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# Electronic Band Structure Effects in the Stopping of Protons in Copper

Abstract

We present an ab initio study of the electronic stopping power of protons in copper over a wide range of proton velocities $$v = 0.02-10~\mathrm{a.u.}$$ where we take into account non-linear effects. Time-dependent density functional theory coupled with molecular dynamics is used to study electronic excitations produced by energetic protons. A plane-wave pseudopotential scheme is employed to solve the time-dependent Kohn-Sham equations for a moving ion in a periodic crystal. The electronic excitations and the band structure determine the stopping power of the material and alter the interatomic forces for both channeling and off-channeling trajectories. Our off-channeling results are in quantitative agreement with experiments, and at low velocity they unveil a crossover region of superlinear velocity dependence (with a power of $$\sim 1.5$$) in the velocity range $$v = 0.07-0.3~\mathrm{a.u.}$$, which we associate to the copper crystalline electronic band structure. The results are rationalized by simple band models connecting two separate regimes. We find that the limit of electronic stopping $$v\to 0$$ is not as simple as phenomenological models suggest and it plagued by band-structure effects.

LLNL-JRNL-680464

NOTE: this paper is now available for download from ArXiv and it will be published in Physical Review B

Among the measurable quantities associated to the interaction between ions and solids, the stopping power $$\mathrm(S)$$ (Ferrell 1977) has received much attention; it provides information regarding the energy transfer between the incoming projectile and the solid target. When a fast ion moves through a material, it loses most of its kinetic energy due to the excitations of the target electrons along its trajectory in what constitutes a fundamentally non-adiabatic process. This energy-loss phenomenon plays an important role in many experimental studies involving radiation in solids, surfaces, and nanostructures (Chenakin 2006, Figueroa 2007, Markin 2008, Kaminsky 1965, Lehmann 1978, Sigmund 2014, Nastasi 1996).