  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.

Materials Science