www.elsevier.com/locate/actamat GRAIN GROWTH IN THIN METALLIC FILMS

Abstract—Grain growth in thin films deposited on a substrate was studied theoretically. The thrust of the model proposed is the effect of vacancy generation accompanying grain growth on the rate of the process. In addition, the magnitude of a tensile stress developing in the film was considered. It was shown that due to the contribution of vacancies to the free energy of the system, discernible grain growth is preceded by an “incubation ” period, during which the grain structure can be considered as stable, as the rate of growth is relatively small over this incubation time. During this time, the vacancy concentration remains nearly constant, staying at a level much higher than the thermal equilibrium concentration. Based on numerical analysis, a simple expression for the incubation time in terms of the vacancy sink spacing, temperature and grain bound-ary characteristics was derived. With this formula, the stability of the grain structure of a thin film can b