Thermoelectric power generation-materials what makes a good thermoelectric: α 2 conflicting ZT = T requirements ρλ α – Seebeck coefficient - large - development of novel materials ρ – resistivity - small - material tailoring – crystal chemistry λ– thermal conductivity - small - composites–microstructure,nanostructure

up-to-date best bulk thermoelectrics: - Bi 2Te 3/Sb 2Te 3, PbTe, Si-Ge

NEW BULK MATERIALS: Skutterudites, Heussler alloys, complex chalcogenides, oxides

Figure of Merit ZT 1 Classical guidelines for thermoelectric materials : - semiconductors, but which???

α, ρ , λ Electronic structure, scattering mechanism, phonon spectrum,…

Two approaches:  Boltzman Equation of transport Kubo formalism…

Increase of ZT α 2 ZT = T ρ λ + λ ( electron lattice ) B.C.

EF To ajust Fermi level EF (optimal doping,…) EG E EF should be at the edge of the band, sharp variation of F DOS,
α ~ ± 200 µV/K

µ 3 B.V. (m* ) 2 highest as possible λ lattice Semiconductors with a high mobility (µ), high effective mass (m*) and low λ 2 thermal conductivity of the lattice ( lattice ) Which materials are interesting ??? – semiconductors – Optimizing power factor highly doped semiconductors

S2σσσ

S

For almost all typical thermoelectric materials, α 2 namely low gap semiconductors , if doping is P = increased, the electrical conductivity increases but f ρ the Seebeck coefficient is reduced. 3 The Thermoelectric Figure of Merit (ZT) Optimizing Figure of merit ZT α 2 α 2 ZT = T Z = minimize the thermal conductivity ρλ ρλ

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

Insulator Semi-conductor Métal requirements α Z λ

ρ α ρ λ e (Electronic thermal conductivity λ Z T = 300 K

λ r (Lattice thermal conductivity 10 14 10 16 10 18 10 20 10 22 Concentration de porteurs (cm 3)

Best compromise still highly doped semiconductors (λ = λ + λ ) e r 4 1930 - 1995 : Classical materials… Limits in ZT (~ 1) …Limits in temperature (T< 250 oC)

1.4

TAGS n 1.2 BiSb (Bi,Sb) (Te,Se) p TAGS : (AgSbTe 2)1-x(GeTe)x 2 3 0.2 T 1 (Pb,Sn)(Te,Se) Si-Ge 0.8 ZT 0.6 61 - 75 0.4 76 - 06

0.2 β-FeSi 2 0 0 200 400 600 800 1000 1200 Temperature (K)

• SC low gap + heavy elements • ZT optimized only for narrow temperature window

• At T ~ 300 K used solutions based on Te, namely (Bi 2Te 3) • ZT ~ 1 standard 5 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

Thermoelectrics based on Identification of new lowered bulk materials…. dimensionality,nanostructuring, … ZT 3 ? 1 2 2

1

0 1940 1960 1980 2000 6 Motivation for Nanotechnology in Thermoelectricity 1 (2D quantum wells, 1D nanowires, 0D quantum dots)

Difficulties in increasing ZT in bulk materials: Seebeck Coefficient Conductivity Temperature S ↑ ⇐⇒ σ ↓ ST2σ ZT = σ ↑ ⇐⇒ S ↓ and κ↑ κ Thermal ⇒ A limit to Z is rapidly obtained in Conductivity conventional materials ZT ~ 3 for desired goal ⇒ So far, best bulk material (Bi 0.5 Sb 1.5 Te 3) 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

7 Low dimensionality- impact on thermopower, thermal conductivity 1

30 nm

3 D 2 D 1 D 0 D D.O.S. D.O.S. D.O.S. D.O.S. E E E E

- (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 λ - chance to decrese lattice due to phonon scattering on interfaces 8 - ZT 0D > ZT 1D > ZT 2D > ZT 3D Theoretical predictions – decrease of the dimensionality 1 Heterostructures PbSeTe/PbTe (MBE) Transport in the ab-plane 4.0 Type n 3.0

~ 100 µm 2.0 ZT

1.0 PbTe massif

0.0 250 300 350 400 450 500 550 600 T (K) Plots de PbSeTe dans des couches de PbTe (Harman et al., J. Electron. Mater., 29 , L1, 2005)

• 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: - Confinement of charge carriers in 2D - Decrease of lattice thermal conductivity due to scattering -EXAMPLE (laboratory): (Harman et al., Science., 297 , 2002)

• Cooling: junction cooled 44 K below RT (31 K pour Bi 2Te 3) • Power generation : 2,2 W/cm 2 for ∆T = 220 K 9

(Harman et al., APL., 88 , 243504, 2006) Superstructures based on (Bi,Sb,Te,Se) - MOCVD

(Venkatasubramanian et al., PRB, 60 , 3091, 2000, Nature, 413 , 2001) 1

1.2

Bi Te , Sb Te 1.0 2 3 2 3 Type p Type n 0.8 Transport Sb Te Bi Te Se µ 2 3 2 3-x x 0,4 – 0,7 m perpendiculaire ~ 20 - 180 Å 0.6 Bi 2Te 3 Bi 2Te 3 (W/mK) R

λ (BiSb)Te 0.4 3

0.2 Type p 0.0 Negligible confinement of charge carriers BUT 0 50 100 150 200 BUT Superlattice period ( Å)

3.5 Interfaces block short wavelength phonons! 3.0 Thermoelectric performance 2.5 ZT Type p : ZT ~ 1,7 - 2,4 à 300 K Type n : ZT ~ 1,4 à 300 K 2.0 Type p 1.5 SPIN off technology 300 320 340 36010 380 400 (www.nextremethermal.com) T (K) Bulk Materials tailoring – decrease of thermal conductivity 1 Alloy Limit of Thermal Conductivity α 2 ZT = T ρλ

Alloy Limit k [W/m-K] k

A B

Impurity and alloy atoms scatter only short - λ phonons 11 that are absent at low T! NANOSTRUCTURING- decrease of thermal conductivity: Phonon Scattering with Imbedded Nanostructures 1

LO ωω TO

Spectral

Frequency, Frequency, TA distribution of LA phonon v energy ( eb) & group velocity (v) @ 300 K 0 Wave vector, K π/a

Phonon Scattering e b Nanostructures α 2 ZT = T Atoms/Alloys ρλ

ω Frequency, ω max

Long-wavelength or low-frequency phonons 12 are scattered by imbedded nanostructures! NANOSTRUCTURING- decrease of thermal conductivity: Phonon Scattering on nanostructure interface 1

phonon ph d > lmfp insulator conductor

electron λ e 13 d < dB ADVANCED BULK MATERIALS 2

Complex material science and advanced synthesis technology: - Open structures and very complex crystal structures with many atoms with different 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.

- - - - - -

« Phonon Glass »  lphonon very low « Electron crystal »  l high λ & electron r very low µ also high

14 Open crystal structures : materials with «cages » 2

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….

Phonon Diffusion

Interesting materials…

Clathrates Skutterudites 15

(Ba 8Ga 16 Ge 30 ) (Co 4Sb 12 ) Decrease of thermal conductivity via Skutterudites (Co Sb ) phonon –phonon scattering 4 12 2 α 2 ZT = T ρλ RATTLING ATOMS

Scattering

Phonon

Clathrates 16 (Ba 8Ga 16 Ge 30 ) Partially filled skutterudites based on Co 4Sb 12 2

1.6

1.4 n-Ba Yb Co Sb 0.05 0.09 4 12 1.2

1.0

0.8 ZT Rich class of compounds, voids, rattling, filling, 0.6 doping,… 0.4 p-Ce Co Fe Sb 0.85 0.5 3.5 12 0.2 Co Sb Materials n et p with ZT > 1 can be obtained… 4 12 0.0 200 300 400 500 600 70017 800 900 T (K) HighHigh TemperatureTemperature OxideOxide ThermoelectricsThermoelectrics New class of compound, metallic oxides, stable 2 chemically at high temperatures, studied are cobaltites and manganites, then chromites,..

• Layered cobaltites - Ca Co O 3 4 9 O - (Bi,Pb) 2Sr 2Co 1.82 Oy ααα > 0 - Na xCoO 2 Ca • 3D - cobaltites Co, Mn • 2D - cuprates

• 3D - Manganites

- Ca 0.95 La 0.05 MnO 3 • 3D - Titanates ααα < 0 - Sr 0.95 La 0.05 TiO 3 • Spinels

18 Gradual increase of ZT during last 60 years…

3.0 Temperatures >> 300 K superstructures 2.5 Temperatures ~ 300 K p-Bi Te /Sb Te SL 2 3 2 3 AgPb SbTe Temperatures < 300 K 10 12

2.0 n-PbSeTe/PbTe SL bulk n,p-PbEuTe/PbTe SL ZT 1.5 Skutterudites n-Bi Te /Bi (Te,Se) SL p-TAGS 2 3 2 3 p-Zn Sb 4 3

optimized alloys 1.0 n, p-PbTe n, p-SiGe (Bi,Sb) Te & Bi (Te,Se) p-CsBi Te 2 3 2 3 4 6 n-BiSb

n, p-Bi Te 0.5 2 3 p-ZnSb p-Bi Te & Bi 2 3 Bi alloys 0.0 1950 1960 1970 1980 1990 2000 2010 Time 19