Generic role of the anisotropic surface free energy on the morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate

Abstract

A systematic study based on self-consistent dynamical simulations is presented for the spontaneous evolution of an isolated thin solid droplet on a rigid substrate, which is driven by the surface drift diffusion induced by the anisotropic capillary forces (surface stiffness) and mismatch stresses. In this work, we studied the effect of surface free energy anisotropies [weak and strong (anomalous)] on the development kinetics of the “Stranski–Krastanow” island type morphologies. The anisotropic surface free energy and the surface stiffness were treated with well accepted trigonometric functions. Although, various tilt angles and anisotropy constants were considered during simulations, the main emphasis was given on the effect of rotational symmetries associated with the surface Helmholtz free energy topography in two-dimensional space. Our computer simulations revealed the formation of an extremely thin wetting layer during the development of the bell-shaped Stranski-Krastanow island through the mass accumulation at the central region of the droplet via surface drift-diffusion. For weak anisotropy constant levels, instead of singlet islanding, we observed formation of doublet islanding, separated by a shallow wetting layer, for a set of specific tilt angles, ϕ=90° and ϕ=45°, respectively, for the twofold and fourfold rotational symmetry axis. No such formation has been detected for the sixfold symmetry. In the strong (anomalous) anisotropy constant domain, we demonstrated the existence of two distinct morphological modes: (i) the complete stability of the initial Cosine-shaped droplet just above a certain anisotropy constant threshold level by spontaneous slight readjustments of the base and the height of the cluster; (ii) the Frank-van der Merwe mode of thin film formation for very large values of the anisotropy constant by the spreading and coalescence of the droplets over the substrate surface. During the course of the simulations, we continuously tracked both the morphology (i.e., the peak height, the extension of the wetting layer beyond the domain boundaries, and the triple junction contact angle) and the energetics (the global Helmholtz free energy changes associated with the total strain and surface energy variations) of the system.