Renormalization-group analysis and simulational studies of groove instability in surface growth

Abstract

The existence of groove instability in linear and nonlinear models of surface growth with diffusion is discussed using renormalization group analysis and computer simulation studies. We present the results of the simulation of a surface growth model with diffusion in which the diffusion of atoms on the surface is controlled by the Hamiltonian of an unrestricted solid-on-solid model. We discuss the dynamic scaling behavior of our model as well as its instability to groove formation. As a more analytical approach to the problem of groove formation, we present a renormalization group analysis in one dimension of a nonlinear Langevin equation for surface growth with diffusion. By eliminating the fast degrees of freedom for the order parameter defined to be the local slope of the surface height, the resulting equation of motion for the coarse-grained order parameter is found to be unstable towards transition to a broken symmetry state consistent with the existence of a grooved phase.