Transport and noise of hot electrons in GaAs using a semi-analytical model of two-phonon polar optical phonon scattering

Recent ab-initio studies of electron transport in GaAs have reported that electron-phonon (e-ph) interactions beyond the lowest order play a fundamental role in charge transport and noise phenomena. Inclusion of the next-leading-order process in which an electron scatters with two phonons was found to yield good agreement for the high-field drift velocity, but the characteristic non-monotonic trend of the power spectral density of current fluctuations (PSD) with electric field was not predicted. The high computational cost of the ab-initio approach necessitated various approximations to the two-phonon scattering term, which were suggested as possible origins of the discrepancy. Here, we report a semi-analytical transport model of two-phonon electron scattering via the Fr\"ohlich mechanism, allowing a number of the approximations in the ab-initio treatment to be lifted while retaining the accuracy to within a few percent. We compare the calculated and experimental transport and noise properties as well as scattering rates measured by photoluminescence experiments. We find quantitative agreement within 15% for the drift velocity and 25% for the $\Gamma$ valley scattering rates, and agreement with the $\Gamma-L$ intervalley scattering rates within a factor of two. Considering these results and prior studies of current noise in GaAs, we conclude that the most probable origin of the non-monotonic PSD trend versus electric field is the formation of space charge domains rather than intervalley scattering as has been assumed.