Quantum dynamics of secondary electron emission from nanographene

Yoshihiro Ueda, Yasumitsu Suzuki, and Kazuyuki Watanabe

Phys. Rev. B 94, 035403 – Published 5 July 2016

Abstract

We have observed secondary electron emission (SEE) from nanographene by applying time-dependent density functional theory simulations in real-time and real-space to electron scattering on target graphene-flakes. We obtained the incident-electron energy dependence and bilayer effect on the amount of secondary electron (SE). The dynamics of SEE and collective density oscillations, which are electronic excitations induced by electron impact, were demonstrated numerically, and elucidated by the time-dependent occupation numbers of the Kohn-Sham electronic levels. The SE yields from graphene flakes are found to be $\sim 0.1$ . The highest energy of SE is $\sim 20$ eV, which is compatible with the characteristics observed in SEE experiments.

Received 24 March 2016
Revised 25 May 2016

DOI:https://doi.org/10.1103/PhysRevB.94.035403

Physics Subject Headings (PhySH)

Graphene

Density functional theory Electron diffraction

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yoshihiro Ueda, Yasumitsu Suzuki, and Kazuyuki Watanabe^*

Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

^*kazuyuki@rs.kagu.tus.ac.jp

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Issue

Vol. 94, Iss. 3 — 15 July 2016

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Images

Figure 1
(a) Schematic view of the calculation box. The target flake is at the center of the box. The initial position of WP is 6.35 Å away from the target. The area surrounded by dashed lines is defined as the flake area. Complex absorbing potentials (CAP) are placed on both ends. (b) Time-space mapping of electric current of $ψ_{wp} (r, t)$ upon scattering with a monolayer target. The red (and yellow) region shows positive current and the blue region shows negative current. The horizontal axis is the $z$ axis defined in (a). The vertical axis is time. The dashed line denotes the target position. The atomic structure of the target ( $C_{54} H_{18}$ ) is given in the inset. The white and black balls correspond to carbon and hydrogen atoms, respectively.
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Figure 2
(a) Time evolution of the electron number in the flake area defined in Fig. 1. The time is set to zero when WP is injected at the initial position. The target $C_{54} H_{18}$ has 234 electrons and the WP one at $t = 0$ . The five curves show the time-dependent electron numbers upon electron impact with different incident kinetic energies. (b) Incident-energy dependent SEE from monolayer (dashed line with triangles) and bilayer (with a gap of 3.4 Å) graphene flakes (solid line with dots). The values depicted are the deficits in the electron numbers at $t = 1.5$ fs in (a). The amounts become negative at 50 eV, because a fraction of the incident electron is still inside the flake area at $t = 1.5$ fs.
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Figure 3
(a) Spatiotemporal current distribution around monolayer graphene upon electron impact of kinetic energy 200 eV. The vertical axis is time ( $0 \sim 1.5$ fs) and the horizontal axis is the $z$ axis defined in Fig. 1. The flake is placed at the center (white line), the flake area is surrounded by dashed lines, and the CAP regions are separated from the scattering region by dotted lines. The blue and red patterns indicate the negative and positive currents, respectively, of $ψ_{1} (r, t) \sim ψ_{N / 2} (r, t)$ integrated over the $x$ and $y$ directions [see Fig. 1]. (b) Time evolution of the current on the target [white line in (a)]. The five curves show the currents for different incident energies. They were shifted to align with the first peak position at $t = 0$ . (c) Fourier transforms (FT) of the current, $j_{z} (ω)$ (blue line) and dipole oscillation, $p_{z}^{wp} (ω)$ (black line) upon electron impact of 200 eV incident energy. Red line shows the dipole excitation induced by an external optical electric field with a $δ$ -function form, $p_{z}^{E} (ω)$ .
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Figure 4
(a) Snapshot of the electron occupation numbers of the target $C_{54} H_{18}$ at $t = 1.5$ fs after electron impact with kinetic energy of 200 eV. Here, spin degrees of freedom 2 is taken into account. Blue dots (see left axis) and red dots (see right axis) denote, respectively, the occupation numbers in the occupied and unoccupied KS levels that are separated by the HOMO-LUMO gap. $E_{H}, E_{L}$ , and $E_{V}$ indicate the energy of HOMO, LUMO, and the vacuum level, respectively. The vacuum level is set to zero and denoted by a dashed line. (b) Time-dependent number of excited electrons at $E$ (dots) and below $E$ (lines) of benzene at $t = 1.5$ fs. The black dots and curves show results for 200 eV incident electrons and the red dots and curves show that for 400 eV. The vacuum level (denoted by $E_{V}$ ) is set to zero. The data for 200 eV in the low energy region are replotted in the inset.
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