Evolution of terrace size distributions during thin-film growth by step-mediated epitaxy

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Abstract
Under certain conditions the process of thin-film epitaxy can be envisioned as atom deposition onto a crystalline substrate with subsequent surface diffusion along the surface terraces and eventual atomic bonding at a surface step. This process of step-mediated growth is currently being explored as a mechanism to form two-dimensional periodic structures. Such schemes require a periodic step distribution, i.e., uniform terrace lengths, to succeed. In this paper we use a model based on step-mediated growth to present an analytical derivation of the approach to uniform terrace lengths on a stepped surface, given a terrace length distribution of finite width at the outset. The results show that growth interruption is of no advantage and that in general the approach to uniform terrace lengths is quite slow. The width of the terrace length distribution varies approximately as the inverse 4th root of the deposited coverage. This will only occur if the atoms attach themselves predominately at the up-step of each terrace. Otherwise, the width of the distribution will grow without bounds. The model further predicts characteristic oscillations of terrace lengths in the vicinity of multiple height steps.

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