Magic Islands and Submonolayer Scaling in Molecular Beam Epitaxy

The characteristic distance $l$ between nucleation sites and the island size distribution are studied for layer-by-layer growth. A derivation is given that the scaling of $l$ with the deposition rate depends only on the size of the smallest stable rather than the largest unstable island. This is important if larger islands are less stable than smaller (“magic”) ones. A new algorithm for simulating molecular beam epitaxy is used to verify this result. It is shown that the size distribution function scales with the average island size only if magic islands are absent. Finite size effects for the density of stable islands and of adatoms are studied and related to the transition to step flow growth on vicinal surfaces.