Contribution to the theory of charge exchange at surfaces

Abstract

The ion fraction P of sputtered or scattered particles is calculated in an independent-electron scheme for exponential variations of atom-substrate coupling matrix elements with a time constant μ-1 along the outward trajectory and, in the scattering case, λ-1 along the inward trajectory, without specific assumptions about the electronic structure of the substrate. If ion formation results from transitions continuous in time, P behaves at small μ as exp (- C1/μ) in most cases. C1 is a certain integral of the function ϕ(ε) = - arg σ(ε) where σ(ε) is the self-energy for the (static) coupled atom-substrate system. The contributing processes are near-resonant (i.e. quasi isoenergetic) as well as far-resonant (implying an energy jump) processes. If transitions are provoked by the discontinuity of the time derivative of coupling matrix elements at t = 0, due to assumed matching conditions, one obtains P ∝ (μ + λ)2 exp (- C 2/μ) or more complicated expressions, with C 2 = 0 for a discrete-level system. The range of validity of the various expressions is delimited. In order to illustrate and corroborate the general results and examine other time dependences of the coupling, three special cases are studied : the case where a rate equation approach is applicable, the wide-band model and the atomic-like two-level model