Relaxation of highly excited carriers in wide-gap semiconductors.

The electron energy relaxation in semiconductors and insulators after high-level external excitation is analysed by a semi-classical approach based on a kinetic equation of the Boltzmann type. We show that the non-equilibrium distributions of electrons and holes have a customary Fermi-like shape with some effective temperature but also possess a high-energy non-Fermian 'tail'. The latter may extend deep into the conduction and valence bands while the Fermi-like component is localized within a small energy range just above the edge of the band gap. The effective temperature, effective chemical potential, and the shape of the high-energy component are governed by the process of electron-phonon interactions as well as by the rates of carrier generation and inter-band radiative recombination.

Electron-phonon relaxation and excited electron distribution in zinc oxide and anatase.

We propose a first-principles method for evaluations of the time-dependent electron distribution function of excited electrons in the conduction band of semiconductors. The method takes into account the excitations of electrons by an external source and the relaxation to the bottom of the conduction band via electron-phonon coupling. The methods permit calculations of the non-equilibrium electron distribution function, the quasi-stationary distribution function with a steady-in-time source of light, the time of setting of the quasi-stationary distribution and the time of energy loss via relaxation to the bottom of the conduction band. The actual calculations have been performed for titanium dioxide in the anatase structure and zinc oxide in the wurtzite structure. We find that the quasi-stationary electron distribution function has a peak near the bottom of the conduction band and a tail whose maximum energy rises linearly with increasing energy of excitation. The calculations demonstrate that the relaxation of excited electrons and the setting of the quasi-stationary distribution occur within a time of no more than 500 fs for ZnO and 100 fs for anatase. We also discuss the applicability of the effective phonon model to energy-independent electron-phonon transition probability. We find that the model only reproduces the trends in the change of the characteristic times whereas the precision of such calculations is not high. The rate of energy transfer to phonons at the quasi-stationary electron distribution also have been evaluated and the effect of this transfer on the photocatalysis has been discussed. We found that for ZnO this rate is about five times less than in anatase.