During molecular beam epitaxy, atoms arrive on the surface, and diffuse over a length ℓs before being incorporated into the crystal. Can we estimate ℓs The solution to this problem is contained in review articles by Stoyanov & Kashchiev (1981) and by Venables et al. (1984).

The simplest case is realized when two diffusing adatoms form an immobile and undissociable pair when they meet, and the resulting cluster grows with a compact shape. Stoyanov & Kashchiev have shown that in this case ℓs ∼ (D/F)1/6, where D is the diffusion constant of adatoms and F the deposition flux. More generally, they have shown that ℓs ∼ (D/F)γ, where γ is a function of the critical nucleus size. The critical nucleus is defined as the largest dissociable atom cluster. The experimental verification is not that easy: the critical nucleus size, and thus γ, depend in an unspecified way on the temperature and the deposition flux. A large host of computer simulation data (Monte Carlo) have anyway confirmed the relation between ℓs, D and F.

Orders of magnitude – The lengths should be less than the distances between defects on the surface, i.e. a few microns at the very best. The temperature must be low–which means below 0 °C for metals–otherwise ℓs becomes too long.

Experimental techniques– Microscopy (STM, LEEM, REM), atom-beam scattering, high-energy electron diffraction.