Critical island size for layer-by-layer growth

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<Ln 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. © 1994 The American Physical Society.