Stochastic continuum model of submonolayer epitaxial growth

The kinetic roughening of growing epitaxial layers is investigated with a phenomenological stochastic differential equation. This nonlinear equation takes account of deposition and surface diffusion, to which we have added a periodic pinning potential that has the vertical crystal lattice period to stabilize the planar crystal surface. If this potential is the dominant term in the equation, the surface roughness shows oscillations that indicate the progressive filing of successive monolayers. The properties of the submonolayer regime obtained from our equation are qualitatively similar to those obtained from kinetic Monte Carlo simulations and seen in experiments.