  To investigate the initial process of Joule heating in semiconductors
microscopically and quantitatively, we developed a theoretical framework for
the ab initio evaluation of the carrier energy relaxation in semiconductors
under a high electric field using a combination of the two-temperature model
and the Boltzmann equation. We employed the method for bulk silicon as a
typical example. Consequently, we found a remarkable difference in the energy
relaxation processes of the electron and hole carriers. The longitudinal
acoustic and optical phonons at the zone boundary contribute to the energy
relaxation of electron carriers, whereas they contribute negligibly to that of
the hole carriers. In addition, at the band edge, the energy relaxation rate is
maximized for the electron carriers, whereas it is suppressed for the hole
carriers. These differences stem from the presence/absence of intervalley
scattering processes and isotropic/anisotropic band structures in electrons and
holes. Our results lay the foundation for controlling the thermal generation in
semiconductors by material design.
