The master and Fokker-Planck equations for surface diffusion were derived from first principles by using a quantum-mechanical approach. The problem of a single ad-particle moving on the corrugated surface of a substrate was studied by considering the coupling of the ad-particle to the substrate phonons. The lattice-gas model was then derived from these principles. Realistic flat-bottomed potential wells were considered as a corrugated surface potential in a study of the diffusion of a single ad-particle along a given surface direction. The temperature dependence of the diffusion coefficient revealed Arrhenius activated behavior; with a compensation effect at higher temperatures.

Microscopic Derivation of the Master and Fokker-Planck Equations for Surface Diffusion. M.Azzouz, H.J.Kreuzer, M.R.A.Shegelski: Physical Review B, 2002, 66[12], 125403 (13pp)