Enhancement and Saturation of Near-Field Radiative Heat Transfer in Nanogaps between Metallic Surfaces

Near-field radiative heat transfer (NFRHT) between planar metallic surfaces was computationally explored over five decades ago by Polder and van Hove [Phys. Rev. B 4, 3303 (1971)]. These studies predicted that, as the gap size ($d$) between the surfaces decreased, the radiative heat flux first increases by several orders of magnitude until $d$ is $\sim 100\mathrm{nm}$ after which the heat flux saturates. However, despite both the fundamental and practical importance of these predictions, the combined enhancement and saturation of NFRHT at small gaps in metallic surfaces remains experimentally unverified. Here, we probe NFRHT between planar metallic (Pt, Au) surfaces and show that RHT rates can exceed the far-field rate by over a thousand times when $d$ is reduced to $\sim 25\mathrm{nm}$. More importantly, we show that for small values of $d$ RHT saturates due to the dominant contributions from transverse electric evanescent modes. Our results are in excellent agreement with the predictions of fluctuational electrodynamics and are expected to inform the development of technologies such as near-field thermophotovoltaics, radiative heat-assisted magnetic recording, and nanolithography.

Figure 1

Experimental setup and devices. (a) Schematic representation of the experimental setup. The bottom chip (made of doped Si coated with Pt, Au, or ${\mathrm{SiO}}_2$) is placed on a piezoelectric actuator to control the gap size between the bottom chip and a microfabricated emitter coated with the corresponding metal or dielectric. The emitter consists of a round, doped-Si mesa ($15\mu \mathrm{m}$ tall, $80\mu \mathrm{m}$ diameter) protruding from the top chip, and a Pt serpentine used as a heater and thermometer [see also (b)]. ${\theta }_x$ and ${\theta }_y$ represent the tip and tilt angles of the emitter to achieve parallelism with the bottom chip. (b) SEM image of a representative emitter device; the round mesa and the nearby Pt serpentine can be seen. (c) Dark-field image (taken with a $50\times$ Zeiss Epiplan objective) of the mesa surface coated with 100 nm of Pt. The image shows a faint particle almost at the center of the active surface, which can be seen more clearly in the inset (more details in [29]). (d) AFM image of the mesa surface. The faint particle seen in (c) can be see more clearly and is circled (see profiles of the particle in [29]).

Figure 2

Heat transfer analysis and measurements. (a) Schematic representation of the experimental system. A heat flux $Q_{\mathrm{gap}}$ is established between the hot emitter and the receiver. Numbers 1–5 identify the five layers involved in the RHT analysis. (b) Thermal resistance network showing the main heat transfer pathways. $Q_{\mathrm{in}}$ is the heat dissipated in the integrated Pt heater, which heats the emitter to an initial temperature $\mathrm{\Delta }{T}_{\mathrm{dc}}$ above the room temperature $T_0$. $G_{\mathrm{th},\text{gap}}$ is the thermal conductance of the gap and $G_{\mathrm{th},\mathrm{beam}}$ is the beam thermal conductance and $Q_{\mathrm{beam}}$ is the heat flow through the beams. As the emitter approaches the receiver, $Q_{\mathrm{gap}}$ increases and the emitter temperature is reduced by $\mathrm{\Delta }{T}_e$. (c) Gap size between emitter and receiver as a function of time. (d) Measured temperature change of the emitter ($\mathrm{\Delta }{T}_e$) as a function of time. Contact of the emitter with the receiver is signaled by a sudden drop in the emitter temperature, marked with a red dashed line.

Figure 3

NFRHT between metallic and polar dielectric surfaces. (a) Gap dependence of the total heat transfer coefficient $h$ measured for Pt (green dots) and ${\mathrm{SiO}}_2$ surfaces (gray dots), compared with the corresponding theoretical calculations (dark green and gray solid lines, respectively). Experimental data displaced by 26–29 nm for Pt surfaces (from six different measurements) and 19 nm for ${\mathrm{SiO}}_2$ surfaces (from two different measurements) to account for the smallest achievable gap size. Dashed and dotted horizontal lines are the blackbody and gray body (Pt) limits, respectively, and correspond to the computed far-field value for surfaces with an area equal to that of the mesa and a temperature difference of $\sim 11.6\mathrm{K}$. The blackbody limit was computed using a view factor of unity and emissivity of 1, and for the gray body we assumed an emissivity of 0.054 [41] for Pt. The $1/d^2$ dependence (gray dotted line) for ${\mathrm{SiO}}_2$ surfaces is also shown. (b) Total heat transfer coefficient $h$ as a function of gap size (black dashed line) for the multilayer system in Fig. 2 with a Pt coating thickness $t=100\mathrm{nm}$. The different contributions from TE and TM modes are also shown. Note that below $1\mu \mathrm{m}$ gaps the major contribution is from evanescent TE modes.

Figure 4

The transmission probability for metals and polar dielectrics. (a),(b) Transmission probability for evanescent TE (${\tau }_s$) and TM modes (${\tau }_p$), respectively, as a function of frequency ($\omega$) and magnitude of the parallel wave vector ($k$) for 100-nm-thick Pt surfaces and a gap size $d=30\mathrm{nm}$. (c),(d) Transmission probability for evanescent TE (${\tau }_s$) and TM modes (${\tau }_p$), respectively, as a function of $\omega$ and $k$ for $2\text{−}\mu \mathrm{m}$-thick ${\mathrm{SiO}}_2$ surfaces when $d=30\mathrm{nm}$. White dashed lines in (c) and (d) correspond to the analytical dispersion relation of the cavity surface phonon polaritons [5, 6]. Notice that TE modes make the dominant contribution for Pt-coated devices, while TM modes are clearly dominant for ${\mathrm{SiO}}_2$-coated devices.