  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: the interrupted coarsening, "facet" bunching, and the lateral drift of the
step perturbations (a traveling wave) when the terrace diffusion is
anisotropic. The nonlinear drift introduces a disorder into the evolution of a
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. Keywords: epitaxial crystal growth;
step flow; meandering instability; molecular precursors; anisotropic diffusion;
nonlinear pde model; convective Cahn-Hilliard equation
