Nonadiabatic effects in a self-consistent Hartree model for electrons under an ac electric field in multiple quantum wells

By deriving a dynamical differential equation for the electron distribution function in the presence of a nonadiabatic sequential-tunneling current under an ac electric field through a multiple-quantum-well system, the self-consistent Hartree model is generalized for the calculation of electronic states with the inclusion of nonadiabatic effects (dependence on the time derivative of the applied ac electric field) in quantum wells. The influences of different doping profiles, temperatures, and amplitudes of an applied ac electric field on the electron distribution function and sequential tunneling are studied. This work provides a fully quantum-mechanical explanation to the previously proposed current-surge model to a leading-order approximation.