http://www.ae.utexas.edu/~ruihuang/papers/PRB1.pdf 

An epitaxial thin film can undergo surface instability and break up into discrete islands. The stress field and the interface interaction have profound effects on the dynamics of surface evolution. In this work, we develop a nonlinear evolution equation with a second-order approximation for the stress field and a nonlinear wetting potential for the interface. The equation is solved numerically in both two-dimensional (2D) and three-dimensional (3D) configurations using a spectral method. The effects of stress and wetting are examined. It is found that the nonlinear stress field alone induces “blow-up” instability, leading to crack-like grooving in 2D and circular pit-like morphology in 3D. For thin films, the blow-up is suppressed by the wetting effect, leading to a thin wetting layer and an array of discrete islands. The dynamics of island formation and coarsening over a large area is well captured by the interplay of the nonlinear stress field and the wetting effect.