Response surface optimization method of power device packaging thermal resistor

Abstract

The invention relates to a response surface optimization method of a power device packaging thermal resistor, and aims to solve the problems of low efficiency and high cost of a traditional optimization method. According to the method, a three-level seven-factor orthogonal standard configuration table is configured, a packaging thermal resistance simulation model is combined, and an orthogonal experiment method is adopted to carry out combined simulation testing on parameters such as the chip area, the chip thickness, the welding layer thickness, the frame thickness, a plastic packaging material, a welding material and a lead frame material which affect thermal resistance. The deviation sum of squares, the degree of freedom and the F ratio of all the factors are calculated through variance analysis, and the factors remarkably influencing the thermal resistance are screened out. And further establishing a thermal resistance prediction model by using a response surface method, analyzing the interactive influence among significant factors in combination with a polynomial regression equation, finding out a parameter combination of a minimum thermal resistance value, and verifying an optimization effect through simulation. According to the method, the efficiency and the precision of packaging thermal resistance optimization are remarkably improved, the experiment cost is reduced, and the method is suitable for optimization design of a power device packaging process.

Description

Technical Field

[0001] The present invention relates to the technical field of power devices, and particularly relates to a response surface optimization method for the thermal resistance of power device packaging. Background Art

[0002] Under high power density operating conditions, the Joule heat generated by the current / voltage effect in power devices will cause the device junction temperature to rise, which will further lead to performance degradation or even failure. As the core index to measure the heat dissipation ability of devices, the packaging thermal resistance directly affects its reliability and stability. The chip packaging structure parameters (such as area, thickness) and the selection of packaging materials (such as solder layer, frame material) are the key factors determining the thermal resistance. Among them, the packaging structure design has become an important direction for thermal resistance optimization due to its flexible adjustability.

[0003] Traditional thermal resistance optimization methods have significant deficiencies:

[0004] Unknown interaction mechanism: Existing research lacks a systematic analysis of the thermal resistance influence mechanism under the coupling action of multiple factors, resulting in the easy omission of key factors during the optimization process and affecting the optimization effect.

[0005] Limited global optimization ability: The single variable method or the orthogonal experiment method can only achieve local parameter optimization and cannot perform global optimization within the full variable range; although the response surface method has the potential for global prediction, the screening of significant factors in existing applications is not accurate enough, resulting in insufficient model accuracy.

[0006] High data cost: Intelligent algorithms rely on a large amount of simulation or experimental data to train models, with high time and economic costs, and it is difficult to meet the requirements of rapid engineering iteration.

[0007] Therefore, there is an urgent need for an efficient and accurate thermal resistance optimization method to globally optimize the packaging thermal resistance under the interaction of multiple factors by scientifically screening significant influencing factors and constructing a high-precision prediction model, so as to provide support for the high-reliability design of power devices. Summary of the Invention

[0008] The purpose of the present invention is to provide a response surface optimization method for the thermal resistance of power device packaging to solve the above problems.

[0009] A response surface optimization method for the thermal resistance of power device packaging includes configuring an orthogonal standard configuration table with 7 factors at 3 levels, and includes the following steps:

[0010] S1. Construct a simulation model for the thermal resistance of the power device packaging according to the power device, and configure an orthogonal standard configuration table with 7 factors at 3 levels;

[0011] S2. The encapsulation thermal resistance simulation model obtains each influencing factor and its parameters in the orthogonal standard configuration table, and uses the orthogonal experiment method to conduct combined simulation tests on the parameters of each influencing factor to obtain the thermal resistance under this combination, and forms an orthogonal result table with this combination and the corresponding thermal resistance;

[0012] S3. Conduct variance analysis calculation on the orthogonal result table to obtain the orthogonal result variance analysis table;

[0013] S4. Compare the significance characteristic values of each influencing factor in the orthogonal result variance analysis table with the significance preset threshold to screen out the significant factors, and integrate the screened significant factors into a significant factor table;

[0014] S5. The encapsulation thermal resistance simulation model obtains different parameters of the significant factors in the significant factor table, combines different parameters of each significant factor, conducts simulation tests to calculate the thermal resistance values between different combinations, and constructs a response surface thermal resistance simulation table;

[0015] S6. Obtain the thermal resistance values in the response surface thermal resistance simulation table as the response values of the second-order polynomial to construct a response surface model expression, and substitute the different parameter combinations and corresponding thermal resistance values of each significant factor in the response surface thermal resistance simulation table into the response surface model expression to obtain the polynomial regression equation of the response surface prediction model;

[0016] S7. Analyze the interaction effects between significant factors, and calculate and find the optimal significant factor parameter combination with the minimum thermal resistance under the parameter constraints of the polynomial regression equation of the response surface prediction model based on the interaction effects between significant factors;

[0017] S8. The encapsulation thermal resistance simulation model obtains the optimal significant factor parameter combination for modeling and simulation, outputs the simulated thermal resistance, and compares and verifies it with the minimum thermal resistance value.

[0018] This application realizes the global optimization of thermal resistance under the interaction of multiple factors through the combination of orthogonal experiments and response surface method. By constructing an encapsulation thermal resistance simulation model, an orthogonal standard configuration table including 7 controllable variables (3 levels) such as chip area, thickness, and solder layer thickness is designed. The thermal resistance values of different parameter combinations are obtained through orthogonal experiments. The F ratios of each factor are calculated through variance analysis, and the key factors significantly affecting thermal resistance (such as chip area, chip thickness, solder layer thickness, and frame thickness) are screened out. A response surface experiment is designed for the significant factors, and a second-order polynomial regression equation with thermal resistance as the response value is constructed. The interaction effects between factors are analyzed, and the optimal parameter combination corresponding to the minimum thermal resistance value is solved under parameter constraints. Finally, the optimization results are verified through simulation to ensure the accuracy of model prediction.

[0019] Further,

[0020] The influencing factors in the orthogonal standard configuration table of 3 levels and 7 factors are controllable variables in the chip packaging process. The controllable variables include chip area, chip thickness, solder layer thickness, frame thickness, encapsulation material, solder material, and lead frame material. Each controllable variable also has its own different parameters.

[0021] Furthermore,

[0022] The orthogonal result variance analysis table includes the control variables and the sum of squared deviations, degrees of freedom, and F ratio corresponding to each control variable. The sum of squared deviations is used to measure the differences caused by various factors or errors. The degrees of freedom represent the number of independent pieces of information. The F ratio is the significance characteristic value of each influencing factor and is used to test the significance of the influencing factors.

[0023] Furthermore,

[0024] The F ratio of each influencing factor satisfies the calculation formula: In the formula, F factor is the F ratio of the influencing factor, SS factor is the sum of squared deviations of the influencing factor, df factor is the degrees of freedom of the influencing factor, SS E is the sum of squared error deviations, and df E is the degrees of freedom of the error.

[0025] Furthermore,

[0026] The comparison of the significance characteristic value with the significance preset threshold is specifically as follows: If the significance characteristic value F of the influencing factor 因素 is greater than the significance preset threshold, it is a significant factor. If the significance characteristic value F of the influencing factor 因素 is less than or equal to the significance preset threshold, it is a normal factor. Based on this, four significant influencing factors are selected.

[0027] Furthermore,

[0028] The setting of the significance preset threshold is determined by referring to the statistical F distribution table.

[0029] Furthermore,

[0030] The expression of the response surface model is: In the formula, y is the response variable, x i is the dependent variable, β0 is the constant term, β i is the linear term, β ii is the quadratic term coefficient, β ij is the quadratic interaction term coefficient, and ò is the error term.

[0031] Furthermore,

[0032] The polynomial regression equation of the response surface prediction model satisfies the calculation formula:

[0033] R jc = 0.6889 - 0.7423A + 0.013B + 0.2565C + 0.0223D + 0.0066AB - 0.3344AC - 0.0209AD -.

[0034] 0.005BC - 0.0027BD - 0.0044CD + 0.4896A 2 - 0.0313B 2 + 0.0027C 2 - 0.0208D 2

[0035] In the formula, the described R jc is the thermal resistance value, and A, B, C, and D represent the parameters of four selected significant factors.

[0036] The beneficial effects of the present invention are as follows:

[0037] 1. Based on significant factors, a response surface model is constructed, and the influence of multi-factor interaction on thermal resistance is described by a second-order polynomial regression equation, breaking through the limitation that traditional orthogonal experiments can only achieve local parameter optimization, and searching for the optimal solution within the full variable range.

[0038] 2. In the orthogonal experiment stage, the number of simulations is reduced through a standardized configuration table (only 18 groups of orthogonal experiments are required), and significant factors are quickly screened by combining variance analysis; the response surface experiment further focuses on 4 key significant factors, avoiding the explosive calculation amount of all-factor combinations. Compared with the massive data training relied on by intelligent algorithms, this method significantly reduces time and economic costs and is suitable for rapid engineering iteration.

[0039] 3. Through the orthogonal experiment design and variance analysis of 7 factors at 3 levels, factors that have a significant impact on thermal resistance are quantitatively screened based on the F ratio, irrelevant variables are eliminated, resources are prevented from being consumed on secondary factors, and the optimization focus is concentrated on the core parameters that truly affect thermal resistance, improving the optimization pertinence. Description of the Drawings

[0040] Figure 1 is the logic flow chart of the present invention;

[0041] Figure 2 is the orthogonal standard configuration table of 7 factors at 3 levels;

[0042] Figure 3 is the orthogonal result table;

[0043] Figure 4 is the orthogonal result variance analysis table;

[0044] Figure 5 is the significant factor table;

[0045] Figure 6 It is the response surface thermal resistance simulation table;

[0046] Figure 7 It is the response surface analysis diagram of the interactive influence of chip area and chip thickness on thermal resistance;

[0047] Figure 8 It is the response surface analysis diagram of the interactive influence of chip area and solder layer thickness on thermal resistance;

[0048] Figure 9 It is the response surface analysis diagram of the interactive influence of chip area and frame thickness on thermal resistance;

[0049] Figure 10 It is the comparison diagram of simulation model verification before and after optimization. Specific implementation manners

[0050] The present invention will be further described in detail below in conjunction with embodiments and the accompanying drawings, but the implementation manners of the present invention are not limited thereto.

[0051] Embodiment, as Figures 1 to 10 shown:

[0052] A response surface optimization method for the thermal resistance of a power device package, including configuring an orthogonal standard configuration table with 7 factors at 3 levels, and including the following steps:

[0053] S1. Construct a thermal resistance simulation model of the power device package according to the power device, and configure an orthogonal standard configuration table with 7 factors at 3 levels;

[0054] S2. The thermal resistance simulation model of the package obtains the influencing factors and their parameters in the orthogonal standard configuration table, and uses the orthogonal experiment method to perform combined simulation tests on the parameters of each influencing factor to obtain the thermal resistance under this combination, and forms an orthogonal result table with this combination and the corresponding thermal resistance;

[0055] S3. Perform variance analysis calculation on the orthogonal result table to obtain an orthogonal result variance analysis table;

[0056] S4. Compare the significance characteristic values of each influencing factor in the orthogonal result variance analysis table with a significance preset threshold to screen out significant factors, and integrate the screened significant factors into a significant factor table;

[0057] S5. The thermal resistance simulation model of the package obtains different parameters of the significant factors in the significant factor table, combines different parameters of each significant factor, performs simulation tests to calculate the thermal resistance values between different combinations, and constructs a response surface thermal resistance simulation table;

[0058] S6. Obtain the thermal resistance values in the response surface thermal resistance simulation table as the response values of the second-order polynomial to construct the expression of the response surface model. Substitute the different parameter combinations of each significant factor and the corresponding thermal resistance values in the response surface thermal resistance simulation table into the expression of the response surface model to obtain the polynomial regression equation of the response surface prediction model.

[0059] S7. Analyze the interaction effects between significant factors. Based on the interaction effects between significant factors, calculate and find the optimal combination of significant factor parameters with the minimum thermal resistance under the parameter constraints of the polynomial regression equation of the response surface prediction model.

[0060] S8. Package the thermal resistance simulation model, obtain the optimal combination of significant factor parameters, perform modeling and simulation, output the simulated thermal resistance, and compare and verify it with the minimum thermal resistance.

[0061] Further, the influencing factors in the orthogonal standard configuration table of 7 factors at 3 levels are controllable variables in the chip packaging process. The controllable variables include chip area, chip thickness, solder layer thickness, frame thickness, molding compound material, solder material, and lead frame material. Each controllable variable also has its own different parameters.

[0062] In one embodiment, the orthogonal standard configuration table of 7 factors at 3 levels is specifically as Figure 2 shown. Each factor corresponds to a code name. The levels in the table refer to the different parameters of the factor. By defining 7 influencing factors including chip area, chip thickness, solder layer thickness, frame thickness, molding compound material, solder material, and lead frame material, the input variables of the experiment are clarified. Each factor has 3 levels (different parameters), which is convenient for designing a standardized orthogonal experiment table. Through the orthogonal experiment method, significant influencing factors can be screened out with fewer experiment times, reducing costs.

[0063] Further,

[0064] The orthogonal result variance analysis table includes the control variables and the sum of squared deviations, degrees of freedom, and F ratio corresponding to each control variable. The sum of squared deviations is used to measure the differences caused by the changes of each factor or error. The degrees of freedom represent the number of independent information. The F ratio is the significance characteristic value of each influencing factor and is used to test the significance of the influencing factor.

[0065] Quantify the influence of each factor on the thermal resistance through indicators such as the sum of squared deviations (SS), degrees of freedom (df), and F ratio. Judge which factors have a significant influence on the thermal resistance through the F ratio, providing a basis for subsequent optimization. Through variance analysis, significant factors can be screened out with less data volume, reducing the computational complexity and the amount of data.

[0066] In one embodiment, its orthogonal result table is as Figure 3 shown, and the orthogonal result variance analysis table is asFigure 4 As shown, according to the orthogonal experiment result table, the sum of squares of deviations, degrees of freedom, and F ratios of each control variable are calculated. For example, for the factor of chip area, its sum of squares of deviations is 1.966, the degrees of freedom is 2, and the F ratio is 12.29. By comparing the F ratio with a preset significance threshold (such as 5), it can be determined whether this factor is significant. If the F ratio is greater than the preset significance threshold, it is considered that this factor has a significant impact on the package thermal resistance and needs further optimization.

[0067] Furthermore,

[0068] The F ratio of each influencing factor satisfies the calculation formula: In the formula, F_factor is the F ratio of the influencing factor, SS_factor is the sum of squares of deviations of the influencing factor, df_factor is the degrees of freedom of the influencing factor, SS E is the sum of squares of error deviations, and df E is the degrees of freedom of error.

[0069] In one embodiment, for the factor of solder layer thickness, its sum of squares of deviations SS 因 factor is 0.515, the degrees of freedom df 因素 is 2, the sum of squares of error deviations SS E is 0.312, and the degrees of freedom of error df E is 8. Substituting into the formula, the calculated F ratio is 3.22. By comparing this F ratio with the preset significance threshold, the significance of the solder layer thickness factor can be determined.

[0070] Furthermore,

[0071] The comparison between the significance characteristic value and the preset significance threshold is specifically as follows: If the significance characteristic value F of the influencing factor 因素 is greater than the preset significance threshold, it is a significant factor; if the significance characteristic value F of the influencing factor 因素 is less than or equal to the preset significance threshold, it is a normal factor. Based on this, four significant influencing factors are screened out.

[0072] Performing significance screening on all influencing factors and eliminating irrelevant influencing factors helps to optimize the significant factors with great influence, improve the optimization efficiency, and avoid wasting time and resources on unimportant factors.

[0073] In one embodiment, through variance analysis, it is found that the F ratios of the four factors of chip area, chip thickness, solder layer thickness, and frame thickness are all greater than the preset significance threshold. Therefore, these four factors are taken as the key research objects for subsequent response surface optimization.

[0074] Furthermore,

[0075] The setting of the significance preset threshold is determined with reference to the statistical F-distribution table.

[0076] This ensures the accuracy and reliability of significance judgment and avoids the influence of subjective factors on the experimental results.

[0077] In one embodiment, according to the degrees of freedom and significance level (such as 0.05) of the experiment, the corresponding F critical value is found from the statistical F-distribution table and used as the significance preset threshold. For example, when the degrees of freedom are 2 and 8 and the significance level is 0.05, the F critical value found from the F table is 4.46. Therefore, 4.46 is used as the significance preset threshold to judge the significance of each influencing factor.

[0078] Furthermore,

[0079] The expression of the response surface model is: where y is the response variable, x i is the dependent variable, β0 is the constant term, β i is the linear term, β ii is the quadratic term coefficient, β ij is the quadratic interaction term coefficient, and ò is the error term.

[0080] The coefficients of each term in the expression of this response surface model are determined by fitting the data in the response surface thermal resistance simulation table.

[0081] In one embodiment, according to the data of the response surface, substituting into the model expression, the values of each coefficient are calculated, thereby obtaining the package thermal resistance response surface prediction model. For example, the regression equation obtained through the model expression is:

[0082] R jc = 0.5 + 0.02A - 0.03B + 0.01C - 0.02D + 0.05AB + 0.003AC + 0.002AD

[0083] + 0.001BC + 0.002BD + 0.001CD + ò

[0084] where, R jc is the minimum thermal resistance value, A, B, C, and D are the chip area, chip thickness, solder layer thickness, and frame thickness respectively, and ò is the error term.

[0085] Furthermore,

[0086] The polynomial regression equation of the response surface prediction model satisfies the calculation formula:

[0087] R jc= 0.6889 - 0.7423A + 0.013B + 0.2565C + 0.0223D + 0.0066AB - 0.3344AC - 0.0209AD -

[0088] 0.005BC - 0.0027BD - 0.0044CD + 0.4896A 2 - 0.0313B 2 + 0.0027C 2 - 0.0208D 2

[0089] wherein the R described in the formula jc is the thermal resistance value, and A, B, C, and D represent the parameters of the four selected significant factors.

[0090] In one embodiment, A, B, C, and D represent the chip area, chip thickness, solder layer thickness, and frame thickness. Among them, the chip area A = 29.053 mm 2 , the chip thickness B = 0.155 mm, the solder layer thickness C = 0.031 mm, and the frame thickness D = 0.474 mm. Substituting these parameters into the polynomial regression equation, the minimum thermal resistance value R jc = 0.343 °C / W.

[0091] It can be understood that the above embodiments are merely exemplary embodiments adopted to illustrate the principle of the present invention / invention. However, the present invention / invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention / invention, and these modifications and improvements are also regarded as the protection scope of the present invention / invention.

Claims

1. A response surface optimization method for the thermal resistance of a power device package, characterized in that, It includes the following steps: S1. Construct a simulation model of the package thermal resistance of the power device according to the power device, and configure an orthogonal standard configuration table with 7 factors at 3 levels; S2. The package thermal resistance simulation model obtains each influencing factor and its parameters in the orthogonal standard configuration table, and uses the orthogonal experimental method to conduct combined simulation tests on the parameters of each influencing factor to obtain the thermal resistance under this combination, and forms an orthogonal result table with this combination and the corresponding thermal resistance; S3. Conduct variance analysis calculation on the orthogonal result table to obtain an orthogonal result variance analysis table; S4. Compare the significance characteristic values of each influencing factor in the orthogonal result variance analysis table with the preset significance threshold to screen out significant factors, and integrate the screened significant factors into a significant factor table; S5. The package thermal resistance simulation model obtains different parameters of the significant factors in the significant factor table, combines different parameters of each significant factor, conducts simulation tests to calculate the thermal resistance values between different combinations, and constructs a response surface thermal resistance simulation table; S6. Obtain the thermal resistance values in the response surface thermal resistance simulation table as the response values of the second-order polynomial to construct a response surface model expression, and substitute the different parameter combinations and corresponding thermal resistance values of each significant factor in the response surface thermal resistance simulation table into the response surface model expression to obtain the polynomial regression equation of the response surface prediction model; S7. Analyze the interaction effects between significant factors, and calculate and find the optimal significant factor parameter combination with the minimum thermal resistance under the parameter constraints of the polynomial regression equation of the response surface prediction model based on the interaction effects between significant factors; S8. The package thermal resistance simulation model obtains the optimal significant factor parameter combination for modeling and simulation, outputs the simulation thermal resistance, and compares and verifies it with the minimum thermal resistance.

2. The response surface optimization method for the thermal resistance of a power device package according to claim 1, wherein, The influencing factors in the orthogonal standard configuration table with 7 factors at 3 levels are controllable variables in the chip packaging process. The controllable variables include chip area, chip thickness, solder layer thickness, frame thickness, molding material, solder material, and lead frame material, and each controllable variable also has its own different parameters.

3. The response surface optimization method for the thermal resistance of a power device package according to claim 1, characterized in that The orthogonal result variance analysis table includes control variables, as well as the sum of squared deviations, degrees of freedom, and F ratio corresponding to each control variable. The sum of squared deviations is used to measure the differences caused by changes in each factor or error, the degrees of freedom represent the number of independent information, and the F ratio is the significance characteristic value of each influencing factor used to test whether the influencing factor is significant.

4. The response surface optimization method for the thermal resistance of a power device package according to claim 3, characterized in that The F ratio of each influencing factor satisfies the calculation formula: In the formula, F factor is the F ratio of the influencing factor, SS factor is the sum of squared deviations of the influencing factor, df factor is the degree of freedom of the influencing factor, SS E is the sum of squared errors, df E is the degree of freedom of error.

5. The response surface optimization method for the thermal resistance of a power device package according to claim 4, wherein, The comparison between the numerical value of the significant feature and the preset threshold for significance is specifically as follows: If the numerical value F of the significant feature of the influencing factor 因素 is greater than the preset threshold for significance, it is a significant factor. If the numerical value F of the influencing factor 因素 is less than or equal to the preset threshold for significance, it is a conventional factor. Based on this, four significant influencing factors are screened out.

6. The response surface optimization method for the thermal resistance of a power device package according to claim 5, wherein The setting of the preset significance threshold is determined with reference to the statistical F distribution table.

7. A response surface optimization method for the thermal resistance of a power device package according to claim 1, characterized in that The expression of the response surface model is as follows: In the formula, y is the response variable, and x i is the dependent variable, β0 is the constant term, and β i is the linear term, and β ii is the quadratic term coefficient, and β ij is the quadratic interaction term coefficient, and ò is the error term.

8. A response surface optimization method for the thermal resistance of a power device package according to claim 5, characterized in that The polynomial regression equation of the response surface prediction model satisfies the calculation formula: R jc = 0.6889 - 0.7423A + 0.013B + 0.2565C + 0.0223D + 0.0066AB - 0.3344AC - 0.0209AD - 0.005BC - 0.0027BD - 0.0044CD + 0.4896A 2 - 0.0313B 2 + 0.0027C 2 - 0.0208D 2 wherein R described above jc is the thermal resistance value, and A, B, C, and D represent the parameters of four selected significant factors.

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