  Coarse-grained modeling of dynamics on vicinal surfaces concentrates on the
diffusion of adatoms on terraces with boundary conditions at sharp steps, as
first studied by Burton, Cabrera and Frank (BCF). Recent electromigration
experiments on vicinal Si surfaces suggest the need for more general boundary
conditions in a BCF approach. We study a discrete 1D hopping model that takes
into account asymmetry in the hopping rates in the region around a step and the
finite probability of incorporation into the solid at the step site. By
expanding the continuous concentration field in a Taylor series evaluated at
discrete sites near the step, we relate the kinetic coefficients and
permeability rate in general sharp step models to the physically suggestive
parameters of the hopping models. In particular we find that both the kinetic
coefficients and permeability rate can be negative when diffusion is faster
near the step than on terraces. These ideas are used to provide an
understanding of recent electromigration experiment on Si(001) surfaces where
step bunching is induced by an electric field directed at various angles to the
steps.
