  Burton-Cabrera-Frank (BCF) theory has proven to be a versatile framework to
relate surface morphology and dynamics during crystal growth to the underlying
mechanisms of adatom diffusion and attachment at steps. For an important class
of crystal surfaces, including the basal planes of hexagonal close-packed and
related systems, the steps in a sequence on a vicinal surface can exhibit
properties that alternate from step to step. Here we develop BCF theory for
such surfaces, relating observables such as alternating terrace widths as a
function of growth conditions to the kinetic coefficients for adatom attachment
at steps. We include the effects of step transparency and step-step repulsion.
A general solution is obtained for the dynamics of the terrace widths, assuming
quasi-steady-state adatom distributions on the terraces. An explicit simplified
analytical solution is obtained under widely applicable approximations. From
this we obtain expressions for the full-steady-state terrace fraction as a
function of growth rate. Fits of the theoretical predictions to recent
experimental determinations of the steady-state and dynamics of terrace
fractions on GaN (0001) surfaces during organo-metallic vapor phase epitaxy
give values of the kinetic coefficients for this system. In Appendices, we also
connect a model for diffusion between kinks on steps to the model for diffusion
between steps on terraces, which quantitatively relates step transparency to
the kinetics of atom attachment at kinks, and consider limiting cases of
diffusion-limited, attachment-limited, and mixed kinetics.
