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We compute the transient dynamics of phonons in contact with high energy"hot" charge carriers in 12 polar and non-polar semiconductors, using afirst-principles Boltzmann transport framework. For most materials, we findthat the decay in electronic temperature departs significantly from asingle-exponential model at times ranging from 1 ps to 15 ps after electronicexcitation, a phenomenon concomitant with the appearance of non-thermalvibrational modes. We demonstrate that these effects result from the slowthermalization within the phonon subsystem, caused by the large heterogeneityin the timescales of electron-phonon and phonon-phonon interactions in thesematerials. We propose a generalized 2-temperature model accounting for thephonon thermalization as a limiting step of electron-phonon thermalization,which captures the full thermal relaxation of hot electrons and holes insemiconductors. A direct consequence of our findings is that, forsemiconductors, information about the spectral distribution of electron-phononand phonon-phonon coupling can be extracted from the multi-exponential behaviorof the electronic temperature.

Theory of Thermal Relaxation of Electrons in Semiconductors