Derivation of a continuum model for the long-ranged elastic interaction on a stepped surface

In heteroepitaxy, the mismatch of lattice constants between the crystal film and the substrate causes a misfit stress in the bulk of the film, driving the surface of the film to self-organize into various nano-structures. Below roughing transition temperature, the surface of a crystal film consists of terraces separated by atomic- height steps, and the misfit results in a long-ranged interaction between surface steps. In this case, the surface morphology is determined by the motion of the steps, and the widely used continuum theories for surface evolution under the elastic effect do not apply directly. In this thesis, we present a continuum model for the surface morphology evolution of a heteroepitaxial film surface. The continuum model is derived rigorously by taking the continuum limit from the discrete model for the interaction between steps, thus it incorporates the atomic features of the stepped surface. Linear instability analysis is performed for surfaces consisting of straight and parallel steps