  Extreme near-field heat transfer between metallic surfaces is a subject of
debate as the state-of-the-art theory and experiments are in disagreement on
the energy carriers driving heat transport. In an effort to elucidate the
physics of extreme near-field heat transfer between metallic surfaces, this
Letter presents a comprehensive model combining radiation, acoustic phonon and
electron transport across sub-10-nm vacuum gaps. The results obtained for gold
surfaces show that in the absence of bias voltage, acoustic phonon transport is
dominant for vacuum gaps smaller than ~2 nm. The application of a bias voltage
significantly affects the dominant energy carriers as it increases the phonon
contribution mediated by the long-range Coulomb force and the electron
contribution due to a lower potential barrier. For a bias voltage of 0.6 V,
acoustic phonon transport becomes dominant at a vacuum gap of 5 nm, whereas
electron tunneling dominates at sub-1-nm vacuum gaps. The comparison of the
theory against experimental data from the literature suggests that
well-controlled measurements between metallic surfaces are needed to quantify
the contributions of acoustic phonon and electron as a function of the bias
voltage.
