  Site-controlled quantum dots formed during the deposition of (Al)GaAs layers
by metalorganic vapor-phase epitaxy on GaAs(111)B substrates patterned with
inverted pyramids result in geometric and compositional self-ordering along the
vertical axis of the template. We describe a theoretical scheme that reproduces
the experimentally-observed time-dependent behavior of this process, including
the evolution of the recess and the increase of Ga incorporation along the base
of the template to stationary values determined by alloy composition and other
growth parameters. Our work clarifies the interplay between kinetics and
geometry for the development of self-ordered nanostructures on patterned
surfaces, which is essential for the reliable on-demand design of confined
systems for applications to quantum optics.
