Island Nucleation, Predictions of
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Under a range of technologically interesting conditions, films of metals, certain oxides, and semiconductors grow or etch via two-dimensional island formation. Atomic-scale control of the resulting island distribution and final morphology of these films depends on a detailed understanding of these early stages of island formation. This, in turn, requires a precise treatment of the environment dependence of adatom or ad-vacancy capture by other adatoms or ad-vacancies and by growing islands. In particular, the evolution of the densities of islands of different sizes (i.e., of the island size distribution) reflects the form of the “capture numbers” and specifically their dependence on island size, which measures the propensity for islands of different sizes (in a variety of environments) to capture diffusing ad-species. One current challenge is the formulation of both an analytic treatment of the observed form of the “capture numbers” and new simulation strategies for analysis of the asymptotic behavior of models of island formation, in the regime of large characteristic lengths, which is still expensive to simulate with conventional algorithms.
Traditional mean-field rate-equation treatments, in which the typical environment of an island is assumed independent of its shape and size, fail to reproduce the form and scaling properties of the island size distributions observed in experimental and simulation studies. This has been a half-century-old challenge. Recent simulation studies revealed not only the well-known spatial correlation of island positions associated with depletion of the population of nearby islands (as a result of competition by islands for diffusing ad-species), which has been incorporated into mean-field approaches, but also a more subtle correlation between the size and separation of islands, which is still missing and is hard to fold into traditional mean-field approaches. It is the latter correlation that controls the individual island growth rates and the island size dependence of the “capture numbers” and thus the selection of the shape of the island size distribution.