Abstract
We study a reaction diffusion model which describes the formation of patterns on surfaces having defects. Through this model, the primary goal is to study the growth process of Ge on Si surface. We consider a two species reaction diffusion process where the reacting species are assumed to diffuse on the two dimensional surface with first order interconversion reaction occuring at various defect sites which we call reaction centers. Two models of defects, namely a ring defect and a point defect are considered separately. As reaction centers are assumed to be strongly localized in space, the proposed reaction-diffusion model is found to be exactly solvable. We use Green's function method to study the dynamics of reaction diffusion processes. Further we explore this model through Monte Carlo (MC) simulations to study the growth processes in the presence of a large number of defects. The first passage time statistics has been studied numerically.
Highlights
Growth processes on surfaces at nanoscales can show a countless varieties of patterns
Random clusters are formed at the location of surface defects present inside the domain boundary
We present here a reaction diffusion model for these growth processes and pattern formation
Summary
Growth processes on surfaces at nanoscales can show a countless varieties of patterns. It has been observed that for the Ge adatoms deposited on the Si surface there is a preferential growth at the domain boundaries.[11] random clusters are formed at the location of surface defects present inside the domain boundary. We present here a reaction diffusion model for these growth processes and pattern formation. This work has been motivated by experimental work on pattern formation in the deposition of Ge on Si(111)-(7 × 7) surfaces[11] as well as several other previous investigations.[2,3,4,5,6,7,8,9,10] We note that ours is a case of reaction-diffusion process in random media.
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