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

Abstract

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 β-Ga2O3. 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 ∼100 eV) and low-energy (below ∼10 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 β-Ga2O3 up to ∼100 eV along with the phonon dispersion, carrier-phonon matrix elements, and dynamic dielectric function. Additionally, using the 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 ∼0.4 and ∼1.0 ps for diamond and β-Ga2O3, respectively, while holes thermalize within ∼0.5 ps for both. We also calculate electron–hole pair creation energies of 12.87 and 11.24 eV, respectively.