ADATOM MOBILITY FOR THE SOLID-ON-SOLID MODEL

The relaxation of a crystal surface through surface diffusion is studied within the solid-on-solid model. Two types of (conserved) dynamics are considered. For Arrhenius dynamics we show that the relevant transport coefficient, the adatom mobility, has a simple analytic form: It is independent of orientation, and depends exponentially on the inverse temperature, for any surface dimensionality d. Together with the expression for the orientation-dependent stiffness this completely determines the macroscopic evolution equation for the surface. The predictions of the macroscopic theory are checked against simulations of profile evolution and roughening in d = 1. For one-dimensional Metropolis dynamics we provide an upper bound on the adatom mobility and obtain numerical estimates of its actual value, which indicate a nontrivial orientation dependence in this case. An alternative derivation of the macroscopic dynamics directly from the master equation is presented and discussed in relation to previous approximate work.