Nonlinear Resonant Tunnelling Through Double Barrier Structures
  We study resonant tunnelling through double-barrier structures under an applied bias voltage, in which nonlinearities due to self-interaction of electrons in the barrier regions are included. As an approximation, we concern ourselves with thin barriers simulated by $\delta$-function potentials. This approximation allows for an analytical expression of the transmission probability through the structure. We show that the typical peaks due to resonant tunneling decrease and broaden as nonlinearity increases. The main conclusion is that nonlinear effects degrade the peak-to-valley ratio but improve the maximum operation frequency of the resonant tunnelling devices. 
Enrique Diez, Francisco Dominguez-Adame, and Angel S\'anchez