Small epitaxial islands Part II: On the significance of dislocations, island size and misfit on contact angles

Abstract

The equilibrium contact angle between a small epitaxial cap-shaped nucleus and its elastic substrate is calculated. A simple one-dimensional model of the Frenkel-Kontorowa type, which emphasises the discrete nature of the atoms and atomic layers of the deposit and substrate, is used rather than Young's equation. The mechanical equilibrium of the nucleus is assumed to be governed by a lowest total energy criterion. Isotropic surface energies are introduced, and the assumption is made that island and substrate have identical physical and chemical properties except for lattice parameters. The considerations show that the contact angle increases with increasing misfit but decreases with increasing island size. The discrete introduction of interfacial dislocations in small islands is shown to be responsible for a sawtooth variation in the contact angle, which is completely analogous to the discontinuous behaviour exhibited, for the same reason, by the average strain in small islands.