Stellar Atmospheres: Radiative Equilibrium 1 Radiative Equilibrium Energy conservation.
Near-field radiative heat transfer : application to energy conversion
description
Transcript of Near-field radiative heat transfer : application to energy conversion
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Near-field radiative heat transfer :application to energy conversion
Jean-Jacques Greffet
Ecole Centrale Paris, CNRS.
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Collaborators
• Rémi Carminati, O. Chapuis, K. Joulain, F. Marquier, J.P. Mulet, M. Laroche, S. Volz
• C. Henkel ( Potsdam)
• A. Shchegrov ( Rochester)
• Y. Chen, S. Collin, F.Pardo, J.L. Pelouard ( LPN, Marcoussis)
• Y. de Wilde, F. Formanek, P.A. Lemoine ( ESPCI)
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Density of energy above a SiC surface at temperature T
Temperature T
z
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20x103
15
10
5
0500x10
124003002001000
ω ( )Hz
1.0
0.8
0.6
0.4
0.2
0.0
=100 z μm
=1 z μm
= 100 z nm
15
10
5
0
T=300 K
z
Density of energy near a SiC-vacuum interface
PRL, 85 p 1548 (2000)
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20x103
15
10
5
0500x10
124003002001000
ω ( )Hz
1.0
0.8
0.6
0.4
0.2
0.0
=100 z μm
=1 z μm
= 100 z nm
15
10
5
0
T=300 K
z
Density of energy near a SiC-vacuum interface
PRL, 85 p 1548 (2000)
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20x103
15
10
5
0500x10
124003002001000
ω ( )Hz
1.0
0.8
0.6
0.4
0.2
0.0
=100 z μm
=1 z μm
= 100 z nm
15
10
5
0
T=300 K
z
Density of energy near a SiC-vacuum interface
PRL, 85 p 1548 (2000)
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T=300 K
z
Density of energy near a Glass-vacuum interface
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What is the physical mechanism responsible for this huge enhancement ?
The density of energy is the product of
- the density of states, - the energy h- the Bose Einstein distribution.
The density of states can diverge due to the presence of surface waves :Surface phonon-polaritons.
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-+ + + + + +-- - -
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+
++
+
+
+-
--
-
---
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Dispersion relation of a surface phonon-polariton
It is seen that the number of modes diverges for a particular frequency. This happens only close to the surface.
PRB, 55 p 10105 (1997)
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Derivation of the thermal emission of a hot body
i) A volume element below the interface contains currents due to the random thermal motion of charges.
ii) Each volume element is equivalent to a dipolar antenna that emits radiation.
iii) The mean field is null.
E(r,ω)=iμ0ω
t G (r,r',ω)⋅ j(r' )d3r'
V∫∫∫
j(r' )d3r'
j(r' ) =0 ⇒ E(r' ) =0
PRL, 82 p 1660 (1999)
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iv) Derivation of the intensity
E(r,ω)2
=μ0ω
2 t G (r,r' ,ω)⋅ j(r' )d3r'
V∫∫∫
2
v) The only quantity needed is the correlation function of the random current. This is given by the fluctuation-dissipation theorem.
jn(r) j
m
* (r' ) = ωπε
0Im(ε)δ
m,nδ(r−r' )
hω
exphωkT[ ]−1
PRL, 82 p 1660 (1999)
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Advantages of the electromagnetic approach
-It is valid in the near field
- It yields the value of the emissivity
- It yields physical insight in Kirchhoff law.
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Direct proof of the coherence of thermal radiation in the near field.
Application to the measurement of the EM LDOS
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Direct experimental evidence of the spatial coherence of thermal radiation in near field
de Wilde et al. to be published in Nature
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Direct experimental evidence of the spatial coherence of thermal radiation in near field
de Wilde et al. to be published in Nature
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Fabrication of a coherent source
of infrared radiation :Infrared antenna
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The thermally emitted fields may be spatially coherent along the interface !
PRL 82, 1660 (1999)
T=300 K
z
M P
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Fabricating an infrared antenna with a microstructured semiconductor.
Thermal currents radiates surface waves
A grating ruled on the surface scatters the surface wave. The scattered wavevector is related to the surface wave wavevector by the relationship :
ksw +
2πd
= 2πλ
sinθs
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Image of the SiC grating taken with an atomic force microscope.
Nature 416, p 61 (2002)
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The emission pattern looks like an antenna emission pattern. The angular width is a signature of the spatial coherence.
Emission pattern of a SiC grating
Green line : theory (300K)Red line : measurement(800K).
Nature 416, p 61 (2002)
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Comparison between theory and measurements
Nature 416, p 61 (2002)
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Thermal emission by a tungsten grating
Opt.Lett. 30 p 2623 (2005)
Angular width : 14 mrad
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Emission mediated by surface waves
1. Excitation of a surface wave.
2. Scattering by a grating.
€
Re Ksp( ) + p2π
a=
2π
λsin θ( )
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• Coherent thermal emission
T
Source : current thermal fluctuations
Greffet et al., Nature (London) 416, 61 (2002), Marquier et al. PRB 69, 155412 (2004)
Emission mediated by surface waves
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The interface as an antenna (1)
• What is an antenna ?i) Increases the emitted power.ii) Modifies the emission pattern.
•How does it work ?
Antenna = Intermediate resonator between the source and vacuum :
i) More energy is extracted from the source because the LDOS is enhanced (Purcell effect)ii) The resonator is a secondary source.
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The interface as an antenna (2)
Example of antenna: a guitar
Source :the string
Resonator
Optical analog : microcavity
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The interface as an antenna (3)
Source : current fluctuations
T
Resonator : the interface+ the grating
i) The output is increased because the LDOS is increased (Purcell effect)
ii) The angular pattern of the antenna depends on the decay length of the SPP.
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Electromagnetic heat transfer in the near field
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Application to radiative heat transfer between two half-spaces
Temperature T1
Temperature T2>T1.
d
h =lim
T1→ T
2
Φ(T
1,T
2)
T1−T
2
Poynting vector yields the radiative enregy flux.
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Radiative heat transfer coefficient, T=300 K.
d
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Monochromatic radiative heat transfer coefficient, d=10 nm, T=300K.
d
Microscale Thermophysical Engineering 6, p 209 (2002)
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Au GaN
Kittel et al. , PRL 95 p 224301 (2005)
Experimental data
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Implications of near-field heat transfer for thermophotovoltaics
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thermal source
T= 2000 K
TPV cell
T= 300 K
d << rad
thermal source
T= 2000 K
TPV cell
T= 300 K
PV cell
T= 300 K
Photovoltaics Thermophotovoltaics Near-fieldthermophotovoltaics
T= 6000K
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potential improvement on the output electric power and efficiency
of near-field thermophotovoltaic devices :
necessity of a quantitative model
thermal sourceT= 2000 K
TPV cell
T= 300 K
d << rad
PR (
W.m
-2 )
d (m)
400
enhanced radiative power transfer
Why near field ?
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Near-field I-V characteristic of a TPV cell
z
€
I = Io eeV / kT −1( ) − Iph
enhanced radiative power (Mulet 2002, Whale 2002, Chen 2003)
€
Io ∝1
τ
modification of the electron-hole pairs lifetime (Baldasaro 2001)
hot source
T= 2000 K
TPV cell
T= 300 K
d << rad
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Near-field radiative power transfer
ω (rad.s-1)
PR(W
. m
-2.
Hz-1
)
d = 10 μmW
T= 2000 K
GaSb cell
T= 300 K
d
ω (rad.s-1)
PR(W
. m
-2.
Hz-1
)
d = 30 nm(near field)
(far field)
1.10-10
3.5.10-10
evanescent waves contribution in the near fieldenhancement by a factor 3
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Near-field effects on the radiative power transfer
d = 30 nm
d = 10 μm
ω (rad.s-1)
PR(W
. m
-2.
Hz-1
)ω (rad.s-1)
PR(W
. m
-2.
Hz-1
)
Drude Metal
T= 2000 K
GaSb cell
T= 300 K
d(far field)
(near field)
9.10-12
6.10-10
evanescent waves contribution in the near fieldenhancement by two orders of magnitudemonochromaticity degraded by the presence of the TPV converter
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Enhanced radiative transfer and photogeneration current in the near field
d (m)
PR (
W.m
-2 )
tungsten source quasi-monochromatic source
PR (
W.m
-2 )
d (m)
d (m)d (m)
I ph (
A.m
-2 )
I ph (
A.m
-2 )
€
PR T1,T2( ) = dω0
∞
∫ PR T1,T2,ω( )
€
Iph = dωEG = 0.7eV
∞
∫PR T1,T2,ω( )
h ω
50
40
400
1000
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Near-field electron-hole pairs lifetime
€
ΓΓn
=1+2π
nωo /cIm Tr G
↔
env
E
r,r,ωo( ) ⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥
hot source
d << rad vacuum
GaSb
z
for both sources : near-field effect on the radiative recombination lifetime of electron-hole pairs negligible
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Near-field output electric power
output electric power enhanced by at least one order of magnitude
tungsten source quasi-monochromatic source
d (m)
50
far field :3.104 W/m2
near field :15.105 W/m2
Pe
l (W
. m
- 2)
d (m)
near field : 2.5.106 W/m2
far field : 1.4.103 W/m2
3000
Pe
l (W
. m
- 2)
BB 2000 KBB 2000 K
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Near-field TPV converter efficiency
€
η =Pel
Pradη (%
)
d (m) d (m)
η (%
)
near field : 27%
far field : 21 %
near field : 35%
significant increase of the efficiency
far field : 8 %
tungsten source quasi-monochromatic source
BB 2000 K BB 2000 K
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Summary
20x103
15
10
5
0500x10
124003002001000
ω ( )Hz
1.0
0.8
0.6
0.4
0.2
0.0
=100 z μm
=1 z μm
= 100 z nm
15
10
5
0
?
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Heat transfer between two nanoparticles
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Heat transfer between two nanoparticles
PRL 94, 85901, (2005)
QuickTime™ et undécompresseur BMP
sont requis pour visionner cette image.
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Radiative heat transfer between a small sphere and an interface
d
Appl.Phys.Lett, 78, 2931 (2001)
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10-6
10-4
10-2
100
102
10-8 10-7 10-6 10-5 10-4
d in m
Far field value
Power absorbed by a SiC sphere as a function of the distance.
Diameter = 10 nm, SiC substrate.
Appl.Phys.Lett, 78, 2931 (2001)
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Emission mediated by surface plasmons
QW luminescenceA. SchererNature Materials 3, p 601 (2004)
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Conclusions
* The existence of surface modes of electromagnetic waves modifies drastically the emission. * Radiative heat transfer can be increased by four orders of magnitude between two plates.* Radiative heat transfer can be very local. * Radiative heat transfer is almost monochromatic at nanoscale.* Radiation emitted by a thermal source is temporally coherent (monochromatic)close to an interface that supports a surface wave.* Radiation emitted by a thermal source is spatially coherent (narrow emitted beams).* Highly directional infrared thermal antennas can be designed.
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Dispersion relation of the surface-phonon polariton
Nature 416, p 61 (2002)
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Introduction
Measurement of the coherence length
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Comparison of calculated and measured emissivity
Calculation with optical dataat 300 K
Calculation with optical dataat 800 K
Phys.Rev.B (2004)
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Application to local heating.
The peak power deposited per unit volume is 100 MWm-3.
A SiC sphere (a=5 nm) is located at a distance 100 nm above a SiC surface.
Contours line are in log scale.
The power decreases as R-6.
R
T=300 K
-0.8
-0.6
-0.4
-0.2
0.0
1.00.80.60.40.20.0
lateral distance in μm
7
5.5
5
4
3.5
3.5
2.5
7 6.5
6
6
5.5
5
4.5
4.5
4.5
4
4
3.5
3
3
3
2.5
2.5
2
Appl.Phys.Lett, 78, 2931 (2001)
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Thermal emission by photonic crystals
PRL 96, 123903 (2006)
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Laboratoire EM2C
2D photonic crystal
PRL 96, 123903 (2006)
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Laboratoire EM2C
Thermal emission assisted by surface waves
Transmission
Absorptionby the crystal
Absorption by the truncated crystal
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Laboratoire EM2C
(a) slab, (b) photonic crystal,(c) truncated PC, (d) amplitude of the surface wave
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Laboratoire EM2C
Design of an isotropic source