Scale invariance and dynamical correlations in growth models of molecular beam epitaxy

Dynamical scaling behavior of the kinetic roughening phenomena in (1+1)- and (2+1)-dimensional models of molecular beam epitaxy (MBE) is studied using kinetic Monte Carlo simulations mostly within the solid-on-solid lattice gas approximation. We relate the simulation results of our finite temperature stochastic Monte Carlo algorithm, which employs local-configuration-dependent thermally activated Arrhenius diffusion, to those obtained from simpler manifestly nonequilibrium dynamical growth models involving instantaneous relaxation. The extracted critical exponents for kinetic roughening are found to be temperature dependent due to finite size and crossover effects, and in particular, the growth (beta) and roughness (alpha) exponents decrease with increasing temperature as diffusion noise becomes stronger relative to the deposition noise. We find strong evidence for anomalous dynamic scaling, with global and local scaling behaviors being substantially different in 1+1 dimensions. Remarkably, the anomalous roughness exponent alpha' (= alpha in the usual dynamic scaling situation) defining the spatial scaling in the height-height correlation function is found to be approximately a temperature-independent constant (approximate to 0.6-0.7 in 1+1 dimensions) in all our models, including the Arrhenius-activated diffusion model. An associated significant result is the marked up-down (h --> -h) asymmetry in our simulated growth morphologies, clearly indicating the presence of nonlinear microscopically irreversible processes dominating local growth features. We study in some detail the recently suggested connection between height fluctuations in MBE growth models and intermittent fluctuations in fluid turbulence by numerically calculating the multiaffine dynamic scaling behavior of higher moments of the height correlation functions and by obtaining the stretched exponential behavior of the step-height distribution functions in our growth models. We critically analyze our growth rules to comment on possible coarse-grained continuum descriptions that could qualitatively account for our MBE simulation results.