Multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated welding spots

Abstract

The invention discloses a multi-objective optimization method for stress-strain and high-frequency crosstalk of a laminated welding spot, which comprises the following steps of: establishing a finite element analysis model and a crosstalk analysis geometric model of the laminated welding spot through simulation software, and respectively carrying out stress-strain analysis and high-frequency crosstalk analysis to obtain a maximum stress-strain value, a near-end crosstalk value and a far-end crosstalk value of the welding spot; a response surface design method is adopted, different structure parameter factor horizontal combinations of the laminated welding spots are designed, simulation analysis is carried out, regression analysis is carried out according to the obtained result, a regression equation of stress strain, near-end crosstalk, far-end crosstalk and welding spot structure parameters is established, a multi-objective optimization model is established, and the welding spot structure parameters are optimized. And then multi-objective optimization is carried out in combination with response surface design and an MOEA / D algorithm, a Pareto optimal solution set is obtained, an optimal welding spot structure parameter combination of multi-objective optimization is obtained through entropy weight TOPSIS decision analysis, and simulation verification is carried out. The multi-objective optimization method is good in optimization effect and multiple in optimization objectives, and has a certain guiding effect on the aspect of welding spot structure optimization.

Description

Technical Field

[0001] The invention relates to the technical field of electronic component packaging interconnection reliability, in particular to a multi-objective optimization method for laminated solder joint stress strain and high-frequency crosstalk. Background Art

[0002] As a key technology in modern microelectronic packaging, laminated solder joints have become the key to miniaturization and high performance of electronic products with their enhanced mechanical strength, improved thermal and electrical properties, and adaptability to high-density packaging. However, the reliability of laminated solder joints will be significantly affected when they are subjected to stress and strain caused by temperature cycles, mechanical assembly, etc., as well as crosstalk in high-frequency working environments. Stress and strain may cause fatigue, cracks, and even breakage of solder joints, while high-frequency crosstalk will reduce signal integrity and affect data transmission quality and speed.

[0003] Existing studies have shown that the structural parameters of solder joints have a direct and important impact on the above-mentioned problems. By optimizing the structural parameters of solder joints, the performance of laminated solder joints in the face of stress, strain and high-frequency crosstalk challenges can be significantly improved, providing strong support for the design and manufacture of high-performance electronic products. Therefore, it is necessary to perform multi-objective optimization of stress, strain and high-frequency crosstalk on laminated solder joints. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-objective optimization method for stress, strain and high-frequency crosstalk of laminated solder joints. The method can optimize the four objectives of stress, strain, near-end crosstalk and far-end crosstalk of laminated solder joints. The optimization effect is excellent and the process is relatively simple, which greatly facilitates the optimization design of solder joint structural parameters.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints comprises the following steps:

[0007] (1) Using ANSYS and HFSS software, a finite element analysis model of the stacked solder joint and a crosstalk analysis geometric model were established, and stress-strain analysis and crosstalk analysis under high-frequency conditions were performed to obtain the maximum stress-strain value, near-end crosstalk, and far-end crosstalk values ​​of the solder joint;

[0008] (2) Using the Box-Behnken design method in response surface design, the combination of different structural parameter factors of the laminated solder joints was designed and simulated;

[0009] (3) Perform polynomial regression analysis to establish regression equations for stress-strain, near-end crosstalk, far-end crosstalk, and solder joint structural parameters;

[0010] (4) Perform variance analysis and significance verification on the regression equation;

[0011] (5) Establish a multi-objective optimization model for the structural parameters of laminated solder joints;

[0012] (6) Combine response surface design and MOEA / D algorithm to optimize the multi-objective optimization model and obtain the Pareto optimal solution set;

[0013] (7) Use the entropy weight TOPSIS decision method to perform decision analysis on the Pareto optimal solution set and obtain the ranking of each combination in the Pareto optimal solution set;

[0014] (8) The top three solder joint structural parameter level combinations in the Pareto optimal solution set were selected for simulation verification and the optimization effects were compared.

[0015] Furthermore, in the finite element analysis model of the laminated solder joints in step (1), the size of the epoxy resin package is 22mm×22mm×1.85mm, the size of the BT substrate is 23mm×23mm×1mm, the chip has a total of 532 solder joints, wherein the solder ball diameter is 0.5mm, the solder joint height is 0.4mm, the solder joint spacing is 0.8mm, the pad diameter is 0.34mm, and the PCB board size is 132mm×77mm×1.6mm. In addition, the geometric model for the crosstalk analysis of the laminated solder joints in step (1) is consistent with the finite element analysis model of the laminated solder joints except that there are only two adjacent laminated solder joints in the number of laminated solder joints.

[0016] Furthermore, when designing the level combination of the laminated solder joint structure parameter factors in step (3), the solder ball diameter, solder joint height, solder joint spacing and pad diameter are selected as the main variables for investigation, and three different levels are set for each variable, namely 0.45mm, 0.50mm, 0.55mm; 0.36mm, 0.39mm, 0.42mm; 0.76mm, 0.79mm, 0.82mm; 0.30mm, 0.33mm, 0.36mm. Finally, there are 29 groups of parameter combinations designed by the response surface.

[0017] Furthermore, the parameters of the MOEA / D algorithm in step (6) are set as follows: population size is 300, neighborhood size Nei max is 20, the crossover probability CR is 0.9, the scaling factor F is 0.5 and the maximum number of iterations t max is 2000.

[0018] Furthermore, the Pareto optimal solution set obtained in step (6) is the optimal level combination set of structural parameters of the laminated solder joint.

[0019] Furthermore, in step (7), when entropy-weighted TOPSIS decision analysis is performed based on the data of the obtained Pareto optimal solution set, the information entropy, difference coefficient, weight value, positive ideal solution distance, and negative ideal solution distance are calculated to obtain the closeness, and the order of each combination in the Pareto optimal solution set is obtained by comparing the size of the closeness.

[0020] In a multi-objective optimization method for stress, strain and high-frequency crosstalk of a laminated solder joint provided by the present invention, a finite element analysis model and a crosstalk analysis geometric model of the laminated solder joint are firstly established by using ANSYS and HFSS software, and stress-strain analysis and high-frequency crosstalk analysis are respectively performed to obtain the maximum stress-strain value, near-end crosstalk and far-end crosstalk value of the solder joint, and a Box-Behnken design method is adopted to design a combination of different structural parameter factor levels of the laminated solder joint and perform simulation analysis, and a regression analysis is performed based on the obtained results to establish a regression equation of stress, strain, near-end crosstalk and far-end crosstalk with the solder joint structural parameters and a multi-objective optimization model, and then the multi-objective optimization model is optimized by combining the response surface design and the MOEA / D algorithm to obtain a Pareto optimal solution set, and then the entropy weight TOPSIS decision analysis is combined to obtain the arrangement order of each group in the Pareto optimal solution set, thereby obtaining the optimal solder joint structural parameter combination under multi-objective optimization.

[0021] This technical solution can perform multi-objective optimization on the stress, strain, near-end crosstalk and far-end crosstalk of laminated solder joints. It has many optimization targets, good optimization effect, clear and simple optimization process, and brings great convenience to the optimization design of solder joint structural parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Schematic diagram of the finite element analysis model of the laminated solder joint in the embodiment;

[0023] Figure 2 The bending-vibration coupling stress distribution cloud diagram of the laminated solder joints in the embodiment;

[0024] Figure 3 The bending-vibration coupling strain distribution cloud diagram of the laminated solder joints in the embodiment;

[0025] Figure 4 Schematic diagram of geometric model for crosstalk analysis of stacked solder joints in the embodiment;

[0026] Figure 5 Schematic diagram of the variation of the crosstalk intensity of the stacked solder joints with the frequency in the embodiment;

[0027] Figure 6 Flowchart of MOEA / D algorithm in the embodiment;

[0028] Figure 7 TOPSIS decision analysis flow chart of entropy weight in the embodiment;

[0029] Figure 8 Multi-objective optimization Pareto frontier graph in the embodiment;

[0030] Fig. 9 Schematic diagram of simulation results of the top 3 combinations in the Pareto optimal solution set in the embodiment. Fig.10 Schematic diagram of the process of the multi-objective optimization method for laminate solder joint stress-strain and high-frequency crosstalk in the embodiment. DETAILED DESCRIPTION

[0031] The present invention is further described below with reference to the accompanying drawings and embodiments, but the present invention is not limited thereto.

[0032] Example:

[0033] A multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints comprises the following steps:

[0034] (1) Use ANSYS software to establish the basic model of finite element analysis of laminated welds. Figure 1 As shown, stress-strain analysis is performed under bending-vibration coupling loading. The material parameters are shown in Table 1. The stress-strain conditions of the solder joints are shown in Figure 2 , Figure 3 As shown in the figure, the geometric model for crosstalk analysis of stacked solder joints is established as Figure 4 As shown, the crosstalk analysis under high-frequency conditions was then performed in the HFSS three-dimensional electromagnetic simulation software, where the solution frequency was set to 10 GHz, the number of iterations was 30, the frequency sweep range was from 1-10 GHz, the step length was 0.05, and interpolation scanning was used to obtain the near-end crosstalk and far-end crosstalk as shown in Figure 5 shown.

[0035] (2) Using the Box-Behnken design method in response surface design, the combination of different structural parameter factors of the stacked solder joints was designed and simulated as shown in Tables 2 and 3.

[0036] (3) According to the combination of the factors of the laminated solder joint structural parameters and their corresponding analysis results shown in Table 3, a polynomial regression analysis was performed, and the regression equation was established to obtain the functional relationship between the bending vibration coupling stress (y1), bending vibration coupling strain (y2), near-end crosstalk (y4) and far-end crosstalk (y4) and the solder joint structural parameters of the solder ball diameter (x1), solder joint height (x2), solder joint spacing (x3) and pad diameter (x4), that is, the regression equations are shown in Formula (1), Formula (2), Formula (3) and Formula (4).

[0037]

[0038]

[0039] (4) The regression equation was subjected to variance analysis and significance verification, as shown in Table 4, which shows that the regression equation has a good predictive effect.

[0040] (5) A multi-objective optimization model for the structural parameters of the stacked solder joints is established, where the independent variables are: solder ball diameter x1 (mm), solder joint height x2 (mm), solder joint spacing x3 (mm) and pad diameter x4 (mm); the constraints and objective functions are shown in Formula (5) and Formula (6).

[0041]

[0042] (6) According to Figure 6 The process uses the MOEA / D multi-objective optimization algorithm combined with response surface design to calculate the multi-objective optimization model, where the parameters are set as: population size is 300, neighborhood size Nei max is 20, the crossover probability CR is 0.9, the scaling factor F is 0.5 and the maximum number of iterations t max is 2000, and the Pareto optimal solution set is shown in Table 5. Figure 7 The Pareto frontier diagram of multi-objective optimization shows that the optimization results have good convergence and uniform distribution, and the bending-vibration coupling stress-strain is almost inversely proportional to the near-end crosstalk and far-end crosstalk.

[0043] (7) The entropy weight TOPSIS decision method is used to perform decision analysis on the Pareto optimal solution set. The specific calculation process is as follows: Figure 8 As shown in Figure 6, by comparing the progress of each group in the Pareto optimal solution set, the arrangement order of each group in the Pareto optimal solution set is obtained as shown in Table 6. The larger the closeness value, the closer the solder joint structure parameter combination is to the optimal parameter combination.

[0044] (8) The top three stacked solder joint structural parameter level combinations in the Pareto optimal solution set in Table 6 are selected, and the finite element analysis model and stacked solder joint crosstalk analysis model corresponding to these three parameter level combinations are re-established. The stress-strain analysis under bending-vibration coupling loading and the crosstalk analysis under high-frequency conditions are completed, and the bending-vibration coupling stress-strain, near-end crosstalk and far-end crosstalk results are obtained as shown in the figure. Fig. 9 As shown in Table 7, the simulation value is compared with the corresponding predicted value in the Pareto optimal solution set. The errors are all less than 2%, which shows that the algorithm has a high prediction accuracy.

[0045] The final multi-objective optimization effect is shown in Table 8. The comprehensive optimization ratio reaches 6.02%, completing the multi-objective optimization purpose and proving the effectiveness of this method.

[0046] Table 1 Material parameters

[0047]

[0048] Table 2. Laminated solder joint structural parameter factor level table

[0049]

[0050] Table 3 Combination of structural parameter factors of laminated solder joints and their corresponding analysis results

[0051]

[0052]

[0053] Table 4 Relevant evaluation indicators of regression equations y1, y2, y3, y4

[0054]

[0055] Table 5 Pareto optimal solution set

[0056]

[0057]

[0058] Table 6 Ranking order of Pareto optimal solution set

[0059]

[0060] Table 7 Comparison results between predicted values ​​and simulated values

[0061]

[0062]

[0063] Table 8 Multi-objective optimization results

[0064]

Claims

1. A multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints, characterized in that: The specific steps include: (1) Using ANSYS and HFSS software, a finite element analysis model of the stacked solder joint and a crosstalk analysis geometric model were established, and stress-strain analysis and crosstalk analysis under high-frequency conditions were performed to obtain the maximum stress-strain value, near-end crosstalk, and far-end crosstalk values ​​of the solder joint; (2) Using the Box-Behnken design method of response surface design, the combination of different structural parameter factors of the laminated solder joints was designed and simulated; (3) Perform polynomial regression analysis to establish regression equations for stress-strain, near-end crosstalk, far-end crosstalk, and solder joint structural parameters; (4) Perform variance analysis and significance verification on the regression equation; (5) Establish a multi-objective optimization model for the structural parameters of laminated solder joints; (6) Combine response surface design and MOEA / D algorithm to optimize the multi-objective optimization model and obtain the Pareto optimal solution set; (7) Use the entropy weight TOPSIS decision method to perform decision analysis on the Pareto optimal solution set and obtain the ranking of each combination in the Pareto optimal solution set; (8) The top three solder joint structural parameter level combinations in the Pareto optimal solution set were selected for simulation verification and the optimization effects were compared.

2. The multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints according to claim 1, characterized in that: In the finite element analysis model of the laminated solder joints in step (1), the size of the epoxy resin package is 22mm×22mm×1.85mm, the size of the BT substrate is 23mm×23mm×1mm, the chip has a total of 532 solder joints, of which the solder ball diameter is 0.5mm, the solder joint height is 0.4mm, the solder joint spacing is 0.8mm, the pad diameter is 0.34mm, and the PCB board size is 132mm×77mm×1.6mm. In addition, the geometric model for the crosstalk analysis of the laminated solder joints in step (1) is consistent with the finite element analysis model of the laminated solder joints except that there are only two adjacent laminated solder joints in the number of laminated solder joints.

3. The multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints according to claim 1, characterized in that: When designing the horizontal combination of the structural parameter factors of the laminated solder joint in step (2), the solder ball diameter, solder joint height, solder joint spacing and pad diameter are selected as the main variables for investigation. Three different levels are set for each variable, namely 0.45mm, 0.50mm, 0.55mm; 0.36mm, 0.39mm, 0.42mm; 0.76mm, 0.79mm, 0.82mm; 0.30mm, 0.33mm, 0.36mm. Finally, there are 29 groups of parameter combinations designed by the response surface.

4. The multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints according to claim 1, characterized in that: The parameters of the MOEA / D algorithm in step (6) are set as follows: population size is 300, neighborhood size Nei max is 20, the crossover probability CR is 0.9, the scaling factor F is 0.5 and the maximum number of iterations t max is 2000.

5. The multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints according to claim 1, characterized in that: The Pareto optimal solution set obtained in step (6) is the optimal level combination set of structural parameters of the stacked solder joints.

6. The multi-objective optimization method for stress-strain and high-frequency crosstalk of laminated solder joints according to claim 1, characterized in that: In step (7), when performing entropy weight TOPSIS decision analysis based on the data of the Pareto optimal solution set, the information entropy, difference coefficient, weight value, positive ideal solution distance, and negative ideal solution distance are calculated to obtain the closeness, and the order of each combination in the Pareto optimal solution set is obtained by comparing the size of the closeness.

Images