基于正交设计和灰色关联的硅通孔互连结构随机振动优化设计

建立了硅通孔（TSV，through silicon vias）互连结构三维有限元分析模型，对该模型进行了随机振动分析.以TSV互连结构的最大等效应力、最大等效应变、一阶固有频率、二阶固有频率为目标函数，选取TSV高度、TSV直径、微凸点高度和微凸点直径四个结构参数为设计变量进行多目标正交优化设计，结合灰色关联分析法获得了优化设计的最优参数组合，使TSV互连结构的最大等效应力降低4.59%，最大等效应变降低22.56%，并且一阶固有频率增加了4.91%，二阶固有频率增加了4.46%.研究表明，可以将正交试验法与灰色关联分析法相结合应用于TSV互连结构优化设计，对提高TSV互连结构在随机振动条件下的综合性能具有较高的实用性.

Optimization design of 3D-TSV interconnect structure under random vibration load based on orthogonal experiment and gray relational analysis

The 3D finite element analysis models of 3D-TSV interconnect structure were developed and done random vibration analysis. The maximum equivalent stress, the maximum equivalent strain, the first order natural frequency and the second order natural frequency as the objective function of the TSV interconnect structure. The TSV height, the TSV diameter, the micro-bump diameter and the micro-bump height as design variable to multi objective optimization design. The multifactorial and multi-objective optimization design based on orthogonal experiment and gray relational analysis, it obtains the optimal parameter level combination. The maximum equivalent stress of the TSV interconnect structure is reduced by 4.59%, the maximum equivalent effect is reduced by 22.56%, and the first order natural frequency is increased by 4.91%, and the second order natural frequency is increased by 4.46%. The research shows:using the combination method based on orthogonal experiment and gray relational analysis it achieved the multi-objective optimization about TSV interconnect structure. It has high practicability to improve the comprehensive performance of TSV interconnect structure under random vibration condition.