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

Abstract

We propose a first-principle 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 external source and the relaxation to the bottom of conduction band via electron-phonon coupling. The methods permits calculations of the non-equilibrium electron distribution function, the quasi-stationary distribution function with 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 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 for ZnO is a fermi-like curve that rises linearly with increasing excitation energy whereas the analogous curve for anatase consists of a main peak and a shoulder. The calculations demonstrate that the relaxation of excited electrons and the setting of the quasi-stationary distribution occur within the time no more than 500 fsec for ZnO and 100 fsec for anatase. We also discuss the applicability of the effective phonon model with energy-independent electron-phonon transition probability. We find that the model only reproduces the trends in changing 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 photocatalyses has been discussed. We found that for ZnO this rate is about 5 times less than in anatase.