Misfit elastic energy and a continuum model for epitaxial growth with elasticity on vicinal surfaces

In heteroepitaxial growth, the mismatch between the lattice constants in the film and the substrate causes misfit strain in the film, making a flat surface unstable to small perturbations. This morphological instability is called Asaro-Tiller-Grinfeld (ATG) instability. In practice, most devices are fabricated on vicinal surfaces which consist of steps and terraces. In this case, the misfit strain causes step bunching and traditional continuum models for the ATG instability do not apply directly. In this paper, we present a continuum model for this elastically driving step bunching. We validate our model by performing linear stability analysis and numerical simulation in the nonlinear regime. We also present a continuum description for the misfit elastic energy on vicinal surface which incorporates the underlying atomic features of the vicinal surface.