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 a.u. where we take into account non-linear effects. Timedependent 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 ∼ 1.5) in the velocity range v = 0.07 − 0.3 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 → 0 is not as simple as phenomenological models suggest and it plagued by band-structure effects.

Effect of Chemical Disorder on the Electronic Stopping of Solid Solution Alloys

“…In the simulations under channeling conditions, S e is 35% smaller than the SRIM prediction at v ∼ 1 a.u.. This difference when comparing channeling and off-channeling S e is expected and consistent with previous simulation works [36,40]. The result for NiCr shows a slightly higher S e when compared with its counterparts (NiFe, NiCo) and Ni across the overall range both for the channeling and off-channeling case, although NiCr has fewer number of valence electrons in the simulation.…”

“…4). From previous work [36,40], we know that for the Period 4 transition metals, projectiles at velocities below 0.8 a.u., for example, depend critically on the electronic structure in a range of ∼ 3.2 eV around the Fermi energy (according to (Fig. 4).…”

“…The maximum of S e for proton and He in the NiCr target is 0.482 E h /a 0 and 1.452 E h /a 0 respectively. According to linear response theory [48], the S e quadratically depends on the projectile ion's effective charge Z * 1 , for a given electronic medium target [36]. This means that the difference in S e between the two fully stripped projectiles, in this case a proton and an alpha particle, should be a factor of 4.…”

Ab initioelectronic stopping power and threshold effect of channeled slow light ions inHfO2

“…It should be noted that SRIM results are obtained semi-empirically by averaging over a number of different incident directions with distinct impact parameters; thus, it does not explicitly account for the channeling conditions studied in our calculations. For this reason, the calculated results are expected to follow a qualitative trend of SRIM data, which has been shown in several previous theoretical studies [48,51,52].…”

Electronic stopping and proton dynamics in InP, GaP, and In0.5Ga0.5P from first principles

“…54 The second observation, that off-channeling projectiles lead to higher stopping than channeling projectiles, has been reported in the literature before and was attributed to stopping contributions from semi-core electrons. 52,55 In order for semi-core electrons to contribute to electronic stopping, protons need to have high enough kinetic energy to excite the semi-core states. In addition, these excitations require spatial proximity of the proton and semi-core wave functions, i.e.…”