Ultrafast dynamics of hot carriers: Theoretical approaches based on real-time propagation of carrier distributions

In recent years, computational approaches which couple density functional theory (DFT)-based description of the electron-phonon and phonon-phonon scattering rates with the Boltzmann transport equation have been shown to obtain the electron and thermal transport characteristics of many 3D and 2D semiconductors in excellent agreement with experimental measurements. At the same time, progress in the DFT-based description of the electron-phonon scattering has also allowed to describe the non-equilibrium relaxation dynamics of hot or photo-excited electrons in several materials, in very good agreement with time-resolved spectroscopy experiments. In the latter case, as the time-resolved spectroscopy techniques provide the possibility to monitor transient material characteristics evolving on the femtosecond and attosecond time scales, the time evolution of photo-excited, nonthermal carrier distributions has to be described. Similarly, reliable theoretical approaches are needed to describe the transient transport properties of devices involving high energy carriers. In this review, we aim to discuss recent progress in coupling the ab initio description of materials, especially that of the electron-phonon scattering, with the time-dependent approaches describing the time evolution of the out-of-equilibrium carrier distributions, in the context of time-resolved spectroscopy experiments as well as in the context of transport simulations. We point out the computational limitations common to all numerical approaches, which describe time propagation of strongly out-of-equilibrium carrier distributions in 3D materials, and discuss the methods used to overcome them.