Nonlinear treatment of many-body effects in double-barrier resonant tunneling structures

TL;DR

This paper presents a simple, solvable nonlinear model for double-barrier resonant tunneling structures that incorporates electron-electron and electron-phonon interactions, successfully explaining experimental features and estimating coupling parameters.

Contribution

The authors introduce a nonlinear effective-mass model for resonant tunneling that includes inelastic scattering effects with a single phenomenological parameter, aligning well with experimental data.

Findings

Observation of a sideband at LO phonon energy in the spectrum.

Good agreement of the model with experimental data for electron-phonon coupling.

Prediction of two negative differential resistance peaks in I-V characteristics.

Abstract

We introduce a simple, solvable model of double-barrier resonant tunneling structure which includes the effects of electron-electron and electron-phonon scattering. The model is based on a generalized effective-mass equation where a nonlinear coupling is introduced to account for those inelastic scattering phenomena. The nonlinear term depends on one parameter which is the only constant in the model to be determined phenomenologically from experimental data. As an example of the application of the model, we discuss GaAs-Ga$_{1-x}$Al$_x$As double-barrier structures. When the nonlinear term is considered, a sideband is observed at an energy of the order of the LO phonon energy in GaAs in addition to and below the main transmission peak. Fitting of the computed spectrum to known experimental results allows to find the value of the nonlinear coupling. As a consequence, we can estimate the electron-phonon coupling from the shift of the main transmission peak in comparison to the linear resonant tunneling. We obtain good agreement with values coming from more sophisticated treatments, which supports our claim that the nonlinear term consistently includes electron-phonon effects. Finally, we use our simple model to study magnitudes of interest for applications, namely $I-V$ characteristics, which are shown to present two negative differential resistance peaks arising from the main transmission peak and the sideband.