Determining energy relaxation length scales in two-dimensional electron gases

TL;DR

This paper measures the energy relaxation length in 2D electron gases using thermovoltage signals, revealing how it varies with carrier density and providing insights into heat transport for nanoelectronics.

Contribution

It introduces a thermometry method to determine energy relaxation length scales in 2DEGs and analyzes their dependence on carrier density and inelastic scattering.

Findings

Energy relaxation length can reach hundreds of microns in high-mobility 2DEGs.

The relaxation length decreases rapidly with decreasing carrier density.

The study offers insights into heat transport mechanisms in low-dimensional systems.

Abstract

We present measurements of the energy relaxation length scale $\ell$ in two-dimensional electron gases (2DEGs). A temperature gradient is established in the 2DEG by means of a heating current, and then the elevated electron temperature $T_e$ is estimated by measuring the resultant thermovoltage signal across a pair of deferentially biased bar-gates. We adapt a model by Rojek and K\"{o}nig [Phys. Rev. B \textbf{90}, 115403 (2014)] to analyse the thermovoltage signal and as a result extract $\ell$, $T_e$, and the power-law exponent $\alpha_i$ for inelastic scattering events in the 2DEG. We show that in high-mobility 2DEGs, $\ell$ can attain macroscopic values of several hundred microns, but decreases rapidly as the carrier density $n$ is decreased. Our work demonstrates a versatile low-temperature thermometry scheme, and the results provide important insights into heat transport mechanisms in low-dimensional systems and nanostructures. These insights will be vital for practical design considerations of future nanoelectronic circuits.