Time-dependent fields on rectangular substrates: modeling anisotropic diffusion and growth

P. Yang and J.A. Venables, Materials Research Soc. 859E (2005) JJ3.2.1-6


In models of nucleation and growth on surfaces, it has often been assumed that surface diffusion is isotropic; however, many cases are known (e.g. Ge clusters or silicide nanowires grown on Si(001)2x1) when anisotropic diffusion, and possibly also attachment, would be more appropriate. Here we explore a method of using the discrete FFT for solving the time-dependent diffusion equation for ad-particles. This method is tested against the known result of diffusion from a 2D point source, with periodic boundary conditions. The FFT method gives a perfect match to the analytical solution for multiple point sources arranged on a lattice, except near (initial) field discontinuities. We solve the time-dependent anisotropic diffusion field with rectangular block sinks to simulate the growth of a regular array of islands using analogous methods. Programs are coded in Matlab 6.5; the calculation is fast, and the evolving diffusion field and island shapes can be seen visually in the form of MatLab movies. Capture numbers are calculated for rectangular islands in the case of restricted corner diffusion.

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Latest version of this document: 22nd February 2010.