A method for optimizing a bga laminated solder joint structure under coupling of extreme temperature and bending load

Abstract

This invention discloses a method for optimizing the structure of BGA stack solder joints under coupled extreme temperatures and bending loads, belonging to the field of electronic packaging reliability analysis and structural design. The method establishes a parametric finite element model, applies extreme temperature cycles from -180℃ to 150℃ and maps the temperature field, and applies a three-point bending displacement of 0.1mm under a 120mm support span to obtain the maximum bending stress of critical solder joints. Using solder ball diameter, solder joint height, pad diameter, solder joint spacing, and PCB board thickness as design variables, Latin hypercube sampling and stepwise regression are used to screen the main variables, establishing a response surface surrogate model containing quadratic and interaction terms. A real-valued genetic algorithm is then used to obtain low-stress parameter combinations, which are verified through finite element back-substitution. This method can identify the main structural variables and reduce local stress concentration under extreme temperature bending conditions while reducing the number of costly finite element calculations.

Description

Technical Field

[0001] This invention relates to the field of thermo-mechanical reliability analysis and structural parameter optimization technology for electronic packaging devices, specifically to a method for optimizing the structure of BGA stack solder joints under extreme temperature and bending load coupling. Background Technology

[0002] Ball grid array (BGA) packaging utilizes arrayed solder joints to achieve electrical interconnection and mechanical support between the chip package and the printed circuit board (PCB). Due to the different thermal expansion properties of the chip, pads, solder, and PCB, temperature changes can generate thermo-mechanical stresses within the solder joints and in the connection area between the solder joint and the pad. While multilayer solder joints increase the interconnect height by arranging multiple interconnected solder balls along the height direction, which helps alleviate some thermal mismatch deformation, localized stress concentrations may still occur at the connection interface and end pad areas.

[0003] Deep space exploration, polar equipment, and wide-temperature-range electronic systems may experience low temperatures below -100°C and large temperature difference cycles, while also being subjected to mechanical loads such as assembly warpage, transportation shocks, structural vibrations, and board-level bending. Extreme temperatures alter the elastic modulus and plastic response of solder, while bending loads change the curvature of printed circuit boards and the shear displacement of solder joints. Therefore, studying only temperature loads or only room-temperature bending loads cannot fully reflect the critical stresses on solder joints under the above-mentioned operating conditions.

[0004] Existing methods for optimizing encapsulation structure parameters typically involve performing full combination finite element calculations on multiple geometric parameters, or establishing a general regression model on a limited number of pre-defined experimental points. The former is computationally intensive, while the latter, if it retains too many weak-contribution variables, can easily increase the complexity of the surrogate model; if only a linear model is used, it is difficult to describe the nonlinear effects of structural variables and the coupling effects between variables.

[0005] Therefore, a method is needed that combines extreme temperature field, plate-level bending load, spatial sampling, variable selection, nonlinear proxy modeling and global optimization to identify key structural variables while reducing the number of finite element calculations and obtain a combination of structural parameters that can reduce the maximum bending stress at dangerous weld points. Summary of the Invention

[0006] The purpose of this invention is to provide a method for optimizing the structure of BGA stacked solder joints under extreme temperature and bending load coupling. The bending stress of critical solder joints is obtained through indirect thermal-structural coupling calculation, finite element samples are formed using Latin hypercube sampling, key structural variables are screened using stepwise regression and a response surface surrogate model is established, and then a combination of low-stress structural parameters is obtained through a genetic algorithm.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] Step S1: Establish a parametric finite element model of the BGA stack-up solder joints. The model includes the chip, stack-up solder joints, pads, and printed circuit board, with solder ball diameter, solder joint height, pad diameter, solder joint spacing, and printed circuit board thickness as design variables.

[0009] Step S2: Perform extreme temperature cycle temperature field analysis. Set temperature-related material parameters and extreme temperature cycle loads, and calculate the temperature distribution of the model at each load step.

[0010] Step S3: Map the temperature field to the structural analysis model and apply a bending load. Set the bending support span and apply a downward displacement at the centerline on the back of the printed circuit board to create a three-point bending deformation in the model.

[0011] Step S4: Identify the critical weld points from the stress field under the combined action of temperature and bending load, and extract the maximum bending stress of the critical weld points.

[0012] Step S5: Use Latin hypercube sampling to form a finite element sample set within the value range of the five design variables.

[0013] Step S6: Establish an initial multiple regression model with the maximum bending stress as the response, and use stepwise regression to introduce and remove variables to screen the main structural variables.

[0014] Step S7: Standardize the main structural variables, construct a response surface surrogate model containing first-order terms, second-order terms, and interaction terms, using the natural logarithm of the maximum bending stress as the response, and verify the accuracy and stability of the surrogate model.

[0015] Step S8: Use a real-number encoded genetic algorithm to search for low-stress solutions of the surrogate model within the constraint space to obtain the target structural parameter combination.

[0016] Step S9: Reconstruct the finite element model based on the combination of target structural parameters, and perform finite element back-substitution verification under the same working conditions. Attached Figure Description

[0017] Figure 1 This is a schematic flowchart of the method of the present invention;

[0018] Figure 2 A schematic diagram of the finite element model of the BGA stacked solder joints;

[0019] Figure 3 The stress-strain curves of SAC305 solder at different temperatures are shown.

[0020] Figure 4 This is a graph showing the extreme temperature cyclic load.

[0021] Figure 5 A schematic diagram of the three-point bending load boundary conditions for BGA stack solder joints;

[0022] Figure 6 This is a diagram showing the stress distribution at the weld joint under the combined effects of extreme temperature and bending load.

[0023] Figure 7 Residual distribution diagram of response surface surrogate model;

[0024] Figure 8 This is a graph showing the convergence curve of the genetic algorithm.

[0025] Figure 9 To optimize the bending stress distribution diagram of dangerous weld points in the structure. Detailed Implementation

[0026] Example:

[0027] like Figure 1 As shown, this embodiment sequentially completes parametric modeling, extreme temperature analysis, temperature field mapping, three-point bending loading, dangerous weld point extraction, Latin hypercube sampling, stepwise regression surrogate modeling, genetic algorithm optimization, and finite element back-substitution verification.

[0028] Step S1: Establish a finite element model of the BGA stacked solder joints, such as... Figure 2 As shown. The chip size is 13mm × 11mm × 0.8mm, the initial solder joint spacing is 0.94mm, the solder ball diameter is 0.60mm, the solder joint height is 0.46mm, the pad diameter is 0.44mm, and the printed circuit board size is 132mm × 77mm × 1.60mm. Thermal analysis was performed using SOLID70 cells, with localized refinement of the solder joints and the transition areas between the upper and lower pads; after the thermal analysis was completed, the thermal cells were converted to SOLID185 structural cells.

[0029] Step S2: The lead-free solder SAC305 was selected as the material for the laminated solder joints. The material parameters of different structures in the model are shown in Table 1. A multilinear isotropic reinforced constitutive model was used to describe the elastoplastic response at extreme temperatures. The stress-strain curves at different temperatures are shown in Table 1. Figure 3 As shown.

[0030] Table 1 Material parameters of the finite element model

[0031]

[0032] Indirect thermal-structural coupling loading was employed. Applying... Figure 4 The temperature cycle shown ranges from -180℃ to 150℃, with heating and cooling times of 300s each, and holding times at both high and low temperatures of 600s each. A single cycle lasts 1800s. The temperature field results are then mapped onto the structural analysis model.

[0033] Step S3: When applying the bending load, the model chip face is downward, the printed circuit board support span is 120mm, and a downward displacement of 0.1mm is applied at the centerline of the back of the printed circuit board. The boundary conditions are as follows. Figure 5 As shown.

[0034] Step S4: Extract the bending stress at 6600s on the fourth temperature cycle. Figure 6 It can be seen that the high-stress area is mainly located in the connection area between the stacked solder joints and the chip-side pads and the printed circuit board-side pads; the maximum stress is located at the corner solder joint of the solder joint array corresponding to the chip in the upper left corner, so this solder joint is identified as a dangerous solder joint.

[0035] Step S5: Select solder ball diameter X1, solder joint height X2, solder pad diameter X3, solder joint spacing X4, and printed circuit board thickness X5 as design variables. Generate 50 sets of samples within a given interval using Latin hypercube sampling, and perform finite element calculations on each set. The maximum bending stress of the samples and critical solder joints is shown in Table 2.

[0036] Table 2. Results of Latin hypercube sampling design and finite element calculation

[0037]

[0038] Step S6: Establish an initial multiple linear regression model using the maximum bending stress Y at the critical weld joint as the response:

[0039] (1)

[0040] The initial model had an R² of 0.9381, and the adjusted R² was 0.9311. The overall F-statistic was 133.4415. The regression coefficients showed that solder ball diameter was positively correlated with maximum bending stress, while solder joint height, pad diameter, solder joint spacing, and printed circuit board thickness were negatively correlated with maximum bending stress.

[0041] Table 3. Parameter estimation results of the initial multiple linear regression model

[0042]

[0043] Table 4 Results of stepwise regression variable selection

[0044]

[0045] Stepwise regression was used to sequentially introduce PCB thickness (X5), solder ball diameter (X1), and solder joint height (X2), while removing pad diameter (X3) and solder joint spacing (X4). The retained variables were then refitted to obtain:

[0046] (2)

[0047] The overall F-statistic of the stepwise regression model is 172.3266, indicating that the simplified model consisting of X1, X2, and X5 has significant explanatory power.

[0048] Step S7: In order to describe the nonlinear effects and interactions of the main structural variables, X1, X2 and X5 are standardized. The standardization method is shown in Table 5.

[0049] Table 5 Structural parameters and standardization methods

[0050]

[0051] Using the natural logarithm of the maximum bending stress as the response, a response surface surrogate model is obtained by progressively filtering through first-order, second-order, and interaction terms:

[0052] (3)

[0053] In the model, z1² reflects the nonlinear effect of the solder ball diameter, and z1z2 reflects the interaction between the solder ball diameter and the solder joint height. The model parameters are shown in Table 6.

[0054] Table 6. Parameter estimation results of the response surface surrogate model with retained variables.

[0055]

[0056] The response surface surrogate model has an R² of 0.9532, an adjusted R² of 0.9479, and an overall F-statistic of 179.3514. After inversely transforming the predicted values ​​to the original stress scale, the RMSE is 0.4935 MPa, the MAE is 0.3568 MPa, and the MAPE is 0.2587%.

[0057] A multicollinearity test was performed on the model, and the variance inflation factor of each explanatory term was less than 10, as shown in Table 7; the residual distribution is as follows. Figure 7 As shown in Table 8, the Breusch-Pagan test results are presented, and the Durbin-Watson statistic is 1.8757. Since this example primarily aims for rapid prediction and optimization, and the surrogate model exhibits relatively small prediction errors, this model is used as the objective function of the genetic algorithm.

[0058] Table 7. VIF test results for each explanatory term in the response surface surrogate model.

[0059]

[0060] Table 8 Results of the Breusch-Pagan heteroscedasticity test

[0061]

[0062] Step S8: In the structural optimization stage, z1, z2, and z5 are used as chromosome genes in the genetic algorithm, and the search is performed within the range of -1 to 1. Since the exponential function is monotonically increasing, minimizing lnŶ is equivalent to minimizing Ŷ. The fitness can be the negative value of the response surface prediction or its monotonically equivalent form. The genetic algorithm parameters are shown in Table 9.

[0063] Table 9 Genetic Algorithm Parameter Settings

[0064]

[0065] The convergence process of the genetic algorithm is as follows: Figure 8 As shown. The standardized optimal variables z1=-1, z2=1, z5=1 were obtained, corresponding to a solder ball diameter of 0.60mm, a solder joint height of 0.52mm, and a printed circuit board thickness of 1.60mm. Based on the negative correlation between pad diameter and solder joint spacing in the initial regression model, the pad diameter was set to 0.50mm and the solder joint spacing to 1.00mm.

[0066] Step S9: Substitute the parameters into the surrogate model to predict the maximum bending stress as 130.95 MPa; reconstruct the finite element model and perform a reverse substitution under the same working conditions to obtain... Figure 9 The stress distribution shown is such that the maximum bending stress is 129.74 MPa. The results before and after optimization are shown in Table 10.

[0067] Table 10 Comparison of maximum bending stress at critical weld points before and after optimization

[0068]

[0069] Compared with the initial structure with a maximum bending stress of 134.52 MPa, the optimized structure has a 3.55% reduction in maximum bending stress, indicating that the technical approach combining stepwise regression variable selection, response surface surrogate modeling, and genetic algorithm can reduce local stress concentration under extreme temperature bending conditions.

[0070] In other implementations, the design variable range, temperature load, and displacement load can be adjusted according to different package sizes, solder materials, and bending fixtures, and the surrogate model can be retrained using Latin hypercube samples. As long as the continuous process of temperature field mapping, critical solder joint response extraction, stepwise regression dimensionality reduction, response surface surrogate optimization, and finite element back-substitution verification is still used, the same type of structural parameter optimization can be achieved.

Claims

1. A method for optimizing BGA stack joint structure under extreme temperature and bending load coupling, characterized in that, Includes the following steps: S1. Establish a parametric finite element model including the chip, pads, at least two solder balls connected along the height direction, and the printed circuit board. Set the solder ball diameter X1, solder joint height X2, pad diameter X3, solder joint spacing X4, and printed circuit board thickness X5 as design variables. S2, perform extreme temperature cycle temperature field analysis on the parameterized finite element model, map the temperature field of each load step to the structural analysis model, set up bending supports on the printed circuit board and apply bending displacement load to obtain the solder joint stress field under the combined action of extreme temperature and bending load. S3, determine the dangerous weld point corresponding to the maximum bending stress from the weld stress field, and use the maximum bending stress of the dangerous weld point as the structural optimization response value; S4. In the range of values ​​of each design variable, Latin hypercube sampling is used to generate multiple sets of design variable samples. Steps S1 to S3 are performed on each set of design variable samples to form a finite element sample set corresponding to the design variable and the maximum bending stress. S5. An initial multiple regression model containing X1 to X5 is established with the maximum bending stress as the response variable, and the main structural variables are screened through the stepwise regression variable introduction and elimination process. S6. The selected main structural variables are centered and scaled, and the natural logarithm of the maximum bending stress is used as the response. The first-order, second-order and interaction terms of the main structural variables are used to construct a response surface surrogate model. S7. Using the response surface surrogate model as the objective function, a real-number encoded genetic algorithm is used to search within the constraint range of the main structural variables to obtain the target structural parameter combination. S8. Reconstruct the finite element model based on the target structural parameter combination. Perform finite element back-substitution under the same temperature cycle and bending boundary conditions as in step S2. When the maximum bending stress obtained by back-substitution is lower than the maximum bending stress of the initial structure, output the target structural parameter combination.

2. The structural optimization method according to claim 1, characterized in that, The minimum temperature of the extreme temperature cycle is -180℃ and the maximum temperature is +150℃. The duration of the heating and cooling phases is 300s each, the duration of the high temperature holding phase and the low temperature holding phase is 600s each, and the duration of a single temperature cycle is 1800s.

3. The structural optimization method according to claim 1, characterized in that, Step S2 adopts an indirect thermal-structural coupling method. The thermal analysis unit is SOLID70, which is converted into the structural unit SOLID185 after temperature field mapping. During bending loading, the chip face is downward, the support span of the printed circuit board is 120mm, and a downward displacement of 0.1mm is applied at the center line on the back of the printed circuit board.

4. The structural optimization method according to claim 1, characterized in that, The laminated solder joints use SAC305 lead-free solder, and a temperature-dependent multilinear isotropic strengthening constitutive model is used to describe the elastoplastic response of SAC305 lead-free solder in the extreme temperature range.

5. The structural optimization method according to claim 1, characterized in that, Step S3 reads the stress field of the solder joint at 6600s during the fourth extreme temperature cycle and identifies the corner stacked solder joints in the solder joint array corresponding to the four chips as dangerous solder joints.

6. The structural optimization method according to claim 1, characterized in that, Step S4 generates 50 sets of Latin hypercube samples, with the design variables taking values ​​in the following ranges: 0.60mm≤X1≤0.75mm, 0.46mm≤X2≤0.52mm, 0.44mm≤X3≤0.50mm, 0.94mm≤X4≤1.00mm, and 0.80mm≤X5≤1.60mm.

7. The structural optimization method according to claim 1, characterized in that, The main structural variables obtained in step S5 are solder ball diameter X1, solder joint height X2, and printed circuit board thickness X5; these main structural variables are standardized according to the following formula: z1=(X1-0.675) / 0.075; z2=(X2-0.490) / 0.030; z5=(X5-1.200) / 0.

400.

8. The structural optimization method according to claim 7, characterized in that, The response surface proxy model established in step S6 is as follows: ln =4.9301+0.0115z1-0.0040z2-0.0257z5-0.0054z1²+0.0087z1z2; in, This is the predicted maximum bending stress value for dangerous weld joints.

9. The structural optimization method according to claim 1, characterized in that, The genetic algorithm in step S7 uses real number encoding, has a population size of 100, a maximum number of iterations of 200, a crossover probability of 0.80, a mutation probability of 0.05, retains 2 elite individuals, and runs 10 times independently.

10. The structural optimization method according to claim 1, characterized in that, The target structural parameter combination is as follows: solder ball diameter 0.60mm, solder joint height 0.52mm, solder pad diameter 0.50mm, solder joint spacing 1.00mm, and printed circuit board thickness 1.60mm; the target structural parameter combination is 3.55% lower than the initial structure.

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