Phonon-Induced Desorption of Adatoms from Crystal Surfaces. I. Formal Theory

Abstract

A three-dimensional multiphonon first-principles theory of the desorption of adatoms from crystal surfaces via interaction with phonons is presented. A central quantity in the theory is the time- and position-dependent displacement-displacement correlation function of the lattice. Explicit expressions are derived for the desorption rate from localized states at low temperatures. Calculations are performed for a Debye substrate and Morse-like interaction between the adatom and substrate atoms. Angular and energy distributions, and temperature dependence, of the single-phonon rate are investigated. Under typical conditions, it is found that the angular distribution deviates strongly from the $cos\theta$ distribution, and that the energy distribution peaks strongly for final adatom energies near zero. At low temperatures the rate is proportional to $e^{-\beta E_0}$, a dependence similar to classical theory.