Step Growth and Meandering in a Precursor-Mediated Epitaxy with Anisotropic Attachment Kinetics and Terrace Diffusion

摘要

Step meandering instability in a Burton-Cabrera-Frank (BCF)-type model forthe growth of an isolated, atomically high step on a crystal surface isanalyzed. It is assumed that the growth is sustained by the molecularprecursors deposition on a terrace and their decomposition into atomicconstituents; both processes are explicitly modeled. A strongly nonlinearevolution PDE for the shape of the step is derived in the long-wave limit andwithout assuming smallness of the amplitude; this equation may be transformedinto a convective Cahn-Hilliard-type PDE for the step slope. Meandering isstudied as a function of the precursors diffusivity and of the desorption ratesof the precursors and adatoms. Several important features are identified, suchas: the interrupted coarsening, "facet" bunching, and the lateral drift of thestep perturbations (a traveling wave) when the terrace diffusion isanisotropic. The nonlinear drift introduces a disorder into the evolution of astep meander, which results in a pronounced oscillation of the step velocity,meander amplitude and lateral length scale in the steady-state that emergedafter the coarsening was interrupted. The mean values of these characteristicsare also strongly affected by the drift. Keywords: epitaxial crystal growth;step flow; meandering instability; molecular precursors; anisotropic diffusion;nonlinear pde model; convective Cahn-Hilliard equation