基于响应曲面法的BGA焊点结构参数优化设计

杨雪霞; 孙勤润; 张伟伟

doi:10.12073/j.hjxb.20220810002

基于响应曲面法的BGA焊点结构参数优化设计

1.
太原科技大学, 太原, 030024
2.
东莞理工学院, 东莞, 523000

基金项目: 国家自然科学基金资助项目(11602157)；山西省自然科学基金面上项目(20210302123220)；广东省普通高校机器人与智能装备重点实验室(2017KSYS009)；东莞理工学院机器人与智能装备创新中心(KCYCXPT2017006).

详细信息

作者简介:
杨雪霞，1985年生，博士，副教授；研究方向为微电子封装材料力学性能及焊点可靠性的优化设计. Email: xuexiayang@tyust.edu.cn

中图分类号: TG 454
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出版历程
- 收稿日期: 2022-08-09
- 网络出版日期: 2023-04-20
- 刊出日期: 2023-11-29

Structure optimization design of BGA solder joints based on surface response method

1.
Taiyuan University of Science and Technology, Taiyuan 030024, China
2.
Dongguan University of Technology, Dongguan 523000, China

摘要

摘要:
球栅阵列(ball grid array package，BGA)封装因其成本低、电气性能好而被广泛应用于集成电路产业中. 文中建立了BGA三维模型，将等效应力作为响应目标，选取焊点直径、焊点高度、焊点间距、芯片厚度作为设计因子，采用响应曲面法设计了25组不同水平组合的焊点结构参数进行仿真计算，并基于遗传算法分析对焊点结构热振可靠性进行了优化. 结果表明，焊点间距对BGA结构热振可靠性有重要影响；优化方案组合为焊点直径0.28 mm，焊点高度0.20 mm，焊点间距0.40 mm.经过优化验证分析，该优化方案较原始设计方案等效应力降低了11.92%，实现了BGA器件焊点参数优化目的.
- BGA焊点 /
- 响应曲面 /
- 回归分析 /
- 有限元
Abstract:
Due to low cost and good electrical performance, BGA packaging is widely used in integrate circuit (IC) industry. Finite element method (FEM) analysis was carried out for evaluation of stress distribution in the Ball Grid Array (BGA) solder joints, and the radial scale, the height, the spacing of the solder joints, the height of chip were selected as design factors. Response surface methodology (RSM) was used to generate 25 designs and finite element modeling was employed to simulate the response of the assemblies to reliability influencing simulation calculations. The equation regression was associated with genetic algorithm (GA) to search for an optimal combination of parameters that meet the thermal vibration quality characteristics. The confirmation results showed that the space played a role in the reliability, and the radical scale 0.28 mm, the height 0.20 mm, the spacing 0.4mm settings of produce optimal assembly which demonstrated potential of reducing equivalent stress of the best design by 11.92%, respectively. The aim of optimizing BGA solder joints parameters was succeeded.
- BGA solder joints /
- RSM /
- the analysis of regression /
- FEM

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图 1 BGA有限元模型

Figure 1. Finite element model of BGA

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图 2 热循环温度载荷曲线

Figure 2. Thermal cycle temperature load curve

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图 3 随机振动加速度功率谱密度曲线

Figure 3. Random vibration PSD curve

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图 4 热循环与随机振动耦合流程图

Figure 4. Flow chart of coupling of thermal cycle and random vibration

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图 5 焊点等效应力云图

Figure 5. Equivalent stress distribution of solder joints

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图 6 因子标准化效应的Pareto图

Figure 6. Pareto plot of normalization effects

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图 7 因子标准化效应正态图

Figure 7. Normal plot of standardized effects

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图 8 目标函数种群均值和最优解变化

Figure 8. Mean and optimal change of objective function

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图 9 最优水平组合焊点等效应力图

Figure 9. Equivalent stress diagram of optimal combination

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表 1 SAC305焊料的Anand模型粘塑性材料参数

Table 1 Visco-plastic parameters of Anand model for SAC305 solder joints

激活能 Q/(J∙mol⁻¹)	气体常数 R/( J∙K⁻¹∙mol⁻¹)	常数 A/s⁻¹	应力乘子 ξ	敏感系数 m	系数 $ \hat{\boldsymbol{S}} $/MPa	指数 n	硬化常数 h₀/MPa	应变指数 α	形变阻抗 S₀/MPa
62022.4	8.314	5.8E6	2.0	0.0942	58.3	0.015	9350	1.50	45.9

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表 2 材料性能参数

Table 2 Property parameters of materials

材料名称	弹性模量E/GPa	泊松比μ	线膨胀系数α/(10⁻⁶K⁻¹)	密度ρ/(kg∙m⁻³)
Si芯片	131	0.30	2.8	2 320
SAC305	38	0.35	25	7 300
PCB板	18.2	0.25	15.0	1 200

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表 3 控制因素及水平因子

Table 3 Control factors and levels

水平	芯片高度h₁/mm	焊点直径 d₁/mm	焊点高度h₂/mm	焊点间距 d₂/mm
1	0.39	0.28	0.19	0.36
2	0.40	0.3	0.2	0.38
3	0.41	0.32	0.21	0.40

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表 4 BBD试验方案及等效应力结果

Table 4 BBD test scheme and equivalent stress results

试验	芯片高度h₁/mm	焊点直径 d₁/mm	焊点高度h₂/mm	焊点间距 d₂/mm	等效应力R/MPa
1	2	2	2	2	0.479 6
2	1	1	2	2	0.527 9
2	3	1	2	2	0.534 6
4	1	3	2	2	0.444 1
5	3	3	2	2	0.456 2
6	2	2	1	1	0.436 7
7	2	2	3	1	0.448 4
8	2	2	1	3	0.588 1
9	2	2	3	3	0.564 8
10	1	2	2	1	0.423 7
11	3	2	2	1	0.434 6
12	1	2	2	3	0.581 7
12	3	2	2	3	0.542 3
14	2	1	1	2	0.582 1
15	2	3	1	2	0.524 9
16	2	1	3	2	0.542 1
17	2	3	3	2	0.446 7
18	1	2	1	2	0.523 3
19	3	2	1	2	0.539 1
20	1	2	3	2	0.470 9
21	3	2	3	2	0.487 2
22	2	1	2	1	0.484 5
22	2	3	2	1	0.419 5
24	2	1	2	3	0.618 8
25	2	3	2	3	0.551 6

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表 5 筛选前方差显著性验证

Table 5 Analysis of variance significance before screening

来源	自由度	调整平方和 SS_Adj	F值	P值
模型	4	0.083 5	27.32	0.001 4
芯片高度	1	0.003 4	0.47	0.586 2
焊点直径	1	0.016 7	75.26	0.000 3
焊点高度	1	0.004 6	19.31	0.000 5
焊点间距	1	0.053 3	237.26	0.000 2

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表 6 筛选前回归方程分析

Table 6 Analysis of regression equation before screening

系数R²(%)	调整系数 R_Adj²(%)	预测系数 R_Pre²(%)	拟合情况
92.14	90.26	81.76	成功

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表 7 筛选后方差显著性验证

Table 7 Analysis of variance significance after screening

来源	自由度	校正平方和 SS_Adj	F值	P值
模型	3	0.079 2	61.47	0.000 6
焊点直径	1	0.016 7	77.49	0.000 2
焊点高度	1	0.004 6	21.25	0.000 3
焊点间距	1	0.053 3	248.14	0.000 1

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表 8 筛选后回归方程分析

Table 8 Analysis of regression equation after screening

系数R²(%)	调整系数 R_Adj²(%)	预测系数 R_Pre²(%)	拟合情况
94.86	93.31	89.93	成功

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