3D堆叠芯片硅通孔的电-热-力耦合构形设计

Constructal Design on Through-Silicon Via of 3D Stacked Chips Based on Electro-Thermo-Stress Coupling

建立了3D堆叠芯片硅通孔(TSV)单元体模型,在单元体总体积和TSV体积占比给定时,考虑电-热-力耦合效应,以最高温度、[火积]耗散率、最大应力和最大形变为性能指标,对TSV横截面长宽比和单元体横截面长宽比进行双自由度构形设计优化。结果表明,存在最佳的TSV横截面长宽比使得单元体的最高温度、[火积]耗散率和最大应力取得极小值,但对应不同优化目标的最优构形各有不同,且TSV两端电压和芯片发热功率越大,其横截面长宽比对各性能指标的影响越大。铜、铝、钨3种材料中,钨填充TSV的热学和力学性能最优,但其电阻率较大。铜填充时,4个指标中最大应力最敏感,优先考虑最大应力最小化设计需求以确定TSV几何参数,可以较好兼顾其他性能指标。

A model of through-silicon via(TSV) element body in 3 D stacked chips was established.With the fixed volume of whole element body and volume proportion of TSV,considering the electro-thermo-stress coupling effect in the chip, and taking the highest temperature, entransy dissipation rate, maximum stress and maximum deformation as performance indexes, constructal design optimization with double-degree-of-freedom was performed on the cross-section aspect ratios of TSV and element body.The results show that there is an optimal cross-section aspect ratio of TSV for the element body, which minimizes the maximum temperature, entransy dissipation rate and maximum stress, but the optimal constructs for different optimization indexes are different, and the greater the electric voltages at both ends of TSV and the chip heating power, the greater the influences of its cross-section aspect ratio on each performance index.Among copper, aluminum and tungsten, TSV filled with tungsten has the best thermal and mechanical properties, but its resistivity is higher.Among the four indexes for TSV filled with copper, the maximum stress is the most sensitive, and it can better take into account other performance indexes by prioritizing the design requirement of maximum stress minimization to determine TSV geometric parameters.