  We study the nucleation of GaN islands grown by plasma-assisted
molecular-beam epitaxy on AlN(0001) in a Stranski-Krastanov mode. In
particular, we assess the variation of their height and density as a function
of GaN coverage. We show that the GaN growth passes four stages: initially, the
growth is layer-by-layer; subsequently, two-dimensional precursor islands form,
which transform into genuine three-dimensional islands. During the latter
stage, island height and density increase with GaN coverage until the density
saturates. During further GaN growth, the density remains constant and a
bimodal height distribution appears. The variation of island height and density
as a function of substrate temperature is discussed in the framework of an
equilibrium model for Stranski-Krastanov growth.
