Hopping conduction in a "superlattice"

We have used the formulation for the "Stark ladder," and a two-well model to describe hopping conduction via acoustical phonons in a "superlattice." Results show that negative differential conductance may occur when the "Stark-ladder" energy $\mathrm{eFd}$ is greater than the energy bandwidth. The mechanism is due to the fact that the transition probability at high fields decreases with the increase of $F$, because the electronic wave functions become more localized.