A First Principles Approach to Closing the “10-100 eV GAP” for Electron Thermalization in Wurtzite GaN

Since the 1960s, when radiation-induced disruption of electronic devices in space was first observed, the study of the effects of ionizing radiation on electronics has grown into an extensive field of its own. The present work is concerned with accurately modelling the energy-loss processes that control the thermalization of hot carriers (electrons and/or electron-hole pairs) that are generated by high-energy radiation in wurtzite GaN, using an ab initio approach. Current physical models of the nuclear/particle physics community cover the high-energy range (kinetic energies exceeding ~100 eV), and the electronic-device community has done extensive work in the lower-energy range (below ~10 eV). However, the processes that control the energy losses and thermalization of electrons and holes in the intermediate energy range of about 10-100 eV are poorly known (the “10-100 eV gap”). The aim of this research is to close this gap. To this end, Density Functional Theory (DFT) is utilized to obtain the band structure of GaN for bands reaching energies above 100 eV. Furthermore, charge-carrier scattering rates for the major charge-carrier interactions (phonon scattering, impact ionization, and plasmon emission) are calculated, using the DFT results and first-order perturbation theory (Fermi’s Golden Rule). With this information, the thermalization of electrons starting at 100 eV is simulated in a Monte Carlo code, allowing the electrons to interact stochastically according to the calculated interaction rates and generate electron-hole pairs as they go, which are also tracked in the simulation. Full thermalization of electrons is complete within 1 ps, and that of holes is complete in approximately half the time. Electrons lose 90% of their energy (90 eV) during the first few ~0.1 fs, due to rapid plasmon emission and impact ionization at high energies. The remainder is lost more slowly as phonon emission dominates at lower energies (below ~10 eV). During the thermalization, hot electrons generate electron-hole pairs with an average energy of ~8.9 eV/pair (11-12 pairs per hot electron). Additionally, upon full thermalization, the average electron displacement from its original position is found to be on the order of 100 nm.