1

Thermoelectric power generation-materials

TZTρλα 2

=what makes a good thermoelectric:

α – Seebeck coefficient - large

ρ – resistivity - small

λ– thermal conductivity - small

- development of novel materials

- material tailoring – crystal chemistry

- composites–microstructure,nanostructure

up-to-date best bulk thermoelectrics: - Bi 2Te3/Sb2Te3, PbTe, Si-Ge

NEW BULK MATERIALS:Skutterudites, Heussler alloys, complex chalcogeni des, oxides

Figure of Merit

ZT

conflicting requirements

2

Classical guidelines for thermoelectric materials :- semiconductors, but which???

TZTlatticeelectron )(

2

λλρα

+=

EF should be at the edge of the band, sharp variation ofDOS,�α ~ ± 200 µV/K

23* )(m

latticeλµ highest as possible

Semiconductors with a high mobility (µ), high effective mass (m*) and lowthermal conductivity of the lattice (λlattice)

B.C.

B.V.

EF

EF

EG

� Boltzman Equation of transport

�Kubo formalism…

To ajust Fermi level EF (optimal doping,…)

Electronic structure, scattering mechanism, phonon spectrum,…

Two approaches:

α, ρ , λ

Increase of ZT

3

For almost all typical thermoelectric materials, namely low gap semiconductorslow gap semiconductors , if doping is increased, the electrical conductivity increases but the Seebeck coefficient is reduced.

S

S2σσσσ

ρα 2

=fP

Which materials are interesting ???– semiconductors –

Optimizing power factor highly doped semiconductors

4Best compromise still highly doped semiconductors (λ = λe + λr)

Insulator Semi-conductor Métal

λe

λr

λα

ρ

Concentration de porteurs (cm 3)

αρλZ

Z

1014 102010181016 1022

(Electronic thermal conductivity

(Lattice thermal conductivity

Ideal material : α ↑, ρ ↓, λ↓ but α ↑ ρ ↑ et ρ ↓ λ↑⇔ ⇔

T = 300 K

The Thermoelectric Figure of Merit (ZT)

ρλα 2

=ZTZTρλα 2

=Optimizing Figure of merit ZT

minimize the thermal conductivity

conflicting requirements

5

1930 - 1995 : Classical materials…Limits in ZT (~ 1) …Limits in temperature (T< 250 oC)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 200 400 600 800 1000 1200

np

ZT

Temperature (K)

β-FeSi2

(Pb,Sn)(Te,Se)

TAGS(Bi,Sb)

2(Te,Se)

3BiSb

Si-Ge

0.2 T

TAGS : (AgSbTe2)1-x(GeTe)x

• SC low gap + heavy elements• ZT optimized only for narrow temperature window• At T ~ 300 K used solutions based on Te, namely (Bi2Te3)• ZT ~ 1 standard

61 - 75

76 - 06

6

Since 1995 - … : New orientations

Environmental problems (Kyoto…), energy, waste heat, etc � New interest in thermoelectricity (USA, Japon, Europe is still on the tail….) Proposal of new concepts to target new matrials, need systems with ZT>1

Identification of new bulk materials….

Thermoelectrics based on lowered

dimensionality,nanostructuring,…

3

2

1

01940 1960 1980 2000

ZT

?1 2

7

Motivation for Nanotechnology in Thermoelectricity

ZTS T=

2σκ

Seebeck Coefficient ConductivityTemperature

ThermalConductivity

ZT ~ 3 for desired goal

Difficulties in increasing ZT in bulk materials:

S ↑ ⇐⇒ σ ↓

σ ↑ ⇐⇒ S ↓ and κ↑

⇒ A limit to Z is rapidly obtained in conventional materials

⇒ So far, best bulk material (Bi0.5Sb1.5Te3)has ZT ~ 1 at 300 K

Low dimensional physics gives additional control:• Enhanced density of states due to quantum confinement effects

⇒ Increase S without reducing σ• Boundary scattering at interfaces can reduce κ more than σ• Possibility of materials engineering to further improve ZT

(2D quantum wells, 1D nanowires, 0D quantum dots)1

8

Low dimensionality- impact on thermopower, thermal conductivity

3 D 2 D 1 D 0 D

- (D.O.S.) more favourable (stronger dependence of DOS on E)

� increase of α without increasing ρ- additional degree of freedom (size) for tailoring of the transport

- possibility to explore the anisotropy of transport properties

- chance to decrese λlattice due to phonon scattering on interfaces

- ZT0D > ZT1D > ZT2D > ZT3D

D.O

.S.

D.O

.S.

D.O

.S.

D.O

.S.

E E E E

30 nm

1

9

Plots de PbSeTe dans des couches de PbTe

Transport in the ab-plane

• Type n : ZT ~ 1,5 à 300 K ( compared to 0,45 pour PbTe bulk), • ZT ~ 3,5 à 570 K• Type p : ZT ~ 1,1 à 300 K.

DUE TO:DUE TO:- Confinement of charge carriers in 2D- Decrease of lattice thermal conductivity due to scattering

-EXAMPLE (laboratory):

• Cooling: junction cooled 44 K below RT (31 K pour Bi2Te3) • Power generation : 2,2 W/cm2 for ∆T = 220 K

(Harman et al., J. Electron. Mater., 29, L1, 2005)

Theoretical predictions – decrease of the dimensionality

Heterostructures PbSeTe/PbTe (MBE)

~ 100 µm

(Harman et al., Science., 297, 2002)

(Harman et al., APL., 88, 243504, 2006)

Type n

0.0

1.0

2.0

3.0

4.0

250 300 350 400 450 500 550 600

ZT

T (K)

PbTe massif

1

10

Superstructures based on (Bi,Sb,Te,Se) - MOCVD

Transport perpendiculaire Bi2Te3

Sb2Te3

Type p Type n

Bi2Te3-xSex

Bi2Te3

~ 20 - 180 Å

Negligible confinement of charge carriers BUTBUT

Interfaces block short wavelength phonons!

(Venkatasubramanian et al., PRB, 60, 3091, 2000, Nature, 413, 2001)

Thermoelectric Thermoelectric performanceperformance

Type n : ZT ~ 1,4 à 300 KType p : ZT ~ 1,7 - 2,4 à 300 K

1.5

2.0

2.5

3.0

3.5

300 320 340 360 380 400

ZT

T (K)

Type p

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200

λ R (

W/m

K)

Superlattice period (Å)

Type p

(BiSb)Te3

Bi2Te3, Sb2Te3

0,4 – 0,7 µm

(www.nextremethermal.com)

SPIN off SPIN off technologytechnology

1

11

Bulk Materials tailoring – decrease of thermal conductivity

k [W

/m-K

]

A B

Alloy Limit

Impurity and alloy atoms scatter only short - λ phonons

that are absent at low T!

TZTρλα 2

=Alloy Limit of Thermal Conductivity

1

12

NANOSTRUCTURING- decrease of thermal conductivity: Phonon Scattering with Imbedded Nanostructures

Frequency, ω ωmax

eb

v

Atoms/Alloys

Nanostructures

Phonon Scattering

Long-wavelength or low-frequency phonons are scattered by imbedded nanostructures!

Spectral distribution of phonon energy ( eb) & group velocity (v) @ 300 K

Fre

quen

cy,ω

Wave vector, K0 π/a

LATA

LO

TO

Fre

quen

cy,ω

Wave vector, K0 π/a

LATA

LO

TO

TZTρλα 2

=

1

13

NANOSTRUCTURING- decrease of thermal conductivity: Phonon Scattering on nanostructure interface

electron

conductorinsulator

d < λdBe

phonond > lmfp

ph

1

14

Complex material science and advanced synthesis technology:-Open structures and very complex crystal structures with many atoms withdifferent mass in unit cell can� identify materials with a weak link between thermal and electric properties� concept of «Phonon Glass Electron Crystal (called PGEC)», G. Slack, 1994.

ADVANCED BULK MATERIALS

� � � � �

� � � � �

� � � � �

--

--

-

-

« Phonon Glass » � lphonon very low λr very low

« Electron crystal » � lelectron highµ also high

&

2

15

Materials with open crystallographic positions which can serve as efficient “host” for inserted atoms , only weakly bonded with basic structural frame �can vibrate around central position (« rattlers ») � heat carrying phonons experience thus important damping from these local Einstein modes….

Open crystal structures : materials with «cages »

Interesting materials…

PhononDiffusion

Skutterudites(Co4Sb12)

Clathrates(Ba8Ga16Ge30)

2

16

TZTρλα 2

=

Phonon

Scattering

RATTLING ATOMS

Clathrates(Ba8Ga16Ge30)

Skutterudites(Co4Sb12)

Decrease of thermal conductivity via phonon –phonon scattering 2

17

Partially filled skutterudites based on Co4Sb12

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

200 300 400 500 600 700 800 900

ZT

T (K)

n-Ba0.05

Yb0.09

Co4Sb

12

Co4Sb

12

p-Ce0.85

Co0.5

Fe3.5

Sb12

Rich class of compounds, voids, rattling, filling, doping,…

Materials n et p with ZT > 1 can be obtained…

2

18

High Temperature High Temperature Oxide Oxide ThermoelectricsThermoelectrics

• Layered cobaltites- Ca3Co4O9

- (Bi,Pb) 2Sr2Co1.82Oy- NaxCoO2

• 3D - cobaltites• 2D - cuprates

• 3D - Manganites- Ca0.95La0.05MnO3

• 3D - Titanates- Sr0.95La0.05TiO3

• Spinels

αααα > 0

αααα < 0

2New class of compound, metallic oxides, stable chemically at high temperatures, studied are cobaltites and manganites, then chromites,..

OCaCo, Mn

19

0.0

0.5

1.0

1.5

2.0

2.5

3.0

1950 1960 1970 1980 1990 2000 2010Time

n-BiSb

p-CsBi4Te

6

Bi alloysp-Bi

2Te

3& Bi

n, p-Bi2Te

3

(Bi,Sb)2Te

3& Bi

2(Te,Se)

3

optimized alloys

p-Bi2Te

3/Sb

2Te

3SL

p-ZnSb

n, p-PbTen, p-SiGe

p-TAGSp-Zn

4Sb

3

Skutterudites

n-PbSeTe/PbTe SL

n-Bi2Te

3/Bi

2(Te,Se)

3SL

n,p-PbEuTe/PbTe SL

AgPb10

SbTe12

ZT

superstructures

bulk

Temperatures >> 300 KTemperatures ~ 300 K

Temperatures < 300 K

Gradual increase of ZT during last 60 years…