COMPARISON OF SILICON-ATOM DIFFUSION ON THE DIMER-ADATOM-STACKING FAULT AND BINNIG ET-AL MODELS OF THE RECONSTRUCTED SI(111)-(7X7) SURFACE

The dynamics of silicon-atom diffusion on the dimer-adatom-stacking fault model (DAS) of the reconstructed Si(111)-(7 x 7) surface suggested by Takayanagi et al. have been investigated using variational phase-space theory methods. The site-to-site jump frequency is obtained from the variationally minimized total flux across a right cylindrical dividing surface whose cross section in the surface plane is formed from straight line and elliptical segments. This minimized flux is corrected for surface recrossings by the computation of trajectories starting from phase-space points in the transition-state region that are obtained in the Markov walk used to evaluate the phase-space integrals in the expression for the total classical flux. The jump frequencies are used as input to the set of differential equations that describes the diffusion rates on the DAS surface. Values of the diffusion coefficient D are computed from the slopes of plots of the time variation of the root-mean-square displacements obtained from the solution of the rate equations. Arrhenius plots of the results at 300, 600, and 1000 K yield D = 0.124 exp[-2.18 eV/kT] cm2/s. These rates are orders of magnitude smaller than the corresponding rates we have previously obtained for silicon-adatom diffusion on the Binnig et al. model of the Si(111)-(7 x 7) surface. In addition, it is found that the diffusion pattern on the DAS surface is uniform with no preferential directions for silicon-atom flow. In contrast, diffusion on the Binnig surface was found to occur via gateways at three of the four corners of the unit cell. This led to preferential directions for adatom flow. These differences lead us to suggest that careful measurements of silicon-adatom diffusion rates on the Si(111)-(7 x 7) surface may be a very sensitive measure of the extent to which these surface models accurately describe the experimental Si(111)-(7 x 7) reconstruction.