Critical island size for layer-by-layer growth

This is the authors' abstract. We don't add key points for this paper.

We show that in epitaxial growth, there is a critical island size Rc at which a second layer nucleates on top of the island. This provides a simple perspective on the conditions for smooth versus rough growth: For island spacing Lₙ, if Rc{L}ₙ$ the islands will nucleate a second layer before coalescence, giving multilayer growth. This occurs when there is a sufficiently large diffusion barrier (the ``Schwoebel barrier'') at the island edge. We demonstrate that surfactants can enforce layer-by-layer growth by reducing the island spacing. The dependence upon temperature is also explained.