Real-time dynamics of electrons in solids under high applied electric fields

The behavior of electrons in solids in the presence of strong external electric fields is central to various electronic applications. However, simulations of this high-field regime are difficult due to competing timescales for collision and field-driven electron dynamics. The dependence of the carrier drift velocity on the applied electric field (so-called velocity-field curve) is particularly important, but it can only be computed with obsolete semi-empirical Monte-Carlo methods requiring many fitting parameters. Therefore, computing velocity-field curves entirely from first principles remains an open challenge. Here we show a novel ab initio approach to investigate ultrafast electron dynamics in the presence of high electric fields in the time-dependent Boltzmann transport equation (BTE) framework. This method, implemented in our Perturbo open source code, enables explicit time-stepping of the electron populations in high electric fields until a steady state is reached, from which we obtain velocity-field curves. We demonstrate calculations of the velocity-field curves in bulk semiconductors (Si and GaAs) and in a 2D material, graphene. Our analysis reveals the dominant electron-phonon scattering mechanisms as a function of applied electric field up to velocity saturation.