Variational phase-space theory studies of silicon-atom diffusion on reconstructed Si(111)-(7×7) surfaces

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Abstract
The dynamics of silicon-atom diffusion on a reconstructed Si(111)-(7×7) surface have been investigated using variational phase-space theory methods with a previously described [J. Chem. Phys. (to be published)] potential-energy surface. A four-layer lattice model of the Binnig et al. (7×7) reconstruction containing 291 atoms is employed for the surface. Canonical Markov walks with importance sampling incorporated are used to evaluate the flux across both right-circular and right-elliptical cylindrical dividing surfaces separating adsorption sites. This flux is minimized with respect to the parameters of the dividing surface to obtain the best estimate of the classical jump frequencies. The minimum jump frequencies so obtained are corrected for recrossings of the dividing surface by the calculation of trajectories that start from phase-space points obtained in the random walk that lie within a specified distance w of the dividing surface. The corrected jump frequencies are then used as input to a set of 225 diffential equations that describe the diffusion rates across the (7×7) surface. Diffusion coefficients D are computed from the slope of plots of the time variation of the root-mean-square displacements obtained from the solution of the rate equations. Arrhenius plots of results obtained at 300, 600, and 1000 K yield D=2.15×10−3 exp (−1.51 eV/kBT) cm2/s. The calculated activation energy of 1.51 eV is in excellent accord with the result obtained by Farrow from molecular-beam pyrolysis data on SiH4 deposition. An examination of the details of the diffusion shows that it is not isotropic on the (7×7) surface. We find that preferential directions of flow exist. These directions correspond to ‘‘gateways’’ at three of the four corners of the (7×7) unit cell. The results suggest that diffusion rates are a sensitive function of the geometry of the (7×7) reconstruction so that careful measurements of diffusion rates and associated activation energies may be able to serve as a means of differentiating different proposed models of the Si(111)-(7×7) reconstruction.