Burton-Cabrera-Frank theory for the influence of off-cut direction on the growth of hcp crystals

Abstract

The precise direction of the off-cut of a vicinal crystal surface determines the azimuth (in-plane angle) of the surface steps and thus their kink density. Here we develop a Burton-Cabrera-Frank (BCF) theory for step-flow crystal growth that includes the effects of step azimuth. We focus on the basal-plane surfaces of hexagonal close-packed (hcp) and related crystal structures, for which surface steps have alternating properties that depend on azimuth. We build on a previous treatment that considered only a single-step azimuth, ϕ=0, that gives alternating steps of pure A and B type. As ϕ increases from zero, the density of kinks on the steps increases. For hcp-type crystals, in addition the structural difference between alternating steps decreases, until they become equivalent at ϕ=30∘. We consider the azimuth dependence of the step transparency, attachment, and repulsion parameters of the BCF model, including the effects of both geometrically required and thermally generated kinks. Example calculations are presented that demonstrate the overall effect of step azimuth on BCF predictions for step spacings during steady-state growth and for their dynamics during growth transients. Effects of symmetric and asymmetric step-step repulsion are discussed. Published by the American Physical Society 2024