The role of processing speed in determining step patterns during directional epitaxy

Abstract

We consider the growth of an epitaxial thin film on a continuously supplied substrate using both the Burton-Cabrara-Frank (BCF) mean-field model and kinetic Monte-Carlo (KMC) simulation. Of particular interest are effects due to the finite size of the deposition zone, which is modeled by imposing an up-and downwind adatom density equal to the adatom density on an infinite terrace in equilibrium with a step. For the BCF model, we find this scenario admits a steady-state pattern with a specific number of steps separated by alternating widths. The specific spacing between the steps depends sensitively on the processing speed and on whether the number of steps is odd or even, with the range of velocities admitting an odd number of steps typically much narrower. These predictions are only partially confirmed by KMC simulations, however, with particularly poor agreement for an odd number of steps. To investigate further, we consider alternative KMC simulations with the interactions between random walkers on the terraces neglected so as to conform more closely with the mean field model. The latter simulations also more readily allow one to disable the step detachment mechanism, in which case they agree well with the predictions of the BCF model.

Emergence of step flow from an atomistic scheme of epitaxial growth in1+1dimensions

“…This flux can be determined via Eqs. (9)- (11). To reduce the discrete equations to BCF-type laws, we need to appropriately scale variables and parameters with the system size, N = a~' (Sec.…”

“…[9][10][11]. It is tempting to explore whether the BCF model can be interpreted as the universal, in some appropriate sense, limit of atomistic processes.…”

“…On the other hand, the studies in Refs. [10,11] concern geometries in 2D with focus on more particular aspects of step flow. For example, in Ref.…”

“…[10] the step position is held fixed; and in Ref. [11] only numerical comparisons of kinetic Monte Carlo (KMC) simulations to the BCF model are pursued. Notably, in Ref.…”

Steric Hindrance of Crystal Growth: Nonlinear Step Flow in 1+1 Dimensions

“…It is worthwhile placing our work in the appropriate context of past literature, e.g. [5][6][7][8][9][10][11][12]. Our goal here is to explore the connection of an atomistic model to mesoscale descriptions of crystals.…”