Time-dependent Boltzmann transport equation for high-field charge transport

Charge transport properties of semiconductors are essential to determining their utility in electronic devices, with transport under high electric fields being especially important in the case of high-power, high-frequency devices. We have developed a first-principles methodology to solve the Boltzmann transport equation (BTE) and find the steady-state charge carrier distribution under an electric field of arbitrary strength. This can be used to calculate transport properties at low fields, such as carrier mobility, as well as at high fields, such as the saturation velocity of carriers. We implement this within the EPW code to leverage its established capabilities to use maximally localized Wannier functions to interpolate electron and phonon properties calculated by DFT and DFPT to fine Brillouin zone sampling grids. Using the time-dependent BTE, we track the time evolution of the charge carrier distribution on femtosecond-scale time-steps under the effect of finite electric fields, electron-phonon scattering, and electron-ionized-impurity scattering. We validate our results in the low-field regime against the established linearized BTE method for mobility calculations. We further compare our results in the nonlinear high-field regime with experimental velocity-field curves for the established semiconductors Si and GaN.