Terrace sizes in molecular beam epitaxy

The order of magnitude of the typical distance ℓ between steps in MBE-grown crystal surfaces in calculated from simple scaling assumptions in the absence of evaporation. This distance is measurable by diffraction methods and yields access to the surface diffusion constant D. At the lowest non trivial temperatures the characteristic distance is of order (D/F)^1/6 where F is the beam flux. At slightly higher temperature, ℓ is given by an algebraic formula which depends on the lifetime T₂ of a bound pair of adatoms at the surface, as well as of the diffusion constant D₂ of these pairs. In certain ranges, ℓ varies as F^1/4 or F^1/5. At higher temperatures yet, ℓ is given by a formula which depends on a larger number of parameters. In special cases, our results are in agreement with the classical formulae of Stoyanov and Kashchiev, but disagree with certain recents works. ℓ is found to increase with temperature more rapidly than an Arrhenius exponential. Monte-Carlo simulations are reported and the discrepancy with certain other authors is clarified.