Simple electron-electron scattering in non-equilibrium Green's function simulations

David O Winge,Claudio Verdozzi,Mauro F Pereira,Andreas Wacker,Martin Franckié

doi:10.1088/1742-6596/696/1/012013

Abstract

In this work we include electron-electron interaction beyond Hartree-Fock level in our non-equilibrium Green's function approach by a crude form of GW through the Single Plasmon Pole Approximation. This is achieved by treating all conduction band electrons as a single effective band screening the Coulomb potential. We describe the corresponding self-energies in this scheme for a multi-subband system. In order to apply the formalism to heterostructures we discuss the screening and plasmon dispersion in both 2D and 3D systems. Results are shown for a four well quantum cascade laser with different doping concentration where comparisons to experimental findings can be made.

Highlights

Since the quantum cascade laser (QCL) was introduced more than 20 years ago [1] it has continuously been improved and redesigned to operate from the mid-infrared all the way down to the Terahertz (THz) range
Compact laser sources at these wavelengths are valuable for spectroscopic applications [2] but a major problem is that THz QCLs do not operate at room temperature
Monte Carlo simulations have shown that electron-electron interaction, beyond the meanfield or Hartree approximation can influence the dynamics of THz QCLs [6, 7, 8]

Summary

Introduction

Since the quantum cascade laser (QCL) was introduced more than 20 years ago [1] it has continuously been improved and redesigned to operate from the mid-infrared all the way down to the Terahertz (THz) range. Published under licence by IOP Publishing Ltd and applied to QCLs, electron-electron scattering has previously been implemented in a low order GW0 approximation employing a purely static screening model [13]. We will describe how we formulate the self-energy expressions for the screened interaction in the single plasmon pole approximation (SPPA).

Results

Conclusion