VOLUME 77, NUMBER 22 PHYSICAL REVIEW LETTERS 25 NOVEMBER 1996 Step-Adatom Attraction as a New Mechanism for Instability in Epitaxial Growth Jacques G. Amar and Fereydoon Family Department of Physics, Emory University, Atlanta, Georgia 30322 (Received 18 June 1996) We show that short-range attraction of adatoms towards clusters and ascending steps leads to an instability towards mound formation in epitaxial growth. This instability is studied both analytically and via Monte Carlo simulations on bccfcc(100) surfaces. The origin of this instability in terms of second-layer nucleation and its implications for surface morphology and interpretation of recent experiments are also discussed. [S0031-9007(96)01674-2] PACS numbers: 68.55.Jk, 68.35.Fx, 68.55.Jk The key to understanding epitaxial growth of materials is the identification and elucidation of processes which control the evolution and the morphology of the surface. Since atomic diffusion is the dominant dynamical process on the surface, much effort has been made to determine the rates of different atomistic diffusive processes on surfaces. For example, measurements of island nucleation, field-ion-microscopy (FIM) studies of atom migration, and theoretical calculations have all been devoted to the determination of energy barriers for diffusion on surfaces. In detailed FIM studies of adatom diffusion on the Ir(111) surface, Wang and Ehrlich [1] have found that there exists a short-range attractive interaction between an adatom diffusing on a terrace and a cluster. In particular, adatoms within a few nearest-neighbor spacings from a cluster were found to diffuse rapidly towards the cluster. This attraction was found to be independent of cluster size and to lead to the rapid incorporation of adatoms near clusters and ascending step edges. The cause of this effect, which has also been observed in embedded atom calculations of diffusion barriers on metal (100) surfaces [2], is an alteration in the potential landscape in the vicinity of a cluster (see Fig. 1). Although it was pointed out that this effect increases the capture radius for a cluster, the consequences of this attraction on epitaxial growth have not been investigated. However, it has already been demonstrated [3,4] that the existence of a potential barrier for an adatom to diffuse from the top of a step to the layer below (often referred to as the Ehrlich-Schwoebel barrier or step barrier [5]) does lead to a morphological instability in epitaxial growth. The question is, does short-range step-adatom or cluster- adatom attraction also have consequences for the surface morphology in epitaxial growth? In this Letter we discuss the effects of step-adatom attraction on the stability and evolution of epitaxial growth. We show that (in the absence of desorption) this effect causes an instability that leads to mound formation even in the absence of an Ehrlich-Schwoebel barrier. In particular, we present an analytic calculation which clearly indicates the existence of an instability due to step- adatom attraction. We also present the results of kinetic Monte Carlo simulations which verify the existence of this instability. Finally, we discuss the physical origin of this instability and its possible implications on the interpretations of various experiments. In order to study the effects of step-adatom attraction on a specific model, we consider the stability of a bcc(100) [or equivalently fcc(100)] surface in the presence of step-adatom attraction. The choice of such a surface is motivated partly by the existence of a variety of experiments on (100) metal surfaces in which unstable growth leading to mound formation has been observed [6,7]. For simplicity we consider a quasi-one-dimensional model consisting of a regular stepped bcc(100) surface [corresponding to a (1 0 l ) facet] with infinitely long straight steps along the [001] direction (see Fig. 1) with terrace length l  1m (in units of 12 the next-nearest- neighbor distance) where l  2j 1 1 and j is the number of exposed rows in each (100) terrace and m is the slope of the surface. We also assume irreversible attachment at ascending steps (site 0). Such a model is appropriate in the case of relatively straight steps when the mound size is significantly larger than the terrace size, and has previously been used [8] to study the critical temperature for mound formation in the case of a step barrier. We note that while our calculations correspond to a specific FIG. 1. Diagram showing stepped bccfcc (100) surface with slope m (terrace width l  1m) and straight step edges along the (001) axis (side view). Even sites correspond to fourfold- hollow sites on terrace. Also shown is a schematic of the potential surface showing decreased potential barrier due to step-adatom attraction near the ascending step along with a possible step barrier at the descending step. 4584 0031-9007 96 77(22) 4584(4)$10.00 © 1996 The American Physical Society