Refining Shockley’s Electron-Hole Pair Equation Using Phonon Dispersions

Abstract

We investigate refining Shockley’s electron-hole pair model by incorporating contributions of optical and acoustic phonons. Using full-band Monte Carlo software, called Anduril, we determine ionization energies in silicon (3.47 ± 0.05), germanium (2.53 ± 0.05), and gallium arsenide (3.98 ± 0.05), as well as their energy loss mechanisms via phonon emission. When compared to phonon dispersions, there is relationship between the energies from the acoustic and optical branches to the preferred energy loss mechanism for hot carriers. This model eliminates the need for expensive software simulations and provides a more physical basis to Shockley’s fitting parameters.