Non-universal mound formation in non-equilibrium surface growth

Abstract

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...

Surface kinetics and generation of different terms in a conservative growth equation

“…With large noise reduction factor however, the observed behaviour of this model corresponds to LDV type GE [31]. We have seen that the form of GE with large enough terraces is indeed LDV type, as in Eq.7.…”

“…In (2+1) dimensions , it may be noted that the slope independent current is not obtained for P A = P B due to the different number of configurations for in-plane and downward hops [31]. Thus for the same set of rules, re-sults in (1+1) dimensions will differ from those in (2+1) dimensions as noted in ref.…”

“…As a result, slope dependent current will dominate the growth changing the universality class with dimensions [31]. In this case, the noise reduction technique helps establish the sign of the current on tilted substrate.…”

Mound morphology of the 2+1 -dimensional Wolf–Villain model caused by the step-edge diffusion effect

“…Mound morphologies are also found [18][19][20][21][22][23][24][25] in several local (no non-local effects exist) non-equilibrium growth models that incorporate no ES barrier. In these models, such as the well-known Wolf-Villain (WV) model [26] (in 2 + 1-dimensions)…”

“…In many common modern deposition techniques, however, many mechanisms can play an important role in defining the surface morphology during growth. Some mechanisms give rise to a mound structure [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] that cannot be described within the context of self-affinity. The origin of this phenomenon is ascribed to a growth instability caused by these mechanisms.…”