Thermalization of radiation-induced electrons in wide-bandgap materials: A first-principles approach

The present study is concerned with simulating the thermalization of high-energy charge carriers (electrons and/or electron-hole pairs), generated by ionizing radiation, in diamond and $\beta$-Ga$_2$O$_3$. Computational tools developed by the nuclear/particle physics and electronic device communities allow for accurate simulation of charge-carrier transport and thermalization in the high-energy (exceeding $\sim100$ eV) and low-energy (below $\sim10$ eV) regimes, respectively. Between these energy regimes, there is an intermediate energy range of about 10-100 eV, which we call the "10-100 eV gap", in which the energy-loss processes are historically not well-studied or understood. To close this "gap", we use a first-principles approach (density functional theory) to calculate the band structure of diamond and $\beta$-Ga$_2$O$_3$ up to $\sim100$ eV along with the phonon dispersion, carrier-phonon matrix elements, and dynamic dielectric function. Additionally, using first-order perturbation theory (Fermi's Golden Rule/first Born approximation), we calculate the carrier-phonon scattering rates and the carrier energy-loss rates (impact ionization and plasmon scattering). With these data, we simulate the thermalization of 100-eV electrons and the generated electron-hole pairs by solving the semiclassical Boltzmann transport equation using Monte Carlo techniques. We find that electron thermalization is complete within $\sim0.4$ and $\sim1.0$ ps for diamond and $\beta$-Ga$_2$O$_3$, respectively, while holes thermalize within $\sim0.5$ ps for both. We also calculate electron-hole pair creation energies of 12.87 and 11.24 eV, respectively.