Heat and Nanotechnologies:Focus on Thermoelectricity

Sebastian VolzYann 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 ParisThermal Nanosciences Group - volz@em2c.ecp.fr

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

Heat carries in non-metals are SOUND PARTICLESHeat carries in non-metals are SOUND PARTICLES or PHONONs, or PHONONs,the quanta of lattice vibrational energythe quanta of lattice vibrational energy

i-1 i i+1

a

un=u.expi(kna-t)

FFijij = K.(u = K.(uj- j- uuii))

Periodic Boundary Conditions:Periodic Boundary Conditions:

k = n . 2k = n . 2/L/LDensity of states

E

kst( ) =hks. nks t( ) +

12

⎛

⎝⎜⎞

⎠⎟

€

∂∂k

=aK

mcos

ka

2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

=2K

amsin

ka

2

⎛

⎝ ⎜

⎞

⎠ ⎟

k

m&&un =−K 2un −un−1 −un+1( )

∂∂k

=aK

m

Acoustics: Coherent Phonons

Continuous limit k=>0

k

ϕ = Cωvω .Λω dω0

ωmax

∫

Heat Flux: the Phonon Gas

ρ&&u = K '

∂2u

∂x2

Phonons form a GAS of particles to propagate heatPhonons form a GAS of particles to propagate heat

Knudsen Transport Applies

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

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

Kn>1Kn>1: Boundary scattering predominates over diffusive scattering : Boundary scattering predominates over diffusive scattering

L

ConfinementConfinement: Cavity modes appear if L< Wavelength: Cavity modes appear if L< Wavelength

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

un ~ ~ expi(kna-t)+ expi(-kna-t) ~ cos(kna)e~ cos(kna)e-i-it

e e ikLikL=e =e ikaika=0 =0

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

The number of phonon modes depends on The number of phonon modes depends on DimensionnalityDimensionnality

Dimension: Number of States /dk:

=1/3 =1/3 CC v 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 conductivitiesNanostructures have exceptional thermal conductivities

Carbon NanotubesCarbon Nanotubes2400-3000 W/mK@RT2400-3000 W/mK@RT

Silicon NanowiresSilicon Nanowires1-3 W/mK@RT1-3 W/mK@RT

WASTED HEAT RECOVERYUS: 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 G. Chen 19981998

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 BalandinAlexander Balandin19981998 ‘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. ChenBOLTZMANN - G. CHEN

Si/Ge superlatticesSi/Ge superlattices

  SV, Saulnier, Chen, Beauchamp, Microelectronics Journal, SV, Saulnier, Chen, Beauchamp, Microelectronics Journal, 3131, 815, 2000., 815, 2000.

According to Molecular Dynamics technique, interfacial roughness explains the experimental trend

Daly, Maris, Imamura, Tamura, PRB, 66, 24301, 2002.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.597p.597

Phonon Scatterers Thermal Phononic Crystals

Phonon ‘Particle’ Phonon ‘Wave’

High ZT Nanoparticles?

OPENING Band GapsDESIGNING 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?Can Nanowires also Improve ZT?

G =κbulk

D2

L

κbulk is the bulk thermal conductivityD : diameterL : lengthΛ : mean free path (100nm in Si)Cv: heat capacityVp : phonon velocity (6000 m/s)

Fourier law

• D,L >>

G =D

κ Bulk

D2

L⎛

⎝⎜⎞

⎠⎟1

e

=1+1DEffective 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 Is the 1D behaviour at low temperatures impacted by reflections at nw/substrate interface?at nw/substrate interface?

1D in k-space1D in k-space

Quantum of ConductanceQuantum of Conductance

K. Schwab, E. A. Henriksen, J. M. Worlockand 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 contributionsThe contact conductance includes nw and substrate contributions

Diffuse Mismatch Model for Transmission:Diffuse Mismatch Model for Transmission:

The contact resistance is predominant compared to the nw oneThe contact resistance is predominant compared to the nw one

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

TL

TR1D DOS

(k)

??

??

T

ExcitedModes

1D WIRE

3D SUBSTRATE

Experiments tend to confirm this trendExperiments tend to confirm this trend

T3

T3T2

Metal nanowires also have predominant contact resistances Metal nanowires also have predominant contact resistances at higher electron densityat higher electron density

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

Is a Nanojunction a good TE system?Is a Nanojunction a good TE system?MEMSMEMS Actuation allows forming and characterizing Actuation allows forming and characterizing NanojunctionsNanojunctions

GS1/2 GS

1/2TATA TS

TH G

€

G = GS

ΔTS

ΔTH − ΔTS( )

The constriction diameter reduces with elongationThe constriction diameter reduces with elongation

Experiments agree with a Experiments agree with a Ballistic Thermal Conductance Ballistic Thermal Conductance ModelModel

before after

30nm

GJex =GS

δTS

δTH −δTS

D=7nm

D=19nm

D=38nm

1

3

5

1

3

5

TheoryGJ

th =Cp vSJ

Experiments

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

Rough Si Nanowires Rough Si Nanowires are relevant candidates for improvedare relevant candidates for improved ZTZT

ZT=S2T/Diameter=48nDiameter=48nmm

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?

20072007

20102010

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)•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

Round Table: Thermoelectric energy conversion, insights, prospects for real applications?

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