Two Species Diffusion Model of Self-Organized Evolution on Patterned GaAs(001) Surfaces*

We report on numerical simulations of the self-organized evolution on GaAs(001) surface, pre-patterned with square arrays of pillars, during homo-epitaxial growth. Our experiments showed that lithographically fabricated, flat-topped cylindrical pillars evolved into a universal, downward paraboloidal shape, for initial diameters of the pillar ranging from 0.7um to several microns. In modeling this behavior, we construct a two-species diffusion model to simulate the growth. We consider the diffusion of both the Ga atom and As$_{2}$ dimers deposited on terraces between the concentric loop steps which make up the sidewall of the pillar. The stoichiometry for incorporating the diffusing Ga atoms and As$_{2}$ dimers into solid GaAs at the step edges produces boundary conditions that couple the flux of both diffusising species. We compare the results of our numerical simulation to the observed self-organization of the topography. *supported by the Lab for Physical Sciences and by~NSF{\#} DMR-0705447.~~