Time-dependent annealing and deposition on substrates with repulsive interactions

J.A. Venables, J. DeGraffenreid, D. Kay and P. Yang
Phys. Rev. B 74 (2006) 075412


In models of nucleation and growth of crystals on surfaces, it is often assumed that the energy surface of the substrate is flat, that diffusion is isotropic, and that capture numbers can be calculated in the diffusion-controlled limit. We lift these restrictions and formulate the general time-dependent problem in a 2D potential field. We utilize the Master Equation Discretization (MED) method to solve the 2D time-dependent diffusion field of adparticles on general non-uniform (rectangular grid) substrates, and compare it against competing algorithms, including the FFT and hybrid-FFT methods previously introduced, for periodic boundary conditions.

The physical context is set by the importance of repulsive interactions in the nucleation and growth of many nanostructures, e.g. metal nanoclusters, hut clusters and nanowires. The programs, realized in Matlab 6.5, are used to obtain quantitative capture numbers, aspect and direct impingement ratios, and other island growth quantities in the presence of potential fields, when particular surface processes are included. The case of no corner rounding is studied in detail. Strongly anisotropic potentials favor wire growth, which can be considerably influenced by alternate deposition and annealing, and the location of neighboring islands. Physical examples are given based on Ge/Si(001) material parameters.

Essentially similar programs, differing only in outputs, are used to visualize the diffusion field and to produce realistic movies of crystal growth. Examples given here are linear deterministic calculations, but the framework allows for inclusion of non-linear and statistical effects for particular applications.

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Latest version of this document: 22nd February 2010.