Impact Parameter Dependence of the Electronic Stopping Power for Channeled Ions

Abstract

I n order to examine the dependence of the electronic stopping power (dE/ds) on the impact parameter p, the energy dissipation of axially channeled ions with curved trajectories is studied theoretically by means of a cluster model. dE/d.x is accounted in the framework of nonlinear molecular dynamics (MD) coupled with the local density approach (LDA) based on the Ihdhard-Winther (LW) theory. A correction factor of 2 is introduced to compensate the lower dE/dx, especially for low-energy ions. B ions are implanted into Si (100) and ( I lo) at incident energy in the region 10 keV 5 E , 5 10 MeV.Results are the following. Firstly two kinds of solid-state effects on the p-dependence of dE/ds are found at high and low En, respectively. A t high E , ( > 100 keV) the core electrons reveal quite different profiles of dE/ds versus p than valence ones, and at low E , ( < 100 keV) the topological difference in the electron distribution among axial channels appears i n those profiles, which cannot be explaincd by nicans of collisions with single atom. Sccondly, the p-dependence of dE/dx is intended to adapt the simple form ciE(p)/d.x = A exp (-.sp/o). The factor s due to core electrons increases distinctly with En, while that due to valence electrons is almost invariant. smaller than 0.3.

A predictive model for the electronic stopping force for molecular dynamic simulation (I)

“…This velocity region is below the Thomas-Fermi velocity and above the specific velocity that gives the maximum nuclear stopping (dE/dx) n , which we call the ''LSS region". We have proposed a model that can do predictive simulation for many semiconductors [8,9]. It is described by the density functional (dE/dx) e for a unit charge and the effective charge following the Brandt-Kitagawa model.…”

“…The (dE/dx) proton is derived from the LW theory as a function of a Muffin-tin type q(r) in a solid, where q(r) is obtained from the Hartree-Fock-Slater approximation [8,9]. The lowest energy taken into account (dE/ dx) e term in a MD is optional, e.g., it was taken around 5 eV [11] or 10 eV [12].…”

“…These terms [8,9] are written as follows using the units of [(dE/dx) e ] = eV/(0.1 nm) and [q(r)] = electrons/(0.1 nm) 3 . The Eq.…”

“…In our MD simulation [8,9], we expressed the term (dE/dx) proton as a function of Muffin-tin type q(r) following the Lindhard and Winther (LW) theory, which revealed a clear dependence of (dE/dx) e on the impact-parameter of particles channeling through IV and III-V semiconductor crystals. Our density functional model had one fitting parameter (a) originated to the (dE/dx) proton of the LW theory, in order to compensate the low value due to LW theory [10].…”