Universal Behaviour of (2+1)-Dimensional Stochastic Equations for Epitaxial Growth Processes

Abstract

We investigate spatially discretized versions of a class of nonequilibrium continuum equations for epitaxial growth processes in (2+1)-dimensions using numerical integration. The epitaxial growth models include the most well-known Villain-Lai-Das Sarma (VLDS) equation and a stochastic differential equation recently proposed by Escudero (Phys. Rev. Lett. 101:196102, 2008). To suppress the instability in the VLDS equation, the nonlinear term is replaced by exponentially decreasing functions. The critical exponents in different regions are obtained. The roughness distributions at the steady states of the growth models show that the two equations are in good agreement with each other. Our results imply that the modified version of the VLDS equation with controlled instability and the equation proposed by Escudero belong to the same universality class. Anomalous scaling behaviour in these growth models are also discussed, and the nontrivial scaling properties are found very weak in (2+1)-dimensions.