Tensile stress generation during island coalescence for variable island-substrate contact angle

During the deposition of films that grow by the Volmer–Weber mechanism, crystallites nucleate as isolated islands, grow larger to impinge with other islands, and eventually coalesce into a continuous film. Tensile stress generation due to grain boundary formation during island coalescence, commonly referred to as island zipping, has been cited as a probable stress generation mechanism in a wide variety of materials, including low- and high-melting point metals, polycrystalline diamond, amorphous semiconductors, and amorphous metallic alloys. For all zipping-based tensile stress models in the literature, with the notable exception of the study of faceted diamond films [Sheldon et al., J. Appl. Phys. 90, 5097 (2001)], the surface of the islands are assumed to approach the substrate at normal incidence, so that the island-substrate contact angle is 90°. We have investigated the importance of the island-substrate contact angle on the tensile stress generated during island coalescence using finite-element calculations. The equilibrium tensile stress as a function of island-substrate contact angle and island radius was calculated numerically. For islands of a given size, the equilibrium stress was found to be strongly dependent on the contact angle, with the stress decreasing with decreasing contact angle. The scaling of the equilibrium stress with island radius was also found to depend on the contact angle. These results suggest that, for a given material, the coalescence stress associated with grain boundary formation should vary significantly for different substrates, depending on detailed differences in wetting behavior.