  We present a model for the interplay between the fundamental phenomena
responsible for the formation of nanostructures by metalorganic vapour phase
epitaxy on patterned (001)/(111)B GaAs substrates. Experiments have
demonstrated that V-groove quantum wires and pyramidal quantum dots form as a
consequence of a self-limiting profile that develops, respectively, at the
bottom of V-grooves and inverted pyramids. Our model is based on a system of
reaction-diffusion equations, one for each crystallographic facet that defines
the pattern, and include the group III precursors, their decomposition and
diffusion kinetics (for which we discuss the experimental evidence), and the
subsequent diffusion and incorporation kinetics of the group-III atoms released
by the precursors. This approach can be applied to any facet configuration,
including pyramidal quantum dots, but we focus on the particular case of
V-groove templates and offer an explanation for the self-limited profile and
the Ga segregation observed in the V-groove. The explicit inclusion of the
precursor decomposition kinetics and the diffusion of the atomic species
revises and generalizes the earlier work of Basiol et al. [Phys. Rev. Lett. 81,
2962 (1998); Phys. Rev. B 65, 205306 (2002)] and is shown to be essential for
obtaining a complete description of self-limiting growth. The solution of the
system of equations yields spatially resolved adatom concentrations, from which
average facet growth rates are calculated. This provides the basis for
determining the conditions that yield selflimiting growth. The foregoing
scenario, previously used to account for the growth modes of vicinal GaAs(001)
during MOVPE and the step-edge profiles on the ridges of vicinal surfaces
patterned with V-grooves, can be used to describe the morphological evolution
of any template composed of distinct facets.
