Crystal plasticity modeling of the heat affected zone of copper micro-wires

Abstract

Due to the ongoing miniaturization of electronic parts, there is the concern that the diameters of micro-wires approach the dimensions of the crystalline microstructure. Owing to fabrication technology and harsh environmental conditions during service, the wires are often exposed to elevated temperature. This leads to grain growth until the cross section of a wire includes only a few grains. In the worst case, wires develop a bamboo-microstructure, where the cross section of a wire is characterized by a single grain. In consequence, depending on the crystallographic orientation, some grains can deform by easy glide. Thereby, the yield stress is drastically reduced compared to polycrystalline materials. In conclusion, the reliability of electronic devices deteriorates. Such effects were studied in detail on the basis of Crystal Plasticity Finite Element simulations. Within this approach, every single grain is modelled according to its own orientation, and crystallographic slip develops on the glide systems with the highest Schmid factors during loading. During glide deformation the dislocation density of activated slip systems increases. This leads to strain hardening, since the dislocations of one glide system appear as forest dislocations for the other systems. In this way, the material strength of a grain depends on its deformation history. A grain embedded in a matrix of neighboring grain shows much higher resistance to plastic deformation than free standing grains. The material parameters of these simulations were chosen from literature to fit experiments for copper single crystals. The results of this study are well illustrated in several deformation plots relating the stress distributions to dislocation densities.