Growth equations, discrete models, and MBE experiments

Abstract

The question of the validity of the scaling ansatz in discrete deposition models and their connection with the scaling exponents of continuum differential equations is addressed. We specifically focus on the scaling properties of the Wolf–Villain type models and, as an extension of this model, on the influence of attractive and repulsive interactions up to second neighbors on the scaling relation. As an example of technological relevance, we present the evolution of steps in the vicinal (100) surface of Si during deposition at relatively low temperatures. We have found that, in general, one should not expect that discrete models, as well as real crystals, exhibit scaling.