Nonlinear effects for island coarsening and stabilization during strained film heteroepitaxy

TL;DR

This paper investigates the nonlinear evolution of strained islands in heteroepitaxial films, identifying regimes of instability, coarsening, and saturation, and highlighting the roles of misfit strain and wetting interactions in island stabilization.

Contribution

It introduces a nonlinear dynamic model for island evolution, revealing how misfit strain and wetting interactions influence island stabilization and saturation.

Findings

Island stabilization occurs at later times for smaller misfit strains.

Wetting interactions constrain island height growth.

Elastic interactions and strain energy drive the nonlinear evolution.

Abstract

Nonlinear evolution of three-dimensional strained islands or quantum dots in heteroepitaxial thin films is studied via a continuum elasticity model and the development of a nonlinear dynamic equation governing the film morphological profile. All three regimes of island array evolution are identified and examined, including a film instability regime at early stage, a nonlinear coarsening regime at intermediate times, and the crossover to a saturated asymptotic state, with detailed behavior depending on film-substrate misfit strains but not qualitatively on finite system sizes. The phenomenon of island stabilization and saturation, which corresponds to the formation of steady but non-ordered arrays of strained quantum dots, occurs at later time for smaller misfit strain. It is found to be controlled by the strength of film-substrate wetting interaction which would constrain the valley-to-peak mass transport and hence the growth of island height, and also determined by the effect of elastic interaction between surface islands and the high-order strain energy of individual islands at late evolution stage. The results are compared to previous experimental and theoretical studies on quantum dots coarsening and saturation.