NEAR-FIELD THERMAL RADIATION
AND POTENTIAL APPLICATION FOR CLEAN ENERGY PRODUCTION
Mathieu Francoeur and M. Pinar Mengüç
UNIVERSITY OF KENTUCKY
College of Engineering
www.uky.edu
NearNear-field radiative heat transfer in 1D layered media
2
N-1
ε r 0 ,T0
kx
k0
z = d1
-11
Blackbody
d = 10 nm
d = 100 nm
d = 1 μm
d = 10 μm
d = 1 m (far-field)
10
-12
10
-13
13
10
14
ω [rad/s]
Propagating modes
Evanescent modes
50
500
600
700
800
900
1000
NanoNano-thermophotovoltaic devices
40
30
20
0
-9
10
15
14
2.4x10
Propagating
Modes
kx < ω/c0
14
2.2x10
light line
in vacuum (kx = k0 = ω/c0)
propagating wave
Near-field radiative heat transfer can potentially be applied to thermophotovoltaic
(TPV) power generators.
-8
-7
10
10
-6
10
-5
10
-4
-3
10
10
d [m]
-2
10
-1
10
0
10
ωres
14
1.6x10
ωTO
surface phonon-polariton
Evanescent Modes
kx > ω/c0
14
10
-7
10
-8
10
-9
surface phonon-polaritons
T1 = 300 K
Far-field
d = 10 nm
-10
T2 = 0 K
Distance between the layers d [m]
V
Tr = 1000 – 2000 K
propagating
waves
evanescent
waves
d ~ nanometers
p-doped region
depletion
region
n-doped region
By using materials supporting surface polaritons, it is possible to achieve quasimonochromatic radiative heat exchanges between the radiator and the PV cells.
If the resonant frequency of the materials matches the bandgap of the PV cells, it
is possible to increase the efficiency of TPV devices.
10
-11
10
-12
10
-13
10
14
1.0x10
= iωμ0 ∫ dV ′∫ dV ′′G (r, r′, ω )G (r, r′, ω ) J (r′, ω ) J (r′′, ω )
Radiator
-1
1.2x10
10
-6
TPV devices are similar to
conventional photovoltaic (PV)
systems, except that the source
of photons is a radiator
maintained
at
temperature
between 1000 and 2000 K. By
spacing the radiator and layer of
PV cells by few nanometers,
more photons are exchanged
due to tunneling of evanescent
waves.
5
6
5.0x10
6
1.0x10
6
1.5x10
2.0x10
1.0x10
-6
9.0x10
-7
8.0x10
-7
7.0x10
-7
6.0x10
-7
5.0x10
-7
4.0x10
-7
3.0x10
-7
Relative near-field
enhancement Y [-]
1.700E-2
1.091E-1
4.497E0
1.853E2
1.190E3
7.636E3
4.902E4
1.0x10
-7
3.147E5
2.020E6
-8
1.0x10
14
1.0x10
14
1.5x10
14
2.0x10
14
10
15
10
Angular frequency ω [rad/s]
2.887E1
-7
13
10
-1
7.005E-1
2.0x10
-14
10
14
2.5x10
3.0x10
Angular frequency ω [rad/s]
References: [1] M. Francoeur, and M.P. Mengüç, “Role of fluctuational electrodynamics in near-field radiative heat transfer”, Journal of Quantitative Spectroscopy and
Radiative Transfer, 109, 280-293 (2008).
[2] M. Francoeur, M.P. Mengüç, and R. Vaillon, “Length scales of transition from near- to far-field radiative heat transfer regime for materials supporting
surface polaritons”, To be submitted to ASME Journal of Heat Transfer (2008).
14
10
11
-2
-1
ωLO
14
1.8x10
r*
m
The FE/FDT is applicable to media in local thermodynamic equilibrium,
where a temperature can be defined at any points.
400
60
10
10
kx [m ]
ωε 0
ε ′′(ω )Θ(ω , T )δ nmδ (r′-r′′)
π r
300
70
Quasi-monochromatic radiant energy exchanges can occur in the near-field when surface phonon- (polar
crystals) or plasmon-polaritons (metals or doped semiconductors) are resonantly excited. SiC is a
material supporting surface phonon-polaritons with resonance at 178.6×1012 rad/s (where kx→∞ in the
dispersion relation. Note that the part of the dispersion relation right to the light line in vacuum corresponds
to evanescent waves contributing to radiative heat transfer only in the near-field.
5
J nr (r′,ω ) J mr* (r′′,ω ) =
2
Net monochromatic radiative heat flux [Wm eV ]
10
Relative contribution [%]
-1
-2
-10
net
10
1.0x10
The link between the ensemble average of the spatial correlation
function of fluctuating currents and the local temperature of the emitting
medium is given by the fluctuation-dissipation theorem (FDT):
These results show that the length
scales of transition are function of
the temperature of the emitting
body, and the materials.
Ag
SiC
GaSb
Au
Wien's law (lc = 2898/T)
100
-9
14
r
n
10
80
Ei (r, ω ) H *j (r, ω )
V
*
⎡ Re(k z 0 ) Re(k zN ) s 2 Re(ε r 0 k z*0 ) Re(ε rN k zN
) p 2⎤
t0 N +
t0 N ⎥
⎢
2
2
2
2
k
n
n
k
0
N
z0
z0
⎣
⎦
z = d N −1
1.4x10
h*
jm
[Θ(ω ,T0 ) − Θ(ω ,TN )]dω ∫ k x d k x ×
4π 2 ω∫=0
k x =0
=
We are currently investigating the
length scales of transition for real
materials that can support surface
polaritons [2].
∞
90
ω [rads ]
V
Computation of the Poynting vector (radiative heat flux) involves
*
calculation of terms Ei H j :
∞
Temperature [K]
10
e
h
q
1
We analyzed radiative heat transfer between two half-spaces (denoted 1 and 2) spaced by a vacuum gap
(medium 0) of thickness d. Both half-spaces are dielectric materials with frequency-independent dielectric
constants (20 + i0.0001) maintained at 800 and 200 K.
14
H (r,ω ) = ∫ dV ′G (r, r′,ω ) ⋅ J r (r′, ω )
net
0N
ε rN , TN
z = d N −2
2.0x10
V
40
z
Half-space
z=0
We studied the length scales of transition from near- to far-field radiative heat
transfer regimes. We have shown that this critical length scale is about three
times larger than Wien’s law for dielectric materials [1].
kx
k zN
10
E(r, ω ) = iωμ0 ∫ dV ′G (r, r′, ω ) ⋅ J r (r′, ω )
kN
...
k z0
Fluctuational electrodynamics
Thermal agitation in a body at temperature greater than 0 K causes a
chaotic motion of charges. These random fluctuations of charges
induce oscillating dipoles generating an electromagnetic field (thermal
radiation field). The fluctuational electrodynamics (FE) is based on a
macroscopic level, where an extraneous stochastic current density term
Jr (due to thermal agitation of charges) is added on the right-hand side
of Ampère’s law (the mean value of this current density term is zero).
Fourier components of the electric and magnetic fields induced by the
random current are given by:
The net radiative heat flux between half-spaces 0 and
N is found from the solution of the dyadic Green’s
function for 1D layered media:
N
Half-space
qω,1-2 [Wm (rad/s) ]
To account for near-field effects of thermal radiation (wave
interference and radiation tunneling), Maxwell’s equations need to
be solved in conjunction with the fluctuational electrodynamics (to
model the emission process).
x
1
Monochromatic radiative heat
-2
-1
net, prop+near
flux qω,1-2
[Wm (rad/s) ]
Radiant energy exchanges between closely spaced bodies can exceed
by several orders of magnitude the values predicted for blackbodies
due to near-field effects. Bodies at temperature greater than 0 K induce
oscillating dipoles emitting far- and near-field components. Far-field
components are propagating waves taken into account in the classical
theory of thermal radiation; near-field components are evanescent
(non-propagating) waves decaying exponentially (over a distance of
about a wavelength) normal to the surface of an emitting body. When
bodies exchanging thermal radiation are spaced in such a way that
their surfaces lay in the evanescent field of their opposite bodies,
radiative heat transfer due to evanescent waves occur (radiation
tunneling).
Length scales of transition
Length scale of transition lc [μm]
NearNear-field effects of thermal radiation
e
in
RADIATIVE TRANSFER LABORATORY
Department of Mechanical Engineering
www.engr.uky.edu/rtl
Radiative Transfer Laboratory, Department of Mechanical Engineering,
University of Kentucky, Lexington, KY 40506-0503
The monochromatic ratio Y of the radiative
heat flux due to evanescent waves and
propagating waves, as a function of d, shows
that most of the energy is transferred around
the resonant frequency at small d.
9
10
d = 10 nm
d = 100 nm
d = 1 mm
Blackbodies
Radiative
heat
transfer
between two half-spaces of
cBN spaced by vacuum
shows that almost 99% of the
energy is exchanged around
0.157 eV for a gap d of 10
nm.
7
10
5
10
3
10
0.12
0.14
0.16
0.18
Energy [eV]
We are in the process of developing an extensive numerical model to compute
efficiencies of nano-TPV devices, and eventually built a prototype. Note that the
model accounts for thermal transport in the PV cells, which has not been studied
so far for nano-TPV devices.
Acknowledgments: MF is grateful to the Natural Sciences and Engineering Research Council (NSERC) for their financial support (ES D3 scholarship).
Contact Information: mfran0@engr.uky.edu (Mathieu Francoeur) and menguc@engr.uky.edu (M. Pinar Mengüç)