Intermediate scaling regime for multilayer epitaxial growth

We explore the layer-by-layer (Frank-van der Merwe) growth regime within th e context of a discrete solid-on-solid kinetic Monte Carlo model. Our resul ts demonstrate a nontrivial scaling of the lattice step edge density, a qua ntity that oscillates about a nominally constant value prior to the onset o f kinetic roughening. This value varies with the ratio of the surface diffu sivity to the deposition flux, R=D/F, as a nearly perfect power law over a wide range of R. This ''intermediate'' scaling regime extends in coverage f rom one to at least a few tens of monolayers, which is exactly the regime o f most importance to the growth of device-quality semiconductor quantum het erostructures. Comparison with lowest-order linear theories for height fluc tuations demonstrates the validity of the Wolf-Villain mean-field theory fo r the description of lattice step density and "in-plane" structure for all coverages down to the first monolayer of growth. However, the mean-field th eory does not fully account for the surface width in this regime and conseq uently does not quantitatively predict the observed step density scaling.