Effective Nonlinear Model of Resonant Tunneling Nanostructures
  We introduce a model of a nonlinear double-barrier structure, to describe in a simple way the effects of electron-electron scattering while remaining analytically tractable. The model is based on a generalized effective-mass equation where a nonlinear local field interaction is introduced to account for those inelastic scattering phenomena. Resonance peaks seen in the transmission coefficient spectra for the linear case appear shifted to higher energies depending on the magnitude of the nonlinear coupling. Our results are in good agreement with self-consistent solutions of the Schr\"odinger and Poisson equations. The calculation procedure is seen to be very fast, which makes our technique a good candidate for rapid approximate analysis of these structures. 
Enrique Diez, Angel Sanchez and Francisco Dominguez-Adame