On Thermometer Operation of Ultrasmall Tunnel Junctions

TL;DR

This paper analyzes the temperature-dependent I-V characteristics of ultrasmall tunnel junctions, proposing their use as thermometers and providing analytical and numerical models for both single and double junction configurations.

Contribution

It introduces analytical solutions and numerical results for the temperature-dependent behavior of single and double tunnel junctions, including co-tunneling effects, for thermometer applications.

Findings

Crossover from Coulomb blockade to ohmic behavior with temperature

Differential conductivity dip enables temperature measurement

Models applicable within specific Coulomb energy ranges

Abstract

The temperature dependence of the I-V characteristics of many single-electron tunneling devices enable thermometer operation of these systems. We investigate two normal conducting kinds of them, {\sl (a)} a single junction in a high-impedance environment, and {\sl (b)} a double junction. The characteristics of both devices show a crossover from Coulomb blockade at low temperatures to ohmic behavior at high temperatures. The related differential conductivity dip allows the determination of the junctions temperature. Both configurations {\sl (a)} and {\sl (b)} are expected to work at least within the range $0.5\le\beta E_{\rm C}\le 10$, where $E_{\rm C}$ is the Coulomb energy of the system under investigation. We present an analytical solution for both low- and high-temperature case of {\sl (a)} and {\sl (b)} as well as numerical results and their fit, including the effect of co-tunneling in case of a double junction.