An underfill BGA solder joint mechanical property optimization method based on RSM-PCA-PSO

Abstract

The application discloses a kind of based on RSM-PCA-PSO's bottom filling BGA weld point mechanical property optimization method, comprising: 1) establish bottom filling BGA weld point under the simulation analysis model of bending vibration coupling load;2) obtain multiple mechanical property index data of weld point;3) using response surface method design test scheme, obtain the mechanical property index data of each test group by finite element simulation;4) using principal component analysis to reduce dimension to multiple mechanical property index, construct standardization comprehensive score Z;5) using response surface method to establish the regression model between weld point structure parameter and standardization comprehensive score Z;6) with regression model as the fitness function of particle swarm optimization algorithm, obtain optimal weld point structure parameter combination;7) verify optimization effect by finite element simulation.The application combines response surface method, principal component analysis and particle swarm optimization algorithm, realize the comprehensive optimization of bottom filling BGA weld point under bending vibration coupling load mechanical property.

Description

Technical Field

[0001] This invention relates to the field of electronic packaging reliability technology, specifically to a method for optimizing the mechanical properties of bottom-filled BGA solder joints based on RSM-PCA-PSO. Background Technology

[0002] Ball Grid Array (BGA) packaging, as a surface mount technology for achieving high-density interconnects, offers advantages such as small solder joint spacing, high I / O density, excellent electrothermal performance, and self-aligned solder joints. BGA devices achieve electrical connection and mechanical support to the printed circuit board (PCB) through BGA solder joints. Solder joints, as a critical weak point connecting the chip and the PCB, are a common cause of electronic device failures. To improve the reliability of BGA solder joints in complex operating environments, an underfill process is often used to reinforce the solder joints, i.e., filling the gaps between BGA solder joints with adhesive.

[0003] In actual service, BGA solder joints often bear both bending loads and random vibration loads simultaneously. The bending-vibration coupling load formed by the bending load and random vibration load leads to complex stress-strain responses within the solder joint, thereby accelerating the initiation and propagation of internal cracks. Therefore, improving the reliability of BGA solder joints under bending-vibration coupling loads is of great significance. Traditional solder joint reliability studies mostly focus on single indicators of stress and strain, and have not fully considered the influence of the first and second natural frequencies on the solder joint's response and durability under dynamic loads, thus failing to comprehensively reflect the overall mechanical properties of the solder joint.

[0004] Existing methods for optimizing solder joint structural parameters mainly include the Taguchi method, orthogonal experimental design, response surface methodology, and genetic algorithms. However, these methods are insufficient for comprehensively evaluating multi-dimensional mechanical performance indicators, making it difficult to simultaneously optimize multiple mechanical performance indicators such as stress, strain, and natural frequency. To address these issues, this invention combines response surface methodology (RSM), principal component analysis (PCA), and particle swarm optimization (PSO) to provide a method for optimizing the bending and vibration coupling mechanical properties of bottom-filled BGA solder joints. Attached Figure Description

[0005] Figure 1 The finite element model of the bottom-filled BGA solder joint provided in the embodiment of the present invention;

[0006] Figure 2 The acceleration power spectral density curve provided in the embodiment of the present invention;

[0007] Figure 3 The stress distribution cloud diagram of the weld joint provided in the embodiment of the present invention;

[0008] Figure 4 The strain distribution cloud map of the weld point provided in the embodiment of the present invention;

[0009] Figure 5 The particle swarm optimization algorithm iterative convergence curve provided in the embodiment of the present invention. Summary of the Invention

[0010] The purpose of this invention is to provide a method for optimizing the mechanical properties of underfill BGA solder joints based on RSM-PCA-PSO, thereby simultaneously optimizing the multi-dimensional mechanical properties of underfill BGA solder joints under bending and vibration coupled loads, including stress, strain, and natural frequency.

[0011] The technical solution to achieve the objective of this invention is:

[0012] A method for optimizing the mechanical properties of underfill BGA solder joints based on RSM-PCA-PSO includes the following steps:

[0013] 1) Establish a simulation analysis model of the bottom-filled BGA solder joints under bending and vibration coupled load;

[0014] 2) Obtain multiple mechanical property data of the weld joint;

[0015] 3) The response surface methodology was used to design the test schemes, and the mechanical performance index data of each test scheme were obtained through finite element simulation.

[0016] 4) Principal component analysis was used to reduce the dimensionality of multiple mechanical performance indicators and construct a standardized comprehensive score Z;

[0017] 5) Based on the normalized comprehensive score Z obtained in step 4), a regression model between the weld joint structural parameters and the normalized comprehensive score Z is established using the response surface methodology;

[0018] 6) Using the regression model obtained in step 5) as the fitness function of the particle swarm optimization algorithm, solve for the optimal combination of solder joint structure parameters;

[0019] 7) Verify the optimization effect of the optimal combination of weld point structural parameters through finite element simulation.

[0020] The structure of the simulation analysis model described in step 1) includes a chip, BGA solder joints, BT substrate, bottom filler layer, and PCB substrate.

[0021] The mechanical performance indicators mentioned in step 2) include maximum equivalent stress, maximum equivalent strain, first natural frequency, and second natural frequency.

[0022] The response surface methodology described in step 3) employs a central composite design method to design the experimental scheme.

[0023] The solder joint structural parameters mentioned in step 5) include solder joint diameter, solder joint height, solder pad diameter, and solder ball spacing.

[0024] The particle swarm optimization algorithm described in step 6) has a population size of 100, a maximum number of iterations of 50, a maximum particle velocity of 0.1, and a learning factor of 2.

[0025] This invention provides a method for optimizing the mechanical properties of underfill BGA solder joints based on RSM-PCA-PSO. The method first uses principal component analysis to objectively reduce the dimensionality of multiple mechanical performance indicators to a single normalized comprehensive score Z. Then, a regression model between the solder joint structural parameters and the normalized comprehensive score Z is established using response surface methodology. Finally, particle swarm optimization is used to optimize the normalized comprehensive score Z to obtain the optimal combination of solder joint structural parameters. This method avoids the subjectivity problem of weight setting in traditional multi-objective weighted methods and achieves simultaneous optimization of the mechanical properties of underfill BGA solder joints under bending and vibration coupled loads. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0027] A method for optimizing the mechanical properties of underfill BGA solder joints based on RSM-PCA-PSO, specifically including the following steps:

[0028] 1) Establish a simulation analysis model of the bottom-filled BGA solder joints under bending and vibration coupled load;

[0029] 2) Obtain multiple mechanical property data of the weld joint;

[0030] 3) The response surface methodology was used to design the test schemes, and the mechanical performance index data of each test scheme were obtained through finite element simulation.

[0031] 4) Principal component analysis was used to reduce the dimensionality of multiple mechanical performance indicators and construct a standardized comprehensive score Z;

[0032] 5) Based on the normalized comprehensive score Z obtained in step 4), a regression model between the weld joint structural parameters and the normalized comprehensive score Z is established using the response surface methodology;

[0033] 6) Using the regression model obtained in step 5) as the fitness function of the particle swarm optimization algorithm, solve for the optimal combination of solder joint structure parameters;

[0034] 7) Verify the optimization effect of the optimal combination of weld point structural parameters through finite element simulation.

[0035] The simulation analysis model described in step 1) includes a chip, BGA solder joints, a BT substrate, a bottom filler layer, and a PCB substrate. The chip model is an STM32F103, consisting of nine chips. The model dimensions are as follows: chip size 10mm × 10mm × 0.65mm; BT substrate size 10mm × 10mm × 0.1mm; BGA solder ball array 12×12, solder joint height 0.3mm, pad diameter 0.3mm, solder joint diameter 0.4mm, solder ball spacing 0.8mm; PCB substrate size 132mm × 77mm × 1mm according to JESD22-B113B standard; and the selected solder joint material is SAC305.

[0036] The mechanical performance indicators mentioned in step 2) include maximum equivalent stress, maximum equivalent strain, first natural frequency, and second natural frequency.

[0037] The response surface methodology described in step 3) employs a central composite design method to design the experimental scheme.

[0038] The solder joint structural parameters mentioned in step 5) include solder joint diameter, solder joint height, solder pad diameter, and solder ball spacing.

[0039] The particle swarm optimization algorithm described in step 6) has a population size of 100, a maximum number of iterations of 50, a maximum particle velocity of 0.1, and a learning factor of 2.

[0040] Example:

[0041] A method for optimizing the mechanical properties of underfill BGA solder joints based on RSM-PCA-PSO, specifically including the following steps:

[0042] 1) Use ANSYS software to create a three-dimensional finite element model of the BGA solder joints at the bottom, such as... Figure 1 As shown in Table 1, the weld joints were modeled using SOLID185 elements, while the remaining structures were modeled using SOLID45 elements. A combination of mapping and sweeping methods was used to mesh the model. The material parameters of each part of the model are shown in Table 1.

[0043] Table 1 Material Parameters

[0044]

[0045] 2) An indirect coupling method was used to apply bending vibration loads to the finite element model with bottom-filled BGA solder joints. Symmetrical supports were installed on the bottom surface of the PCB board with a span of 105mm. A bending displacement load of 1mm was applied along the positive Y-axis at the centerline of the back of the PCB board. Then, the bending analysis results were used as the initial load to continue modal analysis to obtain the natural frequencies of the model. Finally, according to... Figure 2The acceleration power spectral density curve was used to apply random vibration excitation in the positive Y direction to the model, and bending-vibration coupling was solved. Simulation analysis showed that the first natural frequency of the solder joint interconnect structure was 552.4 Hz, and the second natural frequency was 996.3 Hz. The maximum equivalent stress of the solder joint was 16.4 MPa, and the maximum equivalent stress was 4.66 × 10⁻⁶ MPa. -4 The stress distribution cloud diagram of the weld joint is as follows: Figure 3 As shown, the strain distribution contour map is as follows: Figure 4 As shown.

[0046] 3) The four solder joint structural parameters—solder joint diameter D, solder joint height H, pad diameter R, and solder ball spacing E—were used as design variables. Each variable had five levels, as shown in Table 2. The central composite design method (CCD) in response surface methodology was used to design experimental schemes, resulting in 30 experimental combinations. Finite element models were established according to the solder joint structural parameter combinations in each experimental combination, and the same bending-vibration coupling load was applied for simulation analysis. The four mechanical performance indicators of the BGA solder joints—maximum equivalent stress σ, maximum equivalent strain ε, first natural frequency f1, and second natural frequency f2—were read from each model. The simulation results are shown in Table 3.

[0047] Table 2 Factor Level Table

[0048]

[0049] Table 3 Response Surface Design and Simulation Results

[0050]

[0051] 4) To eliminate the influence of differences in dimensions and orders of magnitude on the principal component analysis results, the data of the four mechanical performance indicators in Table 3—maximum equivalent stress, maximum equivalent strain, first natural frequency, and second natural frequency—were first standardized. The standardized data were then subjected to the KMO test and Bartlett's test for sphericity. Passing both tests indicated that the data was suitable for principal component analysis.

[0052] The specific steps of principal component analysis are as follows:

[0053] Step a: Calculate the correlation coefficient matrix of each mechanical performance index;

[0054] Step b: Solve for the eigenvalues ​​and eigenvectors of the correlation coefficient matrix, and sort them in descending order of eigenvalues;

[0055] Step c: Determine the number of principal components based on the cumulative contribution rate, and select the top q principal components with a cumulative contribution rate of 85% or higher;

[0056] Step d: Calculate the score F of each principal component. iThe overall score F is obtained by weighting the variance contribution rate of each principal component.

[0057] Step e: Normalize the overall score F to obtain the normalized overall score Z.

[0058] After the above steps, the standardized comprehensive score Z corresponding to each group of test schemes can be obtained. The larger the Z value, the better the comprehensive mechanical properties corresponding to the weld joint structural parameters of that group.

[0059] The results obtained in this embodiment after following the specific steps of principal component analysis described above are shown in Table 4.

[0060] Table 4. Principal Component Analysis Results

[0061]

[0062] 5) Using the normalized comprehensive score Z as the response value, and the solder joint diameter (X1), solder joint height (X2), pad diameter (X3), and solder ball spacing (X4) as variables, a nonlinear multiple regression was performed using Design-Expert software to obtain the following multiple regression model:

[0063]

[0064] An analysis of variance (ANOVA) was performed on the regression model to test its significance. The ANOVA results showed that the p-value of the regression model in this embodiment after the F-test was 0.0261, which is less than 0.05, indicating that the regression model is significant; the p-value for the lack-of-fit term was 0.9772, which is greater than 0.05, indicating that the model lack of fit was not significant, meaning there was no obvious underfitting problem; the coefficient of determination (R²) was 95.08%, indicating high model fitting accuracy. This information shows that the regression equation in this embodiment can accurately describe the correspondence between variables and response values, providing a reliable computational model for subsequent optimization algorithms.

[0065] 6) Use the regression model obtained in step 5) as the fitness function of the particle swarm optimization (PSO) algorithm. Optimize the four weld point structural parameters with the goal of maximizing the normalized comprehensive score Z. Set the PSO algorithm constraints as follows: 0.40≤X1≤0.48, 0.30≤X2≤0.38, 0.26≤X3≤0.34, 0.74≤X4≤0.82. Set the PSO algorithm parameters as follows: population size 100, maximum number of iterations 50, maximum particle velocity 0.1, and learning factor 2. When the fitness value changes by less than 10 over 20 consecutive iterations... -6 The algorithm was determined to have converged at this point. After iterative optimization, the algorithm finally converged in the 23rd generation, achieving an optimal fitness value of 0.99997. The particle swarm optimization algorithm's iterative convergence curve is shown below. Figure 5As shown, the optimal combination of solder joint structure parameters at this time is: solder joint diameter 0.47mm, solder joint height 0.37mm, pad diameter 0.34mm, and ball spacing 0.80mm.

[0066] 7) Based on the optimal solder joint structural parameter combination obtained in step 6) (solder joint diameter 0.47mm, solder joint height 0.37mm, pad diameter 0.34mm, solder ball spacing 0.80mm), a new finite element model of the bottom-filled BGA solder joint was established, and the same bending-vibration coupling load as in step 1) was applied for simulation analysis. The simulation analysis results were extracted to obtain the maximum equivalent stress, maximum equivalent strain, first natural frequency, and second natural frequency data of the optimized solder joint, and compared with the data of the unoptimized solder joint in step 2) (solder joint diameter 0.4mm, solder joint height 0.3mm, pad diameter 0.3mm, solder ball spacing 0.8mm). The comparison of mechanical performance data before and after optimization is shown in Table 5.

[0067] Table 5 Comparison of mechanical performance data before and after optimization

[0068]

[0069] Reducing stress can decrease the probability of weld joint crack initiation, thereby increasing the service life of the weld joint under bending-vibration coupled loads. Conversely, increasing the natural frequency can reduce the structural response amplitude of the weld joint under dynamic loads, thus enhancing its resistance to bending-vibration coupled loads. As shown in Table 5, after optimization using the method of this invention, the maximum equivalent stress and maximum equivalent strain of the bottom-filled BGA weld joint are effectively reduced, while the first and second natural frequencies are effectively increased, achieving comprehensive optimization of the mechanical properties of the bottom-filled BGA weld joint under bending-vibration coupled loads.

Claims

1. A method for optimizing the mechanical properties of underfill BGA solder joints based on RSM-PCA-PSO, characterized in that, Includes the following steps: 1) Establish a simulation analysis model of the bottom-filled BGA solder joints under bending and vibration coupled load; 2) Obtain multiple mechanical property data of the weld joint; 3) The response surface methodology was used to design the test schemes, and the mechanical performance index data of each test scheme were obtained through finite element simulation. 4) Principal component analysis was used to reduce the dimensionality of multiple mechanical performance indicators and construct a standardized comprehensive score Z; 5) Based on the normalized comprehensive score Z obtained in step 4), a regression model between the weld joint structural parameters and the normalized comprehensive score Z is established using the response surface methodology; 6) Using the regression model obtained in step 5) as the fitness function of the particle swarm optimization algorithm, solve for the optimal combination of solder joint structure parameters; 7) Verify the optimization effect of the optimal combination of weld point structural parameters through finite element simulation.

2. The method according to claim 1, characterized in that: The structure of the simulation analysis model described in step 1) includes a chip, BGA solder joints, BT substrate, bottom filler layer, and PCB substrate.

3. The method according to claim 1, characterized in that: The mechanical performance indicators mentioned in step 2) include maximum equivalent stress, maximum equivalent strain, first natural frequency, and second natural frequency.

4. The method according to claim 1, characterized in that: The response surface methodology described in step 3) employs a central composite design method to design the experimental scheme.

5. The method according to claim 1, characterized in that: The solder joint structural parameters mentioned in step 5) include solder joint diameter, solder joint height, solder pad diameter, and solder ball spacing.

6. The method according to claim 1, characterized in that: The particle swarm optimization algorithm described in step 6) has a population size of 100, a maximum number of iterations of 50, a maximum particle velocity of 0.1, and a learning factor of 2.

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