Diffusion of H atoms on a Si(111) surface with partial hydrogen coverage: Monte Carlo variational phase-space theory with tunneling correction

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Abstract
The diffusion of hydrogen atoms on a partially hydrogen-covered Si(111) surface has been studied by using Monte Carlo techniques with a potential-energy surface based on the available ab initio results and experimental data. The potential describes two kinds of binding sites, a covalent Si–H bond (top site) and an interstitial threefold bonding site (open site). Classical jump frequencies between the top and open sites were calculated using Monte Carlo variation phase-space theory with importance sampling at 300, 600, 900, and 1200 K. A new approach for treating tunneling through two-dimensional diffusional barriers is presented and used to calculate the phonon-assisted tunneling rates. This method assumes continuum-to-continuum WKB tunneling with classical Monte Carlo phase space averaging. Thermal diffusion coefficients are calculated using the jump frequencies. The diffusional barriers between the two binding sites on the equilibrium surface are 2.79 and 0.65 eV for top-to-open site and open-to-top site jumps, respectively. The calculated classical jump frequencies give Arrhenius parameters of A=1.3×1014 and 9.9×1013 s−1 Ea=2.72 and 0.59 eV for top-to-open and open-to-top site jumps, respectively. Monte Carlo techniques were used to compute the minimum energy path; the dynamical barrier is 2.64 eV for top-to-open site jumps. Tunneling rates were calculated at 300 K and estimated at higher temperatures. Due, in part, to the small width of the barrier, the tunneling rate at 300 K is 257 times larger than the classical value. Tunneling is important at room temperature, but its importance relative to the classical rate decreases with increasing temperature. The results indicate that surface phonons significantly enhance the tunneling rate.