Stress analysis and optimization of POP stacked solder joints under thermal cyclic load
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摘要: 建立叠层封装(packaging on packaging，POP)堆叠焊点有限元模型，基于ANAND本构方程，分析了热循环载荷下焊点应力分布状态及热疲劳寿命；基于灵敏度法分析了POP封装结构参数对焊点热应力的影响显著性；基于响应面法建立POP堆叠焊点热应力与结构参数的回归方程，并结合粒子群算法对结构参数进行了优化. 结果表明，焊点与铜焊盘接触处应力最大，该处会率先产生裂纹，上层焊点高度和下层焊点高度对POP堆叠焊点热应力影响较为显著；最优结构参数水平组合为上层焊点高度0.35 mm、下层焊点高度0.28 mm、中层印刷电路板厚度0.26 mm，优化后上、下两层焊点的最大热应力分别下降了0.816和1.271 MPa，延长了POP堆叠焊点热疲劳寿命.Abstract: The finite element model of packaging on packaging(POP) stacked solder joints was established, and the stress distribution state and thermal fatigue life of the solder joints under thermal cyclic load were analyzed based on the ANAND constitutive equation. The significance of the influence of the structural parameters of the POP package on the thermal stress of the solder joints was analyzed based on the sensitivity method. The regression equation of the thermal stress of the POP stacked solder joints and the structural parameters was established based on the response surface method, and the structural parameters were optimized by combining the particle swarm algorithm. The results show that the stress is highest at the contact between the solder joint and the copper solder disc, which is the location of the crack initiation. The upper and lower solder joint heights have a significant effect on the thermal stresses in POP stacked joints. The optimal combination of structural parameter levels is 0.35 mm for the upper solder joint height, 0.28 mm for the lower solder joint height and 0.26 mm for the middle PCB thickness, which reduces the maximum thermal stress of the upper and lower solder joints by 0.816 and 1.271 MPa, respectively, and prolongs the thermal fatigue life of POP stacked joints.
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图 4 上层和下层焊点热应力分布
Figure 4. Thermal stress distribution of upper and lower solder joints. (a) upper solder joints; (b) lower solder joints
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图 5 上层焊点的散点图
Figure 5. Scatter diagram of upper solder joints. (a) thickness of intermediate PCB; (b)thickness of top PCB; (c) height of lower solder joint; (d) height of upper solder joint
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图 7 下层焊点的散点图
Figure 7. Scatter diagram of lower solder joints. (a) thickness of intermediate PCB; (b) thickness of top PCB; (c) height of lower solder joint; (d) height of upper solder joint
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图 10 最优参数组合上层和下层焊点热应力分布
Figure 10. Thermal stress distribution diagram of upper and lower solder joints with optimal parameter combination. (a) upper solder joints; (b) lower solder joints
表 1 POP堆叠焊点尺寸
Table 1 POP stacked solder joint dimensions mm
上层焊点 下层焊点 高度h1 直径d1 间距δ1 高度h2 直径d2 间距δ2 0.30 0.40 0.65 0.23 0.30 0.50 
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表 2 材料参数
Table 2 Material parameters
材料 弹性模量E/GPa 泊松比μ 热膨胀系数α/10−6K−1 SAC305 38.7 − 16.9T 0.35 1.25 芯片 163 0.28 2.5 PCB板 300 0.20 3.5 铜焊盘 117 0.30 14.3
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表 3 SAC305钎料ANAND模型参数
Table 3 SAC305 filler metal ANAND model parameters
初始形变阻抗值 $ {{{S}}_{ \rm{o}}} $ /MPa应力乘子ξ 常数 $A$ /104s−1变形阻力饱和值系数 $ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{S} $ /MPa激活能常数(Q/R)/K−1 硬化/软化常数 $ {{{h}}_{{{\rm{o}}}}} $ /MPa应变率敏感性指数m 饱和值 应力 软硬化 45.9 2 587 58.3 7460 9350 0.0942 1.5 0.015
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表 4 焊点粘塑性应变能密度增量
Table 4 Viscoplastic strain energy density increment of solder joints J/m3
焊点位置 应变能密度增量ΔWave 上层 82 822.671，83 134.183，83 208.574 下层 26 745.566，26 810.497，26 863.966
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表 5 封装体结构参数取值
Table 5 Value of package structure parameters mm
上层焊点高度HS2 下层焊点高度HS1 中层PCB厚度δP2 顶层PCB厚度δP3 0.25 ~ 0.35 0.18 ~ 0.28 0.26 ~ 0.34 0.10 ~ 0.16
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表 6 因素水平表
Table 6 Factor level table
水平 上层焊点高度HS2 /mm 下层焊点高度HS1 /mm 中层PCB厚度δP2 /mm −1 0.25 0.18 0.26 0 0.30 0.23 0.30 1 0.35 0.28 0.34
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表 7 响应面设计组合与热应力分析结果
Table 7 Response Surface design combination and thermal stress analysis results
试验编号 上层焊点高度HS2 /mm 下层焊点高度HS1 /mm 中层PCB厚度δP2 /mm 下层焊点应力y1 /MPa 上层焊点应力y2 /MPa 1 0.25 0.18 0.30 45.726 41.402 2 0.30 0.23 0.30 43.908 40.422 3 0.35 0.18 0.30 45.731 39.720 4 0.35 0.23 0.26 43.876 39.629 5 0.25 0.23 0.26 43.887 41.488 6 0.35 0.28 0.30 42.661 39.681 7 0.30 0.18 0.26 45.453 40.380 8 0.30 0.28 0.26 42.642 40.363 9 0.30 0.23 0.30 43.908 40.422 10 0.30 0.23 0.30 43.908 40.422 11 0.30 0.18 0.34 45.516 40.416 12 0.30 0.28 0.34 42.682 40.451 13 0.30 0.23 0.30 43.908 40.422 14 0.25 0.23 0.34 43.931 41.311 15 0.25 0.28 0.30 42.669 41.356 16 0.35 0.23 0.34 43.923 39.755 17 0.30 0.23 0.30 43.908 40.422
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表 8 响应面分析结果
Table 8 Response surface analysis results
焊点 P值 回归方程系数R2 回归方程调整系数Ra2 回归方程预测系数Rp2 上层 < 0.0001 0.9990 0.9978 0.9847 下层 < 0.0001 0.9983 0.9962 0.9736
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