Mean-field nucleation and growth modeling is important for understanding various adsorbate-substrate systems, particularly in the context of epitaxial growth. Conventional mean-field theory does not take into account nonlocal interactions, but adparticles may interact with strained islands via long range elastic interactions mediated by the substrate. We show that recent extensions of mean-field theory to deal with nonlocal interactions do not describe such processes faithfully. Here, we derive a generally applicable mean-field theory of adparticle dynamics on strained surfaces, when interdiffusion is neglected. This approach enables us to determine the transport coefficients from the microscopic physics; in particular, we find explicit expressions for the diffusion coefficient and drift velocity at all positions relative to an arbitrarily strained island. We demonstrate the role of strain on island growth, using island strain fields that are dynamically updated, for Ge/ Si͑001͒ parameters. This approach has important applications in the modeling of nucleation and growth of many nanostructures, such as metal nanoclusters, semiconductor hut clusters, and silicide nanowires.

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 nonuniform (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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