Comparison of siliconhyphen;atom diffusion on the dimerndash;adatomhyphen;stacking fault and Binnigetal. models of the reconstructed Si(111)hyphen;(7times;7) surface

摘要

The dynamics of siliconhyphen;atom diffusion on the dimerndash;adatomhyphen;stacking fault model (DAS) of the reconstructed Si(111)hyphen;(7times;7) surface suggested by Takayanagietal. have been investigated using variational phasehyphen;space theory methods. The sitehyphen;tohyphen;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 phasehyphen;space points in the transitionhyphen;state region that are obtained in the Markov walk used to evaluate the phasehyphen;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 coefficientDare computed from the slopes of plots of the time variation of the roothyphen;meanhyphen;square displacements obtained from the solution of the rate equations. Arrhenius plots of the results at 300, 600, and 1000 K yieldD=0.124thinsp;explsqb;minus;2.18 eV/kTrsqb; cm2/s. These rates are orders of magnitude smaller than the corresponding rates we have previously obtained for siliconhyphen;adatom diffusion on the Binnigetal. model of the Si(111)hyphen;(7times;7) surface. In addition, it is found that the diffusion pattern on the DAS surface is uniform with no preferential directions for siliconhyphen;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 siliconhyphen;adatom diffusion rates on the Si(111)hyphen;(7times;7) surface may be a very sensitive measure of the extent to which these surface models accurately describe the experimental Si(111)hyphen;(7times;7) reconstruction.