Phenomenological Approach to the Calculation of the Diffusion Coefficient for Si on Si(111) Using Classical Trajectories

摘要

A general method to calculate a lower bound and an estimated upper bound for the surface diffusion coefficient from jump frequencies of an adatom form one absorption site to another has been formulated. This method has been applied to the surface diffusion of Si on Si(111). Keating's potential has been used for the Si(111) lattice. The interaction potential between the adatom and the lattice is a pairwise sum of 60 Morse potentials involving the Si atoms in the first and second layers of the crystal. This potential formulation predicts the existence of two different types of adsorption sites on the Si(111) surface. The jump frequencies from these adsorption sites have been calculated by classical trajectory methods. Using these jump frequencies, a lower bound for the diffusion coefficient is calculated by solving a set of coupled phenomenological kinetic equations describing the jumping of adatoms between adjacent adsorption sites. The results at 800, 1000, 1200, and 1500 K yield a lower bound for the diffusion coefficient of D > (8.53 + or - 1.11)xexp(-(2430 + or - 270)/RT) sq cm/s. At 1500 K, the computed mean-square displacement and velocity autocorrelation function give diffusion coefficients of .0711 and .0869 sq cm/s, respectively, which is in excess of the calculated lower bound at 1500 K by about a factor of 2. This suggests that diffusion of Si on Si(111) involves highly correlated motion. An estimate for the upper bound for the diffusion coefficient is obtained by removing from the set of coupled kinetic equations all terms involving adatom motion which leads back toward the original adsorption site.