Is there a ‘Nano’ Revolution in Thermal Management and Energy Conversion?

Advances in Nanostructure basedThermal Interface and Thermoelectric Materials

Sebastian Volz

Laboratoire EM2C UPR CNRS 288, Ecole Centrale ParisThermal Nanosciences Group - volz@em2c.ecp.fr

EUROTHERM 2012 – Poitiers, France – September 5th 2012

« Nano » wire dConduction

Heat Transfer Laws at Small Scales Deviate from Classical Ones

Ballistic conduction in airKn>>1

L

NEAR FIELD

Radiation When L < the Predominant Photon Wavelength,coupling of Evanescent Surface Waves increases heat flux.

Transition from a regime of propagative waves emitted by charges motions to a direct electrostatic interaction.

STEFAN-BOLTZMANN

European CNRS Network on Thermal Nanosciences and NanoEngineering

ConvectionIf Nu<1, heat conduction in air predominates.If Kn>>1 heat conduction becomes ballistic.

Diffusive to Ballistic transition is well-knownin gases and radiation.

Heat carries in solids are SOUND PARTICLES or PHONONs,the quanta of lattice vibrational energy

i-1 i i+1

a

un=u.expi(kna-wt)

Fij = K.(uj- ui)

Periodic Boundary Conditions:

k = n . 2/L Density of states

E

kst( ) =hωks. nks t( ) +

12

⎛

⎝⎜⎞

⎠⎟

€

∂ω∂k

=aK

mcos

ka

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

ω =2K

amsin

ka

2

⎛

⎝ ⎜

⎞

⎠ ⎟

k

w

m&&un =−K 2un −un−1 −un+1( )

∂ω∂k

=aK

m

Acoustics: Coherent Phonons

Continuous limit k=>0

k

w

ϕ = Cωvω .Λω dω0

ωmax

∫

Heat Flux: the Phonon Gas

ρ&&u = K '

∂2u

∂x2

Phonons form a GAS of particles to propagate heat !

Knudsen Transport Applies

Phonon Wien’s Wavelength: 3nm (300K) Mean free path: 1-1000nm

p(, , pol, )=1/3 C v

Kn>1: Boundary scattering predominates over diffusive scattering

L

Confinement: Cavity modes appear if L< Wavelength

Periodicity: e ik(L+x)=e ikx

un ~ expi(kna-wt)+ expi(-kna-wt) ~ cos(kna)e-iwt

e ikL=e ika=0

a STEADY WAVE has ZERO group velocity=1/3 C v

The number of phonon modes depends on Dimensionnality

Dimension: Number of States /dk:

=1/3 C v

k-space

1D (wire) D(k) ~ 1

2D (film/SR) D(k ) ~ k

3D (bulk) D(k) ~ k2

At nanoscales, thermal resistance arises from boundaries

At nanoscales, thermal resistance arises from boundaries

The KEY is to understand phonon transfer at the surface and between two

systems

Thermal Resistance is an Ambiguous Concept Relating Equilibrium and Non-Equilibrium Quantities

R= (T1-T2)/Q

N1 N2

Q

Heat Bath T1

HeatBath T2

‘Cheating’Seems

Unavoidable

Atomic Simulations involve dubious Non-Equilibrium Conditions

-Thermostats Parameters

-Equilibrium Temperatures:coupling with heat bath?

NEMD - TRANSIENT

-Thermostat Parameters (weaker)

-’Short time’ non-equilibrium

-Equilibrium Temperatures at each time step?

NEMD - STEADY

Equilibrium Temperature Correlation defines Thermal Resistance

τau

FLUCTUATIONAL THERMODYNAMICS

INTERNAL SCATTERING ACF NEGLECTED (?)

JAP, 108, 094324, 2010

A Flux based Thermal Conductance can be equivalently derived

Q t( ) =

ddt

HL =−1ih

HL ,Hsys⎡⎣

⎤⎦

Q t( ) =12

&ui (t) fij (t) − f ji (t)&uj (t)( )i∈Lj∈D

∑

kB

G ω( )=

1N1

+1N2

⎛

⎝⎜⎞

⎠⎟ΔT ω( )

2

ΔT 2 0( )ΔT ω( ) =

Q ω( )

G ω( )

-Interfacial Thermal Resistance only depends on Interactions between Atoms of both Sub-Systems

-Temperatures involved in the definition of resistance are the Temperatures of the Interacting Atoms

Nanostructures have exceptional thermal conductivities

Carbon Nanotubes2400-3000 W/mK@RT

Silicon Nanowires1-3 W/mK@RT

Nanostructures can be used to taylor thermal conductivity

Thermal Interface Materials: Increase

Thermoelectricity: Decrease

ZT =S2σλ

T

Can Carbon Nanotubes be used as Thermal Interface Materials?

Use Carbon Nanotube Pellets

J

€

σ

€

κ3D =σ

72π

ρ

ρ Sgr

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

L2

D

D

L

Isotropy

Isotropic Pellet Thermal Conductivity is promising but….

€

κ3D =σ

144π

ρ

ρ Sgr

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

L2

R

Chalopin, Volz, Mingo, Journal of Applied Physics, 105, 084301, (2009) €

κ3D =σ

72π

ρ

ρ Sgr

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

L2

D

…Measured Thermal Conductivity is more than disappointing

€

κ3D =σ

144π

ρ

ρ Sgr

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2

L2

R

Prasher, Hu, Chalopin, Mingo, Lofgreen, Volz, Cleri, Keblinski, Phys. Rev. Lett.,102, 105901, 2009

CNT Orientation is drastically affecting thermal conductivity

Volkov and Zhigilei Phys. Rev. Lett. 104, 215902 (2010)

Use of Hybrid Charges Imposes Isotropy

Bozlar, He, Bai, Chalopin, Mingo and Volz, Advanced Materials, 21, 1, (2009)

Vertically aligned CNTs appears as the optimized option

CNT-Superstrate contact resistance cancels performances

Applying pressure?

Thermal Conductance is increased when applying Pressure

Chalopin, Srivastava, Mingo, Volz, submitted to APL

Transmission shows the opening of inelastic channels when increasing pressure

Harmonic Green Functions

Fluctuations

Anharmonic Green Functions

G =kB T ω( )dω0

ωmax

∫

Introducing a polymer layer at contact reduces thermal resistance

2.5mm2K/W

Introducing Covalent Bonds Should Increase Conductance

HLK5

CNT-HLK5 resistance is three times lower than CNT-PEMA one

RMDPEMA

RMDHLK 5

=RP1 / NP

RH1 / NH

=3→ 6

Ni, LeKhahn, Bai, Divay, Chalopin, Lebarny,, Volz Appl. Phys. Lett. 100, 193118 (2012)

CONCLUSION on Thermal Interface Materials

Ni, LeKhahn, Bai, Divay, Chalopin, Lebarny,, Volz Appl. Phys. Lett. 100, 193118 (2012)

2007

2010

THANK YOUFOR YOUR ATTENTION

Collaborators:

Team: Y. Chalopin (CNRS)T. Antoni (Ass. Prof.)T. Dumitrica (Inv. Prof.)Pdocs:J. OrdonezO. PokropivnyPhDs: Y. Ni, S. Xiong, L. TranchantW. Kassem, J. JaramilloA. Ramière, H. HanB. Latour, J. Soussi

AbroadG. Chen (MIT)H. Ban (Utah U.)C.W. Chang (National Taiwan Uniiversity)B. Kim (U Tokyo)H. Fujita (U Tokyo)H. Kawakatsu (U. Tokyo)Y. Kosevich (Semenov Inst. Moscow)M. Kazan (U Américaine de Beyrouth)B. Rajabpour (U Teheran)Y. Ciumakov (Moldova)

France:N. Mingo (CEA-LITEN)E. Ollier (CEA-LITEN)A. Ziaei (Thales R&T)L. Divay (Thales R&T)P. Cortona (SPMS, Ecole Centrale Paris)H. Dammak (SPMS, Ecole Centrale Paris)J. Bai (SPMS, Ecole Centrale Paris)L. Aigouy (LPM, ESPCI)B. Palpant (LPQM, ENS Cachan)S. Merabia (LPMNC, U Lyon)P. Chantrenne (MATTEIS, U Lyon)D. Lacroix (LEMTA, U Nancy)J. Amrit (LIMSI, U Orsay)B. LePioufle (SATIE, ENS Cachan)D. Fourmy (Centre de Génétique Mol., Gif)K. Termentzidis (LEMTA, Nancy France)

European CNRS NetworkThermal Nanosciences and NanoEngineering

Quantitative Micro and Nano Thermal Imaging and Analysis

10-12 July 2013

Reims, France

GRESPI

Université de Reims-Champagne-Ardenne

http://qmntia2013.univ-reims.fr/

qmntia2013@univ-reims.fr

QMNTIA 2013