  The formation of nanostructures during metalorganic vapor-phase epitaxy on
patterned (001)/(111)B GaAs substrates is reviewed. The focus of this review is
on the seminal experiments that revealed the key kinetic processes during
nanostructure formation and the theory and modelling that explained the
phenomenology in successively greater detail. Experiments have demonstrated
that V-groove quantum wires and pyramidal quantum dots result from
self-limiting concentration profiles that develop at the bottom of V-grooves
and inverted pyramids, respectively. In the 1950s, long before the practical
importance of patterned substrates became evident, the mechanisms of
capillarity during the equilibration of non-planar surfaces were identified and
characterized. This was followed, from the late 1980s by the identification of
growth rate anisotropies (i.e. differential growth rates of crystallographic
facets) and precursor decomposition anisotropies, with parallel developments in
the fabrication of V-groove quantum wires and pyramidal quantum dots. The
modelling of these growth processes began at the scale of facets and culminated
in systems of coupled reaction-diffusion equations, one for each
crystallographic facet that defines the pattern, which takes account of the
decomposition and surface diffusion kinetics of the group-III precursors and
the subsequent surface diffusion and incorporation of the group-III atoms
released by these precursors. Solutions of the equations with optimized
parameters produced concentration profiles that provided a quantitative
interpretation of the time-, temperature-, and alloy-concentration dependence
of the self-ordering process seen in experiments.
