The role of background impurities in the single particle relaxation lifetime of a two-dimensional electron gas

TL;DR

This paper revisits the scattering lifetimes in 2D electron gases, correcting previous divergences, deriving finite-thickness models, and matching theoretical predictions with experimental data to better understand impurity effects.

Contribution

It introduces a non-divergent model for quantum lifetime in finite-thickness heterostructures and compares theoretical results with experimental data for background impurity scattering.

Findings

Corrected divergence in quantum lifetime calculations.

Derived finite-thickness scattering lifetime model.

Achieved excellent agreement with experimental data.

Abstract

We re-examine the quantum tau_q and transport tau_t scattering lifetimes due to background impurities in two-dimensional systems. We show that the well-known logarithmic divergence in the quantum lifetime is due to the non-physical assumption of an infinitely thick heterostructure, and demonstrate that the existing non-divergent multiple scattering theory can lead to unphysical quantum scattering lifetimes in high quality heterostructures. We derive a non-divergent scattering lifetime for finite thickness structures, which can be used both with lowest order perturbation theory and the multiple scattering theory. We calculate the quantum and transport lifetimes for electrons in generic GaAs-AlGaAs heterostructures, and find that the correct `rule of thumb' to distinguish the dominant scattering mechanisms in GaAs heterostructures should be tau_t/tau_q < 10 for background impurities and tau_t/tau_q > 10 for remote impurities. Finally we present the first comparison of theoretical results for tau_q and tau_t with experimental data from a GaAs 2DEG in which only background impurity scattering is present. We obtain excellent agreement between the calculations and experimental data, and are able to extract the background impurity density in both the GaAs and AlGaAs regions.