Modeling anisotropic energy dissipation of light ions at the atomistic scale

Abstract

Understanding ion-matter interactions at the atomistic level is key to advancing materials for the semiconductor industry, space systems, and nuclear fusion technologies. However, most atomistic frameworks still rely on simplified descriptions of how ions transfer energy to the electronic subsystem, overlooking the sensitivity of this process to the actual ion path. Existing electron-ion interaction models, such as the tensorial unified two-temperature model, were developed to study self-irradiation scenarios, but their suitability for light-ion irradiation remains unexplored. Here, we propose that for light projectiles, stepping back from the tensorial formulation toward a simpler, local model of electronic stopping provides a more efficient and physically transparent trajectory-dependent description. We parameterize and validate both models for hydrogen and helium in tungsten using ab initio electronic stopping data and large-scale ion range simulations, benchmarked against existing experimental data. This provides a consistent framework for including nonadiabatic electronic stopping in atomistic simulations of light-ion energy dissipation.

Figures (8)

• Figure 1: Electronic energy losses of He propagating at $v = 0.3$ a.u. (a) along $\langle 100 \rangle$ center channel, (b) along $\langle 100 \rangle$ off-center channel, (c) through a vacancy, and (d) along $\langle 110 \rangle$ channel in W. In the top panel, the energy profiles obtained from time-dependent (light grey) and ground state calculations (green) are depicted, overlaid with local electron density (orange dotted line with the scale on the right side). The bottom panel shows the difference $E_\text{TDDFT}(r)-E_\text{BOA}(r)$, indicating the net energy transferred to the target electronic system. (e) Energy dissipation strength $S_\text{e}(r)/v$ = $d[E_\text{TDDFT}(r) - E_\text{BOA}(r)]/dr/v$ as a function of the site electron density for all four trajectories.
• Figure 2: Parameterization of the electron-ion interaction models for H and He propagating in W. (a) Numerically optimized H-W and He-W coupling functions $\alpha(\bar{\rho})$ and $\sqrt{\beta(\bar{\rho})}$ and constant electronic stopping values taken from SRIM for comparison. (b) The dissipated energy, calculated with TDDFT (black), in comparison with those, predicted by MD with UTTM and $\beta(\bar{\rho})$-model (color-coded as the corresponding parameterizations in (a)). Results of MD simulations with constant SRIM-derived values $\beta_{\text{SRIM}}$ are presented for comparison.
• Figure 3: MDRANGE-based analysis of H projectile moving along the $\langle100\rangle$ channel in W. (a) Top panel: local electron density and corresponding density-dependent electronic energy dissipation for H and He along the perpendicular line cut indicated by the dashed line in the cross-sectional plots below. Bottom panels: projected $x$-$y$ cross-sections of the 1 keV and 10 keV H trajectories. Cyan and green vertical dashed lines indicate the span of transverse ion oscillations around the center of the channel. The color scale on the right indicates the ion $z$ coordinate. (b) Distribution of local electron densities sampled by the most strongly channeled H trajectories, compared with TDDFT reference values obtained for channeling trajectories within the straight-line approximation.
• Figure 4: Calculated ion range distributions for different initial energies of H projectile moving along the $\langle100\rangle$ channel in W.
• Figure 5: Calculated differential (left) and integral (right) range profiles for 10 keV H implanted in different directions in W. Color coding corresponds to the functional forms shown in Fig. \ref{['FIG:3']}a that served as electronic stopping input for these calculations.