Accurate atomistic first-principles calculations of electronic stopping

André Schleife, Yosuke Kanai, and Alfredo A. Correa

Phys. Rev. B 91, 014306 – Published 20 January 2015

Abstract

We show that atomistic first-principles calculations based on real-time propagation within time-dependent density functional theory are capable of accurately describing electronic stopping of light projectile atoms in metal hosts over a wide range of projectile velocities. In particular, we employ a plane-wave pseudopotential scheme to solve time-dependent Kohn-Sham equations for representative systems of H and He projectiles in crystalline aluminum. This approach to simulate nonadiabatic electron-ion interaction provides an accurate framework that allows for quantitative comparison with experiment without introducing ad hoc parameters such as effective charges, or assumptions about the dielectric function. Our work clearly shows that this atomistic first-principles description of electronic stopping is able to disentangle contributions due to tightly bound semicore electrons and geometric aspects of the stopping geometry (channeling versus off-channeling) in a wide range of projectile velocities.

Received 24 July 2014

DOI:https://doi.org/10.1103/PhysRevB.91.014306

Authors & Affiliations

André Schleife^1,*, Yosuke Kanai^1,2,†, and Alfredo A. Correa^1,‡

¹Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
²Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290, USA

^*schleife@illinois.edu
^†ykanai@unc.edu
^‡correaa@llnl.gov

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Vol. 91, Iss. 1 — 1 January 2015

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Figure 1
Instantaneous electronic stopping (in $E_{H} / a_{B}$ ) from Eq. (3) for hydrogen projectiles of different velocities in aluminum. Black solid lines were obtained for a ( $30.62 \times 30.62 \times 30.62$ ) $a_{B}^{3}$ supercell (256 atoms), red dotted lines for a ( $22.97 \times 30.62 \times 30.62$ ) $a_{B}^{3}$ supercell (192 atoms), green dashed lines for a ( $30.62 \times 22.97 \times 22.97$ ) $a_{B}^{3}$ supercell (144 atoms), and blue dashed lines for a ( $22.97 \times 22.97 \times 22.97$ ) $a_{B}^{3}$ supercell (108 atoms). The region in between the dotted vertical lines is used to extract the stopping. The inset shows the projectile (small circle) in part of the supercell of aluminum atoms (big circles).
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Figure 2
In (a), the electronic total energy for a hydrogen projectile on an off-channeling (random) trajectory in aluminum is shown for $v = 0.1$ (black), 6.0 (red), and 7.44 (blue). In (b), the slopes of linear least-squares fits between $x_{1} = 6$ $a_{B}$ and a given maximum position $x$ is shown as a function of this maximum position. The “kink” between $x$ =0 $a_{B}$ and 6 $a_{B}$ [indicated by the vertical dashed line in (a)] is omitted for the fitting. The vertical dotted line indicates the (converged) average value that we used for the discussion of electronic stopping.
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Figure 3
Electronic stopping calculated as a function of the velocity of a hydrogen projectile in aluminum. The solid blue curve represents experimental results provided by the srim table [52]. Dashed (black and red) curves were computed treating the $3 s^{2} 3 p^{1}$ electrons of aluminum as valence electrons. Solid (black, red, and green) curves were computed including also the $2 s^{2} 2 p^{6}$ electrons in the valence shell. Black curves represent hyper-channeling and red curves correspond to off-channeling projectiles. The solid green line corresponds to the $H^{+}$ charge state (proton) of the projectile.
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Figure 4
Electronic stopping calculated as a function of the velocity of a hydrogen/proton projectile in aluminum. Solid curves were computed for aluminum host material with $2 s^{2} 2 p^{6} 3 s^{2} 3 p^{1}$ electrons in the valence shell for channeling (black) and off-channeling (red) projectiles. Dashed curves are computed using the Lindhard dielectric function for three valence electrons (black), nine valence electrons (green), and 11 valence electrons (blue) per aluminum atom. Finite-size errors due to finite plasmon wavelength in the supercell are estimated within the Lindhard model and indicated at the bottom of the figure. The inset shows the electronic stopping difference between the curves with and without semi-core electrons for off-channeling projectiles.
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Figure 5
Electronic stopping of H (a) and He (b) projectiles in Al: solid (black and red) curves were computed including $2 s^{2} 2 p^{6}$ electrons in the valence shell. Black curves represent hyper-channeling and red curves correspond to off-channeling projectiles. Dotted blue results are calculated results from Ref. [30], dotted green are from Ref. [54], and dashed magenta curves represent experimental data (Ref. [53]). A larger $Δ t$ of 0.69 as was used for the channeling trajectory of He in Al.
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Figure 6
Electronic stopping calculated as a function of the velocity of a helium (solid red)/ ${He}^{2 +}$ (solid green) projectile in aluminum under off-channeling conditions. The solid blue curve represents experimental results provided by the srim table [59]. The solid black curve is computed for a Lindhard dielectric function for three valence electrons per aluminum atom and a $Z_{1} = 2$ projectile.
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