Ab Initio Simulation of Carrier Dynamics in Electric Fields in Bulk Semiconductors

Carrier dynamics in the presence of electric fields governs the performance of semiconductor devices. The carrier drift velocity as a function of electric field (so-called velocity-field curve) has been a key material property since the early days of semiconductor physics. Yet, velocity-field curves cannot be computed from first principles, and their simulation still relies on decade-old semiempirical Monte Carlo approaches. We present a first principles method for solving the Boltzmann Transport Equation (BTE) in the presence of electric fields, which allows us to accurately compute velocity-field curves. The approach extends an efficient scheme we recently developed to solve the BTE with ab initio electron-phonon scattering. Including the electric field is nontrivial – it makes the equations computationally ‘stiff’, a challenge we solve by developing an implicit numerical method to time-step the BTE. We demonstrate the stability of the algorithm, and simulate the relaxation of carriers to steady-state distributions in an electric field. Using GaAs as a case study, we obtain the first fully ab initio velocity-field curves, which correctly exhibit the Gunn effect (negative differential resistance at moderate E-fields) and the drift velocity saturation at high field.