Transport properties of nonlinear double-barrier structures

We introduce a solvable model of a nonlinear double-barrier structure, described by a generalized effective-mass equation with a nonlinear coupling term. This model is interesting in its own right for possible new applications, as well as to help understand the combined effect of spatial correlations and nonlinearity on disordered systems. Although we specifically discuss the application of the model to electron transport in semiconductor devices, our results apply to other contexts, such as nonlinear optical phenomena. Our model consists of finite width barriers and nonlinearities are dealt with separately in the barriers and in the well, both with and without applied electric fields. We study a wide range of nonlinearity coupling values. When the nonlinear term is only present in the barriers, a sideband is observed in addition to the main resonance and, as a consequence, the current-voltage characteristics present two peaks at different voltages. In this case, the phenomenology remains basically the same through all the considered variation of the parameters. When the well is the component exhibiting nonlinearity, the results depend strongly on the nonlinear coefficient. For small values, the current-voltage characteristics exhibit lower and upper voltage cutoffs. This phenomenon is not present at higher nonlinearities, and eventually linear-like behavior is recovered. We complete this exhaustive study with an analysis of the effects of having simultaneously both kinds of nonlinear couplings. We conclude the paper with a summary of our results, their technological implications, and a prospective discussion of the consequences of our work for more complex systems.