Heat and Nanotechnologies:

Focus on Thermoelectricity

Sebastian Volz

Yann Chalopin, Ali Rajabpour, Yuxiang Ni

Gang Chen, Natalio Mingo, Laurent Jalabert, Michel Kazan,

Ravi Prasher, Pawel Keblinski, Deepak Srivastava

Laboratoire EM2C UPR CNRS 288, Ecole Centrale Paris

Thermal Nanosciences Group - volz@em2c.ecp.fr

Nanoelectronics: Concept, theory and Modeling, – Cargèse, France – October 24th 2012

Heat carries in non-metals 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

Eks

t hwks

. nks

t 1

2

w

kaK

mcos

ka

2

w 2K

amsin

ka

2

k

w

m&&un K 2un un1 un1

w

kaK

m

Acoustics: Coherent Phonons

Continuous limit k=>0

k

w

Cwvw .w dw0

wmax

Heat Flux: the Phonon Gas

&&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(, w, 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) dk ~ 1 dk

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

3D (bulk) D(k) dk~ k2 dk

Nanostructures have exceptional thermal conductivities

Carbon Nanotubes

2400-3000 W/mK@RT

Silicon Nanowires

1-3 W/mK@RT

WASTED HEAT RECOVERY

US: 30% of the world energy consumption

The Non-Dimensioned Figure of Merit ZT Qualifies TE Materials

TE Applications are mostly ‘Niche’ Applications

-Laser, PCR

Large scale applications are still expected

CAR INDUSTRY

What are the Physical Mechanisms underlying TE Properties

Nanostructured TE Material Concept was launched by Dresselhaus

…but electron design did not yield significant ZT improvement.

However, phonon thermal conductivity reduction is possible.

Si

Ge

Ge

High ZT Superlattices

Boltzmann Equation Predictions Match Experimental Data

G. Chen

1998

In the thin layer limit, phonon transport within each layer is ballistic, and the TBR

dominates the effective thermal conductivity of superlattices.’ Gang Chen PRB, 57, 23,

1998

Confinement should also contribute to the

thermal conductivity decay in films

Alexander Balandin

1998 ‘We show that strong modification of phonon group velocities due to spatial confinement

leads to a significant increase in the phonon relaxation rates.

Modification of the lattice thermal conductivity by confined phonon modes opens up

a novel tuning capability of thermoelectric properties of heterostructures, and may lead

to a strong increase of ZT in specially designed semiconductor nanostructures.’

Strain Effects strongly affect thermal conductivity showing importance of

interface scattering

Experiences

Experimental results - T. Borca-Tasciuc, G. Chen BOLTZMANN - G. CHEN

Si/Ge superlattices

SV, Saulnier, Chen, Beauchamp, Microelectronics Journal, 31, 815, 2000.

According to Molecular Dynamics technique, interfacial roughness

explains the experimental trend

Daly, Maris, Imamura, Tamura, PRB, 66, 24301, 2002.

EXPERIMENTAL DATA MD DATA

Superlattices have provided a Breakthrough in TE history

ZT=S2T/

Thermal Conductivity of Thermoelectric Material Superlattices

is lower than Bulk ones

p.597

Phonon Scatterers Thermal Phononic Crystals

Phonon ‘Particle’ Phonon ‘Wave’

High ZT Nanoparticles?

OPENING Band Gaps DESIGNING Impurity Size

Alloying scatter high frequency phonons.

How to break middle frequency phonons?

Si/Ge Thermal Phononic Crystal Thermal Conductivity as Low as 0.2W/mK

J.N. Gillet, Y. Chalopin, SV, Journal of Heat Transfer, 131, 043206 (2009)

Can Middle Frequency Phonons be Scattered by 10nm Nanoparticles

Thermal Conductivity below the Alloy Limit was Obtained with Nanoparticles

NPs however deteriorate TE properties

Impact of Nanoparticles on ZT was proven but in conventional TE compounds

Can Nanowires also Improve ZT?

G bulkD2

L

κbulk is the bulk thermal conductivity D : diameter L : length Λ : mean free path (100nm in Si) Cv: heat capacity Vp : phonon velocity (6000 m/s)

regime

Fourier law

• D,L >>

G D

Bulk

D2

L

1

e

1

1

DEffective MFP

• D ~< Λ and L>>

• D < Λ and L<

G CvvpD2

Ballistic regime

3D: Sharvin Law

SMOOTH SURFACES,

NANOJUNCTIONS

1D: Quantum of Conductance

Is the 1D behaviour at low temperatures impacted by reflections

at nw/substrate interface?

1D in k-space

Quantum of Conductance

K. Schwab, E. A. Henriksen, J. M. Worlock

and M. L. Roukes, Nature 404, 974 (2000)

L. G. C. Rego and G. Kirczenow, Phys Rev. Lett. 81, 232 (1998)

Qb Qw

The contact conductance includes nw and substrate contributions

Diffuse Mismatch Model for Transmission:

The contact resistance is predominant compared to the nw one

The density of modes is lower in the substrate at low temperatures

TL

TR 1D DOS

(k)

?

?

T

Excited

Modes 1D WIRE

3D

SUBSTRATE

Experiments tend to confirm this trend

T3

T3 T2

Metal nanowires also have predominant contact resistances

at higher electron density

R. Venkatesh, Y. Chalopin, J. Amrit, SV, PRB 83, 115425 (2011)

Is a Nanojunction a good TE system?

MEMS Actuation allows forming and characterizing Nanojunctions

GS1/2 GS

1/2 TA TA TS

TH G

G GSTS

TH TS

The constriction diameter reduces with elongation

Experiments agree with a Ballistic Thermal Conductance Model

before after

30nm

GJex GS

TSTH TS

D=7nm D=19nm D=38nm

1

3

5

1

3

5

Theory GJth Cp vSJ

Experiments

Jalabert, Sato, Ishida, Fujita, Chalopin, SV, Nanoletters, 12, 5213–5217, 2012

Rough Si Nanowires are relevant candidates for improved ZT

ZT=S2T/ Diameter=48nm

CONCLUSION on NANOWIRES and NANOJUNCTIONS

Quantum of Conductance:

At low temperatures, Heat flux in 1D Si Nanowires is

dominated by CONTACT RESISTANCE .

A similar but less drastic behaviour is observed in

metal nws.

Nanojunctions:

Ballistic Heat Conduction was shown in the 400-500K

range in short nanojunctions.

Conclusions on ZT

-Superlattices, Nanoparticles and Rough NWs present High ZT values

because of enhanced Phonon Scattering.

-Nanostructuraction has yielded unequalled ZT values (ZT=2-3).

-Bulk TE materials can not be obtained by atomic scale fabrication

techniques (MBE) and alternative routes are being explored.

-Large scale applications remain quite out of reach. Restrictions on TE

materials make these expectations even more difficult.

-Cost effective Thermoelectric materials remains an option:

ZT also depends on $

-But how to Improve electronic properties?

2007

2010

THANK YOU

FOR YOUR ATTENTION

Collaborators:

Team:

Y. Chalopin (CNRS)

T. Antoni (Ass. Prof.)

T. Dumitrica (Inv. Prof.)

Pdocs:

J. Ordonez

O. Pokropivny

PhDs:

Y. Ni, S. Xiong, L. Tranchant

W. Kassem, J. Jaramillo

A.Ramière, H. Han

B. Latour, J. Soussi

Abroad

G. 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)

A.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 Network

Thermal Nanosciences

and NanoEngineering

Round Table: Thermoelectric energy conversion, insights,

prospects for real applications?

-2D Electron: Graphene, SrTiO2…

-Magnetic Tunnel Junctions

-3 or 4 terminals devices, Chaos, Fluctuations