Scaling properties of equilibrating semiconductor mounds of various initial shapes

Abstract

A surface below its roughening temperature consisting of two dimensional concentric circular monoatomic steps is discussed under step-flow model. Entropic interactions between the steps are considered and the diffusion equation is solved in two dimensional polar coordinates. It is assumed that the local mass transfer occurs due to surface diffusion only during the evolution of the initial surface. The evolution of initial surfaces bounded by both a sinusoidal and other envelope functions of the form xγ are considered. The evolution of the height of surface as a function of time is analyzed for each surface in Diffusion Limited (DL) regime. We have determined three scaling characteristics of evolution of the height of the surface. For an initial sinusoidal surface profile we have the following findings: The height of surface approximately decreases as τα where α is independent of wavelength and initial height of the surface. The time dependence of the evolution of the height scales with the cube of the wavelength of the initial surface. Finally the normalized height of the initial surfaces of different amplitudes with the same wavelength scales linearly with the amplitude as a function of time. Similar findings are obtained for non-sinusoidal initial surfaces also.