We demonstrate, using well-established nonequilibrium limited-mobility solid-on-solid growth models, that mound formation in the dynamical surface growth morphology does not necessarily imply the existence of a surface edge diffusion bias ("the Schwoebel barrier"). We find mounded morphologies in several nonequilibrium growth models which incorporate no Schwoebel barrier. Our numerical results indicate that mounded morphologies in nonequilibrium surface growth may arise from a number of distinct physical mechanisms, with the Schwoebel instability being one of them.Keywords: Computer simulations; Models of surface kinetics; Molecular beam epitaxy; Scanning tunneling microscopy; Growth; Surface diffusion; Surface rougheningIn vacuum deposition growth of thin films or epitaxial layers (e.g. MBE) it is common [1] to find mound formation in the evolving dynamical surface growth morphology. Although the details of the mounded morphology could differ considerably depending on the systems and growth conditions, the basic mounding phenomenon in surface growth has been reported in a large number of recent experimental publications [1]. The typical experiment [1] monitors vacuum deposition growth on substrates using STM and/or AFM spectroscopies. Growth mounds are observed under typical MBE-type growth conditions, and the resultant mounded morphology is statistically analyzed by studying the dynamical surface height h(r, t) as a function of the position r on the surface and growth time t. Much attention has focused on this ubiquitous phenomenon of mounding and the associated pattern formation during nonequilibrium surface growth for reasons of possible technological interest (e.g. the possibility of producing controlled nanoscale thin film or interface patterns) and fundamental interest (e.g. understanding nonequilibrium growth and pattern formation).The theoretical interpretation of the mounding phenomenon has often been based [1] on the step-edge diffusion bias [2] or the so-called Schwoebel barrier [3] effect (also known as the Ehrlich-Schwoebel [3], or ES, barrier). The basic idea of the ES barrier-induced mounding (often referred to as an instability) is simple : The ES effect produces an additional energy barrier for diffusing adatoms on terraces from coming "down" toward the substrate, thus probablistically inhibiting attachment of atoms to lower or down-steps and enhancing their attachment to upper or up-steps; the result is therefore mound formation because deposited atoms cannot come down from upper to lower terraces and so three-dimensional mounds or pyramids result as atoms are deposited on the top of already existing terraces.The physical picture underlying mounded growth under an ES barrier is manifestly obvious, and clearly the existence of an ES barrier is a sufficient condition [2] for mound formation in nonequilibrium surface growth.Our interest in this paper is to discuss the necessary condition for mound formation in nonequilibrium surface growth morphology -more precisely, we want to ask the inverse qu...

We show that a multiple-hit noise reduction technique involving the acceptance of only a fraction of the allowed atomistic deposition events could, by significantly suppressing the formation of high steps and deep grooves, greatly facilitate the identification of the universality class of limited-mobility discrete solid-on-solid conserved nonequilibrium models of epitaxial growth. In particular, the critical growth exponents of the discrete one-dimensional molecular-beam-epitaxy growth model are definitively determined using the noise reduction technique, and the universality class is established to be that of the nonlinear continuum fourth-order conserved epitaxial growth equation.

We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2 + 1− dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening properties of molecular beam epitaxy. The model exhibits long-lived transient anomalous and multiaffine dynamic scaling properties similar to that found in the corresponding 1 + 1− dimensional problem. Using large-scale simulations we obtain the relevant scaling exponents, and compare with continuum theories.A key issue in kinetic surface roughening [1,2] is making connection between theoretical growth universality classes, as defined by continuum growth equations for example, and experimentally observed rough growth in real surfaces which generally depends on many details such as growth conditions (eg. temperature, surface orientation, growth rate) and atomistic rules controlling attachment, detachment, evaporation, and most importantly, diffusion of the deposited adatoms at the growth front. The concept driving much of the kinetic surface roughening research is that only a few universality classes [1,2] describe the asymptotic growth properties in many seemingly different nonequilibrium surface growth problems as most of the details are irrelevant from a renormalization group viewpoint and do not affect the asymptotic behavior. Much recent work has gone into building simple atomistic discrete nonequilibrium growth models which catch the essential aspects of a complicated growth problem and include only the relevant dynamical processes determining the asymptotic growth behavior. One such nonequilibrium growth model was introduced by one of us in ref. [3] in the context of one dimensional molecular beam epitaxy. This growth model has since been extensively studied [4], and it seems to describe [4] well the low temperature growth properties of realistic stochastic Monte Carlo simulation results of molecular beam epitaxy. Although the growth model introduced in ref. [3] has been fairly extensively studied in the literature [4], almost all of the existing work is in 1 + 1 dimensions where a one dimensional substrate roughens as it grows. We present in this paper results of a systematic study of the growth model of ref.[3] in the physically relevant 2 + 1 dimensions.In our growth model [3], atoms are randomly deposited on an L × L (we have studied system sizes upto L = 10 3 with a maximum of 10 7 deposited layers, which amount to the deposition of upto 10 13 atoms) flat substrate under solid-on-solid deposition and growth conditions. If a randomly deposited atom has at least one lateral nearestneighbor bond (i.e. if its initial coordination number is 2 or more), then it is incorporated at the deposition site and stays there forever. Otherwise the atom could move to a nearest-neighbor lateral site (with no restriction on the number of vertical sites it moves in the growth direction) for incorporation provided it can increase (but not necessarily maximize) its coordination number ...

A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion bias conditions. Simulations using a local coordination dependent instantaneous relaxation of the deposited atoms produce complex surface mound morphologies whose dynamical evolution is inconsistent with all the proposed continuum surface growth equations. For any finite bias, mound coarsening is found to be only an initial transient which vanishes asymptotically, with the asymptotic growth exponent being 0.5 in both 1+1 and 2+1 dimensions. Possible experimental implications of the proposed limited mobility nonequilibrium model for real interface growth under a surface diffusion bias are critically discussed.An atom moving on a free surface is known to encounter an additional potential barrier, often called a surface diffusion bias [1], as it approaches a step from the upper terrace -there is no such extra barrier for an atom approaching the step from the lower terrace (the surface step separates the upper and the lower terrace). Since this diffusion bias makes it preferentially more likely for an atom to attach itself to the upper terrace than the lower one, it leads to mound (or pyramid) -type structures on the surface under growth conditions as deposited atoms are probabilistically less able to come down from upper to lower terraces. This dynamical growth behavior is sometimes called an "instability" because a flat ("singular") two dimensional surface growing under a surface diffusion bias is unstable toward three dimensional mound/pyramid formation. There has been a great deal of recent interest in the morphological evolution of growing interfaces under nonequilibrium growth conditions in the presence of such a surface diffusion bias. In this paper we propose a minimal nonequilibrium cellular automata -type atomistic growth model for ideal molecular beam epitaxial -type random vapor deposition growth under a surface diffusion bias. Extensive stochastic simulation results presented in this paper establish the morphological evolution of a surface growing under diffusion bias conditions to be surprisingly complex even for this extremely simple minimal model. Various critical growth exponents, which asymptotically describe the large-scale dynamical evolution of the growing surface in our minimal discrete growth model, are inconsistent with all the proposed continuum theories for nonequilibrium surface growth under diffusion bias conditions. Our results based on our extensive study of this minimal model lead to the conclusion that a continuum description for nonequilibrium growth under a surface diffusion bias does not exist (even for this extremely simple minimal model) and may require a theoretical formulation which is substantially different from the ones currently existing in the literature. Our results in the initial non-asymptotic transient growth regime (lasting upto severa...

We show from simulations that a limited mobility solid-on-solid model of kinetically rough surface growth exhibits extended self-similarity analogous to that found in fluid turbulence. The range over which scaleindependent power-law behavior is observed is significantly enhanced if two correlation functions of different order, such as those representing two different moments of the difference in height between two points, are plotted against each other. This behavior, found in both one and two dimensions, suggests that the ''relative'' exponents may be more fundamental than the ''absolute'' ones. ͓S1063-651X͑98͒50604-6͔PACS number͑s͒: 47.27. Gs, 05.40.ϩj, 83.20.Jp Scale-invariant spatiotemporal behavior is observed in a wide variety of far-from-equilibrium systems. In analogy with the ''universality'' found in the equilibrium scaling behavior of systems near a second-order phase transition, it is interesting to inquire about the similarities between different nonequilibrium systems exhibiting scale-invariant behavior. In this paper, we point out a remarkable similarity between the scaling behavior of two well-known and extensively studied nonequilibrium systems: turbulent fluids and growing interfaces. Krug ͓1͔ discovered a similarity between the intermittent multiscaling behavior of structure functions in strongly developed turbulence ͓2,3͔ and the scaling properties of correlation functions of height fluctuations in simple solid-on-solid models of kinetically rough epitaxial growth ͓4͔ with limited surface mobility. The multiscaling properties of these growth models have been subsequently investigated in detail ͓5͔ and a mechanism for this behavior has been proposed ͓6͔. In this paper, we demonstrate that the extended self-similarity ͑ESS͒ ͓7͔ exhibited by the structure functions in fluid turbulence is also present in the behavior of correlation functions of height fluctuations in these growth models, and thereby establish that the analogy between deterministic turbulence in fluids and stochastically driven interface growth is remarkably deep. We emphasize that the ESS phenomenology in our discrete stochastic growth model is formally identical to that found in the intermittent fluid turbulence problem, establishing a precise one to one correspondence between these two seemingly completely different physical processes. While the exact reasons for this precise analogy between these two distinct problems remain unclear at this stage, we speculate that the existence of an infinite number of relevant ͑marginal͒ operators in both cases may be the underlying mathematical cause for this analogy ͓6͔.We begin by pointing out the analogy ͓1͔ between fluid turbulence and surface growth. In fully developed turbulence, scaling behavior is observed in the inertial range ӶrӶL, where r is the length scale of interest, L is the outer integral scale at which energy is injected into the system, and is the inner dissipation scale. A measure of the separation between the inner and outer scales is provided by the Reynolds number R...