Thermoelectric materials : Advances and applications

ials Thermoelectric Materials

© 2015 Taylor & Francis Group, LLC

© 2015 Taylor & Francis Group, LLC

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Pan Stanford Series on Renewable Energy — Volume 2

Thermoelectric Materials

Advances and Applications

Enrique Maciá-Barber

© 2015 Taylor & Francis Group, LLC

CRC Press

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Version Date: 20150421

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Contents

Preface ix

1 Basic Notions 1

1.1 Thermoelectric Effects 1

1.2 Transport Coefficients 13

1.2.1 Thermoelectric Transport Matrix 13

1.2.2 Microscopic Description 16

1.2.2.1 Electrical conductivity 16

1.2.2.2 Seebeck effect 17

1.2.2.3 Lattice thermal conductivity 17

1.2.2.4 Phonon drag effect 24

1.2.3 Transport Coefficients Coupling 25

1.3 Thermoelectric Devices 27

1.4 Thermoelectric Efficiency 32

1.4.1 Power Factor 33

1.4.2 Figure of Merit 35

1.4.3 Coefficient of Performance 40

1.4.4 Compatibility Factor 44

1.5 Thermoelectric Materials Characterization 52

1.6 Industrial Requirements 56

1.7 Exercises 60

1.8 Solutions 63

2 Fundamental Aspects 73

2.1 Efficiency Upper Limit 73

2.2 ZT Optimization Strategies 76

2.2.1 Thermal Conductivity Control 77

2.2.2 Power Factor Enhancement 80

2.3 The Spectral Conductivity Function 81

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vi Contents

2.4 Electronic Structure Engineering 92

2.4.1 Regular Electronic Structures 92

2.4.2 Singular Electronic Structures 94

2.4.3 Spectral Conductivity Shape Effect 100

2.5 Exercises 102

2.6 Solutions 103

3 The Structural Complexity Approach 111

3.1 Structural Complexity and Physical Properties 112

3.2 Elemental Solids of TE Interest 115

3.3 Traditional Thermoelectric Materials 122

3.3.1 BiSb Alloys 126

3.3.2 Bi2Te3-Sb2Te3-Bi2Se3 Alloys 128

3.3.3 ZnSb Alloys 131

3.3.4 Lead Chalcogenides 133

3.3.5 SiGe Alloys 136

3.4 Complex Chalcogenides 137

3.4.1 AgSbTe2 Compound 138

3.4.2 TAGS and LAST Materials 139

3.4.3 Thallium Bearing Compounds 141

3.4.4 Alkali-Metal Bismuth Chalcogenides 145

3.5 Large Unit Cell Inclusion Compounds 147

3.5.1 Half-Heusler Phases 148

3.5.2 Skutterudites 155

3.5.3 Clathrates 167

3.5.4 Chevrel Phases 173

3.6 Exercises 175

3.7 Solutions 179

4 The Electronic Structure Role 187

4.1 General Remarks 187

4.2 Electronic Structure of Elemental Solids 192

4.2.1 Bismuth and Antimony 195

4.2.2 Selenium and Tellurium 199

4.2.3 Silicon and Germanium 201

4.3 Electronic Structure of Binary Compounds 203

4.3.1 BiSb Alloys 203

4.3.2 Bismuth Chalcogenides 205

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Contents vii

4.3.3 Antimonides 207

4.3.4 Lead Chalcogenides 208

4.3.5 SiGe Alloys 211

4.3.6 Pentatellurides 211

4.3.7 Rare-Earth Tellurides 215

4.4 The Band Engineering Concept 217

4.4.1 The Thermoelectric Quality Factor 220

4.4.2 Band Convergence Effect 222

4.4.3 Band Gap Size Control 224

4.4.4 Carrier Concentration Optimization 225

4.4.5 Impurity-Induced DOS Peaks 227

4.5 Oxide Semiconductors 228

4.6 Exercises 230

4.7 Solutions 231

5 Beyond Periodic Order 235

5.1 Aperiodic Crystals 237

5.1.1 The Calaverite Puzzle 239

5.1.2 Incommensurate Structures 245

5.1.3 Quasicrystals 248

5.1.4 Complex Metallic Alloys 251

5.2 Decagonal Quasicrystals 254

5.3 Icosahedral Quasicrystals 257

5.3.1 Transport Properties 257

5.3.2 Electronic Structure 263

5.3.3 Band Structure Effects 266

5.4 Exercises 275

5.5 Solutions 276

6 Organic Semiconductors and Polymers 281

6.1 Organic Semiconductors 282

6.2 Physical Properties of Molecular Wires 284

6.2.1 Conducting Conjugated Polymers 285

6.2.2 Transport Properties of DNA 289

6.3 Thermoelectricity at the Nanoscale 296

6.3.1 Transport Coefficients for Molecular

Junctions 299

6.3.2 DNA-Based Thermoelectric Devices 303

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viii Contents

6.4 Exercises 312

6.5 Solutions 313

Bibliography 317

Index 341

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Preface

Environmental concerns regarding refrigerant fluids as well as the

convenience of using non toxic and non expensive materials, have

significantly spurred the interest in looking for novel, high- per￾formance thermoelectric materials for energy conversion in small￾scale power generation and refrigeration devices, including cooling

electronic devices, or flat-panel solar thermoelectric generators.

This search has been mainly fueled by the introduction of new

designs and the synthesis of new materials. In fact, the quest

for good thermoelectric materials entails the search for solids

simultaneously exhibiting extreme properties. On the one hand,

they must have very low thermal- conductivity values. On the other

hand, they must have both electrical conductivity and Seebeck

coefficient high values as well. Since these transport coefficients are

not independent among them, but are interrelated, the required task

of optimization is a formidable one. Thus, thermoelectric materials

provide a full-fledged example of the essential cores of solid state

physics, materials science engineering, and structural chemistry

working side by side towards the completion of a common goal, that

is, interdisciplinary research at work.

Keeping these aspects in mind, the considerable lag between

the discovery of the three main thermoelectric effects (Seebeck,

Peltier and Thomson, spanning the period 1821–1851), and their

first application in useful thermoelectric devices during the 1950s, is

not surprising at all. In fact, such a delay can be understood as arising

from the need of gaining a proper knowledge of the role played

by the electronic structure in the thermal and electrical transport

properties of solid matter. Thus, metals and most alloys (whose

Fermi level falls in a partially filled allowed energy band) yield

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x Preface

typically low thermoelectric conversion efficiencies, as compared

to those observed in semiconducting materials (exhibiting a

characteristic gap between valence and conduction bands).

According to this conceptual scheme, the first two chapters

are devoted to present a general introduction to the field of

thermoelectric materials, focusing on both basic notions and the

main fundamental questions in the area. For the benefit of the non￾acquainted readers, the contents of these chapters are presented in

a tutorial way, recalling previous knowledge from solid state physics

when required, and illustrating the abstract notions with suitable

application examples.

In Chapter 1, we start by introducing the thermoelectric effects

from a phenomenological perspective along with their related

transport coefficients and the mutual relations among them. We also

present a detailed description of the efficiency of thermoelectric

devices working at different temperature ranges. Some more recent

concepts, like the use of the compatibility factor to characterize

segmented devices, or a formulation based on the use of the relative

current density and the thermoelectric potential notions to derive

the figure of merit and coefficient of performance expressions,

are also treated in detail. Finally, several issues concerning the

characterization of thermoelectric materials and some related

industry standards will be presented.

In Chapter 2, we review the two basic strategies adopted in order

to optimize the thermoelectric performance of different materials,

namely, the control of the thermal conductivity and the power

factor enhancement. The electronic structure engineering approach,

nowadays intensively adopted, is introduced along with some useful

theoretical notions related to the spectral conductivity function and

its optimization.

Within a broad historical perspective, the next three chapters

focus on the main developments in the field from the 1990s

to the time being, highlighting the main approaches followed in

order to enhance the resulting thermoelectric efficiency of different

materials. In this way, the low thermal conductivity requirement

has led to the consideration of complex enough lattice structures,

generally including the presence of relatively heavy atoms within

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Preface xi

the unit cell, or to the consideration of nanostructured systems

characterized by the emergence of low-dimensional effects. By

fully adopting this structural complexity approach, in Chapter 3,

we progressively introduce the different kinds of bulk materials

which have been considered, starting from the main properties of

the elemental solids of thermoelectric interest (bismuth, antimony

and tellurium), going through a number of binary and ternary

alloys of growing chemical and structural complexity, to finish with

the promising large unit cell inclusion compounds, including half￾Heusler alloys, skutterudites, clathrates and Chevrel phases.

By all indications, attaining large values of the electrical

conductivity and Seebeck coefficient usually requires a precise

doping control as well as an accurate tailoring of the sample’s

electronic structure close to the Fermi level. Thus, next generation

thermoelectric materials will require more attention to be paid

to enhancing their electronic properties, as the lattice thermal

conductivity of most thermoelectric materials of interest has already

been greatly reduced. To this end, a main goal focuses on obtaining

a fundamental guiding principle, in terms of an electronic band

structure tailoring process aimed at optimizing the thermoelectric

performance of a given material. Following this route, in Chapter

4 we will analyze the role played by the electronic structure in the

thermoelectric performance of the different materials described in

Chapter 3, paying a special attention to the benefits resulting from a

systematic recourse to the band engineering concept.

In Chapter 5, we take a step further along the structural

complexity approach by considering materials able to possess

atomic lattices which are both complex (low thermal conductivity)

and highly symmetric (favorable electronic properties). This leads

us beyond periodic order into the realm of aperiodic crystals

characterized by either incommensurate structures or fully new

lattice geometries based on scale-invariance symmetry and long￾range aperiodic order, as it occurs in quasicrystals and their related

phases.

The inorganic thermoelectric materials we have considered in

the five previous chapters are hindered by issues like high cost of

production, scarcity of constituting elements, or toxicity. Because of

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xii Preface

these problems associated with inorganic compounds, organic elec￾tronic materials have spurred a growing interest in thermoelectric

community. Consequently, in Chapter 6 we consider novel materials

based on organic semiconductors and conducting polymers. We also

explore recent advances in the study of thermoelectric phenomena

at the nanoscale, focusing on the transport properties through

molecular junctions and analyzing the potential of DNA based

thermoelectric devices.

The book contains 58 proposed exercises (highlighted in

boldface through the text) accompanied by their detailed solutions.

I have prepared the exercises mainly from results published and

discussed in regular research papers during the last decade in order

to provide a glimpse into the main current trends in the field.

Although the exercises and their solutions are given at the end of

each chapter for convenience, it must be understood that they are

an integral part of the presentation, either motivating or illustrating

the different concepts and notions. In the same way, most exercises

of Chapters 5 and 6 assume the reader is well acquainted with the

contents presented in the previous four chapters, and may serve as

a control test. Accordingly, it is highly recommended to the reader

that he/she try to solve the exercises in the sequence they appear

in the text, then check his/her obtained result with those provided

at the end of the chapter, and only then to resume the reading of

the main text. In this way, the readers (who are intended to be

both graduate students as well as senior scientists approaching this

rapidly growing topic from other research fields) will be able to

extract the maximum benefit from the materials contained in this

book in the shortest time.

All the references are listed in the bibliography section at the end

of the book. I have tried to avoid a heavily referenced main text by

concentrating most references in the places where they are most

convenient to properly credit results published in the literature,

namely, in the figures and tables captions, in the footnotes, and in the

exercises and their solutions. The references are arranged according

to the following criteria: in the first place, some historical papers are

given, followed by a series of reference textbooks covering different

topics directly related to the materials treated in this book, then I list

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Preface xiii

the reviews and monographs published on related issues during the

last decade. Afterwards, a list of archival research papers is given in

the order they appear in the text from Chapters 1 to 6.

I am gratefully indebted to Professors Esther Belin-Ferre, Jean ´

Marie Dubois, Kaoru Kimura, Uichiro Mizutani, Tsunehiro Takeuchi,

and Terry M. Tritt for their continued interest in my research

activities during the last two decades. Their illuminating advice has

significantly guided my scientific work in the field of thermoelectric

materials.

It is a pleasure to thank Emilio Artacho, Janez Dolinsek, Roberto

Escudero, G. Jeffrey Snyder, Oleg Mitrofanov, and Jose Reyes-Gasga ´

for sharing very useful materials with me.

I am also grateful to Mr. Stanford Chong for giving me the

opportunity to prepare this book and to Ms. Shivani Sharma for her

continued help in dealing with editorial matters. Last, but not least,

I warmly thank M. Victoria Hernandez for her invaluable support, ´

unfailing encouragement, and attention to detail.

Enrique Macia-Barber ´

Madrid

Spring 2015

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Chapter 1

Basic Notions

1.1 Thermoelectric Effects

During the nineteenth century, several phenomena linking thermal

energy transport and electrical currents in solid materials were

discovered within a time interval of 30 years, spanning from 1821

to 1851 (Fig. 1.1). These phenomena are collectively known as

thermoelectric effects, and we will devote this section to briefly

introducing them.a

Let us start by considering an elementary thermal effect:

experience shows us that when a piece of matter is subjected to a

temperature difference between its ends heat spontaneously flows

from the region of higher temperature, TH , to the region of lower

temperature, TC (Fig. 1.2a). This heat current is maintained over

time until thermal equilibrium (TH = TC ≡ T ) is reached and

the temperature gradient vanishes (Fig. 1.2b). It was Jean Baptiste

Joseph Fourier who first introduced the mathematical formulation

describing this well-known fact in 1822. According to the so-called

Fourier’s law, the presence of a temperature gradient ∇T (measured

aIn addition to the phenomena described in this section, we may also observe

the so-called galvanomagnetic (when no temperature gradients are present) or

thermomagnetic (when both thermal gradients and magnetic fields are present)

effects. These phenomena, however, will not be covered in this book.

Thermoelectric Materials: Advances and Applications

Enrique Macia-Barber ´

Copyright c 2015 Pan Stanford Publishing Pte. Ltd.

ISBN 978-981-4463-52-2 (Hardcover), 978-981-4463-53-9 (eBook)

www.panstanford.com

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2 Basic Notions

Figure 1.1 Chronogram showing the portraits and life span of the main

characters in the origins of thermoelectric research. The ticks indicate

the date when the corresponding thermoelectric phenomenon was first

reported.

in Km−1) induces in the material a heat current density h (measured

in Wm−2 units) which is given bya

h = −κ ∇T, (1.1)

where κ is a characteristic property of the considered material, re￾ferred to as its thermal conductivity (measured in Wm−1K−1 units).

In general, the thermal conductivity depends on the temperature of

the material, that is, κ(T ), and it always takes on positive values

(κ > 0), so that the minus sign in Eq. (1.1) is introduced to

properly describe the thermal current propagation sense. Indeed, if

we reverse the temperature gradient (∇T → −∇T ) in Eq. (1.1) we

get a heat flow reversal (h → −h), so that heat always diffuses the

same way: from the hot side to the cold one.

Five years after the publication of Fourier’s work, Georg Simon

Ohm reported that when a potential difference, V (measured in V),

aThroughout this book boldface characters will denote vectorial magnitudes.

© 2015 Taylor & Francis Group, LLC