Step growth and meandering in a precursor-mediated epitaxy with anisotropic attachment kinetics and terrace diffusion


Step meandering instability in a Burton-Cabrera-Frank (BCF)-type model for the growth of an isolated, atomically high step on a crystal surface is analyzed. It is assumed that the growth is sustained by the molecular precursors deposition on a terrace and their decomposition into atomic constituents; both processes are explicitly modeled. A strongly nonlinear evolution PDE for the shape of the step is derived in the long-wave limit and without assuming smallness of the amplitude; this equation may be transformed into a convective Cahn-Hilliard-type PDE for the step slope. Meandering is studied as a function of the precursors diffusivity and of the desorption rates of the precursors and adatoms. Several important features are identified, such as: interrupted coarsening, ``facet" bunching, and the lateral drift of step perturbations (a traveling wave) when the terrace diffusion is anisotropic. The nonlinear drift introduces disorder into evolution of step meander, which results in a pronounced oscillation of the step velocity, meander amplitude and lateral length scale in the steady-state that emerged after the coarsening was interrupted. The mean values of these characteristics are also strongly affected by the drift.


Mechanics of Materials | Non-linear Dynamics | Other Materials Science and Engineering | Partial Differential Equations | Statistical, Nonlinear, and Soft Matter Physics