Abstract
We calculate the d.c.-current of a semiconductor superlattice in the hopping conduction picture. Electronic transport in this regime is described by hopping transitions between the partially localized Wannier–Stark states. In our numerical model we start from the exact wavefunctions of the superlattice and include both impurity and acoustic phonon scattering. We then obtain the electron drift velocity by considering the thermal in-plane distribution function of the Wannier–Stark levels and by summing over all possible hopping processes. Our results deviate significantly from those of the Esaki–Tsu model and the solutions of the Boltzmann equation. We can identify three different regimes of field dependence of the drift velocity, obeying power lawsF−n. For low to moderate fieldsnis apparently 1, in agreement with the high field limit obtained from the models based on a description in momentum space. For intermediate fieldsnis large, resulting from increasing field dependent localization of the wavefunctions. In the high field limit the wavefunctions become equivalent to the Wannier functions of the superlattice and the localization saturates. Therefore, a lower exponentnis obtained.
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