Radiation
heat transfer at the nanoscale
During the past two decades, there have been tremendous
developments in near-field imaging and local probing techniques.
Examples are the Scanning Tunneling Microscope (STM), Atomic Force
Microscope (AFM), Near-field Scanning Optical Microscope (NSOM),
Photon Scanning Tunneling Microscope (PSTM), and Scanning Thermal
Microscope (SThM). Today, the Scanning Probe Microscopy (SPM) family
has become ubiquitous for applications from surface topography and
surface modification nanoscale thermal imaging, to bio-molecular
sensing, atomic-level detection, and nanolithography. Near-field
radiation may play a significant role in the heat transfer process
between the SPM cantilever tip and the surface over which it scans,
due to photon tunneling through evanescent modes and surface-waves
(such as plasmon or phonon polaritons). Furthermore, the radiative
properties of nanostructured materials may differ significantly from
their bulk properties. Although the existence of near-field
radiation has been known for over 100 years, experimental validation
is required to realize the opportunities with near-field radiation
at the nanometer length scale. The purpose of this research is to
investigate the nanoscale thermal radiation both theoretically and
experimentally.
To better understand micro/nanoscale thermal radiation, a
theoretical study on the direction of the energy flow was performed
by examining the group velocity upon refraction [1]. The surface
polariton phenomenon was analyzed to study its impact on the
radiative properties [2]. More recently, we have performed a
comprehensive investigation of the radiation energy transfer between
two semi-infinite parallel plates at different temperatures,
involving silicon with varying dopant concentrations, when the
distance of separation down to 1 nm [3]. The net radiation heat flux
is calculated by means of the fluctuational electrodynamics. A Drude
model that considers the effects of temperature and dopant
concentration on the free carrier concentrations and scattering
times is adopted, after a careful parameter selection and comparison
with existing optical property data. The calculated results show
that the dopant concentration strongly affects the radiation heat
flux when the two media are separated at nanometer distances.
Enormously enhancement in nanoscale radiation heat transfer has been
found for heavily doped silicon. For heavily doped silicon plates
separated at a distance of 1 nm, the present study predicts a
radiation energy flux of over five orders of magnitude greater than
that between two blackbodies placed far apart. At the separation
distance of 1 nm, the net energy flux can exceed 1 GW/m2
with (n-typed) silicon emitter at 1000 K and receiver at 300
K, for dopant concentrations of 1021 cm-3. The
calculated heat flux is 10 times that of air conduction at
atmospheric pressure. The radiation heat transfer coefficient can be
1 MW/m2×K at 1
nm and 10 kW/m2×K
at 10 nm separation distance. The theoretical understanding gained
from the present research will facilitate the design of experiments
that utilize near-field radiation to enhance heating or cooling at
the nanoscale for applications such as thermal control in
nanoelectronics, energy conversion, and nanothermal probing and
manufacturing.
Figure 1 shows the predicted nanoscale radiation heat transfer
between two n-type phosphorus-doped silicon plates, separated
by a distance L in vacuum. In the far-field, the next
radiative flux is limited by the emissivity of silicon surfaces and
is about half of that between two blackbodies. As L becomes
smaller than 1 mm or so,
near-field effect becomes important and the net heat flux exceeds
that between two blackbodies (in the far field). For two intrinsic
silicon media, the near-field heat flux saturates at about 100 nm,
i.e., further reducing L does not increase the heat flux. The
enhancement is limited to n2, where n is
the refractive index of silicon. When both the emitter and receiver
are heavily doped, the enhancement is much greater in the near field
that does not saturate at L approaches zero. When both media
are doped, the radiative heat flux can be enhanced more than 10,000
times as compared to the far-field heat flux between silicon and
silicon [3].
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Figure 1. Predicted nanoscale radiation heat flux between
two parallel silicon plates [3]. |
The difficulty in controlling a heating source can be overcome
by using a heated cantilever mounted on an atomic force microscope.
Heated cantilevers have been fabricated by Professor W.P. King and
his group at Georgia Tech. Cantilever tips with radius of curvature
as small as 20 nm can be fabricated and the tip temperature can be
raised up to 1000 K. The heated tip provides a highly local heating
source, whose temperature can be controlled. Moreover, the use of
AFM enables the manipulation of the gap between the tip and the
substrate to within a few nanometers. Accurate measurements of the
nanoscale thermal radiation from a heated AFM cantilever require a
sensor that can measure the temperature rise with nanometer spatial
resolution. This requirement will be satisfied with a nanofabricated
thermocouple, in which the wire widths are less than 100 nm. We have
designed on-chip calibration structures to determine the effective
Seebeck coefficient of the nanoscale temperature sensor. The heat
transfer between the cantilever tip and the thermocouple as well as
that between the thermocouple and the substrate will be modeled when
the AFM is operated in a constant distance mode as well as in a
tapping mode. The comparison of the measurement with the simulation
will determine the radiation heat flux between the heated cantilever
tip and the substrate surface with different materials. The success
of this research will clarify the radiation energy transport
mechanism at a distance below 10 nm and at above room temperature.
The knowledge achieved from this study will allow the development of
nanoscale devices, materials, and processes that critically depend
upon near-field radiative interactions.
This work has been supported by the National Science
Foundation and is collaborated with Professor W.P. King and his
group.
Selected Publications
[1] Zhang, Z.M., and Park. K., 2004,
“On the Group Front and Group Velocity in a Dispersive Medium upon
Refraction from a Nondispersive Medium,” Journal of Heat Transfer,
126, pp. 244 - 249.
[2] Park, K., Lee, B.J., Fu, C.J., and
Zhang, Z.M., 2005, “Study of the Surface and Bulk Polaritons with a
Negative Index Material,” Journal of the Optical Society of
America B, 22, pp. 1016-1023.
[3] Fu, C.J., and Zhang, Z.M., 2005,
“Nanoscale Radiation Heat Transfer for Silicon at Different Doping
Levels,” submitted to International Journal of Heat and Mass
Transfer.
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