Real time relaxation dynamics of macroscopically photo-excited electrons toward the Fermi degeneracy formation in the conduction band of semiconductors

摘要

Concerning with the recent experiment of time-resolved two-photonphoto-emission spectral measurements on semiconductors (GaAs, InP), wetheoretically study real time relaxation dynamics of macroscopicallyphoto-excited electrons, toward the Fermi degeneracy formation in an originallyvacant conduction band of these semiconductors. Very soon after thephoto-excitation, the whole electrons are shown to exhibit a quite rapidrelaxation, like an avalanching phenomenon, mainly due to successivemulti-(optical and acoustic) phonon emission from them. Repeating thismulti-phonon process, the whole energy distribution of the electrons is shownto become a multi-peaked structure largely elongated over the lower part of thewide conduction band. However, after around 1 ps from the excitation, thisrelaxation critically slows down, since the emission of a long-wave acousticphonon from electrons around the Fermi level becomes prohibitively difficult.By using the electron temperature approximation, we show that this slowrelaxation is inversely proportional to time. Thus, the formation of thecomplete Fermi degeneracy takes an infinite time. These theoretical results arequite consistent to the aforementioned recent experiment.