A Simple Model for the Formation of Step-Free Surfaces

Abstract

ABSTRACTArrays of step-free regions on the surface of silicon have been created either by evaporating atoms from craters[1] or by depositing atoms on mesas[2]. In most cases the maximum extent of the step-free regions is limited by the occurrence of circular pits or islands in the crater or mesa structures. We model the process of step clearing and nucleation of these pits and islands by approximating the initial surface by an array of circular steps whose movement is mediated by adatoms. BCF (Burton-Cabrera-Frank) theory[3] is used to incorporate the effects of surface diffusion, evaporation and the deposition of atoms on the surface. We include the effects of step curvature and step interactions. If the step spacing is large enough, we find that the innermost step moves outwards to create a step-free region; otherwise it moves inward and leads to large scale smoothening of the surface. Pit or island nucleation in the center of the craters or mesas is also included in the model by using classical nucleation theory. We investigate the effect of deposition flux and temperature on the formation of step-free surfaces and compare the results to reported experiments on silicon and to some of our recent work on sapphire.