CRITICAL ISLAND SIZE FOR LAYER-BY-LAYER GROWTH

We show that in epitaxial growth, there is a critical island size R(c) 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 L(n), if R(c) < 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.