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.
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