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Intermediate scaling regime for multilayer epitaxial growth
Phys. Rev. B 61, 8602 – Published 1 April, 2000
DOI: https://doi.org/10.1103/PhysRevB.61.8602
Abstract
We explore the layer-by-layer (Frank–van der Merwe) growth regime within the context of a discrete solid-on-solid kinetic Monte Carlo model. Our results demonstrate a nontrivial scaling of the lattice step edge density, a quantity that oscillates about a nominally constant value prior to the onset of kinetic roughening. This value varies with the ratio of the surface diffusivity to the deposition flux, as a nearly perfect power law over a wide range of R. This “intermediate” scaling regime extends in coverage from one to at least a few tens of monolayers, which is exactly the regime of most importance to the growth of device-quality semiconductor quantum heterostructures. Comparison with lowest-order linear theories for height fluctuations demonstrates the validity of the Wolf-Villain mean-field theory for the description of lattice step density and “in-plane” structure for all coverages down to the first monolayer of growth. However, the mean-field theory does not fully account for the surface width in this regime and consequently does not quantitatively predict the observed step density scaling.
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