A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories - Ibrahim Ali , Noorbatcha; Lionel M. , Raff; Donald L. , Thompson (American Institute of Physics (AIP), 1985)
A general method to calculate a lower bound and an estimated upper bound for the surface diffusion coefficient from jump frequencies of an adatom from 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±1.11)×exp{-(2430±270)/ RT} cm2/s. At 1500 K, the computed mean-square displacement and velocity autocorrelation function give diffusion coefficients of 7.11×10-4 and 8.69×10-4 cm2/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. The upper bound calculated in this manner at 1500 K is 1.41×10-3 cm2/s, which is a factor of 2 greater than the computed diffusion coefficient. The calculated activation energy for surface diffusion (2.43 kcal/mol) suggests that the experimental value for this quantity obtained from the direct deposition of Si on Si(111) in ultra high vacuum most accurately represents the true zero-coverage limit on a Si(111) crystal free of kinks and steps.