Path-dependent electronic stopping for self-irradiated silicon

The experimentally validated real-time time-dependent density-functional theory (rt-TDDFT) provides a robust framework for studying electronic stopping. Accurate predictions of this directionally sensitive phenomenon are essential for various active research areas and applications, especially in semiconductors. Here we present a path-dependent model of electronic stopping in self-irradiated silicon in the keV-MeV regime. We find a linear relationship between electronic stopping and the mean electron density using rt-TDDFT calculations, performed with the Qball code, along six channels and three incommensurate trajectories. Using this, the model predicts electronic stopping as a function of the local ground-state electron density and the projectile velocity S_e(v, ρ). Our model accurately describes the electronic energy losses along any trajectory, from channels to regions of higher electron density, including the random trajectories measured experimentally. In addition, we provide a comprehensive overview of rt-TDDFT calculations of electronic stopping in self-irradiated silicon, including a detailed description of the requirements of pseudopotentials in all kinematic regimes.