Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques...

Laboratoire EM2C

Laboratoire EM2C

Near-field radiative heat transfer :application to energy conversion

Jean-Jacques Greffet

Ecole Centrale Paris, CNRS.

Laboratoire EM2C

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)

Laboratoire EM2C

Density of energy above a SiC surface at temperature T

Temperature T

z

Laboratoire EM2C

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)

Laboratoire EM2C

T=300 K

z

Density of energy near a Glass-vacuum interface

Laboratoire EM2C

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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-+ + + + + +-- - -

Laboratoire EM2C

+

++

+

+

+-

--

-

---

Laboratoire EM2C

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)

Laboratoire EM2C

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)

Laboratoire EM2C

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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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

Laboratoire EM2C

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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Example of antenna: a guitar

Source :the string

Resonator

Optical analog : microcavity

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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

Laboratoire EM2C

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

Laboratoire EM2C

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 ?

Laboratoire EM2C

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

Laboratoire EM2C

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

Laboratoire EM2C

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

Laboratoire EM2C

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

Laboratoire EM2C

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

Laboratoire EM2C

Near-field output electric power

output electric power enhanced by at least one order of magnitude


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

Laboratoire EM2C

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 %


BB 2000 K BB 2000 K

Laboratoire EM2C

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

?

Laboratoire EM2C

Heat transfer between two nanoparticles

Laboratoire EM2C

Heat transfer between two nanoparticles

PRL 94, 85901, (2005)

QuickTime™ et undécompresseur BMP

sont requis pour visionner cette image.

Laboratoire EM2CPRL 94, 85901, 2005

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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)

Laboratoire EM2C

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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2D photonic crystal

PRL 96, 123903 (2006)

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Thermal emission assisted by surface waves

Transmission

Absorptionby the crystal

Absorption by the truncated crystal

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(a) slab, (b) photonic crystal,(c) truncated PC, (d) amplitude of the surface wave

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Design of an isotropic source

Laboratoire EM2C. Near-field radiative heat transfer : application to energy conversion Jean-Jacques...

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