Nowadays thermoelectric materials

Sylvie HEBERT, Romain VIENNOIS

Cours École TE juin 2014

Nowadays thermoelectric materials


TE glasses and polymers

Chalcogenides

Half-Heusler

Silicides

Nanocage compounds

Zintl compounds

Generality on TE materials

OUTLINE

Dimensionless Figure of Merit for each material

=> Minimization of the lattice thermal conductivity kl

=> Maximization of the power factor a2s

ZT = a2sT/(ke+kl)

Figure of Merit of the TE materials


What type of conducting materials ?

Weakly correlated materials

=> Degenerated semiconductors or semimetals

Charge carrier concentration: about 1019-1020 cm-3

ZT = a2sT/(ke+kr)

Insulators


Metals Semiconductors Semimetals

Characteristics of good TE semiconductors and semimetals

Effective mass m*j of each j band must be maximized

Mobility mj of each j band must be maximized

b T3/2 Nj m*j3/2mj /kr

Degeneracy of the bands Nj must be maximized => multivalley semiconductors

Antagonist properties to be optimized


Low electronegativity difference

Other points to take into account

Non-parabolicity (especially for degenerate case) => energy dependence of the m*

Scattering diffusion mechanisms of the electrons

Presence of several bands crossing the Fermi level and the bipolar contributions

Boson drag of the electrons (more often at low T)

Ideal electronic structure of poor or low charge carrier density metals


Suitable band structure:

- Broad band with weak m* for increasing s

- Narrow band with large m* for increasing a

Jeong JAP 2012

Mahan PNAS 1996

Depending of the case and of the band structure shape with the 3 following parameters :

Other possibility : Resonant levels

D(E) M(E) = v(E)D(E) vx+ (E)

Tse TE HB 2005

Example of bulk materials:

Applications to bulk materials

Could be a possibility for correlated materials ?

skutterudite RFe4Sb12 (70 mV/K)

Yb14MnSb11 or La3-xCh4 (Ch = S, Se or Te)

Strongly correlated materials

Bentien, EPL (2007)

Effective mass m* renormalization m* by the electronic correlations

Example : cobaltates, Ce- or Yb- based compounds, skutterudites at low T, strongly correlated

semiconductor FeSb2 (a2s = 2,3 mW/K2.cm, record PF)

a is one order of magnitude larger in correlated metals than in normal metals


Minimization of the thermal conductivity

ZT = a2sT/(ke+kr)

kr must be minimized: kr CV vg2 t

Heat carriers = acoustical phonons

Very good TE materials : phonon glass – electron crystal

Slack, CRC Handbook(1995)

The rate of the thermal waves, and therefore vg, must be minimized

The thermal waves must be scattered and therefore one needs to reduce their life time t


ke is proportional to s : ke = T s L L = L0 = p2/3(kB/e)2 for the metals

L depends to electron scattering processes

Possibility of additional bipolar contribution


-Complex crystal structure, heavy atoms vg

-structural unstability, soft modes vg

-alloy point defects, vacancies t

-scattering by low-energy optical modes t

-nanometric size inclusions (nano-composites) t

-structural disorder t

-Large anharmonicity t

-electron-phonon scattering t



The anharmonicity of each vibrational mode is characterized by its Grüneisen parameter g :

w = (V/V0)g

c3(k,k’,k’’) gM/v

The Grüneisen parameter is related to the 3rd order anharmonic force constant c3(k,k’,k’’) :

kU = 𝐴𝑉𝑎𝑡

1/3𝑀𝑎𝑡 𝜃𝐷

3

𝑇𝑛2/3𝛾2

At high T, when the Umklapp process is dominating, one gets :

The Grûneisen parameter is also related to the thermal expansion.

In this case one defines the thermodynamic Grüneisen parameter as follows :

One can see that it is necessary to have large g and low qD


From Biswas NM 2012


Scattering processes scheme

Thermal conductivity kc (= 0,05 W/m.K) very weak in the layered thin film WSe2 Chiritescu, Science (2007)

Thermal conductivity k (= 0,035 W/m.K) very weak for alumine nanoparticles

Hu, APL (2007)

Toberer, JMC 2011

For comparison :

kc = 135 W/m.K in diamond Si


Choice of matérials : science criteria for optimization of ZT

Maximization of the power factor (FP) for :

Objectif :

Minimization of the phonon lpm des phonons lp without changing the electron lpm le !

Bulusu, SLM 2006

- Heavily doped multivalley narrow-gap semiconductors

- Materials with broad and narrow bands at the vicinity of EF

Minimization of the thermal conductivity by phonon scattering:

- By low-energy optical modes

=> materials based on cage and/or with strong atomic contrast

- By point defects => alloys with strong atomic contrast

- By nanostructuration => nanocomposites

- Thanks to complex crystal structure and heavy atoms

- Thanks to the large anharmonicity of the phonons

It is necessary to fully decouple electrons and phonons !

Semiconductors

Poor metals / semimetals


State-of-the art: best ZT

0 200 400 600 800 1000 1200 14000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Bi0.835

Sb0.165

Ba24

In16

Ge84

Ba8Ga

16Ge

30(In,Ce)

yCoSb

3

InyCoSb

3

(R,R',R'')yCoSb

3

SiGe alloys

PbTe-PbS alloys

PbTe alloys

Bi2-x

SbxTe

3 alloys

LaTe1.45

LAST

Mg2Si

0.6Sn

0.4

Mg2Si

0.7Sn

0.3

Half-Heusler n-type

Half-Heusler n-type

ZT

T (K)

Type n

0 200 400 600 800 1000 1200 14000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

CsBi4Te

6

Borides

Ba8Ga

16Ge

30

(Zn,Cd)4Sb

3

CeFe3.5

Co0.5

Sb12

SiGe alloys

Pb1-x

TlxTe

SnTe alloys

Pb1-x

SnxTe

1-ySe

y alloys

Bi2-x

SbxTe

3 alloys Tl

9BiTe

5

SALT

TAGS

Half-Heusler p-type

HMS Ge doped

Zn4Sb

3

ZT

T (K)

Yb14

Mn0.2

Al0.8

Sb11

Type p


Historical summary (non-exhaustive) of new TE families since 90s


1994-1995 : « phonon glass - electron crystal » => cage compounds such as skutterudites (G. Slack)

1996 : large ZT in skutterudites (B. C. Sales)

1997 : large ZT in Zn4Sb3 (T. Caillat)

1998 : large ZT in clathrates (G. Nolas)

2000 : large ZT in CsBi4Te6 (Chung)

2001 : large ZT in cobaltates (Fujita)

2005 : large ZT in half-Heusler alloys (Sakurada)

2006 : confirmation of ZT > 1 in Mg2Si alloys (Zaitsev) ; ZT > 1 in Yb14MnSb11 (Brown)

2009 : large ZT in In4-xSe3 (Rhyee) and in tetrademyte/teraedrite compounds (Skoug)

2010 : large ZT in BiCuSeO (Zhao)

2011 : first report of relatively large ZT in polymers (Bubnova)

2014 : very large ZT in SnSe (Zhao)

Amatya JEM (2012)

The abundance of Tellurium is too weak !

Material choice: technological, economical and ecological criteria


Amatya JEM (2012)

Due to request

Germanium and Gallium are too expensive

Costs of tellurium, selenium and antimony are increasing


Material cost depends on available world reserves, on the request and the production.

Case of germanium :

Although its abundancy is reasonable (1.4-1.8 ppm in the crust),

its production is weak (120 t/y !!!) => hence its high cost

Production of the main elements used in TE (2012)

Te : 215 t/y

Se : 2120 t/y

Pb : 4.4 Mt/y

Bi : 8900 t/y

Sb: 167 000 t/y

Si : 7.3 Mt/y

Particular case of Sb : with the same production there will be less than 10 y reserves !

Other applied fields are also using these elements

Te : metallurgical add, vulcanisation, PV, IR detectors, shape memory alloys

Se : Mn electrolyse, vulcanisation, painted glasses, PV

Bi : use for replacement of Pb in many applications

Sb: flam delayer (oxide), battery and even condensators, shape memory alloys

Ge : electronic including use as substrate, IR detectors, optic fibers


Toxicity issue

Nowadays materials

Elements Water risks Air risks

Dangerous

concentration in air Risk code

Te 3 2 0.1-0.5 mg/m3 T

Bi 20 mg/m3 D

Pb 2 0.5 mg/m3 T, N

Sb 2 3 0.5-1 mg/m3 Xi

Ge 3 20 mg/m3

Si 2 20 mg/m3

As 3 1 0.05 mg/m3 T, N

Tl 3 1 0.05 mg/m3 T+

Se 2 2 0.5 mg/m3 T

High toxicity risks with Tellurium


Thermodynamic stability

Thermogenerator/ sensor HT => HT range

It is fundamental to have knowledge of :

the stability of a material in the HT range and its phase diagram

Doping

Necessary to know the solubility range of the dopants

Necessary to know how the decomposition/melting temperature change with doping

Necessary to know what secondary phases can precipitate

(useful especially for nanocomposites)

Good knowledge of ternary phase diagram will be welcome

HT

Possibility of structural or order/disorder transition

Possibility of broadening ofexistence range of the materials

Evaluation of material aging

Stability and defects

CALPHAD method can be useful


Stoichiometry and defects

Ideal material => no defect

Real materials => presence of defects that can strongly change the physical properties

One can model the presence of defects via Calphad type approach

=> Link with off-stoichiometry and existence domain of the materials

In a binary AB compound, th most simple defects are:

- Vacancy type defect VA et VB.

- Antisites type defect BA et AB.

- Interstitiels type defect IA et IB.

Two types of defects:

-Exended (ex. dislocation)

-Ponctuels

Point defect complexes can exist :

Frenkel defects (VA IA ), multi-vacancies (including the Schottky defects (VA VB ), … .

Intrinsic doping due to the most stable defects

=> Defects can compensate the extrinsic doping


Mechanical stability

Case JEM 2012

Deformation experienced by the contact layer at the interface

Ravi ,JEM 2010

s = a(E/1-n) DT

ec,desaccord = asDT – acDT= DaDT

sc = (E/1-nc2) (DaDT+ DaDTnc)

s = strain due to DT

a = thermal expansion n = Poisson’s parameter E = Young’s modulus

Strain experienced by the contact layer at the interface


Rogl ,JAP 2010

Material E (GPa) a (10-5 K-1)

Si 163 0.25

Ge 128 0.57

PbTe 58 1.98

Bi2Te3 40.4 1.67

Ba8Ga16Ge30 103 1.42

CoSb3 136-148 0.91

LaFe4Sb12 141 1.17

Mg2Si 49-50 1.1

Zn4Sb3: a = 1.9-2*10-5 K-1 Yb14MnSb11: a = 1.9-2*10-5 K-1

Conventional TE materials


Freibert SS 2001


Bi-Sb alloys

Crystal structure and phase diagram

Rhombohedral structure, SG R-3m (166)

Lenoir SS 2001

Band structure of Bi-Sb


Bi-Sb alloys

Band structure and ZT of Bi-Sb


Bi-Sb alloys

Large anisotropy


Zintl-Klemm approach

Generalities

Zintl materials are based on both:

- Electropositive cations Mn+ (often from col. I or II)

- Electronegative anions Xm-

Mn+ gives their n electrons to the Xm- in order to form bonds saturating their valence band (VB)

Classical Zintl phases = semiconductors with balanced valence

Zintl bonding picture ≠ to ionic picture

Zintl-Klemm approach is useful for understanding electronic structure of complex phases

Electronic structure of Zintl phases can contain ionic, covalent and even metallic bondings

In these ideal case, there are only bondings between cations and anions

Ex. : classical 2-6 and 3-5 cubic semiconductors !

Often, the number of electrons given by the cations is too small for filling the valence bands

Kauzlarich et al DT 2007

Toberer et al CM 2010

BUT one does not consider a charge transfer ! This is valence counting


Polar intermetallic phases or Zintl metals = metallic phases with imbalanced valence

Ex.:filled skutterudite, metallic clathrates, La3X4, Yb14MnSb11, Mo3Sb7, …

Formations of bondings between the anions in order to complete the filling of the valence band

Ex. : unfilled skutterudite, La2AX4 or La2X3, ZnSb, Zn4Sb3, …

« Unclassical » Zintl phases = semiconductors with anionic bondings and balanced valence

Example between these different limits :

Ideal Zn6Sb5, …

Possibly, one can have charge transfer from cations Mn+ to polyanionic units

Ex. : semiconducting clathrates, AZn2Sb2, Yb14AlSb11, ,…

By substitution in these metallic phases, one can sometimes get semiconducting behaviour

« Electron crystal – Phonon glass » concept from Glenn Slack in 1993-5

Decoupling between electron and phonon scattering

Suggestion cage-based compounds as ideal case to test the ideas

Atom interacalation in cages without modifying electronic properties

But strongly scattering the atom vibrations

Suggestion that such atoms must have large atomic displcement parameters (ADP)

Suggestion of several families to investigate :

skutterudites, clathrates => excellent results !

Other investigated families but unsuccesfully:

Borides, …

Because of their too low power factor


Nanocage compounds


Skutterudites

Relation with perovskite structure

Sb Ce

Body centered cubic structure space group: Im-3.

CaCu3Ti4O12

CoSb3 structure with M on (0,0,0) site

CoSb3 structure with M on (¼, ¼, ¼) site

CeFe4Sb12


Crystal structure


M coordination X coordination R coordination

Octahedral Deformed tetrahedral

1st layer icosahedral

Atom coordinations

Different atom coordinations are energetic compromise between the different local symetries

When X4 ring = square

Oftedal relation

Simple chemical counting of electrons in skutterudites

Unfilled skutterudites MX3 or M4X12


FILLED SKUTTERUDITES: electronic properties

Filled skutterudites with 69/71 électrons/ R1+/3+ M4X12

Unfilled skutterudites with 72 electrons/M4X12

Filled skutterudites R1+/3+ M4X12

(R = alkaline metals.earths, rare-earths ;M = Fe, Ru, Os ; X = P, As, Sb)

(M = Co, Rh, Ir ; X = P, As, Sb)

=> Paramagnetic metal with 1-3 electrons

=> Diamagnetic semiconductor

UNFILLED SKUTTERUDITES: electronic properties

Weak electronegativity difference:

DX* = 0.1-0.2

Direct nonparabolic narrow-gap semiconductor with rather high mobility => High power factor

Sofo PRB 1998

Cours École TE juillet 2012 Cours École TE juin 2014

Doping

Large non-parabolicity of the VB

m*

Too high thermal conductivity: about 10 W/m.K=> to be reduced !

Several ways:

- Solid solutions

- Partial filling of 2a site with guest atoms

Nolas, APL 2000 Anno, JAP 1999

T = 300 K


UNFILLED SKUTTERUDITES: thermal properties


FILLED SKUTTERUDITES: electronic properties

Nouneh, JAC 2007 LaFe4Sb12

Eg = 0.6 eV

LaFe3CoSb12

Singh, PRB 1997

EF is shifted into the bandgap due to Co alloying, BUT only weak improvement of TE properties

Large thermopower, PF and ZT due to presence of both

heavy and light hole bands (well explained by DFT)

CeyFe4-xNixSb12

Ni/Co alloying => only partial filling on (2a) site

Qiu, JAP 2012

Meisner, PRL 1998

Lower thermal conductivity for partial filling


Full filling of (2a) site in RFe4Sb12

Partial filling of (2a) site in RFe4-xMxSb12

n

p

State-of-the-art of skutterudites in 2005

Uher, HB TE 2005

FILLED SKUTTERUDITES: thermal properties

No improvement for p-type skutterudites

since this time

Defects in unfilled skutterudites


Partial filling of (2a) site in CoSb3 => from intrinsic p type p to extrinsic n type

Maximum filling can be as large as 0.6-0.65 for R+ ions (Na, K)

The lower is the R valence, the higher is the partial filling of the (2a) site

Recent improvement in tellurium alloyed unfilled skutterudites


ZT approaching 1 without intercalating atoms

Long-term stability to check.

Duan, JMS 2014

n-type

p-type

Reduction of kL to about 1.5-3 W/m.K

Deng, JAC 2014

n-type

p-type

Duan, MRB 2012

FeSb2+xTe1-x

Recent improvement in single-intercalated skutterudites


ZT of about 1.3 for Li- and In- intercalated skutterudite

BUT stability problems !

Zhang, AM 2012

Reduction of kL to about 2-3 W/m.K in both

cases

Impossibility to intercalate Li at room pressure => High-pressure-high temperature synthesis

Intercalation of new types of atoms in (2a) site such as Sn and Li (under P) or In

Tang, EES 2014

Li0.3Co4Sb12

Shi, JACS 2011

High increase of ZT with multi-filling

Efficiency of multiple-filling for reducing kL

Use of mischmetal and didymium also reduces the costs, although ZT is lower


Rogl, AM 2014

Oxidization of CoSb3 Zhao, JAC 2010

Sklad, JAC 2010 Oxidization of CeFe4Sb12

Phase diagram of Co-Sb

Stability from 400-500°C must

be more carefully examined


Stability issue

Clathrates

Rogl, TE HB 2005


Si ou Ge sp3 lattice

of diamond symmetry Fd-3m

From Mudryk JPCM 02, Physica B 03

Formation of IV20 cages

with alkaline atoms Pentagon dodecahedra (512)

Clathrates

Clathrates type III

Cs30Na1.33x-10Sn172-x

I42/mnm

Clathrates type II

NaxSi136

Fd-3m

+ cages IV24 (512 62)

et IV26 (512 63)

+ cages IV28 (512 64)

+ cages IV24 (512 62)

Clathrates type I

Ba8Si46, Eu8Ga16Ge30

Pm-3n

Clathrates type IX

Ba24Si100

P4132

Substraction of 4

Si from IV24 cages

Clathrates type VIII

Eu8Ga16Ge30

I-43m Clathrates type ?

Te16Si38

P-43n ou R-3c

1 only type of distorted

IV20+3 cages

Relation between some different types of cubic clathrates


Rogl, TE HB 2005

Four main structure of TE clathrates

Cages of type 1 & 8 clathrates



Crystal structure type for silicon based clathrates

Type-IX M24X100

Si46 => enlarged bandgap from diamond structure

Intercalation of atoms in Si46 => shifting EF

Case of 8 Ba2+/ Na+ in Si46 (Ge46) => adds 16/8 electrons in Si46 (Ge46)

Substitution of 16 Si by 16 Ga (Al) in Ba8Si46 (Ba8Ge46)

remove 16 electrons from Ba8Si46 (Ba8Ge46)

EF inside Eg

Moriguchi PRB 2000 Electronic structure of type 1 clathrates


Zintl picture works well

Same alloying effect in other types of clathrates => here Ba24Ge100

Zerec PRB 2002 Nenghabi PRB 2008


Electronic structure of type 1 and type 9 clathrates

Thermoelectric properties of type 1 clathrates

Best type 1 compound: Ba8Ga16Ge30


Christensen DT 2010

BUT presence of Ge and Ga make expansive the clathrates

Replacement of Ge by Si and Ga by Al reduces the best ZT to 0.4

Roudebush, JSSC 2011

Best type 9 compound: Ba24In16Ge84

Kim JAP 2007


Thermoelectric properties of type 9 clathrates

BUT presence of Ge and Ga make expansive the clathrates

No attempt with Ge replaced by Si

Needs of high pressure – high temperature technique for Si type 9 clathrates

Thermal conductivity of type 1 and type 8 clathrates

Thermal conductivity weaker in type 1 than type 8 clathrates

Suekuni PRB 2008 Paschen PRB 2001


Plateau in k for the case of intercalated atoms in off-center position

Thermal conductivity conversely

proportional to the cage size

Very weak therm. cond. In type 9 clathrate

Kim JAP 2007 Suekuni PRB 2008


Thermal conductivity of type 1 and type 9 clathrates

Case of type 2 clathrate type 2 without intercalation

=> Archetype of large size (although cubic)

Nolas, TE HB 2005


Thermal conductivity of type 2 clathrates

Ritchie, JPCM 2013

Na intercalation does not decrease significantly the kL

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Nowadays thermoelectric materials