3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization

Abstract

The invention relates to the technical field of integrated circuit packaging, and discloses a 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization, and the method comprises the steps: firstly, employing a Taguchi method in combination with finite element analysis to determine a group of optimal structure parameters; then based on the structure, multiple sets of process parameter samples are generated by adopting an optimal Latin hypercube sampling method, and a data set containing process parameters and quality indexes is established through finite element simulation; then, objective weights of all the quality indexes are determined through a CRITIC weight method, and machine learning agent models such as a support vector machine (SVM) are constructed for fitting and screening; and finally, in combination with the objective weight, performing global optimization on the optimal agent model by adopting a multi-objective genetic algorithm (MOGA), and bringing an optimization result back to the finite element model for closed-loop verification. According to the method, iterative finite element simulation is replaced by constructing the machine learning agent model, and global optimization is carried out in combination with the multi-target intelligent algorithm, so that efficient prediction of the optimal process parameter combination is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of integrated circuit packaging technology, in particular to a 3D-IC packaging injection reliability prediction method based on SVM-MOGA collaborative optimization. BACKGROUND

[0002] Three-dimensional integrated circuit packaging is a leading technology for realizing high-density and high-performance chip integration. In its manufacturing process, injection molding is a key process for encapsulating chips and their interconnection structures with epoxy molding compound. This process aims to provide physical protection and electrical insulation for internal precision components, and the molding quality directly determines the long-term working reliability and service life of the final packaged device.

[0003] In the prior art, the evaluation of packaging injection molding quality mainly relies on experimental measurement and numerical simulation. In terms of experimental measurement, optical methods such as thermal shadow moire are used to physically detect the warping deformation of the package. In terms of numerical simulation, the design of experiments and finite element analysis are usually combined to predict the influence of different structures or process parameters on the molding results, and preliminary optimization design is carried out based on this.

[0004] Due to the nonlinear coupling between packaging injection molding quality, packaging structure, material properties, and multi-stage process parameters, the existing technology has obvious shortcomings: on the one hand, physical testing methods such as thermal shadow moire have limited accuracy when evaluating micro-scale warping, and the testing period is long, and the result interpretation depends on personnel experience; on the other hand, relying solely on the combination of design of experiments and finite element analysis for comprehensive optimization will result in unaffordable computational cost due to high parameter dimension and large number of combinations, and the optimization process is often insufficient. The direct consequence of these shortcomings is that it is difficult to efficiently and accurately obtain the globally optimal process parameter combination, making it difficult to control the residual stress and warping deformation within the final product, increasing the risk of device failure due to delamination or cracking during long-term use. SUMMARY

[0005] In view of the shortcomings of the prior art, the present application provides a 3D-IC packaging injection reliability prediction method based on SVM-MOGA collaborative optimization, aiming to solve the problem that traditional optimization methods cannot obtain global optimal solution due to high computational cost and long optimization period in the process of optimizing 3D-IC packaging injection process parameters.

[0006] To achieve the above purpose, the present application realizes the following technical solutions: The present application provides a 3D-IC packaging injection reliability prediction method based on support vector machine SVM and multi-objective genetic algorithm MOGA collaborative optimization, comprising the following steps: First stage: structure parameter optimization This stage is to determine a set of optimal basic parameter combinations from a number of structure and material factors.

[0007] Firstly, a number of core influencing factors affecting the quality of 3D-IC packaging injection molding are determined, which are: gate location, segmented injection parameter setting, substrate material type, epoxy molding material, chip thickness, mold cover thickness, copper pillar height 1, copper pillar height 2, and substrate thickness.

[0008] Subsequently, the core influencing factors are efficiently evaluated by using the Taguchi orthogonal test method. The method sets multiple parameter levels for each factor and generates test combinations according to the orthogonal table, and evaluates the influence of multiple factors through a limited number of tests. For each test combination, a finite element model is established and numerical simulation is performed to obtain the numerical values of three quality evaluation indicators: chip warpage, holding pressure, and volume shrinkage. By performing main effect analysis on the simulation results, the influence degree of each factor on the injection molding quality is quantified, thereby determining a set of structure parameter combinations with optimal comprehensive performance.

[0009] Second stage: Process parameter optimization and verification This stage is to accurately optimize the process parameters based on the optimal structure determined.

[0010] Firstly, the finite element model is reconstructed based on the optimal structure parameter combination, and the optimal Latin hypercube sampling method is used to generate multiple simulation cases within the preset ranges of multiple key process parameters.

[0011] The key process parameters are: melt temperature, mold temperature, injection time, injection pressure, curing time, and curing pressure. The preset ranges are: the range of melt temperature is 170-180°C; the range of mold temperature is 170-180°C; the range of injection time is 5-10s; the range of injection pressure is 5-10MPa; the range of curing time is 60-120s; the range of curing pressure is 5-10MPa. By performing finite element simulation on the multiple simulation cases, the numerical results of the quality evaluation indicators corresponding to each case are obtained, forming a data set.

[0012] Next, to objectively quantify the relative importance of multiple quality evaluation indicators, the CRITIC weight method is used to determine the weights of each indicator based on the data set. The method completely assigns weights based on the statistical characteristics of the data itself, and determines the information quantity by comprehensively evaluating the comparative intensity and conflict of each indicator. The comparative intensity is measured by the standard deviation of the indicator in the data set, reflecting the fluctuation range of the indicator.

[0013] The conflict is measured by the correlation coefficient between the indicators, reflecting the degree of overlap of information. The CRITIC method assigns higher weights to indicators with larger standard deviations and lower correlations with other indicators, thereby obtaining a set of weight coefficients that objectively reflect the relative importance of each quality indicator.

[0014] Then, based on the data set, a plurality of machine learning agent models are constructed to replace the high computational cost finite element simulation. The machine learning agent model includes a support vector machine (SVM) model, a Bayesian network regression model and an artificial neural network model. By comparing the prediction accuracy indicators such as the determination coefficient R2 of each model on the test set, an optimal fitting model is determined.

[0015] Finally, the optimal fitting model is used to construct a comprehensive objective function in combination with the objective weight. A plurality of multi-objective optimization algorithms including multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization algorithm are used to optimize the key process parameters, and a recommended optimal process parameter combination is obtained. The recommended optimal process parameter combination is substituted into the finite element model for simulation verification.

[0016] By comparing the relative error between the simulation true value and the model predicted value of the recommended parameters of different fitting-optimization model combinations, an optimal fitting-optimization model combination with the smallest error and the most stable performance is determined according to the verification result.

[0017] The present application provides a 3D-IC packaging injection reliability prediction method based on SVM-MOGA collaborative optimization. It has the following beneficial effects: 1. The present application converts the high-time-consuming iterative finite element simulation in the process parameter optimization process into low-time-consuming fast model prediction by constructing a support vector machine (SVM) machine learning agent model. This method uses optimal Latin hypercube sampling to generate training data once, and the subsequent optimization process is completely based on the highly efficient agent model, which helps to improve the overall efficiency of obtaining the optimal process parameter combination, thereby reducing the research and development cost.

[0018] 2. The present application uses multi-objective genetic algorithm (MOGA) to perform global optimization on the entire process parameter space, effectively avoiding the limitation of traditional optimization methods that are prone to local optimal solution. At the same time, the CRITIC weight method is introduced to objectively assign weights to multiple quality indicators based on the statistical characteristics of the data, eliminating the subjectivity of human setting, making the selection of optimization results more scientific, and the final parameter combination more balanced between multiple quality targets.

[0019] 3, The application establishes a closed-loop verification mechanism by bringing back the optimal parameter combination recommended by the optimization algorithm to the finite element model for final simulation verification. This step directly checks the final effectiveness of the combination of the surrogate model and the optimization algorithm, ensuring that the output process parameters are not only optimal in model prediction, but also have high credibility at the physical simulation level, providing reliable process guidance for actual production and effectively avoiding product failure risks. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a method flowchart of the application; Figure 2 is a multi-objective genetic algorithm (MOGA) flowchart in the application; Figure 3 is a simulation verification flowchart of the optimal process parameters. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the application will be described below with reference to the drawings in the application specification. Obviously, the described embodiments are only part of the embodiments of the application, not all. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the application.

[0022] Please refer to the drawings in the application specification Figure 1 - the drawings in the application specification Figure 3 The embodiment of the application provides a 3D-IC packaging injection reliability prediction method based on SVM-MOGA collaborative optimization, which comprises the following steps: S1: Selecting a 3D stacked chip package containing through silicon vias (TSV) as the research object, and determining a plurality of key structure and material parameters affecting the quality in the injection molding process as the core influencing factors; S2: Preliminarily dividing the parameter levels of the key influencing factors by using the Taguchi orthogonal test method, combining a finite element analysis (FEA) platform for simulation, and taking the chip warping degree, holding pressure and volume shrinkage rate as the quality evaluation indexes to determine the optimal structure parameter combination of the injection molding; S3: Based on the optimal structure parameter combination determined in S2, reconstructing the finite element model to perform multi-objective optimization on the injection molding process parameters. The optimal Latin hypercube sampling (OLHS) method is used to divide the simulation cases in the setting range of the six key process parameters, i.e. melt temperature, mold temperature, injection time, injection pressure, solidification time and solidification pressure; S4: Finite element simulation is performed on each set of process parameter combinations generated in S3 to obtain numerical results of three key quality indicators, i.e., chip warpage, holding pressure and volume shrinkage, forming a data set. At the same time, the CRITIC weight method is used to objectively assign weights to quantify the comprehensive influence of the three quality indicators on the molding defects, which serves as the basis for the target function of subsequent multi-objective optimization; S5: Based on the data set obtained in S4, three machine learning proxy models, i.e., support vector machine (SVM), Bayesian network regression (BNR) and artificial neural network (ANN), are constructed for data fitting. By comparing the prediction accuracy, generalization ability and stability on the test set, the fitting model with the best effect is obtained. S6: Multi-objective particle swarm optimization algorithm (MOPSO) and multi-objective genetic algorithm (MOGA) are combined with the three machine learning models in S5 to perform multi-objective optimization on the selected key process parameters. The optimal parameters recommended by each "fitting-optimization" combination are brought back to the finite element model for closed-loop simulation verification. By comparing the relative error between the predicted value and the real value of each combination, the optimal fitting-optimization model cluster with the highest precision and best stability is finally determined.

[0023] The steps of the method of the present application will be described in detail below.

[0024] In one specific embodiment of the present application, S1 determines the research object and identifies the key influencing factors. In this embodiment, a 3D stacked chip package with through silicon via (TSV) is used as the research object.

[0025] Through systematic analysis, nine key factors that have a significant impact on the final packaging quality in the injection molding process are determined. The selection of these factors is based on the understanding of thermal-mechanical stress, material flow behavior and curing kinetics in the injection molding process, ensuring that the main variables affecting packaging reliability are covered.

[0026] The above nine key influencing factors are: (A) gate location, (B) segmented injection parameter setting, (C) substrate material type, (D) epoxy molding compound (EMC) material, (E) chip thickness, (F) mold cap thickness, (G) copper pillar height 1, (H) copper pillar height 2 and (I) substrate thickness.

[0027] S2 step determines the optimal structure parameter combination through experimental design and finite element analysis to establish the baseline for subsequent process optimization. S2 step can be divided into the following sub-steps: S2.1: Experimental design The Taguchi Method is used to divide parameter levels for the 9 key influencing factors determined in S1. The reason for using the Taguchi Method is that this method can efficiently explore a wide parameter space with the least number of experiments, and is very suitable for preliminary factor screening in complex manufacturing processes. In this embodiment, different levels are set for each factor based on actual production sample data, and a Taguchi orthogonal table is designed based on these levels.

[0028] The specific control factors and levels are shown in Table 1 below.

[0029] Table 1 Control factors and levels of mixed Taguchi orthogonal experiment

[0030] Note: In Table 1, factor (C) "substrate material type" is only set to two levels, so the corresponding positions of the 3rd and 4th levels are filled with " / " symbols, indicating that these two levels are not applicable to factor (C).

[0031] S2.2: Quality index definition and simulation Chip warpage, holding pressure and volume shrinkage are selected as quality evaluation indexes. All working conditions of the Taguchi orthogonal experiment are simulated using the Moldex3D finite element analysis software, and the main effect analysis is performed using the Minitab software.

[0032] For simulation and main effect analysis using finite element analysis software (such as Moldex3D) and data analysis software (such as Minitab), a person skilled in the art can implement it according to the conventional operation, and the specific method of simulation and main effect analysis is a known technology in the art, which will not be described here.

[0033] S2.3: Main effect analysis and single-index optimal solution The results of the main effect analysis reveal the sensitivity of different factors to each quality index: For chip warpage: the analysis shows that chip warpage is most sensitive to factors D (epoxy molding compound (EMC) material) and E (chip thickness), indicating that these two factors are the key driving factors leading to warpage changes.

[0034] The relative influence degree of the 9 factors on warpage is ranked as: D > E > C > G > I > H > F > B > A. Based on this ranking, the parameter combination that minimizes warpage is A1B3C2D3E1F1G4H3I4.

[0035] For the holding pressure: the analysis shows that the holding pressure is most sensitive to factor D (epoxy molding compound (EMC) material), followed by factor F (mold cover thickness) and B (segmented injection molding parameter setting), indicating that the influence of these three factors is relatively significant. The relative influence degree of the 9 factors on the holding pressure is ranked as: D > F > B > H > C > I > E > G > A. According to the analysis, the parameter combination that can minimize the holding pressure is A2B3C2D2E1F4G2H4I1.

[0036] For the volume shrinkage: the analysis shows that the volume shrinkage is most sensitive to factor D (epoxy molding compound (EMC) material), followed by factor I (substrate thickness) and G (copper pillar height 1).

[0037] The relative influence degree of the 9 factors on the volume shrinkage is ranked as: D > I > G > C > E > H > F > B > A. Similarly, the parameter combination that can minimize the volume shrinkage is A2B2C3D3E4F1G2H3I1.

[0038] S2.4: Determine the comprehensive optimal structure baseline S2.3 The analysis results show that the optimal parameter combination of each quality indicator is different, and there is an optimization conflict between indicators. For example, the optimal EMC material required to minimize the chip warpage (D3) is not the same as the optimal EMC material required to minimize the holding pressure (D2). The purpose of step S2.4 is to determine a comprehensive optimal structure baseline under such conflicts, which will be used for subsequent process parameter optimization. When considering three quality indicators simultaneously, the comprehensive optimal material-geometric parameter combination determined in this embodiment is A2B3C2D3E1F1G4H3I1.

[0039] This embodiment realizes the comprehensive optimization of structure and material parameters under multi-objective conflict by using Taguchi orthogonal test method to systematically screen multiple structure and material factors affecting packaging quality, and combining finite element analysis for main effect analysis, and determines an optimal physical structure baseline. This provides a fixed and reliable starting point for subsequent process parameter optimization, and decomposes a high-dimensional mixed optimization problem into two related but independent low-dimensional optimization stages.

[0040] Step S3 is based on the comprehensive optimal structure baseline determined in step S2.4, reconstructs the finite element model and performs multi-objective optimization design on the injection molding process parameters. The goal of step S3 is to construct a high-quality data set for training and validating the surrogate model. Step S3 achieves this goal by systematically sampling key process parameters on the fixed optimal structure.

[0041] Step S3 can be divided into the following sub-steps: S3.1: Reconstruct the finite element model based on the optimal structure baseline According to the comprehensive optimal material-geometric parameter combination (A2B3C2D3E1F1G4H3I1) determined in S2.4, the finite element analysis model is updated and reconstructed.

[0042] The above steps are key links to realize the two-stage decoupling method from structure to process. By fixing the physical structure, the focus of the optimization problem is completely transferred to the subsequent process parameters.

[0043] S3.2: Determine the process parameters and design space Six key process parameters that directly affect the packaging quality in the injection molding process are determined, which are: melt temperature, mold temperature, injection time, injection pressure, solidification time and solidification pressure. According to production experience and material properties, reasonable value ranges are set for these six process parameters to form a multi-dimensional design space.

[0044] The specific process parameters and their value ranges are shown in Table 2.

[0045] Table 2 Value range of process parameters

[0046] S3.3: Generate test groups using optimal Latin hypercube sampling To ensure that the sampling data in the multi-dimensional design space defined in S2.2 has good uniformity and space filling, thereby improving the accuracy of the subsequent construction of the proxy model and reducing the model error, the optimal Latin hypercube sampling (OLHS) method is used in this embodiment.

[0047] The specific mathematical principles and implementation algorithms of the optimal Latin hypercube sampling method belong to the known techniques in the art, and will not be described here.

[0048] Through the OLHS method, 80 groups of simulation cases are generated within the set range of the six key process parameters shown in Table 2. Each simulation case represents a specific process parameter combination, which will be used for finite element simulation in S4 to obtain corresponding quality index data.

[0049] This embodiment generates 80 groups of evenly distributed test data points within the determined process parameter design space by using the optimal Latin hypercube sampling method. This provides high-quality input for the subsequent establishment of a comprehensive process parameter to quality index database through finite element simulation (S4), and is a necessary basis for the subsequent construction of a high-precision machine learning proxy model (S5) and multi-objective optimization (S6).

[0050] S4 Step S3 generated 80 groups of simulation cases are simulated by finite element method, and the simulation results are processed to generate a database and objective weights for subsequent steps.

[0051] S4 Step S4 can be divided into the following sub-steps: S4.1: Perform finite element simulation and generate quality index database S3.3 generated by the optimal Latin hypercube sampling 80 groups of process parameter combinations are input into the finite element model reconstructed in S3.1 one by one. Use Moldex3D software to perform complete injection molding process simulation for each parameter combination.

[0052] After each simulation is completed, the corresponding values of the three quality evaluation indexes: chip warpage, holding pressure and volume shrinkage are extracted and recorded.

[0053] After repeating the simulation 80 times, a "process parameter-quality index" database containing 80 samples is formed. Each record in the database includes a set of 6 process parameters (P1 to P6) as input, and a set of 3 quality indexes (chip warpage, holding pressure, volume shrinkage) as output. This database not only serves as the data basis for building machine learning agent models in subsequent S5 steps, but more importantly, it constitutes a digital characterization of the process physics under the specific structure.

[0054] In this embodiment, the data in S4.1 database is substituted into the above formula to calculate the objective weight of each quality index, and the specific results are shown in Table 3.

[0055] Table 3 CRITIC weight calculation results

[0056] As can be seen from Table 3, the injection pressure obtains the highest weight (43%), indicating that in this optimization problem, controlling the injection pressure is the primary goal. The weights of volume shrinkage and chip warpage are 32% and 25% respectively. These objectively calculated weights will be used to build a comprehensive objective function in S6 step to guide the optimization direction of the optimization algorithm.

[0057] S4.2: Determine multi-objective objective weight using CRITIC method When performing multi-objective optimization, the relative importance of each optimization objective (i.e. quality index) will directly affect the tendency of the final optimization result. To avoid the subjectivity and uncertainty brought by manually setting weights in traditional optimization methods (such as analytic hierarchy process AHP), the invention introduces the criteria intercorrelation evaluation method (CRITIC) based on standard importance, which is used to objectively calculate the weight of each quality index.

[0058] The correlation evaluation method among criteria determines weights based on the inherent characteristics of the data itself. The core idea is that the objective weight of an indicator is determined by two factors: the volatility of the indicator's own data distribution (reflected in the strength of the comparison) and the conflict between the indicator and other indicators (reflected in the correlation).

[0059] Contrast strength: Measured by the standard deviation of the indicator. The larger the standard deviation of an indicator across 80 samples, the more significant the differences in that indicator can be caused by different combinations of process parameters. Such indicators provide more valuable distinguishing information and therefore should have a higher weight.

[0060] Conflictability: Measured by the correlation coefficient between indicators. The lower the correlation between an indicator and other indicators (the greater the conflict), the more unique the evaluation information reflected by that indicator is, and the less it can be replaced by other indicators. Therefore, it should also have a higher weight.

[0061] In this embodiment, the calculation process of the correlation evaluation method between criteria is as follows: First, calculate the total amount of information contained in the j-th quality indicator. The calculation formula is: ; In the formula, Let be the total information content of the j-th quality indicator; For the first The standard deviation of each quality indicator in 80 sets of sample data generated by S4.1 is used to quantify the comparative strength of the indicators; For the first The and the first The Pearson correlation coefficient between two quality indicators is used to quantify the degree of linear correlation between the two indicators. This represents the conflict between the two indicators; This represents the total number of quality indicators.

[0062] Then, calculate the first based on the comprehensive information content. The final objective weight of each quality indicator The calculation formula is: ; In the formula, For the first The final objective weight of each quality indicator; The first one calculated according to the aforementioned formula The total amount of information contained in each indicator; This represents the sum of all quality indicators' comprehensive information content, used to normalize the weights of each indicator.

[0063] The calculations in step S4.2 yield the objective weight values ​​for the three quality indicators: chip warpage, holding pressure, and volume shrinkage rate. These objective weight values ​​will be used in the multi-objective optimization algorithm in step S6 to construct a comprehensive evaluation function (or fitness function), thereby scientifically and balancedly guiding the optimization algorithm to find the global optimum among multiple conflicting objectives.

[0064] This implementation method constructs a comprehensive mapping database between process parameters and quality indicators by performing finite element simulations in batches.

[0065] Furthermore, this implementation method employs the CRITIC method, which objectively and quantitatively calculates the relative importance weights of each quality indicator based entirely on the simulation data itself. This approach replaces subjective weighting that relies on expert experience with data-driven objective weighting, providing a mathematical basis for the scientific rigor, balance, and reliability of the results in subsequent multi-objective optimization.

[0066] Step S5 builds upon the process parameter and quality index database established in S4 to construct and validate a high-precision machine learning surrogate model. The purpose of constructing the surrogate model is to replace the computationally expensive and time-consuming finite element analysis simulation process with a computationally low-cost mathematical model, thereby enabling large-scale multi-objective optimization in the subsequent S6 step.

[0067] Step S5 can be divided into the following sub-steps: S5.1: Proxy Model Selection Considering the limited number of training samples (80 groups) and the complex nonlinear relationship between process parameters and quality indicators, this invention selects three mainstream machine learning models—Support Vector Machine (SVM), Bayesian Network Regression (BNR), and Artificial Neural Network (ANN)—as candidate proxy models for comprehensive performance evaluation.

[0068] The evaluation process is as follows: The database generated by S4.1 is divided into training and testing sets proportionally. The three models are trained and tested separately, and the evaluation is performed using the coefficient of determination. As an evaluation indicator.

[0069] The specific performance comparison data is shown in Table 4.

[0070] Table 4 Performance Comparison of Three Agency Models

[0071] Table 4 shows that the three models perform well on the training set. The values ​​are all close to 1, indicating that their fitting ability is relatively strong. However, on the test set, which better reflects the model's generalization ability, their performance shows significant differences: Test set of Artificial Neural Network (ANN) models The value dropped significantly, reaching a low of 0.913, indicating that the model exhibits some overfitting and its prediction results have relatively limited reliability.

[0072] The Bayesian Network Regression (BNR) model performed well on its test set. The value is comparable to that of the SVM model.

[0073] The test set of the Support Vector Machine (SVM) model on all three quality metrics The values ​​remained stable between 0.985 and 0.988, demonstrating extremely high prediction accuracy and stability.

[0074] In summary, the SVM model exhibits the most stable and balanced performance across the three metrics, demonstrating stronger universality and reliability in multi-objective optimization scenarios. Therefore, this implementation method ultimately selects the Support Vector Machine (SVM) model as the surrogate model for subsequent process optimization.

[0075] S5.2: Construction of Support Vector Machine (SVM) Model When dealing with regression problems, the core idea of ​​the Support Vector Machine (SVM) model is to find an optimal hyperplane in a high-dimensional feature space that minimizes the total deviation of all sample points from the hyperplane. For the nonlinear problem in this embodiment, SVM introduces a kernel function (such as a Gaussian kernel) to map the original 6-dimensional process parameter space to a higher-dimensional feature space, thereby transforming the nonlinear regression problem into a linear regression problem for solution. This method exhibits good generalization ability and adaptability when handling small-sample, high-dimensional, and nonlinear problems.

[0076] S5.3: Model Training and Validation Using the database of 80 sets of process parameters and quality indicators generated in S4.1, the three candidate models selected in S5.1 were trained and validated respectively. To evaluate the prediction accuracy of the constructed models, this embodiment uses the coefficient of determination. The coefficient of determination is calculated using the following formula: ; In the formula, The coefficient of determination; For the first The true finite element simulation values ​​of each sample point; For the Kriging model to the first Predicted values ​​for each sample point; The average of the true values ​​for all sample points; This represents the total number of sample points used for validation.

[0077] As shown in Table 4, after training and testing, the final selected Support Vector Machine (SVM) model achieved the following test set determination coefficients on the three indicators: chip warpage, holding pressure, and volume shrinkage rate. The values respectively reached 0.985, 0.988 and 0.986. These values are all very close to 1, proving that the SVM model has very high prediction accuracy and can reliably replace finite element simulation.

[0078] The present embodiment successfully converts the complex and time-consuming physical simulation process into a mathematical function of instantaneous calculation by comparing a plurality of candidate models and finally constructing and verifying a high-precision support vector machine SVM model. This method not only models the relationship between process parameters and quality indicators efficiently, but also provides a technical prerequisite for subsequent S6 steps to use intelligent optimization algorithms to quickly and large-scale optimize in a wide process parameter space.

[0079] Step S6: Process parameter optimization and verification based on multi-objective optimization Step S6 is the core execution and verification stage of the present application. This step aims to determine the optimal proxy model based on the support vector machine model determined in S5, and combine the objective weight calculated in S4 to perform global optimization through advanced multi-objective intelligent optimization algorithms. Further, this step determines an optimal process parameter combination with significant optimization effect and high engineering reliability through a complete closed-loop process including optimization, verification and comparison. Step S6 can be divided into the following sub-steps: S6.1: Parallel optimization of multi-objective optimization algorithm To systematically explore the design space and obtain the optimal solution, the present embodiment uses two technically mature multi-objective optimization algorithms in parallel: multi-objective particle swarm optimization algorithm MOPSO and multi-objective genetic algorithm MOGA.

[0080] Both algorithms use the comprehensive objective function embedded with the objective weight as the optimization guide, and perform iterative search within the process parameter boundary defined in S3.2. To fully prove the advancement of the technical path of the present application, not only the optimal support vector machine SVM model is optimized, but also the same optimization calculation is performed on the Bayesian network regression BNR model and artificial neural network ANN model as a reference.

[0081] Table 5 details the best process parameter combinations recommended by the three proxy models driven by the two optimization algorithms.

[0082] Table 5 MOPSO and MOGA recommended process parameters

[0083] The results in Table 5 show that the mathematical properties of the surrogate model and the search mechanism of the optimization algorithm together determine the final convergence point. Therefore, obtaining the recommended parameters is only an intermediate step, and must be verified by subsequent finite element simulation to objectively evaluate which set of parameters can bring the best physical improvement effect, and determine which technical combination has the prediction result closest to the real physical situation.

[0084] S6.2: Finite element verification and effect evaluation of optimization scheme To objectively evaluate the actual physical effect of each set of recommended parameters in S6.1, this step will substitute each set of parameters in Table 5 into the high-precision finite element analysis model established in S3.1 for simulation calculation to obtain the real values of each quality index after optimization.

[0085] Table 6 and Table 7 respectively show the simulation result comparison and improvement rate of each quality index before and after optimization using MOPSO and MOGA algorithms.

[0086] Table 6 Simulation result comparison before and after MOPSO optimization

[0087] Table 7 Simulation result comparison before and after MOGA optimization

[0088] The data analysis of Table 6 and Table 7 reveals the significant difference in optimization robustness of different technical combinations. The support vector machine SVM model shows excellent stability, with the improvement rate of each index remaining at a high and consistent level under both MOPSO and MOGA algorithms, for example, the improvement rate of volume shrinkage is 17.46% under both algorithms.

[0089] In sharp contrast, the optimization effect of the artificial neural network ANN model is strongly dependent on the algorithm and lacks robustness. The chip warpage improvement rate drops from 15.45% under MOPSO to 9.55% under MOGA, and the volume shrinkage improvement rate also drops significantly from 18.11% to 12.06%. This dramatic fluctuation in performance indicates a high risk of uncertainty in the optimization results in actual industrial applications.

[0090] S6.3: Verification of prediction accuracy and reliability of surrogate model This step aims to verify the prediction reliability of the surrogate model at the optimal parameter point, which is the final standard for measuring the credibility of the entire optimization method. The predicted values given by each surrogate model during optimization are compared with the simulation values obtained by finite element simulation in S6.2, i.e. the real values, and the relative error is calculated. Table 8 and Table 9 respectively show the detailed comparison of the prediction results and simulation results based on the MOPSO and MOGA recommended schemes.

[0091] Table 8 Comparison of prediction results and simulation results based on MOPSO recommended scheme

[0092] Table 9 Comparison of prediction results and simulation results based on MOGA recommended scheme

[0093] As shown in Tables 8 and 9, the relative error data is the key basis for determining the final technical scheme. The combination of support vector machine SVM and multi-objective genetic algorithm MOGA shows a decisive comprehensive advantage in this verification. As shown in Table 9, the prediction error of injection molding pressure under this combination is only 0.02%, which is almost completely consistent with the simulation value; at the same time, the prediction errors of the chip warpage and volume shrinkage are also controlled within 2.14%. This balanced ability to achieve extremely low error on all core indicators is something that other technical combinations cannot achieve.

[0094] As a comparison, although the BNR and ANN models can achieve zero error on some single indicators, they cannot maintain consistent high precision on all indicators. In particular, the ANN model has a volume shrinkage prediction error of up to 18.58% under MOPSO, exposing its prediction ability defects in dealing with complex nonlinear problems, which seriously affects the actual credibility of its optimization results.

[0095] In summary, the S6 step optimizes the process parameters through a rigorous closed-loop process including parallel optimization, effect verification and precision verification. This step not only finds multiple sets of candidate parameters that can significantly improve product quality, but more importantly, through double verification of the optimization effect robustness and model prediction reliability, it is fully supported by data to prove that the technical path of combining support vector machine SVM surrogate model and multi-objective genetic algorithm MOGA has the strongest comprehensive advantage in the technical problems solved by the present application.

Claims

1. A method for predicting the reliability of 3D-IC packaging injection molding based on SVM-MOGA collaborative optimization, characterized in that, Includes the following steps: S1: Identify several key factors affecting the injection molding quality of 3D-IC packaging; S2: Based on the aforementioned core influencing factors, the parameter levels are divided using experimental design methods, and combined with finite element analysis, the optimal combination of structural parameters for injection molding is determined; S3: Based on the optimal combination of structural parameters, reconstruct the finite element model and use the experimental design sampling method to generate multiple sets of simulation cases within the preset range of multiple key process parameters; S4: Perform finite element simulation on the multiple sets of simulation cases, obtain the numerical results of the quality evaluation indicators corresponding to each set of simulation cases, form a dataset, and use an objective weight allocation method to determine the weight of each quality evaluation indicator based on the dataset. S5: Based on the dataset, construct various machine learning proxy models, including the support vector machine (SVM) model, and determine the optimal fitting model by comparing the prediction accuracy of each machine learning proxy model. S6: Using the optimal fitting model and the objective weights, construct a comprehensive objective function. Use multiple multi-objective optimization algorithms, including the multi-objective genetic algorithm MOGA, to optimize the key process parameters, obtain the recommended optimal process parameter combination, and input the recommended optimal process parameter combination into the finite element model for simulation verification. Determine the optimal fitting-optimization model combination based on the verification results.

2. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 1, characterized in that, In step S2, the experimental design method is the Taguchi orthogonal experimental design method; the optimal combination of structural parameters is based on chip warpage, holding pressure, and volume shrinkage rate as quality evaluation indicators.

3. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 2, characterized in that, In step S2, the optimal combination of structural parameters for injection molding is specifically as follows: The gate location is a four-vertical gate, the segmented injection molding parameters are set to 50%~60%, the substrate material type parameter is 5.2ppm / k, the epoxy molding compound material parameter is 50ppm / k, the chip thickness is 0.140mm, the mold cover thickness is 0.700mm, the copper pillar height 1 is 0.060mm, the copper pillar height 2 is 0.026mm, and the substrate thickness is 0.185mm.

4. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 1, characterized in that, In step S1, the core influencing factors identified are: The settings include: gate location, segmented injection molding parameters, substrate material type, epoxy molding compound material, chip thickness, mold cap thickness, copper pillar height 1, copper pillar height 2, and substrate thickness.

5. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 1, characterized in that, In step S3, the experimental design sampling method is the optimal Latin hypercube sampling method; the key process parameters are: melt temperature, mold temperature, injection time, injection pressure, curing time, and curing pressure.

6. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 5, characterized in that, The preset range of the key process parameters is as follows: The melt temperature range is 170-180°C; the mold temperature range is 170-180°C; the injection time range is 5-10s; the injection pressure range is 5-10MPa; the curing time range is 60-120s; and the curing pressure range is 5-10MPa.

7. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 2, characterized in that, In step S4, the objective weight allocation method is the CRITIC weighting method; the weights of the determined quality evaluation indicators are: chip warpage weight is 25%, holding pressure weight is 43%, and volume shrinkage rate weight is 32%.

8. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 1, characterized in that, In step S5, the various machine learning agent models also include Bayesian network regression models and artificial neural network models.

9. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 1, characterized in that, In step S6, the various multi-objective optimization algorithms also include a multi-objective particle swarm optimization algorithm.

10. The 3D-IC packaging injection molding reliability prediction method based on SVM-MOGA collaborative optimization according to claim 1, characterized in that, The determination of the optimal fitting-optimization model combination in step S6 specifically includes: Compare the relative errors between the simulated actual values ​​and the model predictions of the optimal process parameter combinations recommended by different fitting-optimization model combinations; The combination of Support Vector Machine (SVM) model and Multi-Objective Genetic Algorithm (MOGA) was determined to be the optimal fitting-optimization model combination.

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