Influence of out-of-plane insulator properties on the interfacial stresses in periodic electronic structures
While the in-plane properties of thin polyimide films can be measured using standard thermal-mechanical testing procedures, the experimental characterization of the out-of-plane properties (elastic constants and coefficient of thermal expansion) is very difficult due to the minute thickness of the film (on the order of one micron). In the present analysis, we treat the out-of-plane mechanical properties of the polyimide as design variables and investigate the effect of these properties on the thermal stresses that develop in a single layer copper-polyimide interconnection structure using a combined finite element-design of experiment method. The single layer interconnection structure is modeled by a three-dimensional representative cell composed of square copper via in a thin polyimide film mounted on top of a silicon substrate. The cell is assumed to be stress free at an elevated temperature, and is subsequently cooled uniformly. In the analysis, we obtain the initial elastic response of the cell for each combination of the out-of-plane polyimide properties called for in the experimental design, and generate response functions for the stress components at key bimaterial interfaces. Additional finite element trials are then performed over a broad temperature range allowing for copper plasticity to investigate the role of the out-of-plane polyimide properties when a material nonlinearity is present in the structure.