Field dependence of the hopping drift velocity in semiconductor superlattices

The electronic transport in biased semiconductor superlattice structures is investigated on the basis of hopping transitions between the partially localized states of the Wannier-Stark ladder. The drift velocity is calculated numerically by summing all transitions between any two states of the ladder according to their respective weight due to the overlap of the superlattice wave functions and the microscopic scattering process. Both elastic (ionized impurity) and inelastic (acoustic and LO phonon) scattering has been taken into account. Two distinct field ranges are observed depending on the relation between the Wannier-Stark spacing eFd and the width of the lowest miniband {Δ}. For moderate fields (eFd<Δ) the drift velocity is inversely proportional to the applied field for all scattering processes. For eFd>Δ the discrete nature of the Wannier-Stark ladder leads to a 1/Fⁿ dependence of the drift velocity on the applied field, where n depends on the scattering mechanism and is larger than 1. Resonances in the drift velocity due to the discrete LO phonon energy and due to resonant tunneling into excited states are observed and discussed in detail. Simplified analytical expressions for the hopping drift velocity at low and high fields are given.