Theory of Thermal Relaxation of Electrons in Semiconductors

We compute the transient dynamics of phonons in contact with high energy "hot" charge carriers in 12 polar and nonpolar semiconductors, using a first-principles Boltzmann transport framework. For most materials, we find that the decay in electronic temperature departs significantly from a single-exponential model at times ranging from 1 to 15 ps after electronic excitation, a phenomenon concomitant with the appearance of nonthermal vibrational modes. We demonstrate that these effects result from slow thermalization within the phonon subsystem, caused by the large heterogeneity in the time scales of electron-phonon and phonon-phonon interactions in these materials. We propose a generalized two-temperature model accounting for phonon thermalization as a limiting step of electron-phonon thermalization, which captures the full thermal relaxation of hot electrons and holes in semiconductors. A direct consequence of our findings is that, for semiconductors, information about the spectral distribution of electron-phonon and phonon-phonon coupling can be extracted from the multiexponential behavior of the electronic temperature.