Ion fractions in the scattering of hydrogen on different reconstructed silicon surfaces

Abstract

A theoretical calculation that accounts for a fairly complete description of the resonant charge-exchange process occurring in H0 scattering by Si surfaces is presented. Two reconstructed surfaces for the target: Si(100)2 · 1 and Si(111)7 · 7, are analyzed in this work. The interacting system is described by an extended spin-less Anderson Hamiltonian where valence as well as core states of the surface atoms are included. The interaction terms are calculated by taking into account the extended features of the surface and the localized atom– atom interactions within a mean-field approximation. The study is focused mainly in the description of the collision process in terms of short range interactions. The density of states for the surface and subsurface atoms are obtained in each case, from a molecular dynamicdensity functional theory in the local density approximation. A binary elastic collision is assumed to fix the projectile trajectory, while the inelastic processes are determined by the interaction of the projectile atom with all the surface atoms ‘seen’ along its trajectory. The ion fractions are calculated by using the Keldysh–Green’s function formalism to solve the time dependent process. We analyze the negative ion fractions of hydrogen measured by Maazouz et al. By including the interaction of the ion projectile with the target atoms seen during its trajectory and averaging over a variety of scattering centers as it may occur in the experimental situation, we obtained a smooth dependence with the exit angle that does not reflect the specific details of the local density of states and the surface topography while reproducing very well the general trends of the experiment. The ion fraction is found to be almost independent on the incoming energy for large values of the exit angles, while in the opposite cases where the projectile spends longer times in contact with the surface, the effect of the parallel component of the velocity has an increasing importance. Thus, the fine details of the surface are ‘better captured’ as the parallel velocity component becomes smaller.