We develop a microscopic theoretical
model of AlN, GaN, and InN film growth by atomic layer epitaxy. To
make the model realistic, we take into account the atomic hydrogen
that is created by the hydrogen plasma commonly used in plasma-assisted
atomic layer epitaxy. This growth technique relies on separate deposition
steps for nitrogen and the group-III cation. Our model addresses the
processes that occur after a complete monolayer of nitrogen has formed,
that is, the deposition, adsorption, surface diffusion, island nucleation,
and island growth of group-III cations. According to our model, the
three nitrides grow in a standard and qualitatively similar manner:
during a brief nucleation phase, a modest attractive interaction leads
to stable island nuclei consisting of just a few atoms. These then
grow in place at a nearly constant island density and with an island
size distribution which obeys an expected universal scaling relationship
that depends only on the critical island size.