogeneous integration packaging in the field of 3D integration as an example. According to research, the process parameter factors among the input variables of the glass through-hole (TGV) structure include the through-hole diameter. Interface height / through-hole diameter aspect ratio Taper angle and the ratio of inner and outer diameters Equal through-hole dimensions; morphological dimensions and pitch between through-holes ; and environmental factors during manufacturing and service, including annealing temperature. The material properties of the through-glass via (TGV) structure include the elastic modulus, Poisson's ratio, plastic stress-strain data, and temperature-dependent electrical conductivity of the copper-filled vias (TGV-Cu) within the TGV structure and the glass substrate. The upper and lower limits of each process parameter are as follows: , , , , , All process parameters with defined upper and lower limits are organized into a structured database, and combined with material properties, the input variable set is constructed.

[0176] 2) The Taguchi orthogonal experimental method was used to determine the different levels of process parameter factors in the input variable set, and the Taguchi OA table was constructed to generate the glass through-hole TGV structure configuration.

[0177] The structural process parameters in the above input variable set include the through-hole diameter of the glass via TGV structure. Interface height / through-hole diameter aspect ratio Taper angle , inner and outer diameter ratio Pitch and annealing temperature Set the number of input variables to 6. Level values ​​can be actual physical quantities (uncoded) or standardized codes (e.g., -1, 0, +1). If level 1 = 5μm and level 3 = 15μm for the actual physical quantity of the through-hole diameter, then the coded value for level 2, calculated using the conversion formula, is:

[0178]

[0179] As shown in Table 1, the Taguchi orthogonal experimental method was used to determine that the input variable set included 6 process parameter factors, and each process parameter factor contained 5 levels.

[0180] Table 1. Factor Level Table of Process Parameters Used in Glass Through-Hole TGV

[0181]

[0182] Because this example involves six five-level process parameter factors, Taguchi L was chosen. 25 (5) 6The OA table effectively reduces the total number of required experiments to 25. Based on these process parameter factors and their levels, orthogonality is determined for all level combinations of each process parameter factor using the orthogonality conditions in the Taguchi orthogonal experimental method, resulting in the Taguchi L... 25 The OA table is shown in Table 2.

[0183] Using Taguchi L as shown in Table 2 25 The OA table parameter combinations produce four glass through-hole TGV structure configurations, such as... Figure 2 The figures shown are (a) cylindrical, (b) annular, (c) trapezoidal, and (d) hollow trapezoidal. Experiment number 7 is the experiment at the taper angle... The trapezoidal glass through-hole TGV structure configuration produced at that time; Experiment number 8 is the outer diameter ratio The annular glass through-hole TGV structure configuration produced at that time; Experiment number 2 is the one at the taper angle And the ratio of inner to outer diameter The hollow trapezoidal glass through-hole TGV structure configuration produced at that time; Experiment number 1 is the one at the taper angle And the ratio of inner to outer diameter The cylindrical glass through-hole TGV structure configuration produced at that time.

[0184] Table 2 L based on Taguchi method 25 OA Parameter Combination Table

[0185] Table 2

[0186]

[0187] 3) Based on the Taguchi OA table, a simulation experiment was performed on the glass through-hole TGV structure configuration using numerical analysis to calculate the maximum principal stress response data of the glass through-hole TGV structure.

[0188] Input includes diameter Interface height / through-hole diameter aspect ratio Pitch Taper angle and the ratio of inner and outer diameters Different horizontal combinations of the internal dimensions were used to construct simulation models of the copper-filled through-hole TGV-Cu and the glass substrate in the glass through-hole TGV structure, respectively, and then assembled to obtain the simulation model assembly of the glass through-hole TGV structure. The numerical element type used was a 4-node bilinear plane stress quadrilateral element (CPS4R). Key material properties, including plastic stress-strain data and temperature-dependent conductivity, were further input. TGV-Cu was set to elastoplastic behavior, while other materials were treated as linear elastic. Boundary conditions were applied to both sides of the simulation model assembly to constrain its displacement in the x and y directions. Then, temperature variation conditions were applied to the entire simulation model assembly in the form of a field, with the temperature variation conditions being the environmental factor annealing temperature from the Taguchi OA table. The process involves meshing to generate nodes for the simulation model assembly and creating an analysis step with the maximum principal stress as the output response file. The output response values ​​for different glass-through-hole TGV structural configurations are calculated using this analysis step, yielding the maximum principal stress response data for all glass-through-hole TGV configurations. The maximum principal stress values ​​for trapezoidal, hollow trapezoidal, cylindrical, and annular glass-through-hole TGV configurations can be viewed in the post-processing results.

[0189] 4) Based on the maximum principal stress response data obtained from the Taguchi OA table in step 3, the contribution rate of each process parameter factor in the input variable set was calculated by the variance analysis method. The results are shown in Table 3.

[0190] Table 3. ANOVA analysis results of maximum principal stress.

[0191] Table 3

[0192]

[0193] Table 3 presents the ANOVA results, representing the statistically significant factors of each process parameter and their interactions, with F-values ​​and P-values. Variables with high F-values ​​and P-values ​​<0.05 (i.e., at a 95% confidence level) are key determinants. It can be concluded that diameter is the most influential process parameter, followed by annealing temperature and inner-outer diameter ratio. A positive correlation can be observed with diameter, annealing temperature, and taper angle. During the heating stage, radial compressive stress at the interface increases due to thermal expansion mismatch, increasing the risk of substrate cracking. During cooling, higher values ​​enhance radial tensile stress, which increases the likelihood of interface delamination as crack propagation stress intensifies. Conversely, an inverse relationship exists with the inner-outer diameter ratio; as the ratio increases, copper volume decreases, thus reducing energy release rate. Furthermore, aspect ratio and pitch have only a slight effect.

[0194] 5) Based on the ANOVA results obtained by the analysis of variance method, the optimal value of the maximum principal stress response is selected by the main effect analysis method, and the optimal configuration of the corresponding TGV structure is obtained.

[0195] Applications such as Figures 3-6 The main effect analysis shown selects the optimal maximum principal stress response. Figure 3 This represents the principal effect diagram of the maximum principal stress corresponding to the six input variables during the heating phase. Figure 4 This is a main effect plot showing the mean signal-to-noise ratio for the six input variables during the heating phase. Figure 5 This represents the principal effect diagram of the maximum principal stress corresponding to the six input variables during the cooling phase. Figure 6 This plot shows the mean main effect diagram of the signal-to-noise ratio for the six input variables during the cooling phase. Based on ANOVA results, the following... Figures 3-6 The principal stress diagram shown yields the optimal parameter combination as follows: diameter 20 μm, aspect ratio 2, inter-hole pitch 160 μm, annealing temperature 200℃, taper angle 0°, and inner-outer diameter ratio 0.8. Based on this, the optimal parameter values ​​within six input variable ranges were selected, resulting in the optimal glass through-hole TGV structure configuration as an annular glass through-hole TGV structure. This structure demonstrates the potential to enhance the mechanical strength and structural integrity of glass through-hole TGVs. This method exhibits a high correlation between process uncertainty and processing quality during the manufacturing process of glass through-hole TGVs and is less susceptible to the influence of processing parameters. In contrast, existing processing design methods that employ a "manufacture first, then trial and error" approach show poor correlation between process and processing quality and are easily affected by processing parameters.

[0196] 6) Based on the optimal configuration of the glass through-hole TGV structure obtained in step 5, determine the length, location, orientation and number of pre-cracks, determine the load type of the optimal configuration of the TGV structure, and determine the interface fracture behavior parameters.

[0197] Based on the obtained optimal glass through-hole TGV structure ring configuration, a system was established. Figure 7Five crack behavior modes are shown to investigate the impact of crack parameters on structural reliability. Except for the variables that need to be controlled, the same parameters are maintained for each behavior mode. Groups 1-3 investigated the dependence of crack length on crack length at six discrete scales, ranging from 7.5% to 50% of the half-interface length (=40 μm). Furthermore, in Groups 1-3, vertical positioning included top, middle, and bottom, while the growth direction was set to three types: upward, downward, and bidirectional modes. Group 4 evaluated multi-crack interactions under thermal cycling, while Group 5 introduced thermoelectric coupling in the same multi-crack configuration as Group 4. Crack length was normalized to a dimensionless ratio relative to the interface length for generalized interpretation, and the crack length size set [1.5, 3, 4, 6, 8, 10 μm] was preserved in post-processing to ensure dimensional clarity. In summary, to reveal the dependence of fracture behavior on multi-crack interactions and thermoelectric coupling effects, the interface fracture behavior parameters were determined and are shown in Table 4.

[0198] Table 4 reveals the dependence of fracture behavior on multi-crack interaction and thermoelectric coupling effects.

[0199] Table 4

[0200]

[0201] 7) Calculate the fracture mechanics parameters of the crack tip at each location using the contour integral method.

[0202] Based on the interface fracture behavior parameters obtained above, simulation experiments were conducted using J-integral as the fracture mechanics index. The J-integral of the fracture mechanics index at the crack tip of each part was calculated using the contour integral method to determine its propagation trend. Figure 8 The J-integral calculation results for single crack tips of different lengths under thermal cycling conditions are presented. Specifically, Figure 8 The behavior of Type 1 cracks, which propagate vertically along the top of the copper-glass interface, is described. The J-integral at the crack tip increases with increasing crack length, and its growth rate gradually increases with crack propagation. Notably, during cooling, the J-integral exhibits a non-monotonic change with increasing crack length, initially decreasing and then increasing. When the crack length exceeds 1.5 μm, it surpasses the maximum value of the previous stage, indicating that the crack near the upper surface of the interface gradually propagates under thermal contraction conditions. Figure 9 The Von Mises stress contour plot, i.e., the contour plot of the heating stage, shows that the multi-crack configuration critically redistributes the stress-strain field under thermal cycling. The stress field coupling between adjacent crack tips generates a locally non-uniform stress distribution, directly promoting accelerated crack propagation.

[0203] The potential gradient values ​​corresponding to different crack states were further calculated using the thermoelectric coupling method.

[0204] Figure 10The potential gradient distribution of a multi-cracked glass through-hole TGV structure under thermal cycling and thermo-electric coupling loading is shown. Under constant current loading, the peak gradient is reached at the crack tip. The proximity of adjacent cracks causes potential coupling between the tips, amplifying the local Joule heating generated by the current flux and accelerating crack propagation / branching.

[0205] 8) Based on the fracture mechanics parameters of the crack tips in each part and the potential gradient values ​​corresponding to different crack states, the defect exclusion zone range of the TGV structure is obtained.

[0206] Due to the unavoidable initial defects introduced during the manufacturing process of the glass through-hole TGV structure, in this invention, the size and range of the defect removal area are specifically determined by the crack length, the location of the defect removal area is specifically determined by the crack position, and the limitation range of the distance between defects is determined according to the number of cracks. Figure 11 The process of defining the crack exclusion zone is explained. Figure 11 In (a), the crack location is normalized to the interface length, while Figure 11 (b) gives the J-integral value for a single crack at the corresponding location. Cracks located at the interface edge ( Figure 11 (b1) exhibits a critically high J integral value, indicating severe scaling sensitivity. At a normalized distance of 6% ( Figure 11 (b2)), the J integral value remains high, indicating a continued risk of crack-driven interface delamination. Conversely, at distances of 12% and 15% ( Figure 11 (b3) and (b4)), the J integral value drops significantly. Notably, during the cooling phase (2-3s), the J integral is still lower than that during the heating phase (0-1s), verifying the effectiveness of the exclusion zone. Figure 11 (c) shows the distribution of thermal stress and potential gradient between multiple cracks under thermoelectric coupling. At a 3% spacing ( Figure 11 (c1)), the strong coupling between thermal stress and potential gradient amplifies single crack propagation. However, at an 8% spacing ( Figure 11 (c2) The coupling effect is significantly weakened, accompanied by a significant reduction in thermal stress and potential gradient.

[0207] In summary, the defect removal zone under the input parameters of this invention requires a minimum interface length margin of 6%, i.e., 2.5 μm from the interface end. Furthermore, a minimum crack spacing of 3% of the interface length is obtained, at which point the coupling effect between cracks is significantly weakened, and the thermal stress and potential gradient are significantly reduced. When the application scenario changes, the results of adaptive adjustment of the comprehensive process parameter range and adaptive optimization of the structural configuration are iteratively used to ensure that all input variables meet the fracture mechanics indices considering thermoelectric coupling, thus achieving adaptive response analysis of the glass through-hole defect removal zone.

[0208] This method integrates process variables such as the parameters of the through-hole itself and the parameters between through-holes during the manufacturing of glass through-hole TGV, environmental variables during heat treatment, and initial cracks and thermoelectric coupling effects during service. It significantly improves the efficiency of the collaborative design of glass through-hole manufacturing and service performance. The fracture index J integral is significantly reduced in the area outside the final crack exclusion zone, and the thermal stress coupling effect and potential gradient coupling effect are significantly weakened. That is, the propagation trend caused by initial interface defects is significantly suppressed in the manufacturing and service stages, thereby improving the product quality and yield from the source of production.

[0209] Although experimental studies have shown that trapezoidal glass via TGV structures exhibit better process robustness and thermomechanical reliability under high-temperature conditions through geometric configuration reconstruction, a systematic mechanical numerical model was developed to explain the differences in failure behavior of different glass via TGV configurations. Furthermore, by utilizing the quantitative mapping law between via morphology parameters (taper angle, inner-outer diameter ratio) and failure modes, a morphology optimization design paradigm applicable to mechanically driven micro-interconnect structures such as glass via TGV was developed.

[0210] The system of this invention can be widely used in the analysis of heterogeneous structures and the analysis of the strength, stability and vibration characteristics of interconnect structures in the design of heterogeneous structures in mechanical engineering, aerospace and semiconductor electronic device design, and has important engineering application value.

[0211] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. An adaptive analysis method for glass through-hole defect exclusion zone, characterized in that, include: Obtain the process parameters of the glass through-hole TGV structure, determine the material properties of the glass through-hole TGV structure, and construct the input variable set. The Taguchi orthogonal experimental method was used to determine the different levels of each process parameter factor in the input variable set, and the Taguchi OA table was constructed to obtain the glass through-hole TGV structure configuration. Based on the TaguchiOA table, the thermal stress simulation of the glass through-hole TGV structure configuration was carried out using numerical analysis to calculate the maximum principal stress response of the glass through-hole TGV structure. Based on the maximum principal stress response data of the glass through-hole TGV structure, the contribution rate of each process parameter factor in the input variable set was calculated using the analysis of variance method. Based on the contribution rate of each process parameter, the optimal value of the maximum principal stress response is selected by the main effect analysis method, and the optimal configuration of the corresponding glass through-hole TGV structure is obtained. Based on the optimal configuration of the glass through-hole TGV structure, the morphological parameters of the pre-crack in the glass through-hole are determined, the load type of the optimal configuration of the glass through-hole TGV structure is obtained, and the interface fracture behavior parameters are determined. Based on the interface fracture behavior parameters, the fracture mechanical properties of the crack tip at each part of the glass through-hole TGV structure are calculated using the contour integral method, and the potential gradient value corresponding to different crack states is calculated using the thermoelectric coupling method. Based on the fracture mechanics parameters of the crack tip at each location and the potential gradient values ​​corresponding to different crack states, the defect exclusion zone range of the glass through-hole TGV structure is obtained, and the defect exclusion zone range is adaptively adjusted according to the glass through-hole TGV structure configuration.

2. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 1, characterized in that, Factors that determine the process parameters of a glass through-hole TGV structure include the external dimensions of the through-holes, the morphological dimensions between the through-holes, and environmental factors during manufacturing and service. Material properties include elastic modulus, Poisson's ratio, plastic stress-strain data, and temperature-dependent electrical conductivity.

3. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 1, characterized in that, By determining the different levels of each process parameter factor in the input variable set, constructing the TaguchiOA table, and obtaining the glass through-hole TGV structure configuration, including: Based on all process parameter factors whose upper and lower limits have been defined, set the level of each process parameter factor in the input variable set; Convert the actual physical quantities of each process parameter factor level into standardized codes; Based on the standardized coding of each process parameter factor and its level in the input variable set, the Taguchi OA table is constructed using the Taguchi orthogonal experimental method. Based on different combinations of process parameter factors in the TaguchiOA table, various glass through-hole TGV structural configurations are generated, including trapezoidal, annular, hollow trapezoidal, and cylindrical configurations.

4. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 3, characterized in that, At taper angle At this time, a trapezoidal glass through-hole TGV structure configuration is generated; In outer diameter ratio At this time, an annular glass through-hole TGV structure configuration is generated; At taper angle And the ratio of inner to outer diameter At this time, a hollow trapezoidal glass through-hole TGV structure configuration is generated; At taper angle And the ratio of inner to outer diameter At this time, a cylindrical glass through-hole TGV structure configuration is generated.

5. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 1, characterized in that, Thermo-stress simulation of the glass-through-hole TGV structure was performed using numerical analysis to calculate the maximum principal stress response of the glass-through-hole TGV structure, including: Numerical analysis and simulation were performed using the ABAQUS / Standard finite element solver to construct a simulation model assembly of the glass through-hole TGV structure. An analysis step was established to calculate the output response values ​​under different glass through-hole TGV structural configurations, and the maximum principal stress response corresponding to all glass through-hole TGV configurations was obtained.

6. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 5, characterized in that, Calculate the output response values ​​under different glass through-hole TGV structural configurations, including: Solve for the displacement field of the nodes in the simulation model assembly; The strain of the glass through-hole TGV configuration was calculated by the gradient of the displacement field at the nodes. By utilizing the constitutive relations of the material, the strain of the glass through-hole TGV configuration is updated to the stress of the glass through-hole TGV configuration; The maximum principal stress response of the glass through-hole TGV configuration is calculated based on the updated stress of the glass through-hole TGV configuration.

7. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 1, characterized in that, The contribution rate of each process parameter factor in the input variable set was calculated using analysis of variance, including: Calculate the total sum of squares and the sum of squares of each process parameter factor; Calculate the sum of squared deviations of the average values ​​corresponding to different levels of each process parameter factor; Calculate the sum of squared errors to obtain the deviation between the total sum of squares and the sum of squared deviations; Calculate the mean square and error mean square of each process parameter factor; Calculate the contribution rate of each process parameter factor to obtain the ANOVA table.

8. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 1, characterized in that, The optimal value of the maximum principal stress response was selected by using the main effect analysis method. The average value of the maximum principal stress response at all levels of each process parameter factor was calculated by selecting the minimum signal-to-noise ratio among four signal-to-noise ratios, including the minimum, maximum, and two minimum ratios. All process parameter factors are sequentially screened from highest to lowest contribution rate, and the optimal combination of process parameter factors corresponding to the optimal value of the maximum principal stress response is selected to obtain the optimal configuration of the glass through-hole TGV structure.

9. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 1, characterized in that, The morphological parameters of the pre-existing cracks in the glass through-hole were determined, the load type of the optimal configuration of the glass through-hole TGV structure was obtained, and the interface fracture behavior parameters were determined, including: Determine the morphological parameters of the glass through-hole, including the length, location, and orientation of the pre-fabricated single crack; A multi-crack model was set up based on the single crack morphology, and load types including thermal cycling field and thermoelectric coupling field were applied to determine the behavioral parameters of single crack parameters, multi-crack mode and thermoelectric coupling load interface fracture.

10. The adaptive analysis method for glass through-hole defect exclusion zone according to claim 1, characterized in that, Fracture mechanical properties at crack tips in various locations of a glass-through-hole TGV structure were calculated using the contour integral method. The potential gradient values ​​corresponding to different crack states were calculated using the thermoelectric coupling method, including: Set the pre-existing crack parameters, including length, location, orientation, and number, and perform J-integral calculation: in, It is a closed crack tip profile. This refers to the profile of the closed crack tip that spans from the bottom to the top crack surface. Represents outline Enclosed area The outer normal vector, Represents elastic strain energy density. For unit tensors, Indicates stress, For equivalent displacement, It is a unit vector on the contour, traction force. ; The potential gradient values ​​corresponding to different crack states were calculated using the thermoelectric coupling method.

Images