Understanding the Average Electron-Hole Pair-Creation Energy in Silicon and Germanium Based on Full-Band Monte Carlo Simulations

The thermalization process of sub-10-eV charge carriers is examined with treating carrier transport with full-band Monte Carlo simulations. The average energy loss (3.69 eV in Si and 2.62 eV in Ge) required to create a thermalized electron-hole pair, obtained from the simulations, is very close to the experimentally measured radiation-ionization energies of Si and Ge irradiated with high-energy particles. These results suggest that only interactions that occur after the radiation-generated charge carriers decay to energies of similar to 10 eV or less determine the fundamental property of the radiation-ionization energies. In addition to an energy loss equal to the band gap energy via impact ionization, acoustic-phonon emission, which has been omitted in prior work, contributes 30% of the remaining carrier energy loss, while optical-phonon emission contributes the other 70%.