Channeling electronic stopping power of lithium ions in diamond: Contribution of projectile inner-shell electrons

The electronic energy loss of Li ion in diamond under a channeling condition is studied using real-time time-dependent density functional theory. Simulations with and without inner-shell electrons explicitly considered in describing the electron configuration of projectile Li ions are performed to understand their contribution to the dissipation mechanism. It is found that the explicit involvement of inner-shell electrons is particularly important in describing the charge state of the projectile during collision, especially in the high velocity regime where the inner-shell orbital is indeed far from fully occupied during collision. Due to the overestimate of the electronic screening, Li ions with inner-shell electrons that are frozen show only a reduced and hydrogenlike capability in perturbing the host electronic system.

Figure 1

Evolution of electrons bound to the $1s$ orbital for initial neutral and bare incident Li ions with velocity 1.2 a.u. along the whole trajectory, respectively. The region between the gray lines is inside the diamond crystal.

Figure 2

Electronic stopping power (black open squares and circles) for channeled Li ions as a function of velocity along the centroid trajectory of the $\langle 100\rangle$ direction, together with the SRIM-2013 predictions (solid line), experimental data (solid symbols) by Santry [35], Lin [36], Andersen [37], Mertens [38, 39], Liu [40], and also TDDFT simulation results by Ojanperä [26] for Li in graphene. For comparison, the simulated electronic stopping for the channeled proton along the same trajectory is also plotted. The inset shows the sketch of the centroid trajectory along the $\langle 100\rangle$ direction.

Figure 3

Electron number (left axis, red hollow symbols and line) on the specific orbital of Li1 and Li3 and the effective charge states (right axis, blue hollow symbols) of the Li1, Li3, and proton. The charge states (right axis, blue solid symbols) for the Li ion's impact with graphene by Ojanperä [26] are also plotted.

Figure 4

The instantaneous distribution of the carriers induced by projectiles with velocities of 0.9 a.u. at $t=1.2$ fs; the Fermi energies are set to zero eV. The inset shows the displacement-resolved number of excited electrons. The region between the blue dashed lines in the inset is inside the target.

Figure 5

The velocity-resolved number of electrons excited per unit of ion path and excitation rate for Li3 and Li1. See more details in the text.

Figure 6

The velocity-resolved average energy loss per excitation and the corresponding values scaled by velocity for Li3 and Li1. See more details in the text.

Figure 7

Velocity-resolved ratio between Li3 and Li1, and ratio between Li1 and proton for the calculated electronic stopping power and projectile effective charge state. The dashed gray lines represent ratios of 3 and 1, respectively, which is expected from linear-response theory when assuming a fully ionized charge state.