Equilibration of crystal surfaces

The relaxation towards equilibrium of various profiles imprinted on a crystal surface is studied above and below the roughening temperature of that surface. Evaporation kinetics and, above roughening, surface diffusion are considered. Continuum theory and step models are compared with the results of Monte Carlo simulations. Above roughening, the simulational data are well understood in the framework of the continuum theory, and the oscillatory profiles characteristic of surface diffusion are easily seen. Below roughening, the current continuum theories do not treat the top-step annihilation process correctly. That process is described using a Langevin theory for step fluctuations. In addition, the opposing effects of the anisotropic mobility and surface free energy on the profile shapes are emphasized and illustrated in a phenomenological extension of the continuum theory with small rounding parameters. Although these extensions of the continuum theory improve understanding of the Monte Carlo data below roughening, finite-size and lattice effects still preclude a quantitative fit of the theory to the Monte Carlo data.