Dynamical theory of low-energy ionization of inert-gas atoms at surfaces

Abstract

A quasi-ab-initio calculation of the ionization probability of a low-energy He atom at the surface of a linear chain of n atoms (modeling Si) has been made using the technique of numerical solution of the equations of motion for ${\mathrm{scrN}}_{\mathrm{ij}}$(t)\ensuremath{\equiv}〈${\ensuremath{\Psi}}_{S}$(t)\ensuremath{\Vert}${c}_{i}$${c}_{j}$\ensuremath{\Vert}${\ensuremath{\Psi}}_{S}$(t). The low-energy-ionization effect below 1 keV has been explained on the basis of impact scattering, in which the projectile valence orbital overlaps the target core orbitals. Two conditions are established for seeing the effect: (1) The hopping integral ${V}_{\mathrm{ak}}$(z) between the orbitals centered on the He atom and the target atom must go through zero at distances z\ensuremath{\simeq}${R}_{C}$ (the distance of closest approach). (2) The diabatic level centered on the projectile must shift up to near ${\ensuremath{\varepsilon}}_{F}$ there. Fortunately, the first condition will be rather generally encountered, because of the oscillations in the target valence orbitals at small radius. On the other hand, feature (2) is more specific to the projectile-target material combination and leads to some target material dependencies. At energies higher than 2 keV, the ionization probabilities with and without the level shift \ensuremath{\Delta} become identical, and only condition (1) is necessary. Thus, in this energy region the surface ionization effect will be more generally expected for such systems as, e.g., the He\ensuremath{\rightarrow}Cu surface, which has a noncrossing energy-level diagram or \ensuremath{\Delta}=0, in good agreement with experiment. For energies greater than 50 or 100 keV, neither condition is necessary, and ${P}_{\mathrm{ion}}$ oscillates as a function of ${E}_{0}$, representing the quasiresonant ionization process. It is also found that the ionization probability ${P}_{\mathrm{ion}}$ in surface scattering (n\ensuremath{\ge}30) is nearly 1 order of magnitude greater than that in a binary collision (n=1), at an energy of 1 keV. The effect of the energy-band occupation has also been shown to be of essential importance.