Heating Effects in a Chain of Quantum Dots

TL;DR

This paper develops a kinetic theory to analyze heating effects in chains of quantum dots caused by inelastic electron cotunneling, revealing measurable temperature profiles, hysteresis, and potential for sensitive thermometry.

Contribution

It introduces a quantitative model for heating in quantum dot chains, including analytical solutions and substrate effects, advancing understanding of nanoscale thermal behavior.

Findings

Pronounced heating effects in nanoscale grains.

Analytical solutions for stationary heat flux at different voltages.

Demonstration of hysteresis in large-current regimes.

Abstract

We study heating effects in a chain of weakly coupled grains due to electron-hole pair creation. The main mechanism for the latter at low temperatures is due to inelastic electron cotunneling processes in the array. We develop a quantitative kinetic theory for these systems and calculate the array temperature profile as a function of grain parameters, bias voltage or current, and time and show that for nanoscale size grains the heating effects are pronounced and easily measurable in experiments. In the low- and high-voltage limits we solve the stationary heat-flux equation analytically. We demonstrate the over-heating hysteresis in the large-current or voltage regimes. In addition we consider the influence of a substrate on the system which acts as a heat sink. We show that nano dot chains can be used as highly sensitive thermometers over a broad range of temperatures.