First-principles study of semicore electron excitation in the electronic energy loss of ZnO for protons

The electronic stopping power of zinc oxide for protons is presented over a wide range of velocities by using real-time time-dependent density functional theory. We calculated the electronic stopping power of energetic protons for both channeling and off-channeling trajectories, and revealed the microcosmic mechanism of semicore $3d$-electron excitation in ZnO. In the low-energy regime, the stopping power obtained from channeling geometry is in a quantitative agreement with the measured data, which reproduced not only the experimental threshold velocity of the stopping power, but also the deviation from velocity-proportional electronic stopping power which is considered to be caused by excitation of the tightly bound $3d$ electrons. In the high-energy regime, we examined the impact parameter dependence of semicore $3d$-electron excitation of ZnO, and showed that the stopping power obtained from off-channeling geometry greatly improves the simulation results in comparison with the channeling results. We also demonstrated that the electronic energy loss of protons is not only related to the number of electrons excited, but also associated with the energy distribution of excited electrons and holes after collisions.

Figure 1

(a) Total energy and (b) instantaneous electronic stopping power as a function of proton displacement along the center channeling trajectory at velocity of 0.1 a.u.

Figure 2

Electronic stopping power as a function of velocity of protons moving along (a) the center and (b) the midpoint channeling trajectories, respectively. The solid lines are the linear fitting of triangles. The experimental data are from Ref. [27]. The insets show the top view of the incidence geometries of channeling trajectories. The gray circles indicate zinc atoms, the red circles present oxygen atoms, and the black circles show the incident positions.

Figure 3

Electronic stopping power as a function of velocity of protons traveling along the off-channeling trajectory in ZnO.

Figure 4

Electronic stopping powers obtained from RT-TDDFT calculations are shown as a function of proton velocity for channeling (including both center and midpoint trajectories, and considering $3d^{10}$ electrons or not) and off-channeling trajectories, together with SRIM predictions, experimental data from Refs. [27, 41], and SLPA-DFT calculations from Ref. [41].

Figure 5

Density of carrier population as a function of energy for 0.5 a.u. proton channeling along the midpoint trajectory for both pseudopotentials. The positive and negative values show the density of excited electrons and holes, respectively. $E_{\mathtt{VMB}}$ represents the energy of VMB of ZnO.

Figure 6

Density of carrier population as a function of energy for protons channeling along center (upper panel) and midpoint (lower panel) trajectories with zinc containing also $3d$ electrons. The negative and positive values refer to the density of holes and excited electrons, respectively. $E_{\mathtt{VMB}}$ represents the energy of VMB of ZnO.