Electronic stopping power and electronic energy-loss mechanism for a low-energy ion in TiN under channeling conditions

Abstract

The electronic stopping power of a low-energy proton in a crystalline TiN film is investigated by computer simulation based on the time-dependent density-functional theory. The calculated results show that the electronic stopping power of the small impact parameter coincides with the experimental data. By evaluating the channeling electronic density and the stopping force in different channels, the direction dependence of the electronic stopping power is explored and revealed. Along the $\ensuremath{\langle}110\ensuremath{\rangle}$ channel, the electronic stopping power of the proton is lower than that of the $\ensuremath{\langle}100\ensuremath{\rangle}$ and $\ensuremath{\langle}111\ensuremath{\rangle}$ channels; this trend is mainly attributed to the discrepancy in the channeling electronic density. In addition, our research gives evidence that the threshold velocity ${v}_{th}=0.1294\phantom{\rule{0.16em}{0ex}}\text{a.u.}$ is closely related to the indirect band gap. That result suggests that only the valence band's electrons across the band gap can contribute to the electronic energy dissipation; therefore, we discuss that the defect state induced in the gap by the passing ion serves like an elevator ferrying the valence-band electrons across the indirect band gap. Last, we investigate the charge accumulation and depletion as an energy-loss model by intuitive charge-density difference. Furthermore, the intensity of the chemical bond between the projectile and the host atoms around the channel is indirectly investigated and analyzed by obtaining the amplitude of the electron localization function. The shortening and elongation of the chemical bond are deemed a mechanism of the electronic energy loss in the process of the ion-solid interaction, which can contribute to the electronic stopping power. These results supply reference data for the application of the excellent material TiN in ion-beam irradiation.