Electronic heat tunneling between two metals beyond the WKB approximation

TL;DR

This paper investigates electronic heat transfer between metals at nanometer scales, emphasizing the importance of accurate tunneling barrier modeling beyond the WKB approximation for realistic heat flux predictions.

Contribution

It introduces a detailed modeling approach for electronic tunneling heat transfer that surpasses traditional approximations, crucial for nanoscale thermal analysis.

Findings

Heat flux and current density are highly sensitive to barrier shape and height.

Beyond-WKB models significantly alter heat flux estimates, differing by orders of magnitude.

The approach aids in interpreting scanning-thermal-microscopy experiments.

Abstract

Two metals at different temperatures separated by large gaps exchange heat under the form of electromagnetic radiation. When the separation distance is reduced and they approach contact (nanometer and sub-nanometer gaps), electrons and phonons can tunnel between the bodies, competing and eventually going beyond the flux mediated by thermal photons. In this transition regime the accurate modeling of electronic current and heat flux is of major importance. Here we show that, in order to quantitatively model this transfer, a careful description of the tunneling barrier between two metals is needed and going beyond the traditional WKB approximation is also essential. We employ analytical and numerical approaches to model the electronic potential between two semi-infinite jellium planar substrates separated by a vacuum gap in order to calculate the electronic heat flow and compare it with its radiative counterpart described by near-field radiative heat transfer. We demonstrate that the results for heat flux and electronic current density are extremely sensitive to both the shape and height of the barrier, as well as the calculation scheme for the tunneling probability, with variations up to several orders of magnitude. Using the proximity force approximation, we also provide estimates for tip-plane geometries. The present work provides realistic models to describe the electronic heat flux, in the scanning-thermal-microscopy experiments.