POP stack welding spot thermal stress dual-objective optimization method based on Taguchi test-grey correlation analysis method

Abstract

The invention discloses a Taguchi test-grey correlation analysis method-based POP stack welding spot thermal stress dual-objective optimization method, and relates to the technical field of electronic component packaging interconnection reliability. The method comprises the steps that a POP stack welding spot simulation analysis model is established based on ANSYS software, power cycle loading finite element analysis is applied to the model, the maximum thermal stress value of welding spots on the upper layer and the lower layer of the POP model is obtained, various parameters influencing the thermal stress value are determined, and the thermal stress of the welding spots serves as target values; 27 groups of test combinations with different parameter levels are designed by adopting a Taguchi test method, modeling simulation is carried out, then double-target optimization is carried out on the upper layer welding spot stress and the lower layer welding spot stress by utilizing a grey correlation method, and the accuracy of an optimization result is verified through simulation. The method is simple and convenient in calculation and good in performance, and certain reference significance is provided for optimization design of interconnection structure parameters of other welding spots.

Description

Technical Field

[0001] This invention relates to the field of electronic component packaging interconnect reliability technology, specifically to a dual-objective optimization method for thermal stress of POP stack solder joints based on Taguchi test-grey relational analysis. Background Technology

[0002] With the continued rapid growth of the electronics and information industry, integrated circuits have evolved from small-scale, medium-scale, and large-scale to ultra-large-scale and very-large-scale. In line with this trend, electronic packaging has gradually shifted from traditional 2D packaging to 3D high-density packaging. Package-on-package (POP) stacking, due to its high integration, miniaturization, and lightweight advantages, is the mainstream 3D packaging technology in the industry and has been widely applied in aerospace, automotive, and communications fields. During service, POP-packaged electronic devices are subjected to varying power levels due to periodic power switching, and the temperature fluctuations caused by these instantaneous power changes subject the devices to cyclical temperature loads. Because the thermal expansion coefficients of the chip, substrate, and solder joints differ, POP solder joints may crack or even break under cyclical temperature changes, leading to the failure of the entire packaged device. Good thermal design can extend the service life of POP stacked solder joints, thereby improving the reliability of electronic products.

[0003] Taguchi experimental design is a statistical method primarily used for robust product and process design. This method identifies key factors in a product or process through experimental design and assesses their impact on product performance. The core of Taguchi experimental design lies in "parametric design," which reduces sensitivity to changes in the external environment by altering controllable parameters of the product or process. It emphasizes considering product performance under different conditions during the design phase to optimize product performance. The method includes the following steps: identifying key quality characteristics of the product or process; identifying factors that may affect these quality characteristics; arranging experiments using orthogonal experimental design to assess the impact of each factor on the quality characteristics; analyzing the experimental results to determine which factors are the main influencing factors; and adjusting the design based on the analysis results to reduce variation and improve the stability of the product or process. The advantage of Taguchi experimental design lies in its systematic nature, enabling rapid identification and optimization of key factors, improving the reliability and robustness of products or processes. It also helps reduce the number of experiments, saving time and costs. This method has wide applications in many fields, including electronics, machinery, and chemical engineering.

[0004] Grey relational analysis is a multivariate statistical analysis method that simplifies the analysis process by transforming complex multi-factor problems into single-factor problems. Its basic idea is to convert the raw data of each indicator into a dimensionless grey series to eliminate the influence of dimensions between different indicators, and then measure the similarity or correlation between the indicators through the calculation of grey relational degree. The calculation of grey relational degree typically includes the following steps: dimensionless processing of the indicator data to generate reference and comparison series; calculation of the grey relational degree between each comparison series and the reference series; and determining the degree of influence of each indicator on the decision objective based on the magnitude of the correlation degree. The numerical range of grey relational degree is [0,1]. The larger the value, the stronger the correlation between the indicator and the objective. The advantage of this method is its low dependence on data, allowing for effective analysis even when data is incomplete or uncertain. Grey relational analysis is applicable not only to single-objective decision problems but also to complex system optimization and parameter selection problems involving multiple parameters and objectives. It can help decision-makers identify key factors, optimize resource allocation, and improve the scientific nature and effectiveness of decision-making. Summary of the Invention

[0005] This invention aims to overcome the shortcomings of existing technologies and provide a dual-objective optimization method for thermal stress of POP stack solder joints based on Taguchi experiment-grey relational analysis. This method combines Taguchi experiment and grey relational analysis to reduce the maximum thermal stress in POP stack solder joints. The method has good performance and is easy to calculate, which greatly facilitates the optimization design of POP stack solder joint structural parameters. The optimized simulation results are quite ideal.

[0006] The technical solution to achieve the objective of this invention is:

[0007] A dual-objective optimization method for thermal stress of POP stack solder joints based on Taguchi experiment-grey relational analysis includes the following steps:

[0008] Step 1: Establish a simulation analysis model of POP stacked solder joints based on ANSYS and perform power cyclic loading analysis;

[0009] Step 2: Obtain the maximum values ​​of thermal stress in the upper and lower layers of the POP stack solder joint model, as well as the stress-time curve and temperature-time curve;

[0010] Step 3: Determine the structural parameters that affect the thermal stress of the POP stack solder joints and the level values ​​of each structural parameter;

[0011] Step 4: Using the Taguchi experimental method, design 27 sets of horizontal combinations of POP stack solder joint structural parameters, and establish 27 sets of simulation models to apply power cycles for finite element analysis;

[0012] Step 5: The obtained simulation results of 27 groups of POP stacked solder joints are subjected to dimensionless normalization based on the range transformation method;

[0013] Step 6: Based on the principle of grey relational analysis, set the weight coefficient λ of each POP stack solder joint to 0.5, and perform grey relational analysis on the 27 sets of POP stack solder joint simulation results after range transformation processing obtained in Step 5 to obtain the grey relational coefficient.

[0014] Step 7: Calculate the average correlation degree of each factor based on the 27 sets of grey relational coefficients obtained in Step 6. The level value with the highest average correlation degree of each factor is the optimal parameter level combination.

[0015] Step 8: Combine the optimal values ​​obtained in Step 7, i.e. the optimal parameter levels of the POP stacked solder joints under power cyclic load, and use ANSYS to establish an optimized POP stacked solder joint analysis model for simulation verification.

[0016] The POP stack solder joint simulation analysis model described in Step 1 includes two layers of solder joints, two layers of pads, two layers of chips, and three layers of PCB boards. The top layer has 72 solder joints, and the bottom layer has 120 solder joints. The top layer chip dimensions are 7.15mm × 7.15mm × 0.20mm, the middle layer chip dimensions are 4.5mm × 4.5mm × 0.20mm, the top layer PCB board dimensions are 7.15mm × 7.15mm × 0.13mm, and the middle layer PCB board dimensions are 7.15mm × 7.15mm × 0.20mm. The lower PCB board has dimensions of 9.1mm × 7.15mm × 1.2mm. The upper solder joint diameter is 0.40mm, the upper solder joint height is 0.30mm, and the upper solder joint spacing is 0.65mm. The lower solder joint diameter is 0.30mm, the lower solder joint height is 0.23mm, and the lower solder joint spacing is 0.50mm. The upper copper pad is φ0.28mm × 0.02mm, and the lower copper pad is φ0.21mm × 0.02mm. Both upper and lower solder joints are made of SAC305.

[0017] The power cyclic loading analysis described in step 1 uses a thermal-structural coupling approach to simulate the power cyclic loading of the POP stack solder joints. First, all structural units of the POP stack solder joint model are set as thermal units (SOLID70) for thermal analysis. Cyclic thermal power is applied to the chip in the form of power density. A value of 5 W / (m²) is set on the surface of the POP stack solder joint model. 2The air convection heat transfer coefficient (K) was calculated. The initial temperature was set to 20℃. Thermal analysis was performed to obtain the temperature field. Subsequently, structural analysis was conducted. The solder joint structural element was set to VISCO107, and other structural elements were set to SOLID45. The temperature field was applied as a volume load to the POP stack solder joint model for analysis. The boundary condition applied to the POP stack solder joint model was to constrain all four edges of the bottom surface of the PCB board.

[0018] The structural parameters of the POP stacked solder joints mentioned in step 3 include one or more of the following: upper layer solder joint height, lower layer solder joint height, top layer PCB thickness, and middle layer PCB thickness. The level of each structural parameter is 4.

[0019] The dimensionless normalization formula mentioned in step 5 is as follows: In the formula, X represents the original data, x represents the data after range transformation, max(x) and min(x) are the minimum and maximum values ​​in the original data sequence, respectively, and all data are in the range [0,1] after processing.

[0020] The formula for the grey relational degree weighting coefficient of the all-factor level combination experiment scheme described in step 6 is R = λ1q i,1 +λ2q i,2 The calculation formula for grey relational analysis is: In the formula, i = 1, 2, ..., 16, j = 1, 2, ρ is the resolution coefficient, usually taken as 0.5, z j =max(y 1,j y 2,j ), j = 1, 2, the idealized combination of structural parameter levels is used as the reference sequence, and the 27 experimental combinations designed by Taguchi are used as the comparison sequence, denoted as q. i,j Let be the correlation coefficient between the i-th comparison sequence and the j-th index in the reference sequence Z.

[0021] This invention provides a dual-objective optimization method for thermal stress of POP stack solder joints based on Taguchi experiments and grey relational analysis. This method combines Taguchi experiments and grey relational analysis to reduce thermal stress of POP stack solder joints under power cyclic loading. Twenty-seven sets of experiments were designed using the Taguchi experiment method, and data was obtained through ANSYS modeling and simulation. The maximum thermal stress value of the obtained POP stack solder joints was then dimensionlessized using range analysis to prevent order-of-magnitude differences caused by varying structural parameters. Finally, grey relational analysis was used to perform dual-objective optimization on the maximum values ​​of the dimensionless upper and lower layer solder joint stresses, achieving the goal of optimizing the structural parameters of the POP stack solder joints. This method reduces the maximum stress of the upper and lower layer solder joints in the POP stack, providing theoretical guidance for improving the interconnect reliability of POP stack solder joints. Attached Figure Description

[0022] Figure 1 This is a flowchart of the method of the present invention;

[0023] Figure 2 This is a simulation analysis model diagram of POP stacked solder joints provided in an embodiment of the present invention;

[0024] Figure 3 The power density curve provided for the embodiments of the present invention;

[0025] Figure 4 The stress-time curve of the POP stack solder joint provided in the embodiment of the present invention;

[0026] Figure 5 The temperature-time curve of the POP stack solder joint provided in the embodiment of the present invention;

[0027] Figure 6 The stress values ​​of the upper and lower solder joints of the POP stacked solder joint provided in the embodiments of the present invention;

[0028] Figure 7 The optimal parameter horizontal combination provided in this embodiment of the invention refers to the stress values ​​of the upper and lower layers of solder joints in the POP stack. Detailed Implementation

[0029] The specific embodiments of the present invention will be described in more detail below with reference to the schematic diagrams, but this is not intended to limit the invention. The advantages and features of the present invention will become clearer from the following description and claims. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0030] Example:

[0031] like Figure 1 As shown, a dual-objective optimization method for thermal stress of POP stack solder joints based on Taguchi experiment-grey relational analysis includes:

[0032] Step S1: Establish an ANSYS simulation analysis model for POP stacked solder joints, such as... Figure 2As shown, the top layer chip size is 7.15mm×7.15mm×0.20mm, the middle layer chip size is 4.5mm×4.5mm×0.20mm, the top layer PCB board size is 7.15mm×7.15mm×0.13mm, the middle layer PCB board size is 7.15mm×7.15mm×0.30mm, the bottom layer PCB board size is 9.1mm×7.15mm×1.2mm, the upper layer solder joint diameter is 0.40mm, the upper layer solder joint height is 0.30mm, the upper layer solder joint spacing is 0.65mm, the lower layer solder joint diameter is 0.30mm, the lower layer solder joint height is 0.23mm, the lower layer solder joint spacing is 0.50mm, the upper layer copper pad is φ0.28mm×0.02mm, the lower layer copper pad is φ0.21mm×0.02mm, and both the upper and lower layer solder joints are made of SAC305.

[0033] POP stack solder joints were simulated using a thermal-structural coupling approach with power cyclic loading. First, all structural units of the POP stack solder joint model were set as thermal units (SOLID70) for thermal analysis. Cyclic thermal power was applied to the chip in the form of power density. A value of 5 W / (m²) was set on the surface of the POP stack solder joint model. 2 The air convection heat transfer coefficient (K) was calculated, and the initial temperature was set to 20℃. Thermal analysis was performed to obtain the temperature field, and the power cycle curve is shown below. Figure 3 As shown, the highest power density of this curve is 55 × 10⁻⁶. 6 W / m 3 The minimum power density is 1.2 × 10⁻⁶. 6 W / m 3 One cycle of high and low power operation lasts 10 minutes, and the power increase and decrease time is 5 minutes, with a total of 6 power cycles. Structural analysis was then performed, with the solder joint structural elements set to VISCO107 and other structural elements set to SOLID45. The temperature field was applied as a volume load to the POP stack solder joint model for analysis. Specific material parameters are shown in the table below.

[0034] Table 1 Material parameters of POP stack solder joint interconnection structure model

[0035]

[0036] To more accurately analyze the stress distribution of POP stack solder joints under power cyclic loading, the ANAND viscoplastic model was used to analyze the inelastic compressibility-related deformation behavior of the solder. The ANAND model parameters of SAC305 solder are shown in Table 2.

[0037] Table 2 SAC305 ANAND Model Parameters

[0038]

[0039] Step S2: Following step S1, the stress-time curves of the POP stack solder joints and the temperature-time curves of the POP chip under power cyclic loading were obtained, as shown below. Figure 4 and Figure 5 As shown, stress distribution cloud maps of the upper and lower solder joints of the POP stacked solder joint model were obtained, as follows. Figure 6 As shown, the maximum stress value of the upper layer solder joint was 14.3 MPa, and the maximum stress value of the lower layer solder joint was 15.075 MPa.

[0040] Step S3: Determine the structural parameters affecting the thermal stress of POP stack solder joints under power cyclic load and the level values ​​of each structural parameter. These parameters include the upper layer solder joint height H1, the lower layer solder joint height H2, the top layer PCB thickness D1, and the middle layer PCB thickness D2. The level value for each structural parameter is 3, as shown in the table below:

[0041] Table 3. POP stacking package structure parameters and levels

[0042]

[0043]

[0044] Step S4: Construct an orthogonal array L using the Taguchi experiment method. 27 (3 4 Twenty-seven test schemes with different structural parameters and level combinations were determined. The 27 test combinations are shown in the table below:

[0045] Table 4. Orthogonal array and simulation results of the Taguchi experiment.

[0046]

[0047] Step S5: The stress of the upper and lower solder joints in the POP stack solder joint model under power cyclic loading is dimensionless by range analysis, as shown in the following formula:

[0048]

[0049] In the formula, X represents the original data, x represents the data after range transformation, and max(x) and min(x) are the minimum and maximum values ​​in the original data sequence, respectively. All data are within the range [0,1] after processing. The range transformation processed data is shown in the table below:

[0050] Table 5 Range Transformation Processing

[0051]

[0052]

[0053] Step S6: Based on the principle of grey relational analysis, the weight coefficient λ of each POP stack solder joint is set to 0.5. Grey relational analysis is then performed on the data after range transformation to obtain the grey relational coefficients, as shown in the table below:

[0054] Table 6. Grey Relation Coefficient and Relation Degree of the Two-Objective System

[0055]

[0056]

[0057] Step S7: When performing dual-objective optimization of the solder joint stress of POP stack under power cyclic load, it is necessary to reduce the stress of the upper and lower solder joints simultaneously. Therefore, when determining the optimal parameter level combination for POP stack packaging, it is necessary to analyze the average correlation of each parameter level. The maximum average correlation is the optimal parameter level. The average correlation of each parameter level with the solder joint stress is calculated as shown in the table below:

[0058] Table 7 Average Correlation of Stress at POP Stack Solder Joints

[0059]

[0060] As shown in the table above, the optimal levels for each structural parameter are: upper layer solder joint height H1 = 0.35 mm, lower layer solder joint height H2 = 0.28 mm, top layer substrate thickness D1 = 0.1 mm, and middle layer substrate thickness D2 = 0.3 mm. In other words, the optimal parameter combination for simultaneously optimizing the stress of the upper and lower layer solder joints in POP stacked packaging is H13, H23, D11, and D22.

[0061] Step S8: Combine the optimal structural parameters of the POP stacked solder joints under power cyclic loading obtained in Step S7, and use ANSYS to establish an optimized POP stacked solder joint analysis model for simulation verification. The stress distribution diagrams of the upper and lower solder joints in the optimized POP stacked solder joint model are shown below. Figure 7 As shown;

[0062] Under power cyclic loading, the maximum stress value of the upper layer of the optimal combination of structural parameters for POP stacked solder joints is 13.92 MPa, and the maximum stress value of the lower layer is 14.658 MPa. Compared with the original combination of structural parameters of 14.3 MPa and 15.075 MPa, the values ​​are reduced by 2.7% and 2.8%, respectively. This indicates that by optimizing the structural parameters of POP stacked solder joints through grey relational analysis, the thermal reliability of POP stacked solder joints has been greatly improved.

[0063] In summary, the dual-objective optimization method for thermal stress of POP stacked solder joints based on Taguchi experiment-grey relational analysis provided in this embodiment of the invention first establishes a simulation analysis model of POP stacked solder joints based on ANSYS, and performs power cyclic loading analysis to obtain the maximum thermal stress value. Then, it determines the structural parameters that affect the thermal stress value of POP stacked solder joints, designs 27 sets of horizontal combinations of POP stacked solder joint structural parameters using the Taguchi experiment method, and then uses the range analysis method to perform dimensionless processing on the obtained maximum thermal stress value of POP stacked solder joints. Finally, it uses grey relational analysis to perform dual-objective optimization on the maximum values ​​of the upper and lower layer solder joint stresses after dimensionless processing, and performs simulation verification on the optimal horizontal combination of structural parameters. The simulation results show that the maximum thermal stress value of the optimized POP stacked solder joints is reduced by 2.7% and 2.8% compared with the original combination, verifying the accuracy of the method.

[0064] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the scope of protection of the present invention.

Claims

1. A POP stack joint thermal stress double-target optimization method based on Taguchi experiment-gray correlation analysis method, characterized in that, Comprising the following steps: Step 1: based on ANSYS, a POP stack solder joint simulation analysis model is established and power cycle loading analysis is carried out; Step 2: the maximum value of the thermal stress of the upper and lower solder joints of the POP stack solder joint model, and the stress-time curve and temperature-time curve are obtained; Step 3: the structural parameters affecting the thermal stress of the POP stack solder joint and the level values of each structural parameter are determined; Step 4: 27 groups of POP stack solder joint structural parameter level combinations are designed by using Taguchi test method, and 27 simulation models are established respectively to apply power cycle for finite element analysis; Step 5: the 27 groups of POP stack solder joint simulation results obtained are normalized based on range transformation method; Step 6: according to the principle of grey correlation method, the weight coefficient λ of each POP stack solder joint is set to 0.5, and the grey correlation analysis of the 27 groups of POP stack solder joint simulation results obtained by range transformation is carried out to obtain the grey correlation coefficient; Step 7: the average correlation degree of each factor is calculated according to the 27 groups of grey correlation coefficients obtained in step 6, and the level value with the largest average correlation degree is the optimal parameter level combination; Step 8: the optimal value obtained in step 7, i.e. the optimal parameter level combination of the POP stack solder joint under power cycle load, is used to establish an optimized POP stack solder joint analysis model by ANSYS for simulation verification.

2. The POP stack joint thermal stress double-target optimization method based on the Taguchi experiment-gray correlation analysis method according to claim 1, characterized in that, The POP stack solder joint simulation analysis model in step 1 comprises two layers of solder joints, two layers of pads, two layers of chips and three layers of PCBs, the upper layer has 72 solder joints and the lower layer has 120 solder joints, wherein the top chip has a size of 7.15mmx7.15mmx0.20mm, the middle chip has a size of 4.5mmx4.5mmx0.20mm, the top PCB has a size of 7.15mmx7.15mmx0.13mm, the middle PCB has a size of 7.15mmx7.15mmx0.30mm, the lower PCB has a size of 9.1mmx7.15mmx1.2mm, the upper solder joint has a diameter of 0.40mm, the upper solder joint has a height of 0.30mm, the upper solder joint has a spacing of 0.65mm, the lower solder joint has a diameter of 0.30mm, the lower solder joint has a height of 0.23mm, the lower solder joint has a spacing of 0.50mm, the upper copper pad has a size of φ0.28mmx0.02mm, the lower copper pad has a size of φ0.21mmx0.02mm, and the upper and lower solder joints are both made of SAC305.

3. The POP stack joint thermal stress double-target optimization method based on the Taguchi experiment-gray correlation analysis method according to claim 1, characterized in that, The power cycle loading analysis described in Step 1 uses a thermal-structural coupling method to simulate the power cycle loading of the POP stack solder joint. All structural elements of the POP stack solder joint model are first set as thermal elements SOLID70 for thermal analysis. The chip is subjected to cyclic thermal power in the form of power density. An air convection heat transfer coefficient of 5 W / (m 2 K) is set on the surface of the POP stack solder joint model, the initial temperature is set to 20℃, and the temperature field is obtained by loading thermal analysis. Subsequently, structural analysis is performed, the solder joint structural elements are set as VISCO107, and other structural elements are set as SOLID45. The temperature field is applied as a body load to the POP stack solder joint model for analysis. The boundary conditions applied to the POP stack solder joint model are that all 4 edges of the PCB board bottom surface are constrained.

4. The POP stack joint thermal stress double-target optimization method based on the Taguchi experiment-gray correlation analysis method according to claim 1, characterized in that, The POP stack solder joint structural parameters in step 3 include one or more of the upper solder joint height, the lower solder joint height, the top PCB thickness and the middle PCB thickness, and the level of each structural parameter is 4.

5. The POP stack joint thermal stress double-target optimization method based on the Taguchi experiment-gray correlation analysis method according to claim 1, characterized in that, The non-dimensional normalization processing formula described in step 5 is In the formula, K is the original data, x is the data after range transformation processing, max(x) and min(x) are the minimum and maximum values in the original data sequence respectively, and all data is processed to be in [0, 1].

6. The POP stack joint thermal stress double-target optimization method based on the Taguchi experiment-gray correlation analysis method according to claim 1, characterized in that, The grey correlation degree weight coefficient formula of the test scheme of all factor level combinations in step 6 is R = λ1q i,1 + λ2q i,2 The calculation formula of the grey correlation analysis is In the formula, i = 1, 2, …, 16, j = 1, 2, ρ is a resolution coefficient, usually taken as 0.5, z j = max(y 1,j , y 2,j ), j = 1, 2, the idealized structure parameter level combination is taken as a reference sequence, and the 27 test combinations of the Taguchi design are taken as comparison sequences, and q i,j is the correlation coefficient between the ith comparison sequence and the jth index in the reference sequence Z.

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