Competition between the electronic and phonon-mediated scattering channels in the out-of-equilibrium carrier dynamics of semiconductors: an ab-initio approach

The carrier dynamics in bulk Silicon, a paradigmatic indirect gap semiconductor, is studied by using the Baym-Kadanoff equations. Both the electron-electron(e-e) and electron-phonon(e-p) self-energies are calculated fully ab-initio by using a semi-static GW approximation in the e-e case and a Fan self-energy in the e-p case. By using the generalized Baym-Kadanoff ansatz the two-time evolution is replaced by the only dynamics on the macroscopic time axis. The enormous numerical difficulties connected with a real-time simulation of realistic systems is overcame by using a completed collision approximation that further simplifies the memory effects connected to the time evolution. The carrier dynamics is shown to reduce in such a way to have stringent connections to the well-known equilibrium electron-electron and electron-phonon self-energies. This link allows to use general arguments to motivate the relative balance between the e-e and e-p scattering channels on the basis of the carrier energies.