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.

We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface roughening in ideal molecular beam epitaxy. We find essentially all the earlier conclusions regarding the universality class of DT and WV models to be severely hampered by slow crossover and extremely long-lived transient effects. We identify the correct asymptotic universality class(es) that differs from earlier conclusions in several instances.

We study, through large-scale stochastic simulations using the noise reduction technique, surface growth via vapor deposition, e.g., molecular beam epitaxy ͑MBE͒, for simple nonequilibrium limited mobility solid-onsolid growth models, such as the Family model, the Das Sarma-Tamborenea model, the Wolf-Villain ͑WV͒ model, the larger-curvature ͑LC͒ model, and other related models. We find that (dϭ2ϩ1)-dimensional surface growth in several noise reduced models ͑most notably the WV and LC models͒ exhibits spectacular quasiregular mound formation with slope selection in their dynamical surface morphology in contrast to the standard statistically scale-invariant kinetically rough surface growth expected ͑and earlier reported in the literature͒ for such growth models. The mounding instability in these epitaxial growth models does not involve the Ehrlich-Schwoebel step-edge diffusion barrier. The mounded morphology in these growth models arises from the interplay between the line tension along step edges in the plane parallel to the average surface and the suppression of noise and island nucleation. The line tension tends to stabilize some of the step orientations that coincide with in-plane high-symmetry crystalline directions, and thus the mounds that are formed assume quasiregular structures. The noise reduction technique developed originally for Eden-type models can be used to control the stochastic noise and enhance diffusion along the step edge, which ultimately leads to the formation of quasiregular mounds during growth. We show that by increasing the diffusion surface length together with supression of nucleation and deposition noise, one can obtain a self-organization of the pyramids in quasiregular patterns. The mounding instability in these simple epitaxial growth models is closely related to the cluster-edge diffusion ͑as opposed to step-edge barrier͒ driven mounding in MBE growth, which has been recently discussed in the literature. The epitaxial mound formation studied here is a kinetic-topological instability ͓which can happen only in (dϭ2ϩ1)-dimensional, or higher dimensional, growth, but not in (dϭ1 ϩ1)-dimensional growth because no cluster diffusion around a closed surface loop is possible in ''onedimensional'' surfaces͔, which is likely to be quite generic in real MBE-type surface growth. Our extensive numerical simulations produce mounded ͑and slope-selected͒ surface growth morphologies which are strikingly visually similar to many recently reported experimental MBE growth morphologies.

We study, using noise reduction techniques, layer by layer epitaxial growth in limited mobility solid-on-solid nonequilibrium surface growth models, which have been introduced in the context of kinetic surface roughening in ideal molecular beam epitaxy. Multiple hit noise reduction and long surface diffusion length lead to qualitatively similar layer by layer epitaxy in 1+1 and 2+1 dimensional limited mobility growth simulations. We discuss the dynamic scaling characteristics connecting the transient layer by layer growth regime with the asymptotic kinetically rough growth regime.