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Edited by the initiators of a priority research program funded by the German Science Foundation and written by an international team of key players, this is the first book to provide an overview of nanostructured thermoelectric materials -- putting the new developments into perspective alongside conventional thermoelectrics. As such, it reviews the current state of research on thermoelectric Bi2Te3 nanomaterials, covering advanced methods of materials synthesis, characterization of materials structures and thermoelectric properties, as well as advances in the theory and modeling of transport properties. Nanomaterials-based thermoelectric devices are also discussed with respect to their properties, their suitability for different energy generation applications, and in light of their commercialization potential. An outlook on the chances, challenges and future directions of research rounds off the book, giving a straightforward account of the fundamental and technical problems - plus ways to overcome them.

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Table of Contents

Cover

Title Page

Related Titles

Copyright

Preface

List of Contributors

Acknowledgments

Chapter 1: Old and New Things in Thermoelectricity

1.1 Three Thermoelectric Effects

1.2 Semiconductors

1.3 My Entry into Thermoelectricity

1.4 Peltier Cascades

1.5 Challenge of Materials Science

References

Part I: Synthesis of Nanowires, Thin Films, and Nanostructured Bulk

Chapter 2: Electrodeposition of Bi2Te3-Based Thin Films and Nanowires

2.1 Introduction

2.2 Fundamentals of Bi

2

Te

3

-Based Electrodeposition

2.3 Electrodeposition of Bi

2

Te

3

Thin Films

2.4 Electrodeposition of Thermoelectric Nanowires

2.5 Conclusion

References

Chapter 3: Bi

2

Te

3

Nanowires by Electrodeposition in Polymeric Etched Ion Track Membranes: Synthesis and Characterization

3.1 Introduction

3.2 Synthesis of Bi

2

Te

3

NWs with Controlled Size and Crystallography

3.3 Conclusions

References

Chapter 4: Fabrication and Comprehensive Structural and Transport Property Characterization of Nanoalloyed Nanostructured V

2

VI

3

Thin Film Materials

4.1 Situation/State of the Art before the Start of Our Combined Research Project

4.2 Motivation for Research on V

2

VI

3

Multilayered Structures

4.3 Conclusion and Outlook

Acknowledgments

Chapter 5: Structure and Transport Properties of Bi

2

Te

3

Films

5.1 Introduction

5.2 Structural Aspects of the Tetradymite-type Lattice

5.3 MBE Film Deposition

5.4 Structural Characterization of Bi

2

Te

3

Films

5.5 Transport Properties of Films on Sapphire Substrates

5.6 Conclusion

Acknowledgment

References

Chapter 6: Bulk-Nanostructured Bi

2

Te

3

-Based Materials: Processing, Thermoelectric Properties, and Challenges

6.1 Success of

ZT

Enhancement in Nanostructured Bulk Materials

6.2 Methodology at Fraunhofer IFAM-DD: Previous Research

6.3 High-Energy Ball Milling Technology, SPS Technology, and Thermoelectric Characterization

6.4 Control of Crystallite Size and Mass Density

6.5 Nanostructure –Transport Properties – Correlations in Sintered Nanomaterials

6.6 Summary and State of the Art

6.7 Outlook Second Generation SPS Prepared Nanomaterials

References

Part II: Structure, Excitation, and Dynamics

Chapter 7: High Energy X-ray and Neutron Scattering on Bi

2

Te

3

Nanowires, Nanocomposites, and Bulk Materials

7.1 Introduction

7.2 Review of Published High-Energy X-ray and Neutron Scattering Studies on Bi

2

Te

3

and Related Compounds

7.3 Element Specific Lattice Dynamics in Bulk Bi

2

Te

3

and Sb

2

Te

3

7.4 Nanostructure and Phonons in a Bi

2

Te

3

Nanowire Array

7.5 Nanocomposites and Speed of Sound

7.6 Perspectives of High-Energy X-ray and Neutron Scattering

Acknowledgments

References

Chapter 8: Advanced Structural Characterization of Bi

2

Te

3

Nanomaterials

8.1 From Bulk to Nanomaterials

8.2 Synthesis of Nanomaterials and Transport Measurements

8.3 Relevance of Advanced Microscopy and Spectroscopy for Bi

2

Te

3

Nanomaterials

8.4 Nanostructure–Property Relations in Bulk and Nanomaterials

8.5 Simulation of Electron Transport and Electron Scattering in Bi

2

Te

3

-Based Materials

8.6 Experimental Techniques and Simulation

References

Part III: Theory and Modeling

Chapter 9: Density-Functional Theory Study of Point Defects in Bi

2

Te

3

9.1 Introduction

9.2 Thermoelectric Properties

9.3 The Lattice Structure of Bi

2

Te

3

9.4 Point Defects in Bi

2

Te

3

-Related Materials

9.5 Concentration of Point Defects

9.6 Calculation of Formation Energies from First Principles

9.7 Recent DFT Results for the Point Defect Energies in Bi

2

Te

3

9.8 Summary and Outlook

Acknowledgments

References

Chapter 10: Ab Initio Description of Thermoelectric Properties Based on the Boltzmann Theory

10.1 Introduction

10.2 Transport Theory

10.3 Results

10.4 Summary

References

Part IV: Transport Properties Measurement Techniques

Chapter 11: Measuring Techniques for Thermal Conductivity and Thermoelectric Figure of Merit of V–VI Compound Thin Films and Nanowires

11.1 Introduction

11.2 Methods for the Investigation of the In-plane Thermal Conductivity of Thin Films

11.3 Steady-State Measurements of the Cross-Plane Thermal Conductivity of Thin Films

11.4 Investigation of Cross-Plane Thermal Conductivity of Nanowire Arrays

11.5 Characterization of Thermal Conductivity and Thermoelectric Figure of Merit of Single Nanowires

Acknowledgments

References

Chapter 12: Development of a Thermoelectric Nanowire Characterization Platform (TNCP) for Structural and Thermoelectric Investigation of Single Nanowires

12.1 Introduction

12.2 TNCP Initial Design

12.3 First and Second Generations of TNCP

12.4 Nanowire Assembly Utilizing Dielectrophoresis

12.5 Ohmic Contact Generation

12.6 Summary and Outlook

References

Appendix

Index

End User License Agreement

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Guide

Cover

Table of Contents

Preface

Begin Reading

List of Illustrations

Figure 1.1

Figure 1.2

Figure 1.3

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Figure 2.11

Figure 2.12

Figure 2.13

Figure 2.14

Figure 2.15

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 3.11

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Figure 7.2

Figure 7.1

Figure 7.4

Figure 7.3

Figure 7.6

Figure 7.5

Figure 7.7

Figure 8.1

Figure 8.2

Figure 8.4

Figure 8.3

Figure 8.5

Figure 8.7

Figure 8.6

Figure 9.1

Figure 9.2

Figure 9.3

Figure 9.4

Figure 10.1

Figure 10.2

Figure 10.3

Figure 10.4

Figure 10.5

Figure 10.6

Figure 10.7

Figure 10.9

Figure 10.8

Figure 10.10

Figure 10.11

Figure 10.12

Figure 11.1

Figure 11.2

Figure 11.3

Figure 11.4

Figure 11.5

Figure 11.6

Figure 11.7

Figure 11.8

Figure 11.9

Figure 11.10

Figure 11.11

Figure 11.12

Figure 11.13

Figure 11.14

Figure 11.15

Figure 11.16

Figure 11.17

Figure 11.18

Figure 11.19

Figure 11.20

Figure 11.21

Figure 11.22

Figure 12.1

Figure 12.9

Figure 12.2

Figure 12.3

Figure 12.4

Figure 12.5

Figure 12.6

Figure 12.7

Figure 12.8

Figure 12.10

Figure 12.11

Figure 12.12

Figure 12.13

Figure 12.14

Figure 12.15

Figure 12.16

List of Tables

Table 2.1

Table 2.2

Table 2.3

Table 2.4

Table 2.5

Table 3.1

Table 5.1

Table 5.2

Table 6.1

Table 6.2

Table 6.3

Table 8.1

Table 8.2

Table 8.3

Table 8.4

Table 9.1

Edited by Oliver Eibl, Kornelius Nielsch, Nicola Peranio, and Friedemann Völklein

Thermoelectric Bi2Te3 Nanomaterials

 

 

 

 

 

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Editors

Oliver Eibl

E.-Karls-University Tübingen

Institute of Applied Physics

Auf der Morgenstelle 10

72076 Tübingen

Germany

Kornelius Nielsch

University of Hamburg

Institute of Applied Physics

Jungiusstr. 1

20355 Hamburg

Germany

Nicola Peranio

E.-Karls-University Tübingen

Institute of Applied Physics

Auf der Morgenstelle 10

72076 Tübingen

Germany

Friedemann Völklein

Hochschule RheinMain

Institut für Mikrotechnologien

Am Brückweg 26

65428 Rüsselsheim

Germany

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.

© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

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Preface

Thermoelectric effects have been known since the beginning of the nineteenth century. In 1795, Alessandro Volta conducted the very first experiments investigating this phenomenon. In 1821, Thomas Johann Seebeck reported the magnetic polarization of metals and ores by a temperature difference and published the report in 1825. The Peltier effect was discovered later in 1834 by Jean C.A. Peltier. With the introduction of semiconductors in the 1950s and later the introduction of solid solutions as thermoelectric materials, one was able to obtain appreciable performance of thermoelectric devices. However, the enthusiasm began to wane when since the 1950–1960s no bulk material could be found that actually exceeded the thermoelectric figure of merit, ZT, of the materials and the related energy conversion efficiencies of the thermoelectric devices. The reason is that the common fundamental parameters of electron and phonon systems yield inversely interrelated transport properties and thus limitations to further increase the thermoelectric figure of merit ZT in bulk materials. Much later, in the mid-1990s, research in the field of thermoelectrics experienced a renaissance due to theoretical predictions that thermoelectric efficiency could be greatly enhanced through quantum confinement effects and scattering of phonons induced by nanostructural engineering. However, in practice, reduction of thermal conductivity proved to be the more important effect of nanostructuring as was demonstrated by reports on nanoscale Bi2Te3/Sb2Te3 superlattices. Currently, most of the activities in thermoelectric materials research are dedicated to the further improvement of the performance of thermoelectric materials by exploiting the beneficial effects of nanostructuring and reduced dimensionality on the transport properties, extending the range of applications for thermoelectric devices.

Thermoelectric generators convert thermal energy into a “more useful” form, electric energy. They can be used as large module arrays to harvest energy from heat sources in industrial processes, plants, and automobiles or in the form of small assemblies to power energy autarkic sensor networks. Thermoelectric coolers are used for cooling solid-state lasers or computer processors and are also available in multiple sizes ranging from tens of centimeters down to several hundred micrometers. Thermoelectric sensors are widely used for the detection of radiation, heat flux, or reaction heat of chemical processes.

Advances in micro-electro-mechanical systems engineering have enabled the fabrication of thin-film-based microscale modules, which enable high cooling power densities. Due to small thermal mass of these modules, the desired temperatures can be attained extremely fast, usually within ∼100 ms.

Bi2Te3-based compounds are widely used for room temperature thermoelectric applications since they yield materials and thus devices with the highest energy conversion efficiencies at room temperature. These compounds have a large number of structural and chemical degrees of freedom that affect thermoelectric properties. This requires a systematic approach in terms of materials synthesis, structural characterization, thermoelectric characterization, and theory. The German Science Foundation (DFG) initiated and granted a Priority Program 1386 “Nanostructured Thermoelectric Materials: Theory, Model Systems and Controlled Synthesis” in 2009 that will be carried on until 2015. As part of this program, a workshop was held on “thermoelectric properties related to nanostructure and dimensionality in Bi2Te3 nanomaterials,” 5th and 6th July 2012, at the GSI Darmstadt (Helmholtz center for heavy ion research), Darmstadt, Germany. The aims of the workshop were (i) to summarize highlights of different Bi2Te3 clusters of the DFG priority program, (ii) to identify limiting mechanisms for the thermoelectric figure of merit, ZT, and (iii) to propose promising routes for further improvement of ZT. The workshop documented the advances that have been achieved with respect to (i) sample synthesis, (ii) various characterization methods, (iii) thermoelectric property measurements, and (iv) theoretical modeling.

The following topics were covered during this workshop and are also discussed in the different parts of this book:

PART I. Synthesis of Nanowires, Thin Films, and Nanostructured Bulk

Preparation of Bi

2

Te

3

nanowires

Preparation of Bi

2

Te

3

thin films and superlattices

Preparation of Bi

2

Te

3

nanostructured bulk

Part II. Structure, Excitation, and Dynamics

X-ray and neutron scattering and diffraction

Imaging, diffraction, and energy-dispersive X-ray spectrometry in a transmission electron microscopy (TEM) instrument

Investigation of lattice dynamics

Excitations analyzed by electron energy-loss spectroscopy in a TEM

Part III. Theory and Modeling

Modeling the band structure and excitations

Modeling thermal transport

Modeling thermoelectric properties

Part IV. Transport Properties Measurement Techniques

Establish measurement techniques for Seebeck coefficient, electrical conductivity, and thermal conductivity of thin films and single nanowires

Development of a characterization platform for combined structural characterization in the TEM and thermoelectric investigation of single nanowires

Edited by the initiators of the priority research program SPP 1386, funded by the German Science Foundation (DFG), and written by an international team of key players, this is the first book to provide an overview of nanostructured thermoelectric materials – putting the new developments into perspective alongside conventional thermoelectrics.

As such, it reviews the current state of research on thermoelectric Bi2Te3 nanomaterials, covering advanced methods of materials synthesis, characterization of materials structures, and thermoelectric properties, as well as advances in the theory and modeling of transport properties. Nanomaterial-based thermoelectric devices are also discussed with respect to their properties, their suitability for different energy conversion applications, and in light of their commercialization potential. An outlook on the chances, challenges, and future directions of research rounds off the book, giving a straightforward account of the fundamental and technical problems, plus ways to overcome those problems.

List of Contributors

Zainul Aabdin

Eberhard Karls University of Tuebingen

Institute of Applied Physics

Auf der Morgenstelle 10

Tübingen

Germany

 

Kilian Bartholomé

Fraunhofer Institute for Physical Measurement Techniques IPM

Heidenhofstr 8

Freiburg

Germany

 

Svenja Bäßler

University of Hamburg

Institute of Applied Physics

Jungiusstrasse 11

Hamburg

Germany

 

Wolfgang Bensch

Christian-Albrechts-Universität zu Kiel

Institute of Inorganic Chemistry

Max-Eyth-Str 2

Kiel

Germany

 

Dimitrios Bessas

European Synchrotron Radiation Facility

F-38043 Grenoble

France

 

Harald Böttner

Fraunhofer Institute for Physical Measurement Techniques IPM

Heidenhofstr 8

Freiburg

Germany

 

Torben Dankwort

Christian-Albrechts-Universität zu Kiel

Synthesis and Real Structure

Institute for Materials Science

Kaiserstr 2

Kiel

Germany

 

Michael Dürrschnabel

Eberhard Karls University of Tuebingen

Institute of Applied Physics

Auf der Morgenstelle 10

Tübingen

Germany

 

Oliver Eibl

Eberhard Karls University of Tuebingen

Institute of Applied Physics

Auf der Morgenstelle 10

Tübingen

Germany

 

Christian Elsässer

Fraunhofer-Institut für Werkstoffmechanik IWM

Wöhlerstraße 11

Freiburg

Germany

 

Lynn Endicott

University of Michigan

Department of Physics

Ann Arbor, MI 48109

USA

 

Arthur Ernst

Max-Planck-Institut für Mikrostrukturphysik

Weinberg 2

Halle

Germany

 

Henrik Görlitz

Fraunhofer Institute for Manufacturing and Advanced Materials (IFAM-DD)

Winterbergstrasse 28

Dresden

Germany

 

Adham Hashibon

Fraunhofer-Institut für Werkstoffmechanik IWM

Wöhlerstraße 11

Freiburg

Germany

 

Raphael P. Hermann

Jülich Centre for Neutron Science JCNS and

Peter Grünberg Institute PGI, JARA-FIT

Forschungszentrum Jülich GmbH

Jülich

Germany

and

Faculte des Sciences

Universite de Liege

B-4000 Liege

Belgium

 

Nicki F. Hinsche

Martin-Luther-Universität

Halle-Wittenberg

Institut für Physik

Halle/Saale

Germany

 

Martin Hölzer

Max-Planck-Institut für Mikrostrukturphysik

Weinberg 2

Halle

Germany

 

Rudolf P. Huebener

Eberhard Karls Universität Tübingen

Faculty of Science

Physikalisches Institut

Auf der Morgenstelle 14

Tübingen

Germany

 

Lorenz Kienle

Christian-Albrechts-Universität zu Kiel

Synthesis and Real Structure

Institute for Materials Science

Kaiserstr 2

Kiel

Germany

 

Benedikt Klobes

Jülich Centre for Neutron Science JCNS and

Peter Grünberg Institute PGI, JARA-FIT

Forschungszentrum Jülich

Jülich

Germany

 

Jan D. König

Fraunhofer Institute for Physical Measurement Techniques IPM

Heidenhofstr 8

Freiburg

Germany

 

Janina Krieg

GSI Helmholtzzentrum für Schwerionenforschung

Materials Research Department

Planckstrasse 1

Darmstadt

Germany

 

Michael Kroener

University of Freiburg

Department of Microsystems Engineering – IMTEK

Laboratory for Design of Microsystems

Georges-Köhler-Allee 102

Freiburg

Germany

 

Xi Liu

Christian-Albrechts-Universität zu Kiel

Institute of Inorganic Chemistry

Max-Eyth-Str 2

Kiel

Germany

 

Andreas Meier

RheinMain University of Applied Sciences Wiesbaden

Department of Engineering

Institute for Microtechnologies

Am Brückweg 26

Rüsselsheim

Germany

 

Ingrid Mertig

Martin-Luther-Universität

Halle-Wittenberg

Institut für Physik

Halle/Saale

Germany

and

Max-Planck-Institut für Mikrostrukturphysik

Weinberg 2

Halle

Germany

 

S. Hoda Moosavi

University of Freiburg

Department of Microsystems Engineering – IMTEK

Laboratory for Design of Microsystems

Georges-Köhler-Allee 102

Freiburg

Germany

 

Kornelius Nielsch

University of Hamburg

Institute of Applied Physics

Jungiusstrasse 11

Hamburg

Germany

 

Vicente Pacheco

Fraunhofer Institute for Manufacturing and Advanced Materials (IFAM-DD)

Winterbergstrasse 28

Dresden

Germany

 

Nicola Peranio

Eberhard Karls University Tübingen

Institute of Applied Physics

Auf der Morgenstelle 10

Tübingen

Germany

 

Oliver Picht

GSI Helmholtzzentrum für Schwerionenforschung

Materials Research Department

Planckstrasse 1

Darmstadt

Germany

 

Eckhard Pippel

Max-Planck-Institute of Microstructure Physics

Weinberg 2

Halle

Germany

 

Heiko Reith

RheinMain University of Applied Sciences Wiesbaden

Department of Engineering

Institute for Microtechnologies

Am Brückweg 26

Rüsselsheim

Germany

 

Matthias Schmitt

RheinMain University of Applied Sciences Wiesbaden

Department of Engineering

Institute for Microtechnologies

Am Brückweg 26

Rüsselsheim

Germany

 

Ulrich Schürmann

Christian-Albrechts-Universität zu Kiel

Synthesis and Real Structure

Institute for Materials Science

Kaiserstr 2

Kiel

Germany

 

Maria-Eugenia Toimil-Molares

GSI Helmholtzzentrum für Schwerionenforschung

Materials Research Department

Planckstrasse 1

Darmstadt

Germany

 

William Töllner

University of Hamburg

Institute of Applied Physics

Jungiusstrasse 11

Hamburg

Germany

 

Ctirad Uher

University of Michigan

Department of Physics

Ann Arbor, MI 48109

USA

 

Friedemann Völklein

RheinMain University of Applied Sciences Wiesbaden

Department of Engineering

Institute for Microtechnologies

Am Brückweg 26

Rüsselsheim

Germany

 

Guoyu Wang

University of Michigan

Department of Physics

Ann Arbor, MI 48109

USA

 

Zhi Wang

University of Freiburg

Department of Microsystems Engineering – IMTEK

Laboratory for Design of Microsystems

Georges-Köhler-Allee 102

Freiburg

Germany

 

Markus Winkler

Fraunhofer Institute for Physical Measurement Techniques IPM

Heidenhofstr 8

Freiburg

Germany

 

Peter Woias

University of Freiburg

Department of Microsystems Engineering – IMTEK

Laboratory for Design of Microsystems

Georges-Köhler-Allee 102

Freiburg

Germany

 

Peter Zahn

Helmholtz-Zentrum Dresden – Rossendorf

Bautzner Landstr. 400

Dresden

Germany

Acknowledgments

The authors gratefully acknowledge the financial support by the German Research Society DFG, under priority program 1386 “Nanostructured Thermoelectric Materials: Theory, Model Systems and Controlled Synthesis,” managed by Dr. Michael Mößle, 2009–2015. The authors particularly acknowledge Prof. Dr. Peter Rogl from the University of Vienna, Austria, for his contributions to the annual status meetings.

The chapters presented here are based on talks given by the authors on a workshop entitled “Thermoelectric Properties Related to Nanostructure and Dimensionality in Bi2Te3 Nanomaterials.” The workshop took place on July 5 and 6, 2012, at GSI Darmstadt (Helmholtz Center for Heavy Ion Research), Darmstadt, Germany, and it was organized by O. Eibl, Dr. N. Peranio, and Dr. E. Toimil–Molares. The authors and participants of the workshop gratefully acknowledge GSI Darmstadt, particularly Prof. Dr. Ch. Trautmann, for their hospitality and a guided tour through their facility.

1Old and New Things in Thermoelectricity

Rudolf P. Huebener

The three thermoelectric phenomena, which are associated with the names Seebeck, Peltier, and Thomson and are due to the simultaneous presence of an electric field and a temperature gradient in a material, have been studied for almost 200 years. In 1821, Thomas Johann Seebeck discovered the effect named after him. This effect appears if two different electric conductors A and B are connected as shown in Figure 1.1a and if the two junctions are kept at different temperatures T1 and T2. In this case, a thermoelectric voltage develops in the circuit, which can be measured between the two ends of the conductor A. The Peltier effect shows up if two conductors A and B are connected in series and are kept at uniform temperature (Figure 1.1b). If an electric current of density J passes through the two conductors, heat will be generated or absorbed at the junction depending on the current direction and the junction area will be heated or cooled. The Peltier effect was discovered in 1834 by Jean Charles Athanase Peltier. The third thermoelectric effect occurs if an electric current of density J flows in an electric conductor in which a temperature gradient exists along the current direction (Figure 1.1c). This effect was predicted theoretically in 1854 and observed experimentally in 1856 by William Thomson, also known as Lord Kelvin. In the following, we look a bit closer at these thermoelectric phenomena. A more detailed treatment of these subjects has been given earlier by the author [1].

Figure 1.1 The thermoelectric effects: (a) Seebeck effect, (b) Peltier effect, and (c) Thomson effect.

1.1 Three Thermoelectric Effects

1.1.1 Seebeck Effect

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