[Paper Review] Giant near-field mediated heat flux at the nanometer scale

Konstantin Kloppstech, Nils Könne+5 more|arXiv (Cornell University)|Oct 21, 2015

Thermal Radiation and Cooling Technologies3 citations

TL;DR

This study reports direct, quantitative measurements of near-field radiative heat flux between a gold-coated near-field scanning thermal microscope (NSThM) tip and a planar gold sample at nanoscale gaps (0.2–7 nm), revealing a heat flux more than five orders of magnitude larger than black-body radiation and four orders of magnitude above predictions from conventional fluctuational electrodynamics. The observed enhancement cannot be explained by existing theories of phonon tunneling, indicating a need for new models of heat transfer at atomic-scale vacuum gaps.

ABSTRACT

In this Letter, we report on quantitative measurements of the absolute near-field mediated heat flux between a gold coated near-field scanning thermal microscope (NSThM) tip and a planar gold sample at nanometer distances of 0.2 nm- 7 nm. We find an extraordinary large heat flux which is more than five orders of magnitude larger than black-body radiation and four orders of magnitude larger than the values predicted by conventional theory of fluctuational electrodynamics. Additionally, we compare our data with different theories of phonon tunneling which might explain a drastically increased heat flux, but are found not to be able to reproduce the distance dependence observed in our experiment. The findings demand modified or even new models of heat transfer across vacuum gaps at nanometer distances.

Motivation & Objective

• To directly measure absolute radiative heat flux across vacuum gaps at nanometer-scale distances, bridging the gap between near-field and conductive heat transfer regimes.
• To test the validity of established theoretical models—particularly those based on fluctuational electrodynamics and phonon tunneling—under extreme sub-10 nm separations.
• To resolve the discrepancy between theoretical predictions and experimental observations in the crossover regime from radiative to conductive heat transfer at atomic-scale separations.
• To develop a calibrated, high-sensitivity NSThM probe capable of measuring heat fluxes down to 4 nW with 6 nm lateral resolution and 24 pW/K conductance sensitivity.

Proposed method

• A custom-built near-field scanning thermal microscope (NSThM) with a Pt-Ir wire tip coated in 100 nm of Au was used, featuring a self-formed thermocouple at the Au-Pt interface for local thermovoltage detection.
• Heat flux was quantified via calibration of the thermovoltage-to-heat-flux ratio (ε = 0.43 µW/µV) using a 1ω hot-wire method, enabling absolute measurement with ~14% relative uncertainty.
• Measurements were performed in ultra-high vacuum (10⁻¹⁰ mbar) to minimize thermal and mechanical noise, with stepwise approach/retraction at 0.08 nm resolution to map gap-dependent heat flux.
• A finite-element boundary-integral method based on fluctuating surface currents was used for numerical modeling, with geometry discretized using Rao-Wilton-Glisson (RWG) basis functions and material response modeled via the Drude model for gold.
• The probe was calibrated in situ and measurements were averaged over 100 cycles per direction, with drift controlled by ensuring piezo stroke differences <50 pm between start and end.
• The sample was a 200 nm Au film on mica, prepared to achieve a monocrystalline Au(111) surface with atomic flatness and 22×√3 reconstruction, cooled to 120 K while the probe remained at ambient temperature (ΔT = 160 K).

Experimental results

Research questions

• RQ1 What is the magnitude of radiative heat flux between two gold surfaces separated by 0.2–7 nm, a regime where conventional theories break down?
• RQ2 How does the measured heat flux compare to predictions from fluctuational electrodynamics and phonon tunneling models at sub-10 nm gaps?
• RQ3 Can existing theories of near-field heat transfer, including those incorporating phonon tunneling, reproduce the observed distance dependence of the heat flux?
• RQ4 To what extent does the geometry of the probe (conical tip vs. spherical approximation) influence the predicted heat flux in the near-field regime?
• RQ5 What is the role of electronic wave function overlap and quantum effects in enhancing heat transfer at atomic-scale vacuum gaps?

Key findings

• The measured heat flux exceeds black-body radiation by more than five orders of magnitude at 0.2 nm gap distance, indicating a super-Planckian enhancement far beyond classical predictions.
• The measured heat flux is approximately four orders of magnitude larger than the values predicted by conventional fluctuational electrodynamics, even at the smallest measured gap of 0.2 nm.
• No existing theory of phonon tunneling—including those by Prunnila et al., Mahan, Budaev & Bogy, Sellan et al., and Chiloyan et al.—can reproduce the observed distance dependence of the heat flux.
• The numerical model based on fluctuating surface currents shows good agreement with experiment, while the simpler point-approximation model (PA) overestimates the contribution of the tip apex and overall flux.
• The calibration method achieves a relative uncertainty of ~14% in absolute heat flux measurements, enabling reliable quantification of radiative heat transfer at the nanoscale.
• The probe achieves a heat flux sensitivity of 4 nW and a conductance sensitivity of 24 pW/K at 50 Hz bandwidth, enabling detection of near-field effects at atomic-scale separations.