A solder joint reliability analysis optimization method based on Latin hypercube and prediction model

Abstract

This invention discloses a solder joint reliability analysis and optimization method based on Latin hypercube and a prediction model, applicable to semiconductor packaging design. The method uses the thermal fatigue life of the solder joint in a ball grid array (BGA) package as the dependent variable, and the solder ball diameter, pad diameter, and solder joint height as independent variables. Sample points are generated through Latin hypercube sampling, and a three-dimensional finite element model is established. The maximum shear strain range of corner critical solder joints is extracted through thermo-mechanical coupling simulation, and a simulation database is constructed based on the fatigue life model. Multiple candidate prediction models are constructed and evaluated, and a solder joint reliability prediction model is selected. Further Sobol global sensitivity analysis and genetic algorithm optimization are performed to obtain the optimal combination of independent variables, which is then verified by finite element analysis. This invention can reduce the number of simulations and improve the efficiency of solder joint reliability analysis and packaging parameter optimization.

Description

Technical Field

[0001] This invention relates to the field of microelectronic packaging reliability analysis and optimization design technology, and in particular to a solder joint reliability analysis and optimization method for predicting, sensitivity analysis and structural parameter optimization of solder joints under thermal cycling load in ball grid array packaging structures. Background Technology

[0002] In semiconductor packaging devices, solder joints serve both electrical interconnection and mechanical support functions, and their reliability directly affects the service life of the package structure. As electronic products evolve towards miniaturization, high density, and high reliability, the coupling relationships between design parameters such as solder ball diameter, solder ball pitch, substrate thickness, pad diameter, solder joint height, and solder joint material in the package structure are becoming increasingly complex. Under thermal cycling loads, due to the mismatch in thermal expansion coefficients among materials such as the chip, packaging substrate, solder balls, and PCB board, stress concentration easily occurs at the corner solder joints of the package, leading to the initiation and propagation of solder joint cracks, ultimately causing thermal fatigue failure. Therefore, accurate analysis and optimized design of the reliability of semiconductor package solder joints under thermal cycling loads are of great significance.

[0003] Existing methods for analyzing the thermal fatigue life of solder joints typically rely on finite element thermo-mechanical coupling simulations. This involves establishing a package structure model and applying thermal cycling loads to obtain the thermal fatigue life of the solder joints. However, when there are many design variables with a wide range of values, using full factorial design or parametric scanning methods requires extensive finite element simulations, resulting in high computational costs and long cycles, which cannot meet the needs of rapid design and optimization of package structures. Furthermore, traditional optimization processes often rely on engineering experience to select key design variables, making it difficult to quantitatively evaluate the independent impact of each design variable on the thermal fatigue life of the solder joints and the interactions between variables, leading to an unclear optimization direction.

[0004] In terms of optimization algorithms, while commonly used intelligent optimization algorithms such as particle swarm optimization, genetic algorithms, and simulated annealing can be used to optimize package structure parameters, the computational burden becomes excessive if finite element simulation software is called for thermo-mechanical coupling analysis in each iteration. Furthermore, when there is strong nonlinear coupling between solder ball diameter, pad diameter, and solder joint height, relying solely on traditional optimization methods can easily lead to low optimization efficiency, inaccurate identification of key variables, and getting trapped in local optima. Therefore, how to accurately predict the thermal fatigue reliability of solder joints, quantitatively identify key design variables and their interactions, and obtain a more reliable combination of package structure parameters while reducing the number of finite element simulations has become an urgent problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to address the above-mentioned shortcomings by providing a solder joint reliability analysis and optimization method based on Latin hypercube and prediction model. By combining Latin hypercube sampling, thermo-mechanical coupled finite element simulation, prediction model, Sobol global sensitivity analysis and genetic algorithm optimization, this method can reduce the number of finite element simulations while achieving prediction of solder joint thermal fatigue life, identification of key structural parameters and optimization of package structural parameters.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides a solder joint reliability analysis and optimization method based on a Latin hypercube and prediction model, applied to a semiconductor packaging design terminal. The semiconductor packaging design terminal is used to call finite element simulation software and perform thermal cycling reliability analysis on solder joints in a ball grid array (BGA) packaging structure. The method includes the following steps:

[0008] S1. Determine the thermal fatigue life of the solder joint under thermal cycling load as the dependent variable, and determine three continuous structural design variables affecting the thermal fatigue life as independent variables. The three continuous structural design variables are solder ball diameter, solder pad diameter, and solder joint height. The solder ball diameter ranges from 0.50 mm to 0.70 mm, the solder pad diameter ranges from 0.45 mm to 0.65 mm, and the solder joint height ranges from 0.40 mm to 0.60 mm.

[0009] S2 uses the Latin hypercube sampling method to generate a set of sample points within the range of values ​​for the solder ball diameter, solder pad diameter, and solder joint height, and establishes a corresponding three-dimensional finite element model for each sample point in the set of sample points.

[0010] S3 uses a semiconductor packaging design terminal to call finite element simulation software, applies thermal cycling loads to the three-dimensional finite element model corresponding to each sample point and performs thermo-mechanical coupled finite element simulation, extracts the maximum shear strain range of corner dangerous solder joints, and calculates the thermal fatigue life of the solder joint corresponding to each sample point based on the fatigue life model, thereby constructing a solder joint reliability simulation database.

[0011] S4, the solder joint reliability simulation database is divided into a training dataset and a test dataset, and the independent and dependent variables in the training dataset and the test dataset are normalized.

[0012] S5 constructs multiple candidate prediction models based on the normalized training dataset to obtain an approximate mapping relationship between solder ball diameter, solder pad diameter, solder joint height and solder joint thermal fatigue life, and calculates the prediction accuracy of each candidate prediction model based on the normalized test dataset.

[0013] S6, Select a weld joint reliability prediction model from the multiple candidate prediction models based on the prediction accuracy.

[0014] S7. Based on the solder joint reliability prediction model, the Sobol global sensitivity analysis method is used to calculate the first-order Sobol index and the total-order Sobol index corresponding to the solder ball diameter, solder pad diameter and solder joint height, respectively. The importance ranking of the influence of the solder ball diameter, solder pad diameter and solder joint height on the thermal fatigue life of the solder joint is obtained according to the first-order Sobol index and the total-order Sobol index.

[0015] S8. With the goal of maximizing the thermal fatigue life of the solder joint, a genetic algorithm is used based on the solder joint reliability prediction model to iteratively optimize the solder ball diameter, solder pad diameter, and solder joint height to obtain the optimal combination of independent variables.

[0016] S9. Input the optimal combination of independent variables into the finite element simulation software, and perform verification simulation according to the thermal cycle load and thermo-mechanical coupling finite element simulation conditions in step S3 to obtain the verified thermal fatigue life; when the relative error between the predicted thermal fatigue life obtained by the solder joint reliability prediction model and the verified thermal fatigue life meets the preset error threshold, output the packaging design scheme corresponding to the optimal combination of independent variables.

[0017] Furthermore, the three-dimensional finite element model includes a chip, a packaging substrate, a PCB board, solder balls, and solder pads; wherein, the solder balls adopt the Anand viscoplastic constitutive model, and the chip, packaging substrate, and PCB board are respectively assigned elastic modulus, Poisson's ratio, and coefficient of thermal expansion as a function of temperature, and local mesh refinement is performed in the solder joint area.

[0018] Furthermore, the thermal cycling load is a temperature cycling condition ranging from -55 ℃ to 125 ℃. Each temperature cycle includes a heating phase of 15 minutes from -55 ℃ to 125 ℃, a high-temperature holding phase of 10 minutes at 125 ℃, a cooling phase of 15 minutes from 125 ℃ to -55 ℃, and a low-temperature holding phase of 10 minutes at -55 ℃. After completing three full thermal cycle simulations on the three-dimensional finite element model corresponding to each sample point, the maximum shear strain range of the corner critical weld point is extracted. The thermal fatigue life of the solder joint was calculated based on the Coffin-Manson model. .

[0019] Furthermore, the candidate prediction models include the Kriging model, support vector regression model, backpropagation neural network model, and random forest regression model; the prediction accuracy is measured by the coefficient of determination R0. 2 The root mean square error (RMSE) is used for evaluation. The coefficient of determination R is selected. 2The candidate prediction model with the largest and smallest root mean square error (RMSE) is used as the solder joint reliability prediction model; when the coefficient of determination R... 2 The maximum and minimum root mean square error (RMSE) correspond to different candidate prediction models, with the coefficient of determination R... 2 The maximum value is used as the first selection criterion, and the minimum root mean square error (RMSE) is used as the second selection criterion.

[0020] Furthermore, in the Sobol global sensitivity analysis, the individual contributions of solder ball diameter, solder pad diameter, and solder joint height to the thermal fatigue life of the solder joint are determined based on the first-order Sobol index. The total contribution of solder ball diameter, solder pad diameter, solder joint height, and their interaction to the thermal fatigue life of the solder joint is determined based on the total-order Sobol index. The importance of the influence is then ranked from largest to smallest according to the total-order Sobol index.

[0021] Furthermore, the preset error threshold is 5%. When the relative error is greater than 5%, the optimal combination of independent variables and its corresponding verification thermal fatigue life are added as new samples to the weld joint reliability simulation database, and the dataset partitioning, prediction model construction, sensitivity analysis, genetic algorithm optimization and finite element verification steps are re-executed until the relative error is less than or equal to 5%.

[0022] Compared with the prior art, the present invention has at least the following beneficial effects:

[0023] First, this invention uses solder ball diameter, solder pad diameter, and solder joint height as continuous structural design variables, and uses the Latin hypercube sampling method to generate sample points within a limited range of values. This can cover the main design space with a smaller number of samples and reduce the number of finite element simulations.

[0024] Second, this invention extracts the maximum shear strain range of corner critical weld points through thermo-mechanical coupled finite element simulation, and constructs a weld point reliability simulation database based on the fatigue life model, so that the training data of the prediction model corresponds to the thermal fatigue failure mechanism of the weld point, thereby improving the engineering applicability of thermal fatigue life prediction.

[0025] Third, by constructing and evaluating multiple candidate prediction models, this invention can select a weld joint reliability prediction model with higher prediction accuracy from the candidate prediction models, thereby reducing the number of times the finite element simulation software is directly called in the subsequent optimization process and improving the efficiency of weld joint reliability analysis.

[0026] Fourth, this invention uses the Sobol global sensitivity analysis method to obtain the individual and total contributions of solder ball diameter, solder pad diameter and solder joint height to the thermal fatigue life of the solder joint. It can quantitatively identify the key structural parameters that affect the thermal fatigue life of the solder joint and their interactions, providing a basis for parameter optimization.

[0027] Fifth, this invention aims to maximize the thermal fatigue life of solder joints. Based on the solder joint reliability prediction model, it uses a genetic algorithm for iterative optimization, which can obtain a combination of independent variables with better reliability within the limited range of solder ball diameter, solder pad diameter and solder joint height.

[0028] Sixth, this invention re-inputs the optimal combination of independent variables obtained by the genetic algorithm into the finite element simulation software for verification, and determines whether to output the packaging design scheme based on the relative error between the predicted thermal fatigue life and the verified thermal fatigue life, thereby forming a closed-loop process of prediction, optimization and verification, and improving the credibility of the optimization results. Attached Figure Description

[0029] Figure 1 This is an overall flowchart of the solder joint reliability analysis and optimization method of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Those skilled in the art can make adaptive adjustments to the relevant parameters, models, and algorithm settings without departing from the concept of this invention.

[0031] This invention provides a method for solder joint reliability analysis and optimization based on a Latin hypercube and prediction model. The overall process is as follows: Figure 1 As shown. This method is applied to a semiconductor packaging design terminal, which can call finite element simulation software, machine learning modeling programs, sensitivity analysis programs, and optimization algorithm programs to perform thermal cycling reliability analysis and parameter optimization on the solder joints in the ball grid array packaging structure.

[0032] This embodiment takes a typical ball grid array (BGA) packaging structure as the analysis object. The solder joint reliability index is selected as the thermal fatigue life of the corner solder joints under thermal cycling load. The design variables are solder ball diameter, pad diameter, and solder joint height. The specific implementation process is as follows:

[0033] Step S1: Determine the dependent variable, independent variable, and their range of values.

[0034] The first step in semiconductor packaging design is to determine the thermal fatigue life of the solder joints. As the dependent variable, the thermal fatigue life of the weld joint. This is used to characterize the number of cycles a solder joint can withstand before fatigue failure under thermal cycling loads. Simultaneously, three continuous structural design variables affecting the thermal fatigue life of the solder joint are determined as independent variables: solder ball diameter D, solder pad diameter P, and solder joint height H. In this embodiment, the values ​​of each independent variable are as follows: solder ball diameter D: 0.50 mm to 0.70 mm; solder pad diameter P: 0.45 mm to 0.65 mm; solder joint height H: 0.40 mm to 0.60 mm.

[0035] The above value ranges are determined based on the ball grid array packaging structure design specifications and process constraints. Except for the solder ball diameter D, pad diameter P, and solder joint height H, the chip size, packaging substrate size, PCB board size, solder ball array form, and material parameters in the packaging structure remain unchanged in this embodiment, so as to analyze the influence of the three continuous structural design variables on the thermal fatigue life of the solder joint.

[0036] Step S2: Latin hypercube sampling generates a set of sample points and establishes a corresponding three-dimensional finite element model.

[0037] The Latin hypercube sampling method is used to generate a sample point set within the range of values ​​for solder ball diameter D, solder pad diameter P, and solder joint height H. In this embodiment, the number of sample points is set to 150.

[0038] Specifically, the range of solder ball diameter D (0.50 mm to 0.70 mm) is divided into 150 non-overlapping sub-intervals, the range of solder pad diameter P (0.45 mm to 0.65 mm) is divided into 150 non-overlapping sub-intervals, and the range of solder joint height H (0.40 mm to 0.60 mm) is divided into 150 non-overlapping sub-intervals. A variable value is randomly selected from each sub-interval corresponding to each independent variable, and the variable values ​​corresponding to the three independent variables are then randomly combined to obtain 150 sets of sample points. Each sample point includes a set of values ​​for solder ball diameter D, solder pad diameter P, and solder joint height H. Subsequently, a three-dimensional finite element model corresponding to each sample point in the sample point set is established.

[0039] Compared to full factorial design, Latin hypercube sampling can cover the design space more evenly with a smaller number of samples, thereby reducing the number of calculations required for subsequent finite element simulations.

[0040] Step S3: Simulate and calculate the thermal fatigue life of the weld point corresponding to each sample point and construct a weld point reliability simulation database.

[0041] For each sample point generated in step S2, the semiconductor packaging design terminal calls finite element simulation software to establish a corresponding three-dimensional finite element model of the ball grid array package. The three-dimensional finite element model includes the chip, packaging substrate, PCB board, solder balls, and solder pads. The solder ball diameter D, solder pad diameter P, and solder joint height H are updated according to the values ​​of the current sample point, while the remaining structural parameters remain unchanged.

[0042] In this embodiment, the solder ball material is SAC305 lead-free solder, and its inelastic deformation behavior under thermal cycling load is described using the Anand viscoplastic constitutive model. The Anand viscoplastic constitutive model parameters include initial deformation resistance, the ratio of activation energy to gas constant, pre-exponential factor, strain rate sensitivity index, hardening coefficient, saturation coefficient, and hardening index. These parameters are determined based on experimental data of the solder ball material or calibrated material parameters. The chip, packaging substrate, and PCB are respectively assigned corresponding elastic modulus, Poisson's ratio, and coefficient of thermal expansion as a function of temperature.

[0043] To improve the computational accuracy of the solder joint area, local mesh refinement is applied to the solder joint area, especially at corner solder joints and their connections to pads. Corner solder joints are those located at the outer corners of the solder ball array, which are prone to large strain concentrations under thermal expansion mismatch. The corner critical solder joints are those with the largest maximum shear strain range after thermal cycling simulation.

[0044] After establishing the three-dimensional finite element model, a thermal cycling load is applied to the three-dimensional finite element model corresponding to each sample point. In this embodiment, the thermal cycling load is a temperature cycle condition from -55 ℃ to 125 ℃. Each temperature cycle includes the following four stages: heating stage: heating from -55 ℃ to 125 ℃, taking 15 minutes; high temperature holding stage: holding at 125 ℃ for 10 minutes; cooling stage: cooling from 125 ℃ to -55 ℃, taking 15 minutes; low temperature holding stage: holding at -55 ℃ for 10 minutes. The total duration of each temperature cycle is 50 minutes. After completing three full thermal cycle simulations for the three-dimensional finite element model corresponding to each sample point, the maximum shear strain range of the corner critical weld point in the third thermal cycle is extracted. The calculation results from the third thermal cycle were used to reduce the impact of the initial loading process on the strain response of the weld joint, making the extracted maximum shear strain range closer to the steady-state cycle.

[0045] Subsequently, the thermal fatigue life of the solder joint was calculated based on the Coffin-Manson model. The Coffin-Manson model is shown in equation (1):

[0046]

[0047] In the formula, This refers to the thermal fatigue life of the weld joint, expressed in cycles. This represents the maximum shear strain range of the corner weld point in a critical location. It is the fatigue ductility coefficient; It is the fatigue ductility index. and Pre-calibration is performed based on the solder ball material. In this embodiment, when the solder ball material is SAC305 lead-free solder, and Parameters calibrated through material fatigue testing can be used, for example... Take 0.325, Take -0.442.

[0048] For each sample point, the solder ball diameter D, solder pad diameter P, solder joint height H, and the calculated solder joint thermal fatigue life are used. As a single data record, after performing finite element simulation and life calculation on 150 sample points, a weld joint reliability simulation database containing 150 data records was obtained.

[0049] Step S4: Divide the training dataset and the test dataset and perform normalization processing.

[0050] The solder joint reliability simulation database obtained in step S3 is randomly divided into a training dataset and a test dataset at a ratio of 4:1. The training dataset contains 120 data records, and the test dataset contains 30 data records.

[0051] To eliminate the impact of differences in the units of different variables on model training, the solder ball diameter D, solder pad diameter P, solder joint height H, and solder joint thermal fatigue life in the training and testing datasets were analyzed. Minimum-maximum normalization is performed. The normalization formula is shown in equation (2):

[0052]

[0053] In the formula, These are the variable values ​​before normalization; These are the normalized variable values; This is the minimum value of the variable in the training dataset; This represents the maximum value of the variable in the training dataset.

[0054] To avoid data leakage, the normalization process for the test dataset uses the same method as the training dataset. and Perform the calculation.

[0055] Step S5: Construct candidate prediction models and evaluate prediction accuracy.

[0056] Based on the normalized training dataset, multiple candidate prediction models were constructed to obtain the solder ball diameter D, solder pad diameter P, solder joint height H, and solder joint thermal fatigue life. The approximate mapping relationship between them. In this embodiment, the candidate prediction models include the Kriging model, the support vector regression model, the backpropagation neural network model, and the random forest regression model.

[0057] The Kriging model employs a Gaussian correlation function and fits the model parameters using maximum likelihood estimation. The support vector regression model uses a radial basis function kernel, and the penalty factor and kernel parameters are determined through cross-validation. The backpropagation neural network model uses a three-layer network structure, including an input layer, a hidden layer, and an output layer. The input layer has three nodes, corresponding to the solder ball diameter D, the solder pad diameter P, and the solder joint height H, respectively. The hidden layer has eight nodes, and the output layer has one node, corresponding to the solder joint thermal fatigue life. The random forest regression model consists of 200 decision trees, with a minimum number of leaf nodes set to 3.

[0058] The candidate prediction models were used to make predictions on the normalized test dataset, and the coefficient of determination R was calculated for each model. 2 Root mean square error (RMSE). Coefficient of determination R0 2 The formulas for calculating the root mean square error (RMSE) are shown in equations (3) and (4):

[0059]

[0060]

[0061] In the formula, For the first The actual thermal fatigue life of the solder joints of the test sample; For the first Predicted thermal fatigue life of solder joints for each test sample; This represents the average thermal fatigue life of the actual solder joints in the test samples. This represents the number of test samples.

[0062] Step S6: Select a solder joint reliability prediction model.

[0063] Based on the prediction accuracy of each candidate prediction model on the test dataset, a solder joint reliability prediction model is selected from the candidate prediction models. Specifically, the model with a determination coefficient R is given priority. 2 The candidate prediction model with the largest and smallest root mean square error (RMSE) is used as the solder joint reliability prediction model.

[0064] When the coefficient of determination R 2 The maximum and minimum root mean square error (RMSE) correspond to different candidate prediction models, with the coefficient of determination R... 2 The maximum value is used as the first selection criterion, and the minimum root mean square error (RMSE) is used as the second selection criterion. In this embodiment, after evaluation on the test dataset, the prediction accuracy comparison of the candidate prediction models is shown in Table 1, and the determination coefficient R of the Kriging model is... 2 The Kriging model is chosen as the solder joint reliability prediction model because it has the highest accuracy and the lowest root mean square error (RMSE).

[0065] Table 1 Comparison of prediction accuracy of candidate prediction models

[0066]

[0067] Step S7: Sobol global sensitivity analysis.

[0068] Based on the solder joint reliability prediction model selected in step S6, the first-order Sobol index and the total-order Sobol index corresponding to the solder ball diameter D, the solder pad diameter P, and the solder joint height H are calculated using the Sobol global sensitivity analysis method.

[0069] The first-order Sobol index is used to characterize the individual contribution of a single independent variable to the thermal fatigue life of the solder joint; the total-order Sobol index is used to characterize the total contribution of a single independent variable and its interaction with other independent variables to the thermal fatigue life of the solder joint.

[0070] In this embodiment, the global Sobol sensitivity analysis is estimated using Monte Carlo sampling, with the number of samplings set to 100,000. After calculation, the importance of the solder ball diameter D, solder pad diameter P, and solder joint height H on the thermal fatigue life of the solder joint is ranked according to the total Sobol exponent from largest to smallest.

[0071] In this embodiment, the global Sobol sensitivity analysis is shown in Table 2. The calculated first-order Sobol exponent and total-order Sobol exponent of the solder ball diameter D are both greater than the pad diameter P and the solder joint height H, indicating that the solder ball diameter D is the main structural parameter affecting the thermal fatigue life of the solder joint. The total-order Sobol exponent of the solder joint height H is significantly greater than its first-order Sobol exponent, indicating that there is an interaction between this independent variable and other independent variables.

[0072] Table 2 Global Sensitivity Analysis of Sobol

[0073]

[0074] Step S8: Optimize structural parameters based on genetic algorithm.

[0075] Based on the thermal fatigue life of the solder joint With the goal of maximizing, based on the solder joint reliability prediction model selected in step S6, a genetic algorithm is used to iteratively optimize the solder ball diameter D, solder pad diameter P, and solder joint height H.

[0076] The optimization variables and boundary conditions of the genetic algorithm are as follows: solder ball diameter D: 0.50 mm ≤ D ≤ 0.70 mm; solder pad diameter P: 0.45 mm ≤ P ≤ 0.65 mm; solder joint height H: 0.40 mm ≤ H ≤ 0.60 mm.

[0077] In this embodiment, the genetic algorithm parameters are set as follows: population size is 100, crossover probability is 0.8, mutation probability is 0.1, and maximum number of generations is 50. Each individual in each generation represents a combination of solder ball diameter D, solder pad diameter P, and solder joint height H. For each individual, it is input into the solder joint reliability prediction model to obtain the predicted thermal fatigue life of the solder joint, and this predicted thermal fatigue life is used as the fitness value. After selection, crossover, and mutation operations, the optimal combination of independent variables that maximizes the predicted thermal fatigue life of the solder joint is obtained.

[0078] For example, in this embodiment, after 50 generations of evolution, the optimal combination of independent variables obtained by the genetic algorithm is: solder ball diameter D = 0.68 mm, solder pad diameter P = 0.62 mm, and solder joint height H = 0.55 mm. Inputting this optimal combination of independent variables into the solder joint reliability prediction model, the predicted thermal fatigue life of the solder joint is 1620 cycles.

[0079] Step S9: Finite element verification simulation and result output.

[0080] The optimal combination of independent variables obtained in step S8 is input into the finite element simulation software, and the verification simulation is performed according to the modeling method, material parameters, thermal cycle load and thermo-mechanical coupling finite element simulation conditions in step S3 to obtain the verification thermal fatigue life.

[0081] In this embodiment, the optimal combination of independent variables—a solder ball diameter D of 0.68 mm, a solder pad diameter P of 0.62 mm, and a solder joint height H of 0.55 mm—was input into finite element simulation software for verification simulation, yielding a verified thermal fatigue life of 1550 cycles. The predicted thermal fatigue life was 1620 cycles, and the verified thermal fatigue life was 1550 cycles, resulting in a relative error of 4.52%.

[0082] In this embodiment, the preset error threshold is 5%. Since 4.52% is less than 5%, it is considered that the prediction results of the solder joint reliability prediction model are in good agreement with the finite element verification simulation results, and the optimization results are reliable. The semiconductor packaging design terminal outputs the packaging design scheme corresponding to the optimal combination of independent variables.

[0083] When the relative error is greater than 5%, the optimal combination of independent variables and its corresponding verification thermal fatigue life are added as new samples to the solder joint reliability simulation database, and steps S4 to S9 are re-executed, namely, re-dividing the dataset, constructing candidate prediction models, selecting solder joint reliability prediction models, performing Sobol global sensitivity analysis, using genetic algorithm optimization and performing finite element verification, until the relative error is less than or equal to 5%.

[0084] Through the above steps, this invention can establish the mapping relationship between solder ball diameter, solder pad diameter, solder joint height and solder joint thermal fatigue life with relatively few finite element simulations. It also uses Sobol global sensitivity analysis to identify key structural parameters, obtains the optimal combination of structural parameters for solder joint thermal fatigue life through a genetic algorithm, and finally verifies the optimization results through finite element verification simulation, thus forming a closed-loop process of solder joint reliability prediction, sensitivity analysis, optimization and verification.

[0085] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for solder joint reliability analysis optimization based on Latin hypercube and prediction model, characterized in that, Includes the following steps: S1: Determine the thermal fatigue life of the solder joint under thermal cycling load as the dependent variable, and determine three continuous structural design variables affecting the thermal fatigue life as independent variables. The three continuous structural design variables are solder ball diameter, solder pad diameter, and solder joint height. The solder ball diameter ranges from 0.50 mm to 0.70 mm, the solder pad diameter ranges from 0.45 mm to 0.65 mm, and the solder joint height ranges from 0.40 mm to 0.60 mm. S2: Using the Latin hypercube sampling method, a set of sample points is generated within the range of values ​​for the solder ball diameter, solder pad diameter, and solder joint height, and a corresponding three-dimensional finite element model is established for each sample point in the set of sample points. S3: By calling the finite element simulation software through the semiconductor packaging design terminal, thermal cycling load is applied to the three-dimensional finite element model corresponding to each sample point and thermal-mechanical coupled finite element simulation is performed. The maximum shear strain range of the corner dangerous solder joint is extracted, and the thermal fatigue life of the solder joint corresponding to each sample point is calculated based on the fatigue life model, thereby constructing a solder joint reliability simulation database. S4: Divide the solder joint reliability simulation database into a training dataset and a test dataset, and normalize the independent and dependent variables in the training dataset and the test dataset. S5: Construct multiple candidate prediction models based on the normalized training dataset to obtain an approximate mapping relationship between the solder ball diameter, solder pad diameter, solder joint height and the thermal fatigue life of the solder joint, and calculate the prediction accuracy of each candidate prediction model based on the normalized test dataset. S6: Select a weld joint reliability prediction model from the multiple candidate prediction models based on the prediction accuracy; S7: Based on the solder joint reliability prediction model, the Sobol global sensitivity analysis method is used to calculate the first-order Sobol index and the total-order Sobol index corresponding to the solder ball diameter, solder pad diameter and solder joint height, respectively, and the importance ranking of the influence of the solder ball diameter, solder pad diameter and solder joint height on the thermal fatigue life of the solder joint is obtained according to the first-order Sobol index and the total-order Sobol index. S8: With the goal of maximizing the thermal fatigue life of the solder joint, a genetic algorithm is used based on the solder joint reliability prediction model to iteratively optimize the solder ball diameter, solder pad diameter and solder joint height to obtain the optimal combination of independent variables. S9: Input the optimal combination of independent variables into the finite element simulation software, and perform verification simulation according to the thermal cycle load and thermo-mechanical coupling finite element simulation conditions in step S3 to obtain the verified thermal fatigue life; when the relative error between the predicted thermal fatigue life obtained by the solder joint reliability prediction model and the verified thermal fatigue life meets the preset error threshold, output the packaging design scheme corresponding to the optimal combination of independent variables.

2. The Latin hypercube based with predictive model for solder joint reliability analysis optimization method of claim 1, wherein, The three-dimensional finite element model in steps S2 and S3 includes a chip, a packaging substrate, a PCB board, solder balls, and solder pads; wherein, the solder balls adopt the Anand viscoplastic constitutive model, and the chip, packaging substrate, and PCB board are respectively assigned elastic modulus, Poisson's ratio, and coefficient of thermal expansion as a function of temperature, and local mesh refinement is performed in the solder joint area.

3. The Latin hypercube based with prediction model based solder joint reliability analysis optimization method of claim 1, wherein, The thermal cycling load in step S3 is a temperature cycle condition from -55 ℃ to 125 ℃. Each temperature cycle includes a heating stage from -55 ℃ to 125 ℃ for 15 minutes, a high-temperature holding stage at 125 ℃ for 10 minutes, a cooling stage from 125 ℃ to -55 ℃ for 15 minutes, and a low-temperature holding stage at -55 ℃ for 10 minutes. After completing three full thermal cycle simulations for the three-dimensional finite element model corresponding to each sample point, the maximum shear strain range of the corner critical weld point is extracted. The thermal fatigue life of the solder joint was calculated based on the Coffin-Manson model. .

4. The Latin hypercube based with prediction model based solder joint reliability analysis optimization method of claim 1, wherein, The candidate prediction models in step S5 include the Kriging model, support vector regression model, backpropagation neural network model, and random forest regression model; the prediction accuracy is measured by the coefficient of determination R. 2 The root mean square error (RMSE) is used for evaluation; in step S6, the determination coefficient R is selected. 2 The candidate prediction model with the largest and smallest root mean square error (RMSE) is selected as the solder joint reliability prediction model. 2 When the maximum and the minimum root mean square error (RMSE) correspond to different candidate prediction models, the coefficient of determination R... 2 The maximum value is used as the first selection criterion, and the minimum root mean square error (RMSE) is used as the second selection criterion.

5. The solder joint reliability analysis and optimization method based on the Latin hypercube and prediction model according to claim 1, characterized in that, In step S7, the individual contributions of the solder ball diameter, solder pad diameter, and solder joint height to the thermal fatigue life of the solder joint are determined according to the first-order Sobol index. The total contribution of the solder ball diameter, solder pad diameter, and solder joint height and their interaction to the thermal fatigue life of the solder joint is determined according to the total-order Sobol index. The importance of the influence is then ranked from largest to smallest according to the total-order Sobol index.

6. The Latin hypercube based with prediction model based solder joint reliability analysis optimization method of claim 1, wherein, In step S9, the preset error threshold is 5%. When the relative error is greater than 5%, the optimal combination of independent variables and its corresponding verified thermal fatigue life are added as new samples to the weld joint reliability simulation database, and steps S4 to S9 are re-executed until the relative error is less than or equal to 5%.

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