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
Fij = K.(uj- ui)
a
i-1
i
i+1
ka 
K
sin 
am  2 
ka 
w
aK

cos 
 2 
k
m
w
&n  K 2un  un1  un1 
mu&
w 2

un=u.expi(kna-wt)

k
Periodic Boundary Conditions:
k = n . 2/L
Density of states
Eks

1
t  hw ks . nks t  
2



Phonons form a GAS of particles to propagate heat
Acoustics: Coherent Phonons
w
Continuous limit k=>0
2u
u&& K ' 2
x
w
aK

k
m
k
Heat Flux: the Phonon Gas

w max

Cw vw .w dw
0
Knudsen Transport Applies
Phonon Wien’s Wavelength: 3nm (300K)
Mean free path: 1-1000nm
Kn>1: Boundary scattering predominates over diffusive scattering
L
=1/3 C v 
p(, w, pol, )
Confinement: Cavity modes appear if L< Wavelength
Periodicity: e ik(L+x)=e
ikx
e ikL=e
ika=0
un ~ expi(kna-wt)+ expi(-kna-wt) ~ cos(kna)e-iwt
=1/3 C v 
a STEADY WAVE has ZERO group velocity
The number of phonon modes depends on Dimensionnality
k-space
Dimension:
Number of States /dk:
1D (wire)
2D (film/SR)
D(k) dk ~ 1 dk
D(k ) dk ~ k dk
3D (bulk)
D(k) dk~ k2 dk
=1/3 C v 
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.
High ZT Superlattices
Ge
Si
Ge
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
Experimental
results
- T. Borca-Tasciuc, G. Chen
BOLTZMANN
- G. CHEN
Experiences
Si/Ge superlattices
SV, Saulnier, Chen, Beauchamp, Microelectronics Journal, 31, 815, 2000.
According to Molecular Dynamics technique, interfacial roughness
explains the experimental trend
EXPERIMENTAL DATA
Daly, Maris, Imamura, Tamura, PRB, 66, 24301, 2002.
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
High ZT Nanoparticles?
Alloying scatter high frequency phonons.
How to break middle frequency phonons?
DESIGNING Impurity Size
Phonon Scatterers
Phonon ‘Particle’
OPENING Band Gaps
Thermal Phononic Crystals
Phonon ‘Wave’
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?
• D,L >> 
regime
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)
• D ~< Λ and L>> 
Effective MFP
• D < Λ and L< 
Fourier law
1
1 1
 
e  D
G   bulk
 D2
L
D
 D2 
G    Bulk

L 
Ballistic regime
3D: Sharvin Law
G  Cvvp D2
1D: Quantum of Conductance
SMOOTH SURFACES,
NANOJUNCTIONS
Is the 1D behaviour at low temperatures impacted by reflections
at nw/substrate interface?
1D in k-space
K. Schwab, E. A. Henriksen, J. M. Worlock
and M. L. Roukes, Nature 404, 974 (2000)
Quantum of Conductance
L. G. C. Rego and G. Kirczenow, Phys Rev. Lett. 81, 232 (1998)
The contact conductance includes nw and substrate contributions
Qw
Qb
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
(k)
?
TL
?
TR
1D DOS
Excited
Modes
1D WIRE
3D
SUBSTRATE
T
Experiments tend to confirm this trend
T2
T3
T3
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
G  GS
TS
TH  TS  T
H
TA
GS1/2
TS
G
GS1/2
TA
The constriction diameter reduces with elongation
Experiments agree with a Ballistic Thermal Conductance Model
Jalabert, Sato, Ishida, Fujita, Chalopin, SV, Nanoletters, 12, 5213–5217, 2012
Experiments
GJex  GS
Theory
TS
TH  TS
GJth   Cp vSJ
D=7nm
5
D=19nm
3
1
D=38nm
1
before
after
3
5
30nm
Rough Si Nanowires are relevant candidates for improved ZT
Diameter=48nm
ZT=S2T/
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?
Collaborators:
2007
European CNRS Network
Thermal Nanosciences
and NanoEngineering
2010
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
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)
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)
THANK YOU
FOR YOUR ATTENTION
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