Simulation of Grain Coarsening Process in Copper Wiring by Phase Field Method

Abstract

We simulated heat treatment of the fine copper wiring containing impurities by the phase field method. We evaluated effects of the initial grain size and the impurity concentration on the final average grain size and confirmed qualitative agreement between simulation and previous experimental results. Our claim was supported that the increase in interfacial driving force (due to grain refinement) and the effect of grain boundary pinning (due to impurities) are the main factors in grain coarsening in ultra-fine wiring. We clarified that the refinement of the initial grain size has a particularly strong effect on the growth rate at the initial stage of the heat treatment (i.e., 0–60 s), and has a slight effect on the subsequent growth stage (60–600 s). On the other hand, the impurity concentration affects the entire heat treatment process. This indicates that it is difficult to obtain coarse crystal grains by long-time heat treatment (about 30 min as in a conventional process) without lowering the impurity concentration, and that the high-purity plating process gives coarse grains by short-time heat treatment (about 3 min in rapid thermal annealing).