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 en
force layer-by-layer growth by reducing the island spacing. The depend
ence upon temperature is also explained.