Institute of Solid State Chemistry, Urals Branch of the Russian Academy of Sciences, Pervomayskaya 91, GSP-145, Yekaterinburg, Russia.
J Phys Condens Matter. 2012 Oct 10;24(40):405802. doi: 10.1088/0953-8984/24/40/405802. Epub 2012 Sep 12.
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.
我们提出了一种基于第一性原理的方法，用于评估半导体导带中激发电子的时变电子分布函数。该方法考虑了外部源对电子的激发以及通过电子-声子耦合弛豫到导带底部的过程。该方法允许计算非平衡电子分布函数、具有恒定时间光源的准稳态分布函数、准稳态分布的建立时间以及通过弛豫到导带底部损失能量的时间。实际计算是在锐钛矿结构的二氧化钛和纤锌矿结构的氧化锌中进行的。我们发现，准稳态电子分布函数在导带底部附近有一个峰值，在其尾部，最大能量随激发能量的增加呈线性上升。计算表明，对于 ZnO，激发电子的弛豫和准稳态分布的建立时间不超过 500 fs，对于锐钛矿不超过 100 fs。我们还讨论了有效声子模型在能量独立电子-声子跃迁概率中的适用性。我们发现，该模型仅再现了特征时间变化的趋势，而这种计算的精度不高。我们还评估了准稳态电子分布中电子向声子的能量转移速率，并讨论了这种转移对光催化的影响。我们发现，对于 ZnO，这种速率比锐钛矿低约五倍。
