Layer-by-layer epitaxy in limited mobility nonequilibrium models of surface growth

Modeling of nonequilibrium surface growth by a limited-mobility model with distributed diffusion length

Kinetic Monte Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy experiments. In parallel, simplified approaches such as limited mobility (LM) models characterized by a fixed diffusion length have been studied. Here we investigate an extended LM model to gain deeper insight into the role of diffusional processes concerning the growth morphology. Our model is based on the stochastic transition rules of the Das Sarma-Tamborena model but differs from the latter via a variable diffusion length. A first guess for this length can be extracted from the saturation value of the mean-squared displacement calculated from short KMC simulations. Comparing the resulting surface morphologies in the sub- and multilayer growth regime to those obtained from KMC simulations, we find deviations which can be cured by adding fluctuations to the diffusion length. This mimics the stochastic nature of particle diffusion on a substrate, an aspect which is usually neglected in LM models. We propose to add fluctuations to the diffusion length by choosing this quantity for each adsorbed particle from a Gaussian distribution, where the variance of the distribution serves as a fitting parameter. We show that the diffusional fluctuations have a huge impact on cluster properties during submonolayer growth as well as on the surface profile in the high coverage regime. The analysis of the surface morphologies on one- and two-dimensional substrates during sub- and multilayer growth shows that the LM model can produce structures that are indistinguishable to the ones from KMC simulations at arbitrary growth conditions.

Growth instability due to lattice-induced topological currents in limited-mobility epitaxial growth models

The energetically driven Ehrlich-Schwoebel barrier had been generally accepted as the primary cause of the growth instability in the form of quasiregular moundlike structures observed on the surface of thin film grown via molecular-beam epitaxy (MBE) technique. Recently the second mechanism of mound formation was proposed in terms of a topologically induced flux of particles originating from the line tension of the step edges which form the contour lines around a mound. Through large-scale simulations of MBE growth on a variety of crystalline lattice planes using limited-mobility, solid-on-solid models introduced by Wolf-Villain and Das Sarma-Tamborenea in 2+1 dimensions, we show that there exists a topological uphill particle current with strong dependence on specific lattice crystalline structure. Without any energetically induced barriers, our simulations produce spectacular mounds very similar, in some cases, to what have been observed in many recent MBE experiments. On a lattice where these currents cease to exist, the surface appears to be scale invariant, statistically rough as predicted by the conventional continuum growth equation.

Persistence in nonequilibrium surface growth

Persistence probabilities of the interface height in ( 1+1 ) - and ( 2+1 ) -dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the molecular beam epitaxy (MBE) universality class. Both the initial transient and the long-time steady-state regimes are investigated. We show that for growth models in the MBE universality class, the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady-state regimes. For the MBE universality class, the positive and negative persistence exponents in the steady-state are found to be theta(S)(+) =0.66+/-0.02 and theta(S)(-) =0.78+/-0.02, respectively, in ( 1+1 ) dimensions, and theta(S)(+) =0.76+/-0.02 and theta(S)(-) =0.85+/-0.02, respectively, in ( 2+1 ) dimensions. The noise reduction technique is applied on some of the ( 1+1 ) -dimensional models in order to obtain accurate values of the persistence exponents. We show analytically that a relation between the steady-state persistence exponent and the dynamic growth exponent, found earlier to be valid for linear models, should be satisfied by the smaller of the two steady-state persistence exponents in the nonlinear models. Our numerical results for the persistence exponents are consistent with this prediction. We also find that the steady-state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state. The dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form.