Heat Transfer Modelling in the Crossover Regime Between Conduction and Radiation

Fluctuational electrodynamics (FED) theory describes the near field radiative heat transfer for separation distances below the thermal wavelength (some microns at ambient temperature), where the heat flow between two solids at different temperatures can exceed the far field limit by several orders of magnitude, in particular when the bodies exchanging heat support surface resonant modes, such as surface phonon-polaritons or surface plasmons.<br/>At even smaller distances, in the so-called extreme near field (distances in the nanometer range and below) the physics is expected to change radically. Interestingly, two recent scanning thermal microscopy (SThM) experiments, approaching gold tips to gold substrates, reach apparently opposite conclusions. While one of them shows large deviations from FED for separation distances of few nanometers, another experiment shows no deviations from FED even at sub-nanometer gaps, where acoustic phonons and electrons are expected to contribute as further channels to the heat exchange.<br/><br/>Here we introduce a theoretical framework to investigate the heat transfer mediated by photons, phonons and electrons between two metallic bodies. We quantify the role of electron tunnelling currents by paying attention to the role played by the shape of the electronic barrier in the presence of electron-electron screening interactions. Using an approach based on the elastic theory, we address the role of acoustic phonons coupled through the Van der Waals and the electrostatic forces. Finally, we employ FED to study the role played by photons, by taking into account the contribution of non-local effects.<br/>This theoretical work allows us to outline the relative weight of the different carriers with respect to the separation distance, and to highlight the crucial role played by the external bias voltage on the heat flux carried by the three types of carriers.