  We present a zinc-blende lattice gas model of II-VI(001) surfaces, which is
investigated by means of Kinetic Monte Carlo (KMC) simulations. Anisotropic
effective interactions between surface metal atoms allow for the description
of, e.g., the sublimation of CdTe(001), including the reconstruction of
Cd-terminated surfaces and its dependence on the substrate temperature T. Our
model also includes Te-dimerization and the potential presence of excess Te in
a reservoir of weakly bound atoms at the surface. We study the self-regulation
of atomic layer epitaxy (ALE) and demonstrate how the interplay of the
reservoir occupation with the surface kinetics results in two different
regimes: at high T the growth rate is limited to 0.5 layers per ALE cycle,
whereas at low enough T each cycle adds a complete layer of CdTe. The
transition between the two regimes occurs at a characteristic temperature and
its dependence on external parameters is studied. Comparing the temperature
dependence of the ALE growth rate in our model with experimental results for
CdTe we find qualitative agreement.
