Thermoelectricity and Advanced Thermoelectric Materials 9780128199848, 9780128204399, 0128199848

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Thermoelectricity and Advanced Thermoelectric Materials

Woodhead Publishing Series in Electronic and Optical Materials

Thermoelectricity and Advanced Thermoelectric Materials Edited by Ranjan Kumar Professor, Physics Department, King Abdulaziz University, Kingdom of Saudi Arabia Professor, Department of Physics, Panjab University, Chandigarh, India

Ranber Singh Department of Physics, Sri Guru Gobind Singh College, Chandigarh, India

An imprint of Elsevier

Woodhead Publishing is an imprint of Elsevier The Officers’ Mess Business Centre, Royston Road, Duxford, CB22 4QH, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom Copyright © 2021 Elsevier Ltd. All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-819984-8 ISBN: 978-0-12-820439-9 For information on all Woodhead publications visit our website at https://www.elsevier.com/books-and-journals

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Contributors

Aditya Bhardwaj Department of Metallurgy Engineering and Materials Science, IIT Indore, Indore, Madhya Pradesh, India Zhi-Gang Chen Centre for Future Materials, University of Southern Queensland, Springfield Central; School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD, Australia Shobhna Dhiman Department of Applied Sciences, Punjab Engineering College (Deemed to be University), Chandigarh, India Enamullah Department of Physics, School of Applied Sciences, University of Science and Technology, Meghalaya, India Rajesh Ghosh Department of Physics, Gauhati University, Guwahati, Assam, India Min Hong Centre for Future Materials, University of Southern Queensland, Springfield Central; School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD, Australia Neha Jain Department of Physics, Dr. Hari Singh Gour University Sagar, Sagar, India Prafulla K. Jha Department of Physics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, India Hemen Kalita Department of Physics, Gauhati University, Guwahati, Assam, India Manish K. Kashyap School of Physical Sciences, Jawaharlal Nehru University, New Delhi; Department of Physics, Kurukshetra University, Kurukshetra, Haryana, India Kulwinder Kaur Department of Applied Sciences, Punjab Engineering College (Deemed to be University), Chandigarh, India Ravneet Kaur Centre for Advanced Studies in Physics, Department of Physics, Panjab University, Chandigarh, India Shakeel Ahmad Khanday Department of Physics, National Taiwan UniversityTaipei, Taipei, Taiwan

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Contributors

Pushpendra Kumar CSIR-National Chemical Laboratory, Pune, India Rajesh Kumar Department of Physics, Panjab University, Chandigarh, India Ranjan Kumar Physics Department, King Abdulaziz University, Kingdom of Saudi Arabia; Department of Physics, Panjab University, Chandigarh, India Ajay K. Kushwaha Department of Metallurgy Engineering and Materials Science, IIT Indore, Indore, Madhya Pradesh, India Mushtaq Ahmad Malik Department of Chemistry, Govt. Degree College Pulwama, Jammu and Kashmir, India Khalid Bin Masood Department of Physics, Dr. Hari Singh Gour University Sagar, Sagar, India Sudhir K. Pandey School of Engineering, Indian Institute of Technology Mandi, Kamand, India Anuradha Saini Department of Physics, Panjab University, Chandigarh, India Biplab Sanyal Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden Shivprasad S. Shastri School of Engineering, Indian Institute of Technology Mandi, Kamand, India Jai Singh Department of Physics, Dr. Hari Singh Gour University Sagar, Sagar; Department of Pure and Applied Physics, Guru Ghasidas University, Chhattisgarh, India Jaspal Singh Department of Physics, Mata Sundri University Girls College, New Delhi, India Ranber Singh Department of Physics, Sri Guru Gobind Singh College, Chandigarh, India Sukhdeep Singh Centre for Advanced Studies in Physics, Department of Physics, Panjab University, Chandigarh, India Renu Singla Department of Physics, Kurukshetra University, Kurukshetra, Haryana, India Siddhartha Suman Department of Metallurgy Engineering and Materials Science, IIT Indore, Indore, Madhya Pradesh, India

Contributors

xi

S.K. Tripathi Centre for Advanced Studies in Physics, Department of Physics, Panjab University, Chandigarh, India Manoj K. Yadav National Research, Training and Innovation Center; St. Xavier’s College, Maitighar, Kathmandu, Nepal Jin Zou School of Mechanical and Mining Engineering; Centre for Microscopy and Microanalysis, The University of Queensland, Brisbane, QLD, Australia

Introduction and brief history of thermoelectric materials

1

Anuradha Sainib, Rajesh Kumarb, and Ranjan Kumara,b a Physics Department, King Abdulaziz University, Kingdom of Saudi Arabia, bDepartment of Physics, Panjab University, Chandigarh, India

1.1

Introduction

Thermoelectrics is an energy conversion technology that involves the direct conversion of thermal energy into heat energy and vice versa via thermoelectric materials. It is an environmentally friendly, compact, low-cost, pollutant-free energy conversion technology with use over wide temperature ranges. Thermoelectric materials are basically solid-state devices with immobile parts, hence provide noise-free, reliable, and maintenance-free operation. These materials have a variety of applications in temperature measurements, refrigeration, power generation, and waste heat recovery [1–5]. Power generation via thermoelectric materials is based on the Seebeck effect, which is the generation of an electrical voltage due to a temperature gradient across a material. The inverse of the Seebeck effect is the Peltier effect, i.e., the appearance of a temperature gradient with an applied electric voltage, which is used for cooling applications. According to various reports, nearly two-thirds of all available energy is lost as heat in various industrial and household processes. This waste heat, an untapped, low-cost source of sustainable energy, can lead to several economic benefits where the cost of most other sustainable energies such as wind, solar, geothermal, etc., is very high [6]. Therefore, there is an increased interest in finding cost-effective technologies to generate electricity from this waste heat. Thermoelectrics is a promising energy conversion technology enabling the conversion of heat into electricity, but its applications are limited due to the very low conversion efficiency compared with conventional heat engines. Presently, it has niche applications in areas where energy availability, stability, and reliability of operations are mainly important, not the efficiency or cost of energy conversion. Examples of such fields include space missions, optoelectronics, laboratory equipment, and several medical applications [7–9]. With the advent of newer technologies, the potential fields of applicability of thermoelectric materials are also increasing. In this chapter, we focus on introducing thermoelectricity while discussing its historical background. Next, we introduce the thermoelectric phenomenon and various thermoelectric effects, such as the Seebeck effect, the Peltier effect, and the Thomson effect. Then, we provide a brief history of thermoelectric materials. Afterward, we discuss thermoelectric efficiency and the figure of merit, which is the parameter Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00012-6 Copyright © 2021 Elsevier Ltd. All rights reserved.

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Thermoelectricity and Advanced Thermoelectric Materials

driving thermoelectric material research. We also discuss the various parameters affecting the figure of merit. Finally, we discuss the current energy scenario and the relevance of thermoelectricity in this background.

1.2

Historical background

Even though the discovery of the first thermoelectric effect in 1821 is considered to be the beginning of thermoelectricity, there exists evidence of conversion between thermal and electrical energy prior to that. In the late 1780s, while conducting experiments to study the effect of electricity on animals, Italian scientist, physician, and philosopher Luigi Aloisio Galvani observed muscular contractions in a dead frog sample subjected to an electric discharge [10]. This observation motivated him to conduct several experiments to study the effect of electricity on living beings. He assumed that nerves and muscles were unbalanced electrically, and contraction of muscles occurred when this electrical equilibrium is restored by short-circuiting the nerves and muscles with metal. Therefore, he concluded that muscles in living beings reserve electricity. Although Galvani failed to find a correct explanation for this phenomenon, his work inspired Alessandro Gi€ usepe Antonio Anastasio Volta who conducted similar experiments and studied the efficacy of arcs made by different metals at inducing muscular contractions. In pursuit of the cause of these muscular contractions, he finally identified that an electromotive force generated due to a temperature difference between the junctions of two conducting materials leads to muscular contractions in a dead frog, which was a manifestation of the thermoelectric effect [11]. Around 20 years later, German physicist Johann Seebeck observed deflections in a compass magnet placed near a closed circuit made of two different metals when their junctions were at a temperature gradient. He believed magnetism induced due to the temperature differences to be the cause of the observed phenomenon. He rejected the electrical origin of the observed phenomenon. He termed this as thermomagnetism [12]. The presently used term “thermoelectric” was later coined by Danish physicist Hans Christian Orsted. With the help of Jean Baptiste Fourier, Orsted made the first thermoelectric pile, which was made of bismuth and antimony [13]. Two Italian physicists, Leopoldo Nobili and Macedonio Melloni, later improved this thermoelectric device and presented it at the French Academy of Science. Their device consisted of many thermocouples of antimony and bismuth that were used for infrared radiation and temperature measurements. The phenomenon of the generation of electromotive force due to temperature gradients was called the Seebeck effect, although it was discovered much earlier by Alessandro Volta. A few years later, in 1834, French watchmaker and physicist Jean Charles Athanase Peltier observed that heat is either liberated or absorbed across an isothermal junction of two different metals when a current was passed through them [14]. He tried to explain the observed phenomenon using the Joule theory of heat dissipation but failed to find a satisfactory explanation. In 1838, Russian physicist Heinrich Freidrich Emil Lenz proved that the effect observed by Peltier was not directly related to the Joule effect but instead was an autonomous phenomenon

Introduction and brief history of thermoelectric materials

3

involving the release or absorption of heat by junctions of dissimilar conductors when a current passed through them [15]. This effect came to be known as the Peltier effect. Later in 1851, Heinrich Gustav Magnus observed that the Seebeck voltage is independent of the distribution of temperature across the metals between the junctions, which indicated that the thermopower is a thermodynamic state function [16]. However, a comprehensive description of these two effects, the Seebeck and Peltier effect, was provided by British physicist William Thomson (Lord Kelvin), who in 1854 discovered the third thermoelectric effect known as the Thomson effect [17]. The Thomson effect is nothing but the release or absorption of heat in a currentcarrying conductor subjected to a temperature difference. He observed that the quantity of heat exchanged is proportional to both the electrical current and temperature gradient, and he also concluded that their mutual direction determines if the heat is absorbed or liberated. Thomson also established that the three thermoelectric effects are related to each other. The discovery of thermoelectric effects opened a new field of science and engineering focusing on the conversion between thermal and electrical energy. In 1885, British physicist John William Strutt Rayleigh suggested the generation of power using the Seebeck effect [18]. Numerous thermoelectric devices were designed in the second half of the 19th century, mainly comprising elements such as zinc, antimony, bismuth, etc., for power generation, cooling, temperature measurements, etc. A few of them that became popular include Cox’s pile consisting of bars of a mixture of bismuth and antimony, the Gulcher thermopile, and the Clammond pile [19]. On the other hand, the practical applications of the Peltier effect could be realized only after the discovery of semiconductors, which account for larger efficiency of conversions. The devices based on the Peltier effect came to be known as Peltier coolers. Later in 1909, German physicist Edmund Altenkirch derived the expression for the efficiency of a thermoelectric generator using a constant property model, according to which the thermoelectric properties of the thermocouples were assumed to be independent of temperature. He found that the efficiency of thermoelectric conversion is proportional to Carnot’s cycle efficiency. He also suggested that a thermoelectric material should have a high Seebeck coefficient and electrical conductivity so as to achieve minimum Joule heating, and it should also have low thermal conductivity to keep a large temperature gradient. In 1922, he derived the coefficient of performance (COP) for a Peltier cooler [20]. The advent of quantum mechanics and nonequilibrium thermodynamics in the first half of the 20th century helped to develop a microscopic description of the three thermoelectric effects. In 1931, American physical chemist Lars Onsager formulated a theory describing the transport phenomenon in a nonequilibrium system using a quasiequilibrium approximation [21,22]. The transport theory of Onsager has been extensively applied to thermoelectricity. The development of the modern theory of semiconductor physics by Russian physicist Abram Fedorovic Ioffe during the 1940s turned attention toward semiconductors for thermoelectric applications. In 1949, he introduced the dimensionless thermoelectric performance measuring parameter known as the figure of merit (zT) (for details, see Section 1.5). He observed that maximization of zT leads to maximized conversion efficiencies for thermoelectric

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Thermoelectricity and Advanced Thermoelectric Materials

generators and coolers. In his classic book, Semiconductor, Thermoelements, and Thermoelectric Cooling, Ioffe postulated that heavily doped semiconductors are the best materials for thermoelectric conversion [23]. Progress in semiconductor technology during World War II led to several major breakthroughs in thermoelectrics. In 1947, Hungarian-American scientist Maria Telkes fabricated a thermoelectric generator based on PbS and ZnSb with a conversion efficiency of 5% for a temperature gradient of 400 K [24]. In 1954, Hiroshi Julian Goldsmid designed a thermoelectric device based on Bi2Te3 thermocouples, exhibiting 0°C cooling [25]. He was one of the first to realize the importance of high carrier mobility and effective mass in combination with low thermal conductivity of materials in determining thermoelectric performance. During the 1950s, the Soviet Union invented and commercialized thermoelectric generators of ZnSb Constantan thermocouples to convert heat produced by kerosene lamps and to power radio receivers in rural areas [26]. A few years later, in 1959, Chasmar and Straton introduced a material parameter known as the “material quality factor” denoted by β to quantify the thermoelectric performance of materials depending on effective mass, carrier mobility, doping, temperature, and thermal conductivity [27]. They were the first to study the effect of energy band gap on the zT of a material. They concluded that a large band gap results in high thermal conductivity, and low mobility of charge carriers, hence is not desired for a high zT. By the end of the 1960s, progress in thermoelectrics slowed down due to the very low thermoelectric conversion efficiencies (about 5%). Various attempts to commercialize thermoelectric devices failed miserably. Gradually, thermoelectrics became restricted to niche applications. Because thermoelectric devices are solid-state devices without any moving parts, they provide reliable and maintenance-free operation. This advantage motivated the use of thermoelectric devices in such areas where availability of source, reliability, and durability of operation were prerequisites rather than efficiency and cost. Hence, over a period of time, thermoelectrics found applications in optoelectronics for precise and accurate cooling of electronic components and in deep space missions to generate power at distances where photovoltaic converters become inoperative. The thermoelectric generators used in space probes generate electricity by converting heat generated from the decay of a radioactive material, which came to be known as radioisotope thermoelectric generators (RTG) [28]. In 1961, the United States launched the first RTG, SNAP-III-equipped spacecraft, Transit-4A, into space. Afterward, several other space missions such as Voyager 1, Voyager 2, Galileo, Ulysses, Cassini, etc., had RTGs aboard them. Later during the 1970s, thermoelectric generators found applications in the biomedical sector to power cardiac pacemakers. However, these generators were soon replaced with lithium batteries due to nuclear waste disposal issues [29]. In 1979, Slack proposed the concept of “Phonon-Glass-Electron-Crystal” (PGEC), stating that the best thermoelectric material should possess thermal conductivity, as in the case of glass, and electrical conductivity, as in the case of crystalline solids, which led to the investigation of several material systems with complex crystal structures [30]. In the 1990s, the pioneering works of L. D. Hicks and M. Dresselhaus proposed

Introduction and brief history of thermoelectric materials

5

that reducing dimensionality and nanostructuring can lead to zT values, which rejuvenated thermoelectric research. They stated that quantum confinement effects in low dimensional materials lead to a considerable enhancement in the electronic properties of materials without affecting their thermal properties, therefore leading to increased thermoelectric efficiency [31,32]. Today, the ever-increasing global demand for energy and the need for environmentally friendly sustainable sources of energy have focused attention toward thermoelectricity. Thermoelectrics have very low efficiencies compared with conventional heat engines, but they could play an important role in waste heat recovery by enabling direct conversion of waste heat into useful electrical energy, such as that found in power plants and factories. With new emerging fields of applicability such as cooling of microelectronic components, use of thermoelectric generators in wearable electronics, etc., thermoelectric material research needed to be speeded up [33,34]. Developing high performance, environmentally friendly, and sustainable thermoelectric materials for specific temperature ranges is critical to the widespread commercialization of thermoelectricity. Researchers throughout the world are constantly working in this direction, exploring several different classes of materials such as chalcogenides, skutterudites, oxides, clathrates, Heusler compounds, Zintl phases, superlattices, nanocomposites, nanowires, etc. Besides the challenges of developing thermoelectric materials with high zT values, hence higher conversion efficiencies, designing cheap thermoelectric devices is also one of the challenges that also need to be addressed. To find a place in everyday life, they need to be cost-competitive with other devices available in the market. With a vast sea of opportunities for applications, thermoelectrics is a technology that has not yet been fully explored.

1.3

Thermoelectric phenomenon and effects

1.3.1 Basic principle When two ends of a material are kept at different temperatures, a temperature gradient is generated across the material, and the resulting movement of charge carries from the hot end to the cold end generating a potential difference. Conversely, when an electric current or voltage is applied across a material, the release or absorption of heat occurs at the two ends of the material, depending on the direction of the current. This phenomenon is known as a thermoelectric effect.

1.3.2 Thermoelectric effects [i] Seebeck Effect: The discovery of the Seebeck effect in the year 1821 marked the birth of thermoelectricity. Seebeck found that electrical voltage is produced in a circuit of two different metals when a temperature difference is present between the two junctions (Fig. 1.1) [12]. The voltage produced is proportional to the temperature difference between the two junctions. The proportionality constant is known as the

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Thermoelectricity and Advanced Thermoelectric Materials

Fig. 1.1 The Seebeck effect—Two metals.

Seebeck coefficient, which is an inherent property of the circuit. Mathematically, we can write it as: V ¼ α ðTH  TC Þ

(1.1)

where V is the voltage developed across the junctions of the circuit, α is the Seebeck coefficient, and (TH  TC) represents the temperature difference between the hot and cold junctions. [ii] Peltier Effect: In 1834, Peltier discovered that a current flowing in the circuit of two dissimilar materials results in a temperature difference across two junctions [14]. This effect represents the calorific effect of an electrical current at the junction of two different metals (Fig. 1.2). The direction of the current would determine the heating or cooling of the junction. The rate of heat absorbed or emitted at either of the two junctions in the circuit is given by: Q ¼ Π AB I ¼ ðΠ B  Π A ÞI

(1.2)

where I is the electrical current and Π AB is the Peltier coefficient. [iii] Thomson Effect: Finally, in 1851, Thomson observed the release or absorption of heat occurs across a current-carrying conductor with a temperature gradient [15].

Fig. 1.2 The Peltier effect—Two metals.

Introduction and brief history of thermoelectric materials

7

This is known as the Thomson effect. The rate of absorption or release of heat is determined by the temperature gradient and the current density across the conductor. If a current density J is passed through a conductor, the heat produced per unit volume is: q ¼ ρJ 2  μJ

dT 0 dx

(1.3)

where ρ is the resistivity of the material, dT/dx is the temperature gradient along the conductor, and μ is the Thomson coefficient that has the same units as the Seebeck coefficient. These three thermoelectric coefficients are related to each other such that: Π ¼ ST μ¼T

dS dT

(1.4) (1.5)

These three effects, in combination, give rise to the thermoelectric phenomenon as a whole. These effects are present in all metals and semimetals and are not exclusive to thermoelectric materials. In selected combinations of dissimilar semimetals (thermoelectric materials), these effects are more pronounced and become important from an application point of view.

1.4

Brief history of thermoelectric materials

Ever since the discovery of the first thermoelectric effect almost two centuries ago, different classes of materials have been investigated for thermoelectric applications to date. The journey of thermoelectric material research began with the study of simple metals for temperature and radiant energy measurements that possessed very low values of Seebeck coefficients on the order of few tens of μV/K [35]. It was the development of semiconductor physics during the first half of the 20th century around World War II that turned attention toward semiconductors for thermoelectric applications. Semiconductors possessed high Seebeck coefficient values, and the phonons dominated heat transport in them. In 1952, Ioffe postulated that the thermal conductivity of semiconductors depends on atomic weight such that large atomic weight semiconductors have low thermal conductivity. Goldsmid studied the variations in electrical conductivity with a crystal structure and electron mobility [36]. He found that the ratio of mobility and thermal conductivity is a function of atomic weight. Selecting high Seebeck coefficients and high atomic weights from studying material properties of some common semiconductors, Goldsmid discovered bismuth telluride (Bi2Te3) in 1954 [25]. Bi2Te3 is a metal chalcogenide, which crystallizes in a hexagonal-layered structure with atomic layers Te1-Be-Te2-Bi-Te3 held together via the Van der Waal forces. There exists mixed ionic-covalent bonding along the lattice planes. The nearly two-dimensional crystal structure of Bi2Te3 results in strongly

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Thermoelectricity and Advanced Thermoelectric Materials

anisotropic properties such that the ratio of conductivity along the c-axis and perpendicular to it is very different for both the electrical conductivity and thermal conductivity. Bi2Te3 has a small indirect bandgap of 0.15 eV at room temperature and a low melting point of 585°C, the reason why its applications are limited to a lowtemperature regime only [37]. Although discovered in the 1950s, Bi2Te3 continues to remain the focus of thermoelectric material research even today. In 1956, Ioffe et al. proposed that alloying a semiconductor with an isomorphic substance could result in increased thermoelectric performance by lowering the thermal conductivity without changing electrical conductivity. It was proposed that alloying would lead to increased phonon scattering as a result of the lattice distortions caused of the order of the interatomic distances [38]. Consequently, a number of semiconductor alloys were explored for thermoelectric applications over wide temperature ranges. p-type Bi2–xSbxTe3 and n-type Bi2Te3–xSex emerged as the best materials for thermoelectric applications that have zT values of 1 at 300 K. These materials have been in use for several decades now [39–41]. Another important thermoelectric material that drew attention during the 1950s is lead telluride (PbTe), which belongs to the class of materials known as lead chalcogenides such as PbS, PbSe, and their alloys. It is a thermoelectric material best suited for medium temperature ranges (600–800 K) owing to its high temperature stability and the anomalous temperature dependence of its energy bandgap [42,43]. PbTe crystallizes in the cubic NaCl-type crystal structure with Pb atoms at the cationic sites and Te atoms at the anionic sites. PbTe has an energy band of 0.32 eV at 300 K, which increases with an increase in temperature and thus contributes to enhanced thermoelectric performance at higher temperatures [44–46]. Various developments in band structure engineering techniques such as the introduction of resonant impurities, increased band convergence, and alloying, have led to remarkable improvements in the electronic properties and hence, in the thermoelectric performance of lead chalcogenides in recent years. For example, Heremens et al. reported a high zT value of 1.5 at 773 K in Tl-doped PbTe due to the presence of resonance states near the Fermi level [47]. Similarly, Pei et al. reported a zT of 1.8 at 850 K in Na-doped PbTe0.85Se0.15, which was attributed to increased band degeneracy at high temperatures caused by alloying with selenium [48]. Because Pb is very toxic, GeTe-rich alloys such as TAGS (GeTe-AgSbTe2) having zT  1 in the same temperature range of operation are investigated as an alternative to PbTe. These alloys possess the same rock-salt cubic structure of PbTe but undergo a phase transition to a rhombohedral structure when the concentration of GeTe exceeds 70% [49]. The ternary chalcogenide AgSbTe2 used to form TAGS is considered to be a promising material for low-to-medium temperature applications [50]. Recently, a p-type thermoelectric material was developed by preparing solid solutions of PbTe and AgSbTe2. These are represented by AgPbmSbTe2+ m (m ¼ 10, 12) and are known as “LAST” (Lead-Antimony-Silver-Tellurium alloys). These alloys have high crystal symmetry and low thermal conductivity values [51,52]. Yet another class of p-type thermoelectric material has been developed by adding Sn atoms to “LAST,” represented by the general formula AgPbmSnnSbTe2+ m+ n and known as “LASTT” (Lead-Antimony-Silver-Tellurium-Tin alloys). The transport properties of these alloys can be

Introduction and brief history of thermoelectric materials

9

tuned by varying the Pb:Sn ratio. Replacing all Pb atoms with Sn atoms leads to AgSnmSbTem+2, which is less toxic compared with PbTe [53]. At temperatures above 700 K, SiGe alloys have been in use since the 1960s. Despite elemental Si and Ge being very poor thermoelectrics due to their very high thermal conductivity, their alloy SiGe has shown considerably good thermoelectric performance. SiGe alloys, which have long been used in RTGs, are high-temperature (600–1300 K) thermoelectric materials owing to their excellent high temperature stability (melting point 1027°C). However, these alloys have very high thermal conductivities at room temperature [54]. No significant progress could be made in the efficiency of SiGe alloys from 1960 to 2000. It was only the introduction of nanotechnology that led to considerable gains in the efficiency of these materials. Recently, a maximum zT of 1.3 at 1173 K in n-type nanostructured phosphorus-doped SiGe bulk alloy was achieved, a 40% increase compared with that of pristine SiGe alloys (0.7) [55]. Other than Si and SiGe alloys, several other silicon-based materials such as Mg2Si and its solid solutions, higher manganese silicides (HMS), etc., have been explored for thermoelectric applications [56–58]. Mg2Si and its solid solutions represented by the general formula (Mg, Ca)2 (Si, Ge, Sn) are low-cost, environmentally friendly, thermoelectric materials. The constituent elements of Mg2Si are environmentally friendly and are among the most abundant elements in the Earth’s crust. For example, Si is the second most and Mg the eighth most abundant element. Mg2Si-based solid solutions have a very low mass density of the order of 2–3 g/cm3, which is roughly a factor of 3 lower than other thermoelectric materials such as PbTe- and CoSb3-based skutterudites that work in the same temperature region. Mg2X (with X ¼ Si, Ge, Sn) compounds are therefore especially promising where weight is crucial, such as space and airborne applications. The other Si-rich compounds in the Mn-Si binary system HMS have attracted attention as they consist of less-toxic and naturally abundant elements. These are found to be chemically and thermally stable. In 1979, Slack proposed that the materials that exhibit electronic properties, like those observed in crystalline solids, and phonon properties, like those observed in amorphous solids such as glass, are generally known PGEC materials, which made the best thermoelectric materials [30]. This observation set the stage for extensive research into materials with complex structures such as clathrates, skutterudites, etc., having large voids in their crystal structures. Clathrates are generally low thermal conductivity materials having complex cage-like crystal structure consisting of guest atoms. These guest atoms, known as “rattlers,” act as phonon scattering sites reducing the thermal conductivity of these materials. Depending on the type of tetrahedral coordination of families of clathrates with Al, Ga, Si, Ge, or Sn to form an open framework, this material system is subdivided into different types such as type I (A8E46), type II (A24E136), and type III (A30E172) clathrates. Clathrates are promising materials at temperatures above 600°C. Framework element substitution in clathrates results in the reduction of thermal conductivity through the introduction of ionized impurities and lattice defects into these materials [59–62]. Another important PGEC material skutterudites are represented by the general formula TX3, where T is a transition metal such as cobalt, iron, etc., and X is a metalloid

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Thermoelectricity and Advanced Thermoelectric Materials

element belonging to group 15 of the periodic table such as phosphorus, antimony, or arsenic. Skutterudites were first identified by Oftedal in 1928 as materials having an octahedral structure with voids at its center (space group Im3). Filling these voids with large cations such as ions of rare-earths known as rattlers facilitates modification of both electronic and lattice properties, hence enhances the figure of merit. These rattlers serve to optimize the carrier concentration and reduce the otherwise high thermal conductivity (10 W m1 K1) in these materials. Multiple filling of these voids significantly reduces the lattice thermal conductivity and hence enhances the thermoelectric performance [63–65]. The highest reported zT of 1.8 for a skutterudite was obtained in Ba0.08Yb0.04La0.05Co4Sb12, a multiple-filled skutterudite system [66]. Filled skutterudites are among the most efficient thermoelectric materials in the temperature range of 400–850 K. In addition to clathrates, Half-Heusler (HH) alloys are another important intermetallic compound investigated for thermoelectric applications. HH alloys are represented by the general formula XYZ, where X and Y are transition elements, and Z is the main group element. These alloys, having exceptionally high mechanical and thermal stability, are promising materials for high temperature applications. HH alloys are characterized by narrow band gaps and have a high room-temperature Seebeck coefficient (300 μV/K) and electrical conductivity values (103–104 S/cm). The only drawback of HH alloys is their relatively high thermal conductivity (10 W m1 K1) [67,68]. Scattering of phonons by the introduction of mass fluctuation and strain-field fluctuation effects leads to a lowering of thermal conductivity in them [69,70]. Among the numerous HH alloys, MNiSn and MCoSb systems are the most intensively investigated ones. Other emerging material systems include Zintl phases Zn4Sb3, layered cobaltites NaCo2O4, Ca3Co4O9, layered oxyselenides LaFeAsO, BiCuSeO (earlier explored only as superconductors), Tl9BiTe6, etc. [71–75]. More recently, several organic materials such as PEDOT poly (3, 4-ethylenedioxythiophene), PANI (polyaniline) also have caught attention for thermoelectric applications [76,77]. In 2012, a new concept of “Phonon Liquid Electron Crystal” (PLEC) was proposed by Liu et al. to explain the high thermoelectric performance (zT ¼ 1.5 at 1000 K) in Cu2Se, which has generated interest in binary Cu-based chalcogenides Cu2–δX (X ¼ S, Se, Te) for TE applications [78–81]. Apart from the development of numerous bulk materials with enhanced thermoelectric performance, superlattices, several nanostructured materials such as nanowires, nanocomposites, etc., have been developed with the aim of increased thermoelectric performance. Superlattices are structures consisting of alternating layers of materials that are good thermoelectric materials. Several superlattices such as Bi2Te3/Sb2Te3, Bi2Te3/Bi2Se3, PbSeTe/PbTe quantum dot superlattices, Si/Si1 xGex, and Si/Ge superlattices have been developed with the aim to increase zT [82,83]. Nanostructuring has been found to decrease thermal conductivity with the introduction of nanoscale heterogeneities and nanodispersions. The quantum confinement and energy filtering effects proposed by Hicks and Dresselhaus have been found to be effective in low dimensional material systems such as superlattices, nanowires, quantum dots, thin films, etc. [31,32]. These effects lead to an increased density

Introduction and brief history of thermoelectric materials

11

of states (DOS), leading to enhanced Seebeck coefficient values. On the other hand, the thermal conductivity decreases by scattering of phonons from the nanostructured surfaces or interfaces, consequently improving the zT of the materials. Beginning with the first commercialized thermoelectric material, Bi2Te3, the thermoelectric material family today has grown into a vast family consisting of materials ranging from semimetals and semiconductors to ceramics, from single crystals to polycrystalline materials and nanocomposites, and also materials in varying dimensions including bulk, thin films, and wires, etc. Presently, the search for materials with enhanced thermoelectric materials over wide temperature ranges for widespread commercial applications continues to drive thermoelectric material research.

1.5

Efficiency of thermoelectric materials and figure of merit

Altenkirch was one of the first who derived the efficiency of a thermoelectric generator, which is the ratio of the output power and the heat supplied per unit time to the hot side, using a constant property model according to which the thermoelectric properties of the materials were assumed to be temperature independent. It was Ioffe who in 1949 gave the modern dimensionless parameter, the figure of merit (zT), characterizing the performance of a thermoelectric device using the approximation of constant thermoelectric properties. zT ¼

S2 σ T κ

(1.6)

Where S2σ is the thermopower or the power factor, S is the Seebeck Coefficient, σ is the electrical conductivity, κ is the thermal conductivity of the material, and T is the absolute temperature. Ideal thermoelectric materials should possess a high electrical conductivity (σ), a high Seebeck coefficient (S), and a low thermal conductivity (κ) to have a high zT. The efficiency of a thermoelectric generator and COP of a Peltier cooler expressed in terms of the figure of merit are expressed as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P TH  TC 1 + ZT M  1 η¼ ¼ Q TH pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi TC 1 + ZT M + TH where ηc ¼

(1.7)

TH  TC is the Carnot’s efficiency. TH

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi TC 1 + ZT M  TC T pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H COP ¼ TH  TC 1 + ZT M + 1

(1.8)

12

Thermoelectricity and Advanced Thermoelectric Materials

The product of the Carnot’s efficiency, ηc, and the zT-dependent quantity gives the thermoelectric efficiency, where TH, TC, and TM are the temperatures of the hot side, cold side, and the average temperature at which a TE device is operating, respectively. A maximum zT value leads to maximum conversion efficiency. The conversion efficiency of presently available materials is 10%–15% (i.e., zT  1). The widespread commercial applications of thermoelectrics demand zT  3 or 4. The various parameters affecting zT are discussed as follows:

1.5.1 Carrier concentration The number of charge-carriers in a material affects both the electrical conductivity and the Seebeck coefficient; hence the charge-carrier concentration needs to be optimized to find efficient thermoelectric materials. The carrier concentration of a material can be controlled via extrinsic doping and by tuning the intrinsic point defects. The nature of the dopants and their concentration affect the charge-carrier type and its concentration. The charge-carrier concentration increases with temperature, which can be controlled further by alloying and doping [84,85].

1.5.2 Seebeck coefficient Seebeck coefficient is basically the voltage developed per unit temperature difference applied across a material. It is expressed in μV/K. Metals have very low Seebeck coefficient values (μV/K or less), hence are not suitable candidates for thermoelectric applications. Semiconductors possess Seebeck coefficient values of about 100 μV/K or greater. Seebeck coefficient has positive values for p-type and negative values for n-type semiconducting materials. An ideal thermoelectric must have a high Seebeck coefficient, generally of the order of 150–250 μV/K or greater. The Mott relation for the Seebeck coefficient (S) is given by: S¼

  Π 2 kβ 1 dnðEÞ 1  + E ¼ Ef kβ T n dE μ  3 q

(1.9)

where T is the temperature, n(E) is the carrier density at energy E, μ(E) is the carrier mobility at energy E, Ef is the Fermi energy, and q is the electronic charge. The Seebeck coefficient depends upon the absolute temperature, carrier concentration, and crystal structure of a material. Seebeck coefficient is a linear function of temperature only for small temperature differences; at higher temperatures, it has nonlinear temperature dependence. The carrier concentration influences both the Seebeck coefficient and the electrical conductivity, such that increasing the carrier concentration decreases the Seebeck coefficient and increases the electrical conductivity. Hence, an optimal carrier concentration is required to tune the power factor (S2σ). The various strategies for increasing the Seebeck coefficient include increasing the energy dependence of μ(E) and increasing the energy dependence of n(E) by a local increase in the DOS [47]. The type of dopants and their concentration have a

Introduction and brief history of thermoelectric materials

13

substantial effect on the Seebeck coefficient [86,87]. For example, in the case of Nadoped PbSe, the Seebeck coefficient is reduced with an increase in concentration, whereas Tl-doped PbTe systems have high Seebeck coefficient values that can be attributed to the introduction of resonant energy levels by Tl atoms [47]. K-doped systems have Seebeck coefficient values that are sensitive to dopant concentration.

1.5.3 Electrical conductivity Electrical conductivity is an important material-dependent property, which is the measure of the ability of a material to conduct electrical current. The electrical conductivity (σ) of a semiconductor is given by: σ ¼ eðμe n + μh pÞ

(1.10)

where e is the electronic charge, and μe, μh, n, and p are the electron mobility, the hole mobility, the electron density, and the hole density, respectively. Typical values of the electrical conductivity for a good thermoelectric material are on the order of 105 S/cm. The electrical conductivity of materials can be tuned either by varying the carrier concentration or by varying the carrier mobility. A high carrier concentration is generally required for a high electrical conductivity, which needs to be optimized to have a high thermoelectric performance. This can be achieved through extrinsic doping and tuning of the intrinsic point defects such as vacancies, interstitials, and antisites. High carrier mobility is also desired for efficient conduction of electricity, which is determined by the electronic structure of the materials and the various scattering mechanisms, such as lattice scattering, impurity scattering, alloy scattering, etc. For example, lattice scattering increases with an increase in temperature, which leads to a decrease in carrier mobility. Contrary to this, impurity scattering is dominant at low temperatures. Hence, the type of material, doping, impurities, and temperature determine the electrical conductivity of thermoelectric materials [88,89].

1.5.4 Thermal conductivity The thermal conductivity of a material determines its ability to conduct heat. In semiconductors, the total thermal conductivity κ is the sum of the contributions from the chargecarriers, i.e., electrons or holes, κ c, and the phonons κ l, i.e., κ ¼ κc + κl. The typical values of thermal conductivity for good thermoelectric materials are κ < 2W m1 K1 and κl  κ c. The charge thermal conductivity κ c is related to the electrical conductivity (σ) via the Wiedmann-Franz law, κc ¼ LσT, where L is the Lorentz constant, which is equal to 2.45  108 V2 K2 for metals and 1.5  108 V2 K2 for nondegenerate semiconductors [90]. Hence, an increase in the electrical conductivity, in turn, leads to an increase in the thermal conductivity due to charge-carriers. The charge-carrier thermal conductivity is affected by the bipolar conduction effects when the carrier concentration and mobilities of electrons and holes are comparable to each other.

14

Thermoelectricity and Advanced Thermoelectric Materials

The lattice thermal conductivity κl can be expressed as: κ l ¼ D  Cp  ρ

(1.11)

where D is the thermal diffusivity, Cp is the specific heat, and ρ is the density of the material. The lattice thermal conductivity depends on the crystal structure and lattice parameters of the material. The lattice thermal conductivity is expressed in terms of the lattice parameter, density of the material, and anharmonic lattice vibration as [90]: κl ¼

kβ3 a4 ρΘ3D h3 γ 2 T

(1.12)

where kβ, h, a, ρ, and γ denote the Boltzmann’s constant, Planck’s constant, lattice parameter, material density, and the Gr€ uneisen parameter (a measure of the anharmonicity of the lattice vibration), respectively. The lattice thermal conductivity can be reduced via doping or alloying, which alters the lattice parameter [70].

1.6

Current energy scenario and thermoelectricity

Continuous growth in the world’s population and rapid economic and industrial development in the last century has given rise to a global energy crisis and caused huge environmental degradation. The global demand for energy is growing continuously at a rate of 1% annually and is expected to rise further in the near future. Presently, approximately 80% of this energy demand is met through fossil fuels like coal, oil, and natural gas, and the rest is supplied by renewable sources of energy like biomass (8.9%), heat energy (4.2%), biofuels (1%), hydroenergy (3.9%), and wind, solar, geothermal, and ocean power (2.2%). Renewable energy is slowly replacing conventional fuels in various sectors such as electricity/power generation, motor fuels, rural energy services, etc. Global investments in renewable energy are on the rise in the backdrop of the continuous depletion of fossil fuels, which are nonrenewable sources of energy. As per reports, worldwide investments in renewable technologies reached $289 billion in 2018, with countries like the United States and China making huge investments in wind, solar, hydro, and biofuels [91,92]. These investments in renewable energy are expected to rise to meet the global energy demand. On the other hand, severe environmental problems such as global warming, climate change, ozone layer depletion, etc., caused due to the excessive use of fossil fuels have also necessitated the development of clean, environmentally friendly, sustainable sources of energy. Apart from growing concerns with the usage of fossil fuels, there is a pressing need for efficient sources of energy as nearly two-thirds of all available energy is wasted as heat in various household and industrial processes. Capturing the waste heat coming from various sources such as power plants, automobiles, factories, etc., and converting it into electrical energy can be an important component of energy security and can lead to several economic benefits. Several techniques such as the Rankine cycle, organic

Introduction and brief history of thermoelectric materials

15

Rankine cycle, air preheaters, etc., are in use to harness this waste heat. Among the various technologies developed so far, thermoelectrics is more attractive due to the absence of moving parts and sustainable and reliable operation. Thermoelectrics is an energy conversion technology involving the direct conversion of heat into electricity and vice versa. The various advantages of thermoelectrics include solid-state operation, no toxic residuals, and maintenance-free operation because of the absence of any moving parts or chemical reactions. The thermoelectric devices are highly scalable. Thermoelectrics is expected to play a growing role in increasing energy efficiency by utilizing waste heat. The thermoelectric generator market is projected to grow from USD $460 million in 2019 to USD $741 million by 2025 at a compound annual growth rate (CAGR) of 8.3% driven by the increasing demand to recover waste heat by various industries, growing environmental concerns, and need to increase engine efficiency. Factors such as rapid commercialization of thermoelectric generators in the automotive industry, the need for durable and maintenance-free power sources, increasing demand for miniaturized TEGs, along with increasing adoption of decarbonization technologies to reduce greenhouse gas emissions is expected to be the primary factors driving the thermoelectric generator market [93].

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Theory of energy conversion between heat and electricity

2

Shivprasad S. Shastri and Sudhir K. Pandey School of Engineering, Indian Institute of Technology Mandi, Kamand, India

2.1

Introduction

Thermoelectric materials are one such class of materials with the potential of becoming alternative and green energy generators in selective applications. These materials are useful in extracting heat energy and converting it into electricity, thereby harnessing the waste heat [1, 2]. The application of an electric field can create a temperature gradient in these materials, which makes them useful in refrigeration and cooling applications. Thermoelectric devices are solid-state energy generators so they are easily scalable, noise and vibration free, portable, and less polluting [3, 4]. These features make the thermoelectric materials attractive to bring into application. But, the lower efficiency of thermoelectric devices drives researchers to search for new efficient materials. The efficiency of the thermoelectric generator is mainly decided by its material’s figure of merit zT. The figure of merit is the screening quantity in selecting efficient materials. Generally, materials with zT
1.0 are considered to be suitable for commercial applications. The figure of merit of a material is given by zT ¼

S2 σT : κe + κ‘

(2.1)

Here, the Seebeck coefficient S, electrical conductivity σ, and electronic thermal conductivity κ e are the quantities derivable from an electronic structure, whereas the lattice thermal conductivity κ ‘ is dependent on the lattice vibrations [5]. In search of new thermoelectric materials via computational approach, calculation of these quantities becomes the primary task [6]. Also, the calculated transport coefficients help in explaining the experimental transport data. Therefore, understanding of electronic structure and phonon calculation methods and a transport theory are essential. In this direction, this chapter begins with the Drude description of conduction of electrons. Next, the semiclassical transport theory is presented. The calculation of Seebeck coefficient, electrical conductivity, and electronic thermal conductivity and their relation to electronic band structure are discussed. Similarly, the heat transport through phonons is also discussed. Furthermore, the direct method and density functional perturbation theory (DFPT) of phonon calculations are discussed. Using the direct method calculation of phonon lifetime, thermodynamical quantities and Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00008-4 Copyright © 2021 Elsevier Ltd. All rights reserved.

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Thermoelectricity and Advanced Thermoelectric Materials

thermal expansion are presented. To give an idea of how electronic energy states can be calculated, the key concepts of electronic structure calculation methods, namely, density functional theory (DFT) and DFT + U, are briefly summarized. Some of the important aspects that should be considered in computational predictions are discussed. The given segmentation method of efficiency calculation of thermoelectric generators is useful to evaluate the material for application. In the last section, a short review of the published results that give the applicability of various methods in investigating thermoelectric properties is done, which is useful to readers venturing into the field.

2.2

Electronic transport and its relation to electronic structure

To understand the electronic structure dependence of the figure of merit, it is important to know the following three quantities: (i) Seebeck coefficient S, (ii) electrical conductivity σ, and (iii) electronic part of thermal conductivity κe. Understanding these transport terms gives an insight into the electronic structure of the material since they are derivable from the electronic structure [5]. Then based on the theoretical understanding, modifications to the electronic structure can be predicted, which can improve the figure of merit. These changes to the electronic structure can be made by an appropriate combination of crystal structure, chemical elements, and doping. The first and simple explanation of these electronic transport terms can be made by applying Drude theory. This theory with the Sommerfeld correction is useful for a qualitative picture and explanation of transport properties of metals. Since good thermoelectric materials are doped semiconductors with high carrier concentration close to metals, the Drude model can be applied in many cases. However, for a precise and quantitative description of electronic transport coefficients, a more general theory is useful. The semiclassical transport theory becomes applicable in the quantitative description of electron transport in crystalline solids. The previously mentioned models [7] are described in the following sections.

2.2.1 Electronic transport under free electron theory The electrical conductivity in simple terms can be defined as the ability of materials to conduct electricity. The electrical conductivity is the proportionality constant between current density j and electric field E, which induces that j. According to the Drude theory for free electron gas in metals [7], it is expressed as σ¼

ne2 τ , m

(2.2)

where n is the number of free electrons per unit volume, e is electronic charge, τ is relaxation time, and m is mass of the electron. The relaxation time is a temperature-dependent quantity. In metals, due to electron-phonon scattering, τ

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23

decreases with temperature causing σ to decrease. Normally, the relaxation time varies inversely with temperature (τ ∝ T1). From the measured value of resistivity, one can estimate τ knowing the value of n. The value and sign of n can be obtained from Hall coefficient measurement. The resistivity ρ is related to conductivity as ρ ¼ 1/σ. The energy of an electron in a metal is given by the Sommerfeld model [7] as εðkÞ ¼

ħ2 k 2 , 2m

(2.3)

where k is one-electron level. If kF is the radius of the Fermi sphere, then the number of electrons per unit volume (or ground state electronic density) that does not vary with temperature is given by n¼

kF3 : 3π 2

(2.4)

This is related to Fermi energy, εF, and Fermi velocity, vF, as εF ¼

ħ2 kF2 2m

(2.5)

vF ¼

ħkF : m

(2.6)

and

Therefore, by knowing kF, εF, or vF, n can be calculated using Eqs. (2.4)–(2.6), which finally gives the electrical conductivity in Eq. (2.2). The thermal conductivity gives a notion of how good a material is in heat conduction. The transport of heat within a material occurs mainly through electrons and phonons. So, total thermal conductivity is mainly the sum of electronic and lattice thermal conductivity. According to Drude model in metals, most of the heat is transported by the large number of free electrons present. The application of the Drude model gives the electronic part of thermal conductivity as 1 κe ¼ cv v2 τ, 3

(2.7)

where v2 is the mean square electronic speed, cv is the electronic-specific heat at constant volume, and τ is relaxation time. Using Fermi-Dirac statistics under the Sommerfeld model, cv can be expressed as
 π 2 kB T cv ¼ nkB , 2 εF

(2.8)

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Thermoelectricity and Advanced Thermoelectric Materials

where kB is Boltzmann’s constant. The relation between electronic thermal conductivity of a metal to its electrical conductivity can be explained through the Wiedemann-Franz law. The law says that the ratio of electronic thermal conductivity to electrical conductivity is proportional to absolute temperature. By dividing Eq. (2.7) by Eq. (2.2) and using the expression of cv (Eq. 2.8), the law is given by κe ¼ LT, σ

(2.9)

where L is called Lorenz number, which is generally a constant in the case of metals, whose value is 2.44  108 WΩ K2. Here, the mean square velocity v2 of electrons (Eq. 2.7) can be considered as mean square Fermi velocity v2F , since in case of metals those electrons that are close to Fermi energy play an important role in transport. This formula also finds application in the case of explanation of electronic thermal conductivity of some highly doped semiconductors. The Seebeck coefficient of the material is a measure of induced voltage in the presence of a temperature gradient within the material. Under the Drude theory of metals, Seebeck coefficient is defined as S¼

cv : 3ne

(2.10)

By putting the value of cv equal to 32 nkB (in the classical approach), Eq. (2.10) becomes S¼

kB ¼ 0:43  104 V K1 : 2e

(2.11)

The previous expression gives the constant Seebeck coefficient, which indicates a failure to calculate the S using the classical value of specific heat for metals. By inclusion of Fermi-Dirac statistics, the electronic specific heat obtained under the Sommerfeld model is given by Eq. (2.8). The expression for S can be further derived using Eqs. (2.4), (2.5), and (2.8) in Eq. (2.10) as


 4π 2 kB2  π 2=3 S¼ mT, 3n 3eh2

(2.12)

where m is the mass of the electron. From Eq. (2.12), it is clear that the value of the Seebeck coefficient depends on n, m, and T. Since n and T are positive quantities, then sign of S depends on m only. Can we use this equation for intrinsic semiconductors? In semiconductors, the contribution to the Seebeck coefficient comes from the charge carriers, electrons, and holes. Hence, when applying the expression for intrinsic semiconductors, the m needs to be replaced by effective mass of electrons or holes in the band extrema. The sign of the Seebeck coefficient will be decided by those charge carriers that have dominating effective mass. Therefore, the sign of the Seebeck coefficient

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25

of the materials can be understood using Sommerfeld theory once band feature at the conduction band minimum or valence band maximum is known. This section provided an explanation of electronic transport under free electron theory. But, under this theory, the sign of the Seebeck coefficient cannot be properly predicted. The electronic thermal conductivity of semiconductors cannot be explained. The temperature dependence of the Lorenz number is not properly explained. The temperature and directional dependence of electrical conductivity is difficult to explain with this theory. These difficulties lead one to go for the semiclassical theory of transport. The semiclassical theory that relies on the band structure information of the material is useful in obtaining precise quantitative results of electronic transport. This theory and its relation to electronic band structure is discussed in the following section.

2.2.2 Electronic transport under semiclassical theory Qualitative descriptions on thermoelectric properties of materials can be explained under free electron theory. For quantification of thermoelectric properties, free electron theory is not appropriate. Here, we have to use the band theory to explain the thermoelectric properties more accurately. Here, the concept of conduction in materials can be understood by employing a nonequilibrium distribution function within relaxation-time approximation. In relaxation-time approximation [7], mainly it is assumed that an electron undergoes a collision for a very small time interval dt with the collision rate τ being the function of electron position r, wave vector k, and band index n. The nonequilibrium distribution function gives the probability of occupation of a state of the system when external influences like electric field, magnetic field, and/or temperature gradient, etc. are applied. The evolution of position, wave vector, and band index with time can be calculated once this distribution function is known according to the case. With the necessary modification in distribution function according to the case, how one can reach the equations of electrical conductivity, electronic thermal conductivity, and Seebeck coefficient is presented in this section [7]. This distribution function treats the case in which the electric field and temperature gradient are weak and spatially uniform. The relaxation time is taken to be independent of position because of the spatial homogeneity of electric field and temperature gradient. If the dependence of relaxation time on wave vector is only through εn(k), the τ now becomes τ ¼ τn(ε(k)). The nonequilibrium distribution function g(k, t) for single band under the semiclassical model [7] for the previous case is given as
 ∂f 0 dt0 eðtt Þ=τðεðkÞÞ  ∂ε ∞   εðkÞ  μ rTðt0 Þ ,  vðkðt0 ÞÞ  eEðt0 Þ  rμðt0 Þ  T Z

gðk,tÞ ¼ g0 ðkÞ +

t

(2.13)

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Thermoelectricity and Advanced Thermoelectric Materials

where g0(k) is the local equilibrium distribution function and f is Fermi-Dirac distribution function f ðεÞ ¼

1 : eðεμÞ=kB T + 1

(2.14)

Under equilibrium condition, g(k, t) reduces to Fermi-Dirac distribution function. Now in the presence of the static E and uniform temperature, the nonequilibrium distribution function reduces to:
 ∂f gðkÞ ¼ g ðkÞ  eE  vðkÞτðεðkÞÞ  : ∂ε 0

(2.15)

The electrical current density for a single band is defined as Z

dk vðkÞgðkÞ ¼ σE: 4π 3

j ¼ e

(2.16)

Using the g(k) (Eq. 2.15) in Eq. (2.16) makes it in the form j ¼ σE. The proportionality quantity is the electrical conductivity, which is generally a tensor. So, we find that the electrical conductivity of single band (nth band) is σ ðnÞ ¼ e2

Z


 dk ∂f τ ðε ðkÞÞv ðkÞv ðkÞ  , n n n n 4π 3 ∂ε ε¼εn ðkÞ

(2.17)

where vn(k) is the mean velocity of an electron in a level specified by band index n and wave vector k, and it is written as 1 vn ðkÞ ¼ —k εn ðkÞ: ħ

(2.18)

Here, εn(k) is the energy of an electron in a level given by band index n and wave vector k. It is to be noted that, at T ¼ 0 K, one can obtain the Drude form of electrical conductivity from Eq. (2.17), when effective mass tensor is independent of k, as σ¼

ne2 τ , m∗

(2.19)

where m* is the effective mass of the charge carriers. The total electrical conductivity can be calculated as the sum of contributions from each band and can be written as σ¼

X n

σ ðnÞ :

(2.20)

Theory of energy conversion between heat and electricity

27

When the uniform static electric field and temperature gradient are present, the nonequilibrium distribution in Eq. (2.13) takes the form:  
 ∂f εðkÞ  μ ð—TÞ , gðkÞ ¼ g ðkÞ + τðεðkÞÞ  vðkÞ  eE + ∂ε T 0

(2.21)

—μ : e

(2.22)

where E¼E+

Then the thermal current density is given by X Z dk j ¼ ½εn ðkÞ  μvn ðkÞgn ðkÞ: 4π 3 n q

(2.23)

Electrical current density as in Eq. (2.16) and thermal current density in the form of Eq. (2.23) can be obtained from distribution function (2.21) as j ¼ L11 E + L12 ð—TÞ,

(2.24)

jq ¼ L21 E + L22 ð—TÞ:

(2.25)

Here, the matrices Lij are given in terms of LðαÞ ¼ e2


 dk ∂f  τðεðkÞÞvðkÞvðkÞðεðkÞ  μÞα : 4π 3 ∂ε

Z

(2.26)

So, the matrices Lij now become L11 ¼ Lð0Þ ,

(2.27)

1 L21 ¼ TL12 ¼  Lð1Þ , e

(2.28)

L22 ¼

1 e2 T

Lð2Þ :

(2.29)

The structure of these results can be simplified by defining: Z σðεÞ ¼ e2 τðεÞ

dk δðε  εðkÞÞvðkÞvðkÞ: 4π 3

(2.30)

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Thermoelectricity and Advanced Thermoelectric Materials

Now, Eq. (2.26) in terms of the previous equation becomes L

ðαÞ

Z ¼




 ∂f dε  ðε  μÞα σðεÞ: ∂ε

(2.31)

It is to be noted that the L defined early are for single band and in the case of many bands, summation over the band index needs to be considered. ∂f In the case of metals, the factor ð ∂ε Þ is negligible except within O(kBT) of μ  εF. Therefore, the matrices Lij become L11 ¼ σ ¼ σðεF Þ, L22 ¼

π 2 kB2 T σ ðεF Þ, 3 e2

L21 ¼ TL12 ¼ 

π2 ðkB TÞ2 σ 0 ðεF Þ, 3e

(2.32) (2.33)

(2.34)

where σ0 ¼

  ∂ σðεÞ : ∂ε ε¼εF

(2.35)

It is important to note that thermal conductivity relates the thermal current to the temperature gradient with zero electric current. Hence, Eq. (2.24) becomes E ¼ ðL11 Þ1 L12 ð—TÞ:

(2.36)

On replacing E as given by the previous equation in Eq. (2.25), the thermal current density becomes jq ¼ κe ð—TÞ,

(2.37)

where κe is the thermal conductivity tensor given by κe ¼ L22  L21 ðL11 Þ1 L12 :

(2.38)

By considering the typical order of σ 0 as σ/εF and using Eqs. (2.32)–(2.34) in Eq. (2.38), we get
 kB T 2 κe ¼ L + O : εF 22

(2.39)

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29


 kB T 2 The term O for metals is negligible and hence applying the value of L22 εF (Eq. 2.33) in the previous equation, we can find the well-known Wiedemann-Franz law as
 π 2 kB 2 κe ¼ TσðεF Þ: 3 e

(2.40)

Here, the thermal conductivity tensor is proportional to the electrical conductivity tensor. From the definition of the Seebeck coefficient (or thermopower), it can be expressed as S¼

E : —T

(2.41)

In thermoelectric voltage measurement under a temperature gradient, there is a negligible flow of current (j  0). Hence, from Eq. (2.24) we can find that S¼

L12 : L11

(2.42)

For the case of metals using Eqs. (2.34) and (2.32) in the previous expression, we get the well-known Mott formula of thermopower S¼

π 2 kB2 T σ 0 ðεF Þ : 3 e σðεF Þ

(2.43)

This discussion showed how the transport properties can be obtained as a response to the applied fields or temperature gradient. The heat or electrical energy supplied makes the system shift to nonequilibrium, which is described by a distribution function. Knowing the equation of motion under the semiclassical model, distribution function, and energy of the particles, how the transport coefficients can be calculated was explained in this section. In the next section, the theory of heat transport through phonons in the crystal and its relation to phonon band structure will be discussed.

2.3

Heat transport through phonons and its relation to phonon band structure

In semiconductors or insulators, heat is mainly propagated through the lattice vibrations. The lattice vibrations in a crystalline solid are described using the picture of phonons or normal modes. One can employ the simple kinetic theory to explain the thermal conduction qualitatively like in the case of electrons [7]. If a monatomic

30

Thermoelectricity and Advanced Thermoelectric Materials

Bravais lattice is considered for a simple treatment, then there will be only acoustic phonons. All three acoustic branches can be described by the linear relation ω ¼ vk by applying the Debye approximation. Under a uniform temperature gradient applied, the lattice thermal conductivity κ ‘ is given by 1 κ‘ ¼ cv v2 τ: 3

(2.44)

The κ‘ is dependent on the lattice-specific heat at constant volume cv. The temperature dependence of κ ‘ mainly comes from the cv and phonon relaxation time τ. The phonon speed v does not majorly contribute to the temperature dependence of lattice thermal conductivity [7]. This relation can also be applied to get a simple qualitative idea of lattice thermal conductivity for thermoelectric materials. For a precise quantitative explanation of thermal conductivity as Eq. (2.44) suggests, the three quantities in the right-hand side of the equation need to be calculated using the full phonon spectrum. The calculation of phonon relaxation time, which normally decides the nature of κ‘ and makes it finite in a real crystal, is the crucial and challenging part. One of the methods of calculating lattice thermal conductivity is to directly solve the linearized Boltzmann transport equation (LBTE) [8]
 ∂g0λ ∂g vλ  —T ¼ : ∂t coll ∂T

(2.45)

Here, g0λ is equilibrium Bose-Einstein distribution and vλ is velocity of phonon mode λ. Here, λ denotes a phonon mode with wave vector q and band index j, that is, λ ¼ (q, j). The term on the right-hand side is called collision term, and it gives the scattering of phonon into and out of the state λ. The perturbed distribution function g is obtained as the sum of equilibrium and nonequilibrium distribution functions after imposing a small uniform temperature gradient. Another method of calculation is to use the closed form of lattice thermal conductivity under the supercell approach [9]: κ‘ ¼

1 X cλ vλ vλ τSMRT , λ NV0 λ

(2.46)

which is obtained after solving LBTE under single phonon mode relaxation time (SMRT) approximation. In this expression, V0 is volume of unit cell and N is the number of unit cells in the crystal. The terms cλ and vλ are the mode-dependent heat capaccan be ity and group velocity, respectively. The phonon relaxation time τSMRT λ approximately taken as phonon lifetime τλ. The group velocity and specific heat can be calculated from the harmonic phonon frequency ωλ obtained after solving the eigenvalue equation of dynamical matrix. The information about the full phonon spectrum of a material is given by ωλ and scattering of phonons can be described by the

Theory of energy conversion between heat and electricity

31

phonon lifetime. The phonon lifetime can be calculated from the imaginary part of self-energy, which is obtained by considering the anharmonic term in the expansion of crystal potential energy. In this direction, the following section of the chapter covers the phonon calculation methods that describe how to obtain these two quantities from first principles.

2.4

Phonon calculation methods

The explanation of properties, such as thermal conductivity of insulators (or semiconductors), specific heat, thermal expansion, etc., requires the consideration of lattice vibrations. These lattice vibrations in a solid are described using the concept of phonons. As in the case of electrons, the energy or frequency of phonons is a basic quantity from which other properties can be derived. Therefore, calculation of the phonon spectrum of a material from first-principles becomes important. After recent theoretical and computational developments, two different ways of calculating phonon frequencies in a solid are normally used. One is the direct method and the other is known as DFPT based on the linear-response approach. In direct method, force constant and phonon frequency are calculated by the finite displacement method (FDM) within the supercell structure [10]. For the direct method, the input forces required are taken from the DFT or DFT + U calculations. Here, we discuss both methods of phonon calculations.

2.4.1 Direct method Consider a perfect crystal at rest in which the κth ion in the lth unit cell is at the equilibrium position r(lκ). If the vibrations of ions are introduced by a displacement of u(lκ) with respect to equilibrium position, then the crystal potential energy Φ as a function of these displacements can be written as Φ ¼ Φ0 +

XX lκ

α

Φα ðlκÞuα ðlκÞ +

1XX Φαβ ðlκ,l0 k0 Þuα ðlκÞuβ ðl0 k0 Þ 2 ll0 κκ0 αβ

1 X X + Φαβγ ðlκ, l0 k0 ,l00 k00 Þ  uα ðlκÞuβ ðl0 κ0 Þuγ ðl00 κ00 Þ + ⋯ , 3! ll0 l00 κκ0 κ0 0 αβγ

(2.47)

where α, β, … are the Cartesian indices. Φ0, Φα(lκ), Φαβ(lκ, l0 κ0 ), and Φαβγ (lκ, l0 κ0 , l00 κ 00 ) are zeroth-, first-, second-, and third-order force constants, respectively. The vibrations in the crystal, due to small displacements at constant volume, are understood by using terms up to the second order, which is known as harmonic approximation. The other higher-order terms are taken care using perturbation theory. The higherorder terms capture the anharmonicity of the vibrations. The properties like thermal expansion, thermal conductivity require the inclusion of these terms to explain them. The force can be obtained from the potential energy as

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Thermoelectricity and Advanced Thermoelectric Materials

Fα ðlκÞ ¼ 

∂Φ : ∂uα ðlκÞ

(2.48)

Then the element of second-order force constant using the previous equation is written as ∂2 Φ ∂Fβ ðl0 κ0 Þ ¼  : ∂uα ðlκÞ∂uβ ðl0 κ0 Þ ∂uα ðlκÞ

(2.49)

Within the harmonic approximation, it is possible to understand any dynamical nature of ions by solving the eigenvalue equation of dynamical matrix D(q) DðqÞWqj ¼ ω2qj Wqj or

X βκ 0

βκ0 2 ακ Dαβ κκ 0 ðqÞWqj ¼ ωqj Wqj :

(2.50)

Here, Dαβ κκ 0 ðqÞ ¼

X Φαβ ð0κ,l0 κ0 Þ 0 0 pffiffiffiffiffiffiffiffiffiffiffiffi W iq  ½rðl κ Þrð0κÞ , 0 m m κ κ l0

(2.51)

where mκ is the mass of ion κ, ωqj and Wqj denote the respective phonon frequency and polarization vector of a phonon mode with the wave vector q and band index j, respectively. The phonon density of states (DOS) is obtained after normalizing with number of unit cells N: gðωÞ ¼

1X δðω  ωqj Þ: N qj

(2.52)

The energy E due to any phonon system can be obtained after getting the phonon frequencies of full Brillouin zone at temperature T: E¼

X

 ħωqj

qj

 1 1 + : 2 exp ðħωqj =kB TÞ  1

(2.53)

Here, kB is the Boltzmann constant and ħ is the reduced Planck constant. The group velocity of a phonon mode λ ¼ (q, j) with band index j and wave vector q is calculated from phonon frequency as vα ¼

∂ωλ : ∂qα

(2.54)

The group velocity is a useful quantity in the calculation of lattice thermal conductivity in solids.

Theory of energy conversion between heat and electricity

33

Another important thermodynamical quantity that is required in the calculation of lattice thermal conductivity is mode-dependent constant volume heat capacity cλ. Using the harmonic phonon frequency, cλ is calculated as
cλ ¼ kB

ħωλ kB T

2

exp ðħωλ =kB TÞ ½ exp ðħωλ =kB TÞ  12

:

(2.55)

Here, the temperature dependence of cλ is introduced through the Bose-Einstein distribution function.

2.4.2 Density functional perturbation theory In this method, the ground state energy is perturbed by a very small amount so that the system is shifted very slightly from its ground state [11, 12]. Then the solution of this problem can be addressed by applying perturbation theory. Thus, the lowenergy excitations obtained from lattice vibrations can be understood using DFPT. It has less computational complexities compared with the direct method. The total energy of the crystal with atoms slightly displaced from the equilibrium position can be written as ð0Þ Etot ð fΔτgÞ ¼ Etot

+

! ∂2 Etot Δτaκα Δτbκ0 β + ⋯ : a ∂τb 2 ∂τ 0 κα κ0β bκ β

XX1 aκα

(2.56)

Here, the atom κ of the unit cell a is displaced by an amount Δτaκα along α direction from the equilibrium position of τκ. The matrix element of the interatomic force constants (IFCs) is expressed by ! ∂2 Etot Cκα,κ0 β ða,bÞ ¼ : ∂τaκα ∂τbκ0β

(2.57)

The Fourier transformation of this equation for the N number of cells in the crystal is

1X Cκα,κ0 β ða, bÞeiq  ðRa Rb Þ N ab X ¼ Cκα,κ0 β ð0, bÞeiq  Rb :

C 0 ðqÞ ¼

κα,κ β

(2.58)

b

The eigenvalue equation of dynamical matrix (D κα,κ0 β ðqÞ) can be written using

C κα,κ0 β ðqÞ as X C κα, κ0 β ðqÞUqj ðκ0 βÞ ¼ Mκ ω2 Uqj ðκ0 αÞ, κ0 β

qj

(2.59)

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Thermoelectricity and Advanced Thermoelectric Materials

where the eigenvalues ωqj are known as the harmonic phonon frequencies and Uqj are the eigendisplacements for a phonon mode with wave vector q and band index j. The normalized phonon DOS can be obtained once the phonon frequencies are calculated as gðωÞ ¼

ð2πÞ3 X 3NΩ0 j

Z δðω  ωqj Þdq:

(2.60)

BZ

Using the Bose-Einstein distribution and calculated phonon frequency, the constant volume heat capacity cv as a function of temperature can be obtained as Z cv ¼ ð3NÞkB

ωmax


0

ħω=kB T eħω=2kB T  eħω=2kB T

2 gðωÞdω:

(2.61)

This method gives only harmonic phonon frequencies but without the need for supercell. This makes DFPT computationally faster compared with the direct method. However, the direct method explained before can also address anharmonicity of lattice vibrations. The use of direct method to obtain phonon lifetime is described in the next section.

2.4.3 Phonon lifetime The transport of thermal energy through phonons in a material depends upon the phonon relaxation time. The scattering of phonons makes the heat transport degrade along the length of the material. The calculation of phonon relaxation time is an important aspect in understanding the lattice thermal conductivity of a solid as discussed earlier. This quantity has a strong relation with phonon lifetime. Under pure harmonic theory, phonons have zero scattering with infinite thermal conductivity. Anharmonic lattice dynamics are required to take into account phonon scattering. To calculate this term, the third-order potential term Φ3 (anharmonic term) of Eq. (2.47) can be written using creation and annihilation operators with the concept of three-phonon collisions as [9] Φ3 ¼

X λλ0 λ0 0

Φλλ0 λ0 0 ð^ aλ + a^{λ Þð^ aλ0 + a^{λ0 Þð^ aλ0 0 + a^{λ0 0 Þ,

(2.62)

where the phonon modes (q, j) and (q, j) are expressed by λ and  λ, respectively. 00 The interaction strength of three phonons λ, λ0 , λ in a scattering is denoted by Φλλ0 λ0 0

sffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 XX ħ ¼ pffiffiffiffi Wα ðκ, λÞWβ ðκ0 , λ0 ÞWγ ðκ00 ,λ00 Þ 2mκ ωλ N 3! κκ0 κ00 αβγ sffiffiffiffiffiffiffiffiffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffi ħ ħ X Φαβγ ð0κ, l0 κ 0 ,l00 κ 00 Þ  00 0 0 2mκ ωλ 2m0κ0 ωλ l0 l0 0 0

0 0

 eiq  ½rðl κ Þrð0κÞ 00 00 0 0 0 00  eiq  ½rðl κ Þrð0κÞ eiðq + q + q Þ 

rð0κÞ

Δðq + q0 + q00 Þ:

(2.63)

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35

The Δ(q +q0 +q00 ) ¼ 1 if the sum q +q0 +q00 represents a reciprocal lattice vector, otherwise it will be 0. Here, the imaginary part of self-energy Γ λ(ω) is obtained from Φ3 with the help of many-body perturbation theory. The form of Γ λ(ω) can be written as 18π X |Φλλ0 λ00 |2 fðg0λ0 + g0λ00 + 1Þδðω  ωλ0  ωλ00 Þ ħ2 λ0 λ00 + ðg0λ0  g0λ0 0 Þ½δðω + ωλ0  ωλ00 Þ  δðω  ωλ0 + ωλ0 0 Þg:

Γ λ ðωÞ ¼

(2.64)

Here at equilibrium, the phonon occupation number is given by Bose-Einstein distribution g0λ 1 : exp ðħωλ =kB TÞ  1

g0λ ¼

(2.65)

The relation between phonon lifetime τλ and Γ λ(ωλ) for a particular phonon mode λ can be expressed by τλ ¼

1 : 2Γ λ ðωλ Þ

(2.66)

This calculated phonon lifetime can be approximately considered as single-mode phonon relaxation time in the calculation of lattice thermal conductivity. Once phonon relaxation time is obtained, the lattice thermal conductivity can be calculated using Eq. (2.46) with the help of group velocity (Eq. 2.54) and lattice-specific heat (Eq. 2.55).

2.4.4 Thermodynamical properties Using the direct method discussed earlier, the various thermodynamical properties of the material can be obtained [10]. The different thermodynamic quantities with temperature can be obtained using the following relations once the harmonic phonon frequencies are calculated. The temperature dependence on these quantities is introduced through Bose-Einstein distribution function. 1. Helmholtz free-energy Fph ¼

X 1X ħωqj + kB T ln½1  exp ðħωqj =kB TÞ: 2 qj qj

(2.67)

This phonon part of Helmholtz free-energy gives the phononic total energy of the crystal at a given temperature. This quantity can be used to find the temperature-dependent volume of the crystal as discussed in the next section. 2. Entropy S¼

X 1 X ħωqj coth½ħωqj =2kB T  kB ln½2 sinhðħωqj =2kB TÞ: 2T qj qj

(2.68)

36

Thermoelectricity and Advanced Thermoelectric Materials

The phonon contribution to entropy is given by the previous equation.

In addition to the earlier mentioned thermodynamical quantities mode Gr€uneisen parameter, thermal expansion and heat capacity at constant pressure can also be calculated. Out of these quantities, thermal expansion calculation, which is one of the useful quantities in thermoelectric generator design, will be discussed.

2.4.5 Thermal expansion coefficient The thermal expansion of a crystalline solid is one such property, for the explanation of it inclusion of anharmonic terms in the expansion of crystal potential energy is needed [7]. But the volume dependence on phonon frequencies for thermal expansion can be introduced by applying the harmonic approximation at each volume. This approximation is called the quasiharmonic approximation (QHA) [10]. To calculate the thermal expansion, the volumes of crystal at different temperatures are needed. Once the temperature-dependent volumes are known, the volumetric thermal expansion coefficient β(T) can be calculated. The equilibrium volumes (V (T)) at different temperatures needed to calculate β(T) are obtained by finding the minimum value of free-energy with respect to volumes. The free-energy F(T;V ) at each temperature as a function of volume is approximately taken as FðT;VÞ ’ Uel ðV0 Þ + Fph ðT;VÞ:

(2.69)

Here, Uel(V0) is the ground state total electronic energy and Fph(T;V ) is phonon Helmholtz free-energy. The Uel(V0) is obtained from DFT or DFT + U calculation at ground state equilibrium volume V0. And, at given temperature Fph(T;V ), it is calculated from harmonic phonon frequencies at different volumes. Computationally, the minimum value of free-energy can be found by using an equation of state (EOS) to fit the F(T;V ) versus volume curves at each temperature. The obtained minimum value of free-energy at each temperature corresponds to the equilibrium volume V (T) at that temperature. Now, from these obtained values of V (T), the volumetric thermal coefficient can be calculated as
 1 ∂VðTÞ βðTÞ ¼ : VðTÞ ∂T P

(2.70)

To calculate the thermal expansion coefficient of materials, QHA can be a reasonably good approximation for temperatures below the melting point.

Theory of energy conversion between heat and electricity

2.5

37

Thermoelectric transport in a nutshell

For the calculation of figure of merit, electrical conductivity, Seebeck coefficient, electronic thermal conductivity, and lattice thermal conductivity are needed. The equations of these quantities are summarized in this section. This gives the reader a quick glance of these quantities and the main terms on which they depend. 1. Electrical conductivity σðT,μÞ ¼

X

Z e2

n


 dk ∂f τ ðε ðkÞÞv ðkÞv ðkÞ  : n n n n 4π 3 ∂ε ε¼εn ðkÞ

Here, one can note that the temperature and chemical potential (μ) dependence on the electrical conductivity are introduced through the Fermi-Dirac distribution as f ðεÞ ¼

1 : eðεμÞ=kB T + 1

2. Seebeck coefficient SðT, μÞ ¼

L12 : L11

3. Electronic thermal conductivity κe ðT,μÞ ¼ L22  L21 ðL11 Þ1 L12 : Here, the matrices Lij are given by L11 ¼ Lð0Þ ,

1 L21 ¼ TL12 ¼  Lð1Þ , e 1 ð2Þ 22 L ¼ 2 L : e T

With the LðαÞ defined as LðαÞ ðT, μÞ ¼ e2

Z


 dk ∂f τðεðkÞÞvðkÞvðkÞðεðkÞ  μÞα :  4π 3 ∂ε

This expression introduces the temperature and chemical potential dependence on the Seebeck coefficient and electronic thermal conductivity in calculations. 4. Lattice thermal conductivity κ‘ ¼

1 X cλ vλ vλ τSMRT : λ NV0 λ

38

Thermoelectricity and Advanced Thermoelectric Materials

In the calculation of lattice part of thermal conductivity, temperature dependence is taken care by the Bose-Einstein distribution function. The electronic transport terms mainly depend on electronic eigenvalue (εn(k))derived quantities and electronic relaxation time τn(εn(k)), whereas the lattice thermal conductivity depends on the quantities obtainable from phonon frequency ωλ and pho. These are the material-specific quantities needed as basic non relaxation time τSMRT λ input for the calculations. Generally, electronic transport terms are calculated under constant relaxation time approximation. However, any transport theory cannot tell how to obtain these material-specific quantities. This aspect is addressed by the electronic structure methods. Here, in particular, two methods DFT and DFT + U can be considered. Using DFT or DFT + U as the calculator, the forces on atoms (further using which ωλ and τSMRT are obtained) and εn(k) are calculated ab initio. These λ two methods are briefly presented in the following sections.

2.6

Computational approaches based on DFT

2.6.1 Density functional theory DFT is based on the two famous theorems of Hohenberg and Kohn [13]. It states that if any nonspin-polarized interacting electrons are placed in an external potential (in this case, the Coulomb potential generated due to nuclei), the total energy E of this system is a unique functional of the ground state electronic density ρ as E ¼ E½ρ:

(2.71)

Hohenberg and Kohn theorems also say that the true ground state density ρ is the one that minimizes E[ρ], and the other ground state properties are also the functionals of ρ. Now, in case of spin-polarized system the E can be written as the functionals of spin density of spin-up (ρ") and spin-down (ρ#) electrons E ¼ E½ρ" ,ρ# :

(2.72)

But, the Hohenberg and Kohn theorems do not discuss the form of E[ρ]. To find the form of E[ρ] for the nonspin-polarized case, it is written as the sum of known and unknown terms: E½ρ ¼ T½ρ + Eei ½ρ + EH ½ρ + Eii ½ρ + Exc ½ρ,

(2.73)

where T[ρ] is the single particle kinetic energy, Eei[ρ] denotes the Coulomb interaction between the electrons and the nuclei, EH[ρ] is the Hartree part of electron-electron interaction, Eii[ρ] is the interaction energy between two nuclei that is considered as constant after Born-Oppenheimer approximation, and Exc[ρ] is known as the exchange-correlation (XC) functional, which is smaller than all the other parts but is most important to obtain the proper ground state properties. Here, Exc[ρ] is the

Theory of energy conversion between heat and electricity

39

unknown term and the rest of the terms are the known terms. In DFT, the approximation to electron-electron interaction enters through the XC term. Next, as mentioned by Kohn and Sham, the electron density may be found by the sum of single particle wave functions or orbitals. They also suggested that the ground state energy and density can be found by using variational property with the selfconsistent solution of a set of single particle Schr€ odinger-like equations. These equations are known as Kohn-Sham (KS) equations: fT + Vei ðrÞ + VH ðrÞ + Vxc ðrÞgφi ðrÞ ¼ Ei φi ðrÞ:

(2.74)

The density is obtained by taking the sum over the occupied orbitals as given by ρðrÞ ¼

X

φ∗i ðrÞφi ðrÞ:

(2.75)

occ

In the KS equation, Ei are the Kohn-Sham eigenvalues of corresponding Kohn-Sham orbitals φi(r), Vei is the Coulomb potential between nuclei and electron, VH is the Hartree potential, and Vxc is known as the XC potential. Both VH and Vxc are defined as Z VH ðrÞ ¼ e Vxc ðrÞ ¼

0

ρðr Þ dr , jr  r0 j 0

2

δExc ½ρ : δρðrÞ

(2.76)

(2.77)

It is seen that the form of Exc[ρ] is unknown and approximated in different ways. One of the most simplest and used approximations is known as local density approximation (LDA). The Exc[ρ] can be defined in terms of LDA: Z ELDA xc ½ρ ¼

drρðrÞExc ðρðrÞÞ:

(2.78)

Here, the approximation of Exc(ρ) is carried out by a local function of ρ. Another advanced approximation is known as generalized gradient approximation (GGA), where Exc is the function of both ρ and the gradient of local ρ (i.e., jrρj): Z EGGA xc ½ρ ¼

drρðrÞExc ðρðrÞ, jrðρÞj:

(2.79)

One of the recently developed Exc is known as meta-GGA, where Exc is written as Z ½ρ ¼ EmetaGGA xc where τðrÞ ¼

Pocc 1 i

drρðrÞExc ðρðrÞ,rρðrÞ,τðrÞÞ,

2 jrφi ðrÞj

2

is the positive orbital kinetic energy densities.

(2.80)

40

Thermoelectricity and Advanced Thermoelectric Materials

In DFT, the selection of the proper approximation to XC part becomes important since the form of εn(k) obtained through DFT is going to be dependent on the Exc[ρ]. In turn, this will affect the transport properties to be calculated. The self-consistent solution of Eqs. (2.74), (2.75) estimates the proper Ei of corresponding φi(r) for particular functional Exc. Another crucial aspect for finding the proper eigenvalues of a many-body electron system using the DFT method depends on the selection of basic function. Many methods such as pseudopotential and plane wave method, pseudopotential and projector augmented wave (PAW) method, full-potential linearized muffin tin orbital (LMTO) method, etc. exist depending on the basis set and potential type used. One of the most successful and widely used basis functions for the full-potential (here, all electrons are considered in the calculation) is known as the linearized augmented plane wave (LAPW) method. In this method, the solid is divided into muffin-tin spheres centered around nuclei and interstitial regions outside the muffin-tin spheres. In the muffin-tin sphere (S) and interstitial (I) region, the respective basis functions are defined as

φðrÞ ¼

Ω1=2 Σ G cG eiðG + kÞ:r rI Σ ‘m ½A‘m u‘ ðrÞ + B‘m u_‘ ðrÞY‘m ð^rÞ r  S,

(2.81)

where ‘ and m are the angular and magnetic quantum number, respectively, φ is the wave function, Ω is the unit cell volume, cG and A‘m are expansion coefficients, B‘m are the coefficients of the energy derivative, and u‘ is the solution of radial part of Schr€ odinger equation at the energy E‘. To find the solution of the Kohn-Sham equation (2.74), a proper choice for the Kohn-Sham orbital φi(r) is to be made. This choice is made depending on the computational cost, the type of problem to be addressed, and accuracy. Once a basis function of choice is selected, the Kohn-Sham orbitals are expanded as φi ðrÞ ¼

X α

ciα φα ðrÞ:

(2.82)

Here, φα(r) are the basis functions and ciα are the expansion coefficients. Once the form of basis function is chosen, solving of Eq. (2.74) involves mainly finding the coefficients ciα for the occupied orbitals, which minimize the total energy. This is done using the method of matrix diagonalization. So, after constructing the Kohn-Sham Hamiltonian H and overlapping matrices of Kohn-Sham orbitals, S, the following matrix equation is solved: ðH  Ei SÞci ¼ 0:

(2.83)

This equation is solved at each k-point in the irreducible Brilliouin zone. The size of the matrix is determined by the cut-off decided for basis functions, which in turn fix the number of coefficients ciα. Here, ci are the vectors for each Kohn-Sham orbital i, containing a number of coefficients ciα in Eq. (2.82). This choice of cut-off is decided

Theory of energy conversion between heat and electricity

41

based on the required accuracy and the properties to be studied. The higher the number of coefficients, the larger the matrix size, and the solution process consumes more computational time.

2.6.2 DFT + U DFT calculations with LDA or GGA are not able to estimate the proper ground state properties of the so-called strongly correlated electrons systems. These systems contain a spatially confined open d or f subshell, which is responsible for their localization effect and strong Coulomb repulsion among the d or f electrons [13]. Therefore, DFT based on homogeneous electron gas fails to explain the properties in the case of strongly correlated electron systems. This is because the DFT gives the energy of the occupied and unoccupied orbitals to be the same in the case of partially filled orbitals predicting the metallic ground state. But, in systems with partially filled d or f subshells, the occupied as well as unoccupied electronic energy levels do not have the same energy due to strong correlations or Coulomb interactions. This creates a gap between the occupied and unoccupied levels making the system basically an insulator due to strong correlation. The simple example of one such system is NiO. In NiO with the partially filled 3d-orbital, it is expected to be metallic in nature, but the strong correlation between d electrons makes it an insulator with a band gap of 4.3 eV [14]. Using the hybrid functionals as Exc may be one of the solutions, but it leads to computationally expensive calculations. Another simple and less computational costly method is DFT + U, where U is the on-site Coulomb interaction. In this case, the corrected energy functional for the total N number of d or f electrons can be defined as E ¼ ELDA  UNðN  1Þ=2 +

UX ni nj : 2 i6¼j

(2.84)

Here, ni is the occupation number of orbital i ¼ {ml, σ}. The last term of the previous equation is added to take into account the strong Coulomb interactions, whereas the second term represents a double counting term in one of the approaches, which is subtracted from the LDA total energy to make the correction [15]. This approach is one of the simple approaches of obtaining the total energy of a strongly correlated system. The orbital energies Ei are obtained by taking the derivatives of the previous equation: Ei ¼


 ∂E 1 ¼ ELDA + U  ni : ∂ni 2

(2.85)

Thus, the shifting of LDA orbital energy is observed from Eq. (2.85) by  U/2 (U/2) after inserting ni ¼ 1 (ni ¼ 0) for occupied (unoccupied) orbitals. This can lead to the creation of a gap in the electronic structure. Various general methods are developed where U and J (on-site exchange interaction) are used as input parameters in the calculation. Nowadays, there are two possible ways to calculate this U: (i) constrained

42

Thermoelectricity and Advanced Thermoelectric Materials

density functional theory (cDFT) [16] and (ii) constrained random-phase approximation (cRPA) [17, 18]. Typically, it is observed that the estimated value of U using cDFT for late transition metals is larger than that of cRPA [19, 20]. An example of cRPA calculation shows that the experimental result is quite good in matching the theoretical prediction when the calculated value of fully screened Coulomb interaction (W) is used as U parameter in DFT + U method, which can be seen in the work of Sihi and Pandey [21]. From the earlier two discussed methods, one can calculate electronic eigenvalues as well as forces on atoms. The electronic eigenvalues are the main input in calculating transport properties. The forces obtained from first-principles calculations can be further used as main input to calculate force constants and phonon frequencies. Here, the three most commonly used open source tools for the calculation of thermoelectric quantities are mentioned. For the calculation of electronic transport coefficients from the electronic energy bands, the open-source computational packages like BoltzTraP [22] or BoltzWann [23] exist. The BoltzTraP program, which is based on the Boltzmann theory, is one of the widely used tools to calculate thermoelectric or transport properties. The transport coefficients discussed in the previous section can be calculated by using BoltzTraP. In this code, the transport properties of the materials are calculated by using their dispersion relation as a basic input. The electrical conductivity can be calculated using Eq. (2.17) with the help of the following transformation (k!ε): σðεÞ ¼

e2 X δðε  εn ðkÞÞ : τn ðεn ðkÞÞvn ðkÞvn ðkÞ dε N n, k

(2.86)

In BoltzTraP code, the electronic part of thermal conductivity is calculated using Eq. (2.38). The second term of Eq. (2.39) is negligibly small far from the band-gap region, where the value of εF is very large compared with kBT. Therefore, to minimize the computational cost, electronic thermal conductivity can be approximated through the first term of Eq. (2.38), which is known as Wiedemann-Franz law (Eq. 2.40). The Seebeck coefficient of the materials can be calculated using Eq. (2.42), which is also implemented in BoltzTraP code. For the calculation of phonon frequencies, phonopy [10] is one of the most popular open-source tools. This code is based on the supercell and FDM. Using the harmonic force constants, dynamical matrix is constructed and used to solve the eigenvalue equation to get the polarization vectors and phonon frequencies. Once the phonon frequencies are known, group velocity, thermal properties, and other phonon-related properties are calculated. Phonopy is based on the direct method described earlier. The DFPT method implementation can be found in Abinit [24], Elk [25], or Quantum ESPRESSO [26] open-source packages. The lattice thermal conductivity under relaxation time approximation can be calculated using phonopy [9]. This program is based on the supercell approach. Using the cubic force constants, the imaginary part of self-energy and further phonon lifetime is

Theory of energy conversion between heat and electricity

43

calculated. Other open-source packages like ALAMODE [27] or almaBTE [28] can be used for lattice thermal conductivity calculations.

2.7

The theoretical aspects toward prediction of new thermoelectric materials

The discussed theory and calculation methods of the electronic transport, thermal transport, and electronic structure can be used to understand the experimental thermoelectric properties as well as to search for new thermoelectric materials. The search for new thermoelectric materials can be made either through experimental methods or through computational approaches. However, the experimental route of materials search is time consuming and normally resource consuming. Therefore, in searching for new thermoelectric materials, the computational method is the most preferable. A particular composition of elements and structure are chosen while predicting a new thermoelectric material through the first-principles calculations. A simple preliminary picture of whether the predicted material in that particular composition and structure can be synthesized or not is given by the formation energy and structural stability calculations, respectively.

2.7.1 Formation energy The formation energy value gives an indication of whether the material forms or not for a given composition of chemical elements. The formation energy is the energy needed to dissociate a material into its constituent parts. If, for example, X‘Ym is the chemical formula of the compound, then formation energy Eform is given by Eform ¼ EðX‘ Ym Þ  ½‘EðXÞ + mEðYÞ,

(2.87)

where E(X‘Ym) is the ground state energy of the compound, and E(X) and E(Y ) are the ground state energies of constituent elements in their conventional reference phases [29]. The negative value of Eform suggests the material can be synthesized.

2.7.2 Structural stability The question of whether, for a given crystal structure, the particular arrangement of atoms leads to a stable structure or not can be answered by phonon dispersion [10]. If the small atomic displacements from the equilibrium position leads to a decrease in the crystal potential energy, then the solution of the eigenvalue equation of the dynamical matrix gives the imaginary phonon frequencies. The crystal structure is said to be dynamically or mechanically unstable in this case. This condition is observed through the presence of negative frequencies in the phonon dispersion. Here, it is important to note that this condition is a simple preliminary criteria but not sufficient for structural stability.

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Thermoelectricity and Advanced Thermoelectric Materials

2.7.3 Role of band gap, band features, and prediction of thermoelectric properties DFT is the most commonly used tool in the study or search for new thermoelectric materials. But, when using DFT, the band-gap problem is a pitfall one needs to address in any such investigations because, generally in DFT, the band gap is not accurately obtained. To overcome this, there are other methods such as hybrid functionals, TranBlaha modified Becke Johnson (TB-mBJ) functional, or GW calculations. These are known to give more accurate band-gap values [30]. But, again, usage of hybrid functionals or GW methods is highly limited since they are computationally costlier at the present stage. But, the TB-mBJ functional is computationally cheaper and also found to give more accurate band gap [31]. The reason for the importance of considering proper band gap are understood as following: The calculated electrical conductivity, Seebeck coefficient, and electronic thermal conductivity are dependent on the carrier concentration and chemical potential values. In a semiconductor, the position of chemical potential depends on the value of band gap, which in turn decides the carrier concentration. Thus, for a plausible theoretical prediction of thermoelectric properties, proper band gap plays a key role. Also, one more observed setback when using DFT bands in transport properties calculation is the dependence of the band features on the XC functional used in the calculation. As discussed earlier, these electronic transport properties depend on the form of εn(k) (or band features), and group velocity and effective mass, which are derived from εn(k). Thus, in a prediction of thermoelectric properties, this aspect needs to be properly taken care of when using DFT calculations. Few results related to the role of band gap and band features and their benchmarking are discussed in the short review section, which provide better examples to readers.

2.7.4 Calculation of efficiency Once the thermoelectric figure of merit is calculated from the temperature-dependent thermoelectric quantities, one can evaluate the material for thermoelectric applications for a particular area based on its efficiency calculation. The theoretically calculated value of efficiency gives an indication of the applicability of materials in thermoelectric generators (TEG). This further motivates to experimentally synthesize the material. The maximum efficiency η max of a TEG is given by [32] pffiffiffiffiffiffiffiffiffiffiffiffi Th  Tc 1 + zT  1 pffiffiffiffiffiffiffiffiffiffiffiffi ηmax ¼ , Th 1 + zT + Tc =Th

(2.88)

where T is average temperature, Th is hot end temperature, and Tc is cold end temperature. Here, zT is the figure of merit of the material used. The maximum efficiency is a helpful criterion for the selection of material for TEG fabrication. Eq. (2.88) cannot be applied for a broad temperature range since zT is not the same at all temperatures. Therefore, for the calculation of efficiency, the method of segmentation as given in the work of Gaurav and Pandey [33] can be used. In this method, the working temperature profile of thermoelectric material is divided into n segments or

Theory of energy conversion between heat and electricity

45

slices. The number n of the elemental segments depend upon the Th, Tc, and temperature range ΔT of each segment as, n ¼ (Th  Tc)/ΔT. Then, efficiency of each segment ηi is calculated using the value of zT at temperature T of each segment. For example, the efficiency of segment 1 is obtained as follows. For segment 1, T1 ¼ Th  ΔT and T ¼ Th  ΔT 2 . The efficiency η1 is given by pffiffiffiffiffiffiffiffiffiffiffiffi 1 + zT  1 ΔT : η1 ¼ ΔT pffiffiffiffiffiffiffiffiffiffiffiffi T  ΔT T+ 2 2 1 + zT + ΔT

(2.89)

T+ 2

Similarly, the efficiency ηi of each segment can be obtained. Now, using the efficiency of an individual segment in series, the overall efficiency of TEG is obtained by the following formula: ηoverall ¼ 1  ð1  η1 Þð1  η2 Þð1  η3 Þ…ð1  ηn Þ:

(2.90)

This method can be also applied to calculate the efficiency of a hybrid TEG. The hybrid TEG is a TEG in which two or more thermoelectric materials stacked in series layers have increased efficiency. For a hybrid TEG made up of two materials, the efficiency of each layer of material can be obtained using Eq. (2.90) and overall efficiency is obtained as ηoverall ¼ 1  ð1  ηoverall1 Þð1  ηoverall2 Þ:

(2.91)

The cumulative efficiency is obtained from this formula in a temperature range Tc to Th. In a hybrid TEG, by stacking two materials in layers, the best suitable temperature at the interface that can give maximum efficiency is decided by compatibility factor s. The compatibility factor s is given by pffiffiffiffiffiffiffiffiffiffiffiffi 1 + zT  1 , s¼ αT

(2.92)

where α is Seebeck coefficient. Generally, two materials are said to be compatible for hybridization if the compatibility factors of the two materials at the interface temperature do not differ by a factor of 2 or more.

2.8

Theoretical and computational investigations of thermoelectric properties: A short review

In the earlier sections, the theory of electronic and phonon transports were introduced. These sections showed the relation of the electrical conductivity, electronic thermal conductivity, and Seebeck coefficient to electronic band structure. Similarly, how the lattice thermal conductivity and phonon energies are connected was also shown. The

46

Thermoelectricity and Advanced Thermoelectric Materials

electronic and phonon relaxation time are other important quantities deciding these transport terms. These discussions showed how the electronic transport coefficients are dependent on group velocity, effective mass, band gap, and band features, which also help in understanding the properties of thermoelectric materials. The electronic structure calculation methods, namely, DFT and DFT + U, are presented, which tell how to obtain the main input, electronic eigenvalues εn(k) needed for first-principles transport calculations. Here, the applicability of the methods discussed earlier and many other factors in understanding and explaining the thermoelectric properties are summarized in this section through a review of published results.

2.8.1 Importance of effective mass The effective mass is a band structure-derived quantity. Under simple parabolic 2 approximation, it is given as m* ¼ ħ2 =ðddkE2 Þ. But, the effective mass is a tensor quantity and can be obtained in matrix form at a given k-point. The transport properties to be calculated are going to be dependent on effective mass as shown earlier. Therefore, knowing the effective mass to understand thermoelectric properties becomes essential. Sharma and Pandey [34] gave a first-principles study of electronic structure and effective mass tensors of four materials, namely, PbTe, Mg2Si, FeGa3, and CoSb3. At the bottom of conduction band and top of the valence band, the effective mass tensors were calculated. The specific heat effective mass from band structure at a k-point can be approximately obtained as m*¼jMj1/3, where jMj is the determinant of effective mass tensor matrix M at that k-point. The other approximate method of obtaining the effective mass at the top of valence band and bottom of the conduction band is under parabolic approximation. If the bands in close vicinity of these band extrema are parabolic, one can apply this approximation. In the neighborhood of band extrema, parabola are fitted to get the curvature 2 of a band (ddkE2 ) in a particular direction. Using the definition of effective mass mentioned previously and the value of curvature extracted, one can get the effective mass. The effective mass values obtained from either of the earlier mentioned method can be used for an explanation of the Seebeck coefficient. The application of the latter approach is carried out in the work of Singh et al. in understanding the Seebeck coefficient of LaCoO3 [35] and ZnV2O4 [36] through electronic structure and Boltzmann transport calculation. In this work, the effective mass values at high symmetric points under parabolic approximation were calculated to see the contribution to Seebeck coefficient. The calculated effective mass values can also be used to estimate the temperature-dependent chemical potential and using which proper explanation of the Seebeck coefficient can be given. The relation between chemical potential and effective mass in a nondegenerate semiconductor (Eg ≫ kBT) at any temperature T can be obtained, which is described here. In an intrinsic semiconductor, the number of electrons in conduction band per unit volume (nc(T)) and the number of holes in valence band per unit volume (pv(T)) are given as [7]

Theory of energy conversion between heat and electricity

47

nc ðTÞ ¼ Nc ðTÞeðEc μÞ=kB T ,

(2.93)

pv ðTÞ ¼ Pv ðTÞeðμEv Þ=kB T ,

(2.94)

where Nc ðTÞ ¼


 1 2mc kB T 3=2 , 4 πħ2

(2.95)

Pv ðTÞ ¼


 1 2mv kB T 3=2 : 4 πħ2

(2.96)

Here, kB is Boltzmann constant, μ is chemical potential, Ec (Ev) is the energy at the CBM (VBM), and mc (mv) is the geometric mean of the eigenvalues of effective mass tensor at CBM (VBM), respectively. These effective mass tensors and their eigenvalues can be obtained using electronic structure code such as elk [25]. Then, from the previous relations, the chemical potential μ in an intrinsic semiconductor at any temperature T when the CBM and VBM are nondegenerate is given by
 1 3 mv μ ¼ Ev + Eg + kB T ln , 2 4 mc

(2.97)

where Eg is the band gap of the semiconductor. The application of the previous relation was shown by Singh and Pandey to find the μ value at 300 K in the case of LaCoO3 [35]. But, the mc and mv values only along certain directions obtained by fitting parabola were used. The more accurate estimation of μ can be made by using the geometric mean of the eigenvalues of effective mass tensor at CBM and VBM. In the case where the CBM and VBM are degenerate, then the equations for Nc(T) and Pv(T) will be modified as [7, 37]
 1 2kB 3=2 X α 3=2 Nc ðTÞ ¼ ðmc TÞ , 4 πħ2 α

(2.98)


 1 2kB 3=2 X α 3=2 ðmv TÞ , 4 πħ2 α

(2.99)

Pv ðTÞ ¼

where α denotes the index of the degenerate band at CBM or VBM indicating a sum over each such minimum or maximum. Then, from these relations, the chemical potential μ in the case of an intrinsic semiconductor is given by

48

Thermoelectricity and Advanced Thermoelectric Materials

0X

ðmαv Þ3=2

1

B α C 1 1 C μ ¼ Ev + Eg + kB T ln B @X α 3=2 A: 2 2 ðmc Þ

(2.100)

α

This relation can be used to find the value of temperature-dependent chemical potential in a semiconductor in which CBM and VBM are degenerate. The application of the previous equation to include temperature dependence on μ can be seen in the work of Shastri and Pandey [37]. In this work, the Seebeck coefficient S, electrical conductivity per relaxation time σ/τ, and electronic thermal conductivity per relaxation time κ e/τ of ZrNiSn thermoelectric are calculated by including temperature dependence on μ.

2.8.2 Applicability of two-current model If the thermoelectric material under study is a spin-polarized system, the two-current model can be applied to understand its electronic transport properties. This model is known to explain the transport in some ferromagnetic transition metals, half-metallic ferromagnetic compounds, and antiferromagnetic transition metal oxides. Here, in understanding the transport in spin-polarized systems, how the two-current model can be applied is presented. In a two-current model, below Curie temperature (Tc), two independent parallel currents of spin-up and spin-down electrons are considered for the conduction in ferromagnetic transition metal [38]. In this model, the total electrical conductivity σ in the absence of spin-flip is given by [39] σ ¼ σ" + σ# ,

(2.101)

where, σ " and σ # are the respective conductivities of spin-up and spin-down channels. The total Seebeck coefficient S can be obtained by averaging two channel S, weighted by the respective conductivities as [40, 41] S ¼ ðS" σ " + S# σ # Þ=ðσ " + σ # Þ,

(2.102)

where S" and S# are the Seebeck coefficients of spin-up and spin-down channels, respectively. The effective electronic thermal conductivity κ e is given by the contribution from both the spin channels as [42] κe ¼ κ"e + κ#e :

(2.103)

The Heusler family contains many materials with features suitable to explore for thermoelectric applications [43]. The half-metallic ferromagnetic Heusler compounds are

Theory of energy conversion between heat and electricity

49

expected to be good thermoelectric materials due to their comparatively large Seebeck coefficient. This model was applied to understand the thermoelectric behavior of ferromagnetic Heusler compounds Co2MnGe and Fe2CoSi in the work of Sharma et al. [44, 45]. The transport properties calculated by applying the two-current model under Boltzmann theory for these two compounds are in fairly good agreement with experimental data. This model can also be applied to explain the transport behavior in half-metallic ferromagnetic strongly correlated oxide systems. In the work of Singh et al., two such systems La0.75Ba0.25CoO3 [46] and La0.82Ba0.18CoO3 [47] were investigated using DFT + U method and two-current model to explain the transport. Nice agreement between the experimental and calculated data showed the applicability of DFT + U method, Boltzmann transport theory, and two-current model to explain Seebeck coefficient and electrical conductivity of this kind of system.

2.8.3 Importance of band gap The band gap plays a crucial role in the transport behavior of a material. Because, the value of band gap changes from its T ¼ 0 K value with rise in temperature, it also becomes an important factor in deciding the number of carriers excited into the conduction band. However, in rigid band approximation (RBA) in which the electronic band features and band gap are assumed to be unaffected by temperature, fixed band gap value is used at all temperatures. The DFT or DFT + U method give the ground state band-gap value. This constant band gap is used in the transport calculations for the entire temperature range, which normally leads to the deviation at high temperatures. The deviations observed in the high temperature Seebeck coefficients of ZnV2O4 and LaCoO3 were addressed by Singh et al. [48]. They considered the suitable change in the band gap with temperature and found nice agreement with the experimental Seebeck coefficient values. The possible trend in the change in the values of band gap for both the compounds with temperature was shown. This work clearly showed the importance of considering temperature-dependent band gap in transport studies. Another important aspect when using DFT to calculate electronic dispersion and band gap of a thermoelectric material is that, in DFT, normally proper band gap values are not obtained. The value of band gap depends on the approximation used for the XC functional. In the search for new thermoelectric materials, where the thermoelectric properties are calculated from first-principles, this discrepancy in the band gap may lead to inaccurate predictions, because in electronic transport calculations the value of band-gap decides the position of chemical potential and thus number of carriers. Hence, proper selection of XC functional is an important step in any theoretical predictions using DFT. Such studies addressing the previously mentioned aspect can be found in the work of Shastri and Pandey [49] and Sk et al. [50]. These studies show the suitability of XC functionals in explaining the thermoelectric properties of two nonmagnetic Heuslers with semiconducting ground state Fe2VAl and Fe2TiSn as case examples. These studies suggested that mBJ functional can be used to study band gap and SCAN

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meta-GGA (or PBEsol) XC functional to describe the electronic dispersion of Febased Heusler type of compounds. Based on these results, how the combined two functionals approach can be employed in the prediction of thermoelectric properties can be found in the work of Shastri et al. for Fe2ScX (X ¼ P, As, Sb) compounds [51]. Strongly correlated electron systems with band gap are also one class of thermoelectric materials with potential applications. In the case of strongly correlated electron systems, the insulating gap arises due to the strong Coulomb interaction among the open d or f orbital electrons. The electronic structure of such systems is studied by the DFT + U method. Here, in this method, the selection of suitable value for U parameter is important to find the proper band gap. The studies of a few strongly correlated transition metal oxide systems by Singh et al. can be referred here to see the importance of U in explaining thermoelectric properties [35, 36, 47].

2.8.4 Chemical potential and doping concentration For a thermoelectric material to achieve high figure of merit, the power factor should be higher. This higher power factor can be attained in semiconductor thermoelectric materials by a suitable value of electron (n-type) or hole (p-type) doping. This doping concentration or number of carriers per unit volume in the material is dependent on chemical potential. In other words, in theoretical calculations, knowing the value of chemical potential one can find the carrier concentration. In computational programs like BoltzTraP used to compute thermoelectric properties, the doping is taken into account by the shift in chemical potential. Thus by plotting the calculated power factor as a function of chemical potential, one can find those values of chemical potential that would yield highest power factors. From these values of chemical potentials, one can predict the optimal electron or hole doping values. The predicted carrier concentration values are useful numbers for experimentalists. Such a prediction can be found in the work of Singh et al. for ZnV2O4 [36] and LaCoO3 [35] compounds and in the work of Shastri and Pandey for Fe2ScX (X ¼ P, As, Sb) compounds [51].

Acknowledgments The authors thank Antik Sihi and Shamim Sk for the initial help in writing the chapter. The authors also thank the Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India, for the funding (SERB Project Sanction Order No. EMR/2016/001511).

References [1] G.J. Snyder, E.S. Toberer, Complex thermoelectric materials, Nat. Mater. 7 (2) (2008) 105. [2] G. Snyder, Small thermoelectric generators, Electrochem. Soc. Interface 17 (3) (2008) 54–56. [3] M.S. Dresselhaus, G. Chen, M.Y. Tang, R. Yang, H. Lee, D. Wang, New directions for low-dimensional thermoelectric materials, Adv. Mater. 19 (8) (2007) 1043–1053.

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[4] T.M. Tritt, M.A. Subramanian, Thermoelectric materials, phenomena, and applications: a bird’s eye view, MRS Bull. 31 (3) (2006) 188–198. [5] G.D. Mahan, J.O. Sofo, The best thermoelectric, Proc. Natl Acad. Sci. 93 (15) (1996) 7436–7439. [6] J. Yang, L. Xi, W. Qiu, L. Wu, X. Shi, L. Chen, On the tuning of electrical and thermal transport in thermoelectrics: an integrated theory-experiment perspective, NPJ Comput. Mater. 2 (1) (2016) 1–17. [7] N. Ashcroft, N. Mermin, Solid State Physics, W.B. Saunders Company, Philadelphia, PA, 1976. [8] A. Ward, D. Broido, D.A. Stewart, G. Deinzer, Ab initio theory of the lattice thermal conductivity in diamond, Phys. Rev. B 80 (12) (2009) 125203. [9] A. Togo, L. Chaput, I. Tanaka, Distributions of phonon lifetimes in Brillouin zones, Phys. Rev. B 91 (9) (2015) 094306. [10] A. Togo, I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108 (2015) 1–5. [11] X. Gonze, C. Lee, Dynamical matrices, born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Phys. Rev. B 55 (16) (1997) 10355. [12] S. Baroni, S. De Gironcoli, A. Dal Corso, P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73 (2) (2001) 515. [13] D.J. Singh, L. Nordstrom, Planewaves, Pseudopotentials, and the LAPW Method, Springer Science & Business Media, 2006. [14] G. Sawatzky, J. Allen, Magnitude and origin of the band gap in NiO, Phys. Rev. Lett. 53 (24) (1984) 2339. [15] V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. CzyZ˙yk, G.A. Sawatzky, Densityfunctional theory and NiO photoemission spectra, Phys. Rev. B 48 (1993) 16929–16934. [16] V. Anisimov, O. Gunnarsson, Density-functional calculation of effective Coulomb interactions in metals, Phys. Rev. B 43 (10) (1991) 7570. [17] F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, A. Lichtenstein, Frequency-dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B 70 (19) (2004) 195104. [18] L. Vaugier, H. Jiang, S. Biermann, Hubbard U and Hund exchange J in transition metal oxides: screening versus localization trends from constrained random phase approximation, Phys. Rev. B 86 (16) (2012) 165105. [19] F. Aryasetiawan, K. Karlsson, O. Jepsen, U. Sch€onberger, Calculations of Hubbard U from first-principles, Phys. Rev. B 74 (12) (2006) 125106. [20] T. Miyake, F. Aryasetiawan, Screened Coulomb interaction in the maximally localized Wannier basis, Phys. Rev. B 77 (8) (2008) 085122. [21] A. Sihi, S.K. Pandey, A detailed electronic structure study of Vanadium metal by using different beyond-DFT methods, Eur. Phys. J. B 93 (1) (2020) 1–8. [22] G.K. Madsen, D.J. Singh, Boltztrap. A code for calculating band-structure dependent quantities, Comput. Phys. Commun. 175 (1) (2006) 67–71. [23] G. Pizzi, D. Volja, B. Kozinsky, M. Fornari, N. Marzari, Boltzwann: a code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis, Comput. Phys. Commun. 185 (1) (2014) 422–429. [24] X. Gonze, J.M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G.M. Rignanese, Firstprinciples computation of material properties: the ABINIT software project, Comput. Mater. Sci. 25 (3) (2002) 478–492. [25] http://elk.sourceforge.net.

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[26] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter. 39 (21) (2009) 395502. [27] T. Tadano, Y. Gohda, S. Tsuneyuki, Anharmonic force constants extracted from firstprinciples molecular dynamics: applications to heat transfer simulations, J. Phys. Condens. Matter. 26 (22) (2014) 225402. [28] J. Carrete, B. Vermeersch, A. Katre, A. van Roekeghem, T. Wang, G.K. Madsen, N. Mingo, almaBTE: a solver of the space-time dependent Boltzmann transport equation for phonons in structured materials, Comput. Phys. Commun. 220 (2017) 351–362. [29] V. Stevanovic, S. Lany, X. Zhang, A. Zunger, Correcting density functional theory for accurate predictions of compound enthalpies of formation: fitted elemental-phase reference energies, Phys. Rev. B 85 (11) (2012) 115104. [30] R.M. Martin, L. Reining, D.M. Ceperley, Interacting Electrons: Theory and Computational Approaches, Cambridge University Press, 2016. [31] F. Tran, P. Blaha, Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential, Phys. Rev. Lett. 102 (22) (2009) 226401. [32] B. Sherman, R. Heikes, R. Ure, Calculation of efficiency of thermoelectric devices, J. Appl. Phys. 31 (1) (1960) 1–16. [33] K. Gaurav, S.K. Pandey, Efficiency calculation of a thermoelectric generator for investigating the applicability of various thermoelectric materials, J. Renew. Sustain. Energy 9 (1) (2017) 014701. [34] S. Sharma, S.K. Pandey, A first-principle study of electronic band structures and effective mass tensors of thermoelectric materials: PbTe, Mg2Si, FeGa3 and CoSb3, Comput. Mater. Sci. 85 (2014) 340–346. [35] S. Singh, S.K. Pandey, Understanding the thermoelectric properties of LaCoO3 compound, Phil. Mag. 97 (6) (2017) 451–463. [36] S. Singh, R. Maurya, S.K. Pandey, Investigation of thermoelectric properties of ZnV2O4 compound at high temperatures, J. Phys. D Appl. Phys. 49 (42) (2016) 425601. [37] S.S. Shastri, S.K. Pandey, Thermoelectric properties, efficiency and thermal expansion of ZrNiSn half-Heusler by first-principles calculations, J. Phys. Condens. Matter. 32 (35) (2020) 355705. [38] N.F. Mott, Electrons in transition metals, Adv. Phys. 13 (51) (1964) 325–422. [39] J.W.F. Dorleijn, Electrical conduction in ferromagnetic metals, Philips Res. Rep. 31 (1976) 287. [40] H. Xiang, D.J. Singh, Suppression of thermopower of NaxCoO2 by an external magnetic field: Boltzmann transport combined with spin-polarized density functional theory, Phys. Rev. B 76 (19) (2007) 195111. [41] A. Botana, P.M. Botta, C. De la Calle, A. Pineiro, V. Pardo, D. Baldomir, Non-onedimensional behavior in charge-ordered structurally quasi-one-dimensional Sr6Co5O15, Phys. Rev. B 83 (18) (2011) 184420. [42] G.E. Bauer, E. Saitoh, B.J. Van Wees, Spin caloritronics, Nat. Mater. 11 (5) (2012) 391–399. [43] T. Graf, C. Felser, S.S. Parkin, Simple rules for the understanding of Heusler compounds, Prog. Solid State Chem. 39 (1) (2011) 1–50. [44] S. Sharma, S.K. Pandey, Applicability of two-current model in understanding the electronic transport behavior of inverse Heusler alloy: Fe2CoSi, Phys. Lett. A 379 (38) (2015) 2357–2361.

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[45] S. Sharma, S.K. Pandey, Investigation of the electronic and thermoelectric properties of Fe2ScX (X¼ P, As and Sb) full Heusler alloys by using first-principles calculations, J. Phys. D Appl. Phys. 47 (44) (2014) 445303. [46] S. Singh, D. Kumar, S.K. Pandey, An important role of temperature dependent scattering time in understanding the high temperature thermoelectric behavior of strongly correlated system: La0.75Ba0.25CoO3, J. Phys. Condens. Matter. 29 (10) (2017) 105601. [47] S. Singh, D. Kumara, S.K. Pandey, Experimental and theoretical investigations of thermoelectric properties of La0.82Ba0.18CoO3 compound in high temperature region, Phys. Lett. A 381 (36) (2017) 3101–3106. [48] S. Singh, S.K. Pandey, The importance of temperature dependent energy gap in the understanding of high temperature thermoelectric properties, Mater. Res. Express 3 (10) (2016) 105501. [49] S.S. Shastri, S.K. Pandey, Effect of density functionals on the vibrational and thermodynamic properties of Fe2VAl and Fe2TiSn compounds, Comput. Mater. Sci. 155 (2018) 282–287. [50] S. Sk, P. Devi, S. Singh, S.K. Pandey, Exploring the best scenario for understanding the high temperature thermoelectric behaviour of Fe2VAl, Mater. Res. Express 6 (2) (2018), 026302. [51] S.S. Shastri, S.K. Pandey, Two functionals approach in DFT for the prediction of thermoelectric properties of Fe2ScX (X¼ P, As and Sb) full-Heusler compounds, J. Phys. Condens. Matter. 31 (43) (2019) 435701.

Measurement of thermoelectric properties

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S.K. Tripathi and Sukhdeep Singh Centre for Advanced Studies in Physics, Department of Physics, Panjab University, Chandigarh, India

As is known by now, thermoelectric (TE) materials have shown promising potential as far as conversion of waste heat to electricity is concerned. Figure of merit (FOM) of a material, also called ZT, is a dimensionless number that quantifies the material’s capability for TE application and determines final efficiency (η). It is related to Seebeck coefficient, electrical conductivity, and thermal conductivity of the material by the relation given by [1–3]: ZT ¼

S2 σT kl + ke

(3.1)

where the denominator term represents the total thermal conductivity, kl is the thermal conductivity arising due to the lattice vibrations, and ke is the contribution to the heat transfer due to movement of charge carriers. All the parameters in Eq. (3.1) are temperature-dependent and interlinked to each other. Measurement of these parameters can be done through various methods, but each methodology has its own drawbacks. Thus, a particular method or geometry providing accurate results in the case of one sample can be erroneous for another. A very simple example of this discrepancy is the difference between the measurement techniques adopted for bulk and film sample measurements. Apart from the dimensions, electrical conductivity, surface roughness, etc. can also be decisive factors for choosing a particular method for measurement. This chapter describes the basic principle involved in the measurement of TE properties. A detailed description of the various methods employed at bulk and film scale for the measurement of TE properties are explained.

3.1

Measurement principles of electrical conductivity and thermopower

The basic principle and underlying mechanism in the measurement of electrical conductivity is the electrostatic force experienced by charge carriers under the applied electric field. This force accelerates charge carriers along the line of an applied electric field. In the case of electrons as carriers, this drift is opposite the direction of the electric field where the accelerated carriers suffer collisions due to impurity scattering and/or due to thermal vibration. Hence, the carriers’ velocities are a function of time, Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00004-7 Copyright © 2021 Elsevier Ltd. All rights reserved.

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and an average velocity, namely drift velocity, is assigned to carriers moving under the applied field [4]. Because the current (I) is defined as the amount of charge transported by carriers per unit time interval, there is a direct relation between the current and drift velocity of carriers. Furthermore, the velocity with which a carrier drifts is directly influenced by the material’s structure, defects, impurities, temperature, etc. Obstruction offered to the carrier’s mobility and thus drift velocity is quantified in terms of “resistance” of the material, which is obtained by taking the ratio of the potential difference and current through the material. Because resistance is a function of the material’s dimensions, the material’s ability to resist the flow of current is defined using the term “resistivity.” It is defined as the resistance of the material with a unit area of crosssection and unit length. Electrical conductivity can be further calculated from the reciprocal of resistivity. Thermopower measurement is based on the Seebeck effect where a temperature gradient applied across the material generates a potential at the end of the material. A simple visualization of the effect is depicted in Fig. 3.1 for both n- and p-type materials. Charge carriers move from the hot end to the cold end, which generates a negative potential at the cold end (due to electron majority) for the n-type material with positive at the hot end and vice-versa for p-type material. This effect enables a material to utilize a temperature gradient to generate useful electrical power. The amount of potential difference developed for a unit temperature difference is termed as the Seebeck coefficient of the material.

3.2

Methods of thermal conductivity measurement in bulk materials

Thermal conductivity of an efficient TE material is usually low where the values r1 and “H” is the height of

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Fig. 3.4 Radial heat flow method. From D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials, J. Electron. Packag. Trans. ASME 138 (2016) 1–64. https://doi.org/10.1115/1.4034605.

the sample. As far as testing methodology and requirements for this method are concerned, one can refer to ASTM C335 [14] and ISO 8497 [15] standard report.

3.2.4 Parallel technique This method is usually preferred for the samples that have very small dimensions (mm). It is near impossible to position or support thermocouples and measure the heat flow through them [16]. Hence a support post or a base, as shown in Fig. 3.5, is utilized that bears the weight of thermocouples, heater, and sink. Thermocouples are attached to the end of the post close to the source and other thermocouple is attached to the post close to the sink. Before attaching the sample to the support setup, thermal conductance of the post (Kp) is defined to determine its contribution to losses. Following this, thermal conductance measurements are performed with the sample attached to the post (Kp+s). Thermal conductance of the sample (Ks) is calculated by subtracting the Kp from Kp+s. The value of Ks is used to obtain thermal conductivity by using the expression: k¼

Ks l A

(3.6)

where “A” and “l” are the cross-section area and length of the sample, respectively.

Fig. 3.5 Parallel technique for thermal conductivity measurement. From D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials, J. Electron. Packag. Trans. ASME 138 (2016) 1–64. https://doi.org/10.1115/1.4034605.

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3.2.5 Pulsed technique The schematic for this methodology is depicted in Fig. 3.6 and employs heating the sample through a heating element driven by a periodic current. The current can be of sinusoidal or a simple square wave of constant amplitude and defined period. This method is similar to absolute methodology in geometry of setup but differs due to its transient nature of heating. Apart from construction, the main requirement of the method is that temperature difference between the hot and the cold end should be small. This facilitates a very low drift in the temperature of the cold end and thus can be assumed to be constant. The temperature oscillations (ΔT) produced by the oscillating heat input are plotted as a function of time where the graph of ΔT vs time shows a periodic maxima and minima. The difference between these extremes is designated as ΔTp-p and calculation of thermal conductance is done using the relation: K¼

  RI 2o Kτ tanh 2C ΔTpp

(3.7)

where τ, C, R, and Io is the half-period of the current, volumetric heat capacity of the material, resistance of the heater, and current through the heater, respectively. Eq. (3.7) can be solved numerically to obtain K and the value of thermal conductivity.

3.2.6 Laser flash method All the methods described earlier have a common problem of contact thermal resistance. It arises from the imperfect contact between two surfaces due to the difference in surface roughness. This results in an inefficient heat transfer across the surface due

Fig. 3.6 Pulsed heating method for thermal conductivity measurement. From D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials, J. Electron. Packag. Trans. ASME 138 (2016) 1–64. https://doi.org/10.1115/1.4034605.

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to lattice mismatch or discontinuity. This problem is eliminated in the case of the laser flash (LF) method where a noncontact optical method is utilized. This method was introduced in 1961 by W.L. Parker et al. [17]. LF method, as shown in Fig. 3.7, employs the heating of the sample using an optical (usually laser) pulse where the rise in temperature is detected by a high precision infrared (IR) sensor. Heating induces a temperature rise in the sample that is faster for the samples with higher thermal diffusivities. A graph of the normalized temperature (T/Tm) vs time is plotted where normalization factor is the maximum temperature (Tm). Thermal diffusivity (α) of the sample is calculated using the expression [17]: α¼

1:38d2 π 2 t1=2

(3.8)

where d is the thickness of the sample and t1/2 is the time taken by the sample to reach half of the Tm. The value of “α” can be used further to calculate thermal conductivity from the relation as [19]: k ¼ αρcp

(3.9)

where density (ρ) and specific heat capacity (cp) can be measured through trivial methods. LF method, due to its noncontact nature, has been vastly used in determination of thermal conductivity of TE samples [19–25].

Fig. 3.7 Schematic block for laser flash technique [18].

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3.3

63

Methods of thermal conductivity measurement in thin films

Most of the methods defined earlier (except for the LF method) fail to provide thermal conductivity results when the sample is in a thin film form with thickness in the order of μm. Positioning of thermocouples becomes a hectic task as it can result in the destruction of the delicate film sample. Hence different geometry is employed for the film measurements where the methodology may be steady state or transient-based. Also, thin film thermal conductivity may be dependent upon the direction in which the heat flow is set up or the orientation of the film’s crystal structure. Crystal orientation and grain growth of the film can be controlled in most of the cases by varying the conditions (like temperature, pressure, etc.) at which the films are deposited. It can also be controlled by postdeposition heat treatments like annealing [26–29]. On the other hand, measurements of thermal conductivity can be performed in two directions depending upon the direction in which the heat flow is set up. Measured conductivity is called in-plane thermal conductivity if the heat is set up in the film along the plane, i.e., perpendicular to the thickness of the film. Calculated thermal conductivity is designated as cross-plane thermal conductivity when heat flow is set up perpendicular to the plane of the film.

3.3.1 Steady state methodology The basic construction for the measurement of cross-plane thermal conductivity of thin film samples is shown in the schematic of Fig. 3.8A. A thin metallic strip is deposited onto the substrate before the sample film deposition, and then the film is deposited onto this metallic strip. Following this, another metallic strip is deposited onto the sample film with the same dimensions as that of the lower strip. The metallic strip is thin as far as the width and thickness are concerned, which results in a finite electrical resistance that may be of the order of tens of ohms. A DC current is set up through the upper metallic strip that heats up due to joule heating and heat generated is delivered to the sample. The losses to the environment are minimized by performing the measurements in the evacuated sample holder that is also shielded

Fig. 3.8 Steady state method for thermal conductivity measurement in film samples.

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from the electromagnetic interferences. Heat flows across the thickness of the films and causes a temperature rise in the metallic strip below. The temperature rise in both strips causes a change in the resistance. To have an observable change in resistance, gold (Au) is usually chosen as the strip material due to its high temperature coefficient of resistance (TCR) and inertness to oxidation. Changes in the resistances of strips can be used to calculate the temperature rise of both strips. The temperature of the top strip (T1) and bottom (T2) can be used to calculate the thermal conductivity of the films. On the other hand, sensor strips are deposited in the in-plane direction for in-plane thermal conductivity measurements. The major problem with the in-plane measurements is separating the amount of heat that flows from the film as some of heat flows through the substrate. This problem is overcome by employing the geometry of Fig. 3.8B where the film is transferred onto the support substrate or grown onto the substrate with the substrate below the film etched later. This cuts off the losses of heat to the substrate, and heat is conducted purely through the film. The value of in-plane thermal conductivity can be obtained from the relation [30, 31]: k¼

Ql 2dðT1  T2 Þ

(3.10)

where d is the film thickness and l is the length of the film within the support substrates. However, the methods defined earlier require modification for electrically conducting films as deposition of metallic strips on conducting samples can cause current leaks through the sample. This causes inefficient heating and inaccurate estimation of strip temperatures. Hence an additional insulating layer (usually dielectric) is added between the strip and conducting films sample as an isolator (Fig. 3.9A). Reference geometry, as depicted in Fig. 3.9B for the cross-plane case, is constructed with the same thickness of insulating layer and strips of same dimensions but without the sample film. Measurements are performed on both the sample and reference geometry where the temperature difference of the latter is subtracted from the former to obtain the temperature difference across the film. This difference is further used to calculate the film’s thermal conductivity.

Fig. 3.9 Schematic for thermal conductivity measurement of conducting film samples.

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3.3.2 3ω method Different methods like LF method [19, 25], Time Domain ThermoReflectance (TDTR) [32], etc. have been employed for the measurement of thermal conductivity. Three omega (3ω) method is one of the most reliable methods for thermal conductivity measurements on both bulk and film samples. The basic schematic of the geometry employed for 3ω measurements is depicted in Fig. 3.10. Method involves deposition of a sensor over the sample whose thermal conductivity is to be measured [33]. The sensor is a thin strip of metal (Fig. 3.10A) with contact pads at the end for applying the bias. The linear part (l) of the strip acts simultaneously like a heater and sensor. Sensor deposition over the sample surface can be done by any of the physical vapor deposition techniques. The resistance of the strip is labeled “Rh” in the Fig. 3.10B. The sample is placed in a sample holder and connected to the remaining three resistances of the bridge circuit, shown in Fig. 3.10B, through BNC connectors. Another geometry employs the single arm with the sample on top in series with a reference resistor, and the series combination is driven by a current source [34]. Sample holder is evacuated to minimize heat losses to the environment, and alternating current of frequency “ω” is set through the arms of the bridge [35]. The bridge is balanced using the variable resistance “Rv,” and this ensures a zero voltage at frequency ω. However, AC current passing through the metallic sensor produces heat oscillations in the sensor strip. This in turn results in the resistance oscillations (at frequency 2ω) in the strip (or sensor) and is given by the expression: RðT Þ ¼ Rho ð1 + αΔTAC ÞCos ð2ω + ϕÞ

Fig. 3.10 (A) Geometry of the metal sensor and (B) electric circuital connections for 3ω method.

(3.11)

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where ΔTAC is the amplitude of the temperature oscillations. This gives the relation for the net voltage across the heater given by: 1 Vsensor ¼ Iho Rho ð1 + αΔTDC ÞCos ðωtÞ + αjΔTAC jCos ðωt + ϕÞ 2 1 + αjΔTAC jCos ð3ωt + ϕÞ 2

(3.12)

Rho are the maximum of current and resistance magnitudes at room temperature, whereas α is the TCR of the metallic sensor. ΔTDC is the increase in temperature due to the DC component of heating that is steady, and jΔTAC j is the magnitude of the amplitude of temperature oscillations of the metal sensor. Phase lag between the current and the heat oscillations is denoted by ϕ. The convolution of the current oscillations (at frequency ω) and resistance oscillations (at 2ω) generate a harmonic voltage (V3ω) at frequency 3ω. This signal V3ω, third term in Eq. (3.12), is around 1000 times weaker that the signal at frequency ω (Vω), which is the remnant signal after balancing at the bridge output. Hence the V3ω is acquired using a lock-in amplifier that has a high input impedance and capability to dig out the V3ω signal from the stronger Vω background. This signal is plotted as a function of frequency, and the slope of the graph is used to calculate thermal conductivity. The exact expression relating the 3ω signal with the frequency is given as: 
 V3ω ¼ A ln ð2ωÞ + ln w2h =λ  2ξ + iπ=2

(3.13)

where the λ is the thermal diffusivity of the sample and 2w is the width of the sensor. Parameter “A” in the equation is the slope of the graph of V3ω vs 2ω plot and is given by the following expression: A¼

3 Vho αR1 ¼ ðSlopeÞ 4πlkRho ðRho + R1 Þ

(3.14)

Thus thermal conductivity is calculated by substituting the value of slope (A). Due to highly sensitive and detailed analytical nature of 3ω method, it is a highly preferred method along with LF method. Conventional 3ω methodology discussed earlier fails for most TE samples due to their conducting nature. This is due to the short circuit between sensor and conducting TE film, which causes the current leak through the sample and irregular heating. This problem is overcome by the reference methodology where reference sample shall be exactly same except for the absence of the conducting TE film. Measurements of temperature drop (ΔT) are done across both sample and reference geometry where the latter is subtracted from the former to obtain the ΔT of film. This value is further used to calculate thermal conductivity of film.

Measurement of thermoelectric properties

3.4

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Methods for electrical conductivity measurement

3.4.1 Two probe and four probe methods Magnitude of conductivity is calculated from the resistance of the given dimensions of the sample and resistance is further obtained by utilizing two methods. The methods employed are (1) two probe method and (2) four probe method. The basic schematic for two probe and four probe methods are given in Fig. 3.11. Two probe methods, as shown in Fig. 3.11A, consist of four probes where the current is injected through two of the probes and the resulting voltage is measured using the other two probes. The voltage and current probes are attached at the same point, which makes the two probe setup prone to contact resistance. On the other hand, in four probe methodology (Fig. 3.11B), the current is injected at point D and C, whereas the voltage is measured across points A and B. The resistance (R) is calculated using the ratio of voltage and current, and the conductivity is obtained using the relation: σ¼

l RA

(3.15)

here l is the length and A is the cross-section area of the sample. Conductivity is also related to the charge carrier concentration and carrier mobility through the following equation: σ ¼ neμ n in this expression is the conductivity and μ is the mobility of the carriers.

Fig. 3.11 General circuit for (A) two probe method and (B) four probe method.

(3.16)

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3.4.2 Van der Pauw method It is one of the most efficient methods for electrical conductivity measurement based on the four probe technique. Van der Pauw method employs deposition of four ohmic contacts at each corner of the sample. Fig. 3.12A and B show a film sample with four contacts at each corner of the sample where two of them are used to inject current and other two for potential drop measurement. Two alternate measurements where the first current (I12) is set up through the contacts “1” and “2” using a current source and potential drop (V34) is measured across the terminals “3” and “4.” The ratio of V34 and I12 is taken to obtain resistance, which is designated as RA. Next, the connections are swapped by setting up current (I23) through terminals “2” and “3” and measuring voltage (V14) between “1” and “4.” Ratio of V14 and I23 provides the value of resistance, which is further designated as RB. Sheet resistance (RS) of a sample is defined as the resistivity per unit thickness of a material. It is related to “RA” and “RB” by the relation [36]:  exp

   πRA πRB + exp ¼1 RS RS

(3.17)

This equation can be solved to obtain the value of RS where RS and thickness of film (d) can be further employed to calculate resistivity of the sample using the relation [37]: ρ ¼ RS d

(3.18)

Fig. 3.12 Electrical connections and electrode configuration in Van der Pauw methodology. From M.P. Gutierrez, H. Li, J. Patton, Thin Film Surface Resistivity, 2002.

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Methods for thermopower measurement

Fig. 3.13 shows the schematic of the measurement setup for Seebeck coefficient measurement where the system consists of a sample that may be in the bulk or film form. Measurement geometry consists of a heater attached to one end called the hot end. The other end is attached to a heat sink and denoted as the cold end. The temperatures of both ends are monitored using two thermocouples. One side of the sample is heated using the heater, and the value of the generated emf is acquired by the voltage probes attached to the samples. The thermoemf so generated is usually in the range of μV, and one has to employ a good voltmeter to acquire this signal. The value of Seebeck coefficient is calculated using the relation: S¼

ΔV ΔT

(3.19)

where ΔV is the thermoemf and ΔT is the applied temperature difference. The prime requirement for the accurate measurement of the Seebeck coefficient is that the voltage and temperature should be measured at the same point. As far as the temperaturedependent measurements are concerned, temperature of the sample is first ramped up to target temperature using a primary heater. Following this, a small temperature gradient is induced across the sample by using a secondary heater.

3.6

Test criteria and errors

Different sources of errors may contribute as far measurement of TE properties is concerned. Some of them are listed as follows: l

l

The first and foremost measurement errors arise due to the improper calibration of the instrument, which also includes the zero error adjustment. An incorrect zero error can lead to an inaccurate interpretation of the reading. In addition to this, stability of the sample environment is an important factor where measurements must be acquired once the sample environment has reached a steady state. This factor becomes crucial when the measurements are acquired in a vacuum where the measurement chamber pressure should be stable while taking measurements. Any leak of air can result in the absorption or desorption of species from or on the sample surface. This can cause fluctuations in the results where the effects are more pronounced for thin film.

Fig. 3.13 Basic schematic of the Seebeck coefficient measurement setup.

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Electrodes should not be Schottky but ohmic. Ohmic nature of electrodes can be confirmed by acquiring the conductivity measurements in both directions. Similar values of current and voltage in both directions are taken as evidence of formation of ohmic contacts. Next factor that may add to error is the reaction of the electrode and sample material at elevated temperatures, which may create false results in temperature-dependent measurements of TE properties. Apart from this, electrode material should have a melting point higher than the measurement temperature of interest, which ensures that there is no degradation of the electrode material. Apart from the melting point, electrode materials should have a low diffusion coefficient, which ensures repeatable values in the case of thermal cycling. Another factor that may influence the electrical conductivity measurements is the temperature coefficient of resistance for electrode material, which should be negligible compared with the sample material. As far as the Seebeck coefficient measurements are concerned, potential and temperature measurements should be acquired from the same points on the sample. Ohmic contacts are required for the accurate estimation of thermovoltage. Voltage arising due to contact potential should be addressed. Temperature difference (ΔT) of less than 5–6 K should be applied to the material so as to avoid any nonlinearity in measurements. Small temperature gradient ensures that the plot of ΔV vs ΔT is linear around the temperature at which the value of S is to be calculated. However, for nonlinear relation, Slope generates an inaccurate estimate of Seebeck coefficient. One of the most common sources of error in measurement of thermal conductivity is the loss of heat from the sample to the surrounding. This can be minimized by conducting the measurements in an evacuated setup. Another difficult task is to determine the heat flow where an alternative of reference sample was discussed, which further requires accurate determination of all parameters related to the reference geometry. The most critical part of thermal conductivity measurement by 3ω method is the determination of the temperature coefficient of resistance for the sensor. Another problem is the stabilization of the sample in a vacuum environment and avoiding parasitic effects due to contacts. Measurement of thermal conductivity of conducting samples by 3ω method requires fabrication of sample and reference geometries where both should be identical with the absence of the sample in the latter. This requires a very controlled fabrication process.

References [1] C. Gayner, K.K. Kar, Recent advances in thermoelectric materials, Prog. Mater. Sci. 83 (2016) 330–382, https://doi.org/10.1016/j.pmatsci.2016.07.002. [2] J.C. Zheng, Recent advances on thermoelectric materials, Front. Phys. China 3 (2008) 269–279, https://doi.org/10.1007/s11467-008-0028-9. [3] G. Chen, M.S. Dresselhaus, G. Dresselhaus, J.-P. Fleurial, T. Caillat, Recent developments in thermoelectric materials, Int. Mater. Rev. 48 (2003) 45–66, https://doi.org/10.1179/ 095066003225010182. [4] M.A. Wahab, Solid State Physics Structure and Properties of Materials, Narosa Publishing House, New Delhi, 1999.

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[5] C. Kim, D.H. Lopez, D.H. Kim, H. Kim, Dual defect system of tellurium antisites and silver interstitials in off-stoichiometric Bi2(Te,Se)3+y causing enhanced thermoelectric performance, J. Mater. Chem. A 7 (2019) 791–800, https://doi.org/10.1039/c8ta05261a. [6] J. He, T.M. Tritt, Advances in thermoelectric materials research: looking back and moving forward, Science (80-. ) 357 (2017), https://doi.org/10.1126/science.aak9997. [7] J.R. Sootsman, D.Y. Chung, M.G. Kanatzidis, New and old concepts in thermoelectric materials, Angew. Chem. Int. Ed. 48 (2009) 8616–8639, https://doi.org/10.1002/ anie.200900598. [8] C 177 – 97 Standard Test Method for Steady-State Heat Flux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate, n.d. [9] X. Zhang, P.Z. Cong, M. Fujii, A study on thermal contact resistance at the interface of two solids, Int. J. Thermophys. (2006), https://doi.org/10.1007/s10765-006-0064-z. [10] D5470 – 12 Standard Test Method for Thermal Transmission Properties of Thermally Conductive Electrical Insulation Materials 1, n.d. doi:https://doi.org/10.1520/D547012.2. [11] E 1225 – 04 Standard Test Method for Thermal Conductivity of Solids by Means of the Guarded- Comparative-Longitudinal Heat Flow Technique, 2004. [12] C 518 – 98 Standard Test Method for Steady-State Thermal Transmission Properties by Means of the Heat Flow Meter Apparatus 1, n.d. [13] E1530 – 11 Standard Test Method for Evaluating the Resistance to Thermal Transmission of Materials by the Guarded Heat Flow Meter Technique, n.d. doi: https://doi.org/10. 1520/E1530-11.2. [14] C 335 – 95 Standard Test Method for Steady-State Heat Transfer Properties of Horizontal Pipe, n.d. [15] ISO 8497 Determination of Steady-State Thermal Transmission Properties of Thermal Insulation for Circular Pipes, n.d. [16] D. Zhao, X. Qian, X. Gu, S.A. Jajja, R. Yang, Measurement techniques for thermal conductivity and interfacial thermal conductance of bulk and thin film materials, J. Electron. Packag. Trans. ASME 138 (2016) 1–64, https://doi.org/10.1115/1.4034605. [17] W.J. Parker, R.J. Jenkins, C.P. Butler, G.L. Abbott, Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity, J. Appl. Phys. 1961 (1679), https:// doi.org/10.1063/1.1728417. [18] R.C. Campbell, S.E. Smith, R.L. Dietz, Measurements of adhesive bondline effective thermal conductivity and thermal resistance using the laser flash method, Annu. IEEE Semicond. Therm. Meas. Manag. Symp. 1999 (1999) 83–97. [19] K. Shinzato, T. Baba, A laser flash apparatus for thermal diffusivity and specific heat capacity measurements, J. Therm. Anal. Calorim. 64 (1) (2001) 413–422, https://doi. org/10.1023/A:1011594609521. Akademiai Kiado´, co-published with Springer Science + Business Media B.V., Formerly Kluwer Academic. [20] T. Nishi, H. Shibata, H. Ohta, Y. Waseda, Thermal conductivities of molten iron, cobalt, and nickel by laser flash method, Metall. Mater. Trans. A 34 (2003) 2801–2807. [21] Y. Tada, M. Harada, M. Tanigaki, W. Eguchi, Laser flash method for measuring thermal conductivity of liquids—application to low thermal conductivity liquids, Rev. Sci. Instrum. 49 (1978) 1305, https://doi.org/10.1063/1.1135573. [22] B. Jang, Y. Sakka, N. Yamaguchi, H. Matsubara, H. Kim, Thermal conductivity of EBPVD ZrO2 – 4 mol % Y2O3 films using the laser flash method, J. Alloys Compd. 509 (2011) 1045–1049, https://doi.org/10.1016/j.jallcom.2010.08.162.

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[23] M. Ruoho, K. Valset, T. Finstad, I. Tittonen, Measurement of thin film thermal conductivity using the laser flash method, Nanotechnology 28 (2015) 1–6, https://doi.org/ 10.1088/0957-4484/26/19/195706. [24] H. Ohta, H. Shibata, Y. Waseda, New attempt for measuring thermal diffusivity of thin films by means of a laser flash method, Rev. Sci. Instrum. 60 (317) (1989) 317, https:// doi.org/10.1063/1.1140430. [25] E. Krumov, V. Mankov, N. Starbov, Thermal diffusivity measurements based on laser induced heat transfer in low-conductivity thin films, J. Optoelectron. Adv. Mater. 7 (2005) 2619–2624. [26] W. Zhu, Y. Deng, Y. Wang, B. Luo, L. Cao, Preferential growth transformation of Bi0.5Sb1.5Te3films induced by facile post-annealing process: Enhanced thermoelectric performance with layered structure, Thin Solid Films 556 (2014) 270–276, https://doi. org/10.1016/j.tsf.2014.02.041. [27] Z. Zhang, Y. Wang, Y. Deng, Y. Xu, The effect of (00l) crystal plane orientation on the thermoelectric properties of Bi2Te3 thin film, Solid State Commun. 151 (2011) 1520–1523, https://doi.org/10.1016/j.ssc.2011.07.036. [28] S. Singh, S. Jindal, S.K. Tripathi, High Seebeck coefficient in thermally evaporated Sb-In co-alloyed bismuth telluride thin film high Seebeck coefficient in thermally evaporated Sb-In co-alloyed bismuth telluride thin film, J. Appl. Phys. 127 (2020), https://doi.org/ 10.1063/1.5127108. 055103–1. [29] S. Singh, J. Singh, S.K. Tripathi, High thermopower in (00l)-oriented nanocrystalline BiSb-Te thin films produced by one-step thermal evaporation process, Vacuum 165 (2019) 12–18, https://doi.org/10.1016/j.vacuum.2019.03.055. [30] F. Volklein, H. Reith, A. Meier, Measuring methods for the investigation of in-plane and cross-plane thermal conductivity of thin films, Phys. Status Solidi A 118 (2013) 106–118,https://doi.org/10.1002/pssa.201228478. [31] J. Lee, Z. Li, J.P. Reifenberg, S. Lee, R. Sinclair, M. Asheghi, E. Kenneth, J. Lee, Z. Li, J.P. Reifenberg, S. Lee, R. Sinclair, M. Asheghi, K.E. Goodson, Thermal conductivity anisotropy and grain structure in Ge2Sb2Te5 films, J. Appl. Phys. 109 (2011) 084902, https:// doi.org/10.1063/1.3573505. [32] P. Jiang, X. Qian, R. Yang, Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials, J. Appl. Phys. 124 (2018), https:// doi.org/10.1063/1.5046944. [33] S. Singh, S.K. Tripathi, Designing and investigation of thermal conductivity set-up using 3ω method, AIP Conf. Proc. 2220 (2020) 080020, https://doi.org/10.1063/5.0001848. [34] S. Kudo, H. Hagino, S. Tanaka, K. Miyazaki, Determining the thermal conductivity of nanocrystalline bismuth telluride thin films using the differential 3 x method while accounting for thermal contact resistance, J. Electron. Mater. 44 (2021) 4–6, https:// doi.org/10.1007/s11664-015-3646-3. [35] K.T. Wojciechowski, R. Zybala, R. Mania, Application of DLC layers in 3-omega thermal conductivity method, J. Achiev. Mater. Manuf. Eng. 37 (2009) 512–517. http://yadda.icm. edu.pl/yadda/element/bwmeta1.element.baztech-article-BOS2-0021-0053. [36] M.P. Gutierrez, H. Li, J. Patton, Thin film surface resistivity, in: Mate 210 Experimental Methods in Materials Engineering, 2002. [37] G.P. Panta, D.P. Subedi, Electrical characterization of aluminum (Al) thin films measured by using four- point probe method, Kathmandu Univ. J. Sci. Eng. Technol. 8 (2012) 31–36.

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Min Honga,b, Jin Zoub,c, and Zhi-Gang Chena,b a Centre for Future Materials, University of Southern Queensland, Springfield Central, QLD, Australia, bSchool of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD, Australia, cCentre for Microscopy and Microanalysis, The University of Queensland, Brisbane, QLD, Australia

4.1

Introduction

Thermoelectrics, enabling the direct conversion between heat and electricity, has been considered as one of the ecofriendly energy conversion technologies to replace nonrenewable carbon-based fuels. So far, thermoelectric devices have been successfully applied in the fields of waste heat recovery, refrigeration, and power generation. To achieve wider application of thermoelectric materials, there is a demand to increase energy conversion efficiency, which is evaluated by the dimensionless figure of merit (zT). By definition, zT ¼ S2σT/κ, wherein S is Seebeck coefficient, σ is electrical conductivity, T is temperature, and κ is thermal conductivity [1]. Noteworthy, the combined parameter S2σ is generally referred to as the power factor and κ commonly includes contributions from electrons (κe) and phonons (κ l) [2]. The net increase in zT is, in general, achieved by enhancing S2σ and/or decreasing κl [3, 4]. Motivated by the development of physics, chemistry, and materials science, innovative strategies have been developed to enhance thermoelectric performance. The typical strategy for enhancing S2σ is band convergence, which adopts the contribution from the other lower conducting bands to enhance the overall electronic transport [5]. Moreover, the distortion of density of states near the Fermi level can lead to an enhancement in S2σ. As for decreasing κl, introducing extra phonon scattering centers, such as dislocations [6, 7], interstitial doping [8], stacking faults [9], and planar vacancies [10–12], can lead to an ultralow κl. In addition, the development of material synthesis has also made significant contributions to achieving high thermoelectric performance [13]. Compared with the ingots with zT less than 1 prepared by the conventional zone-melting method, zT of the ball-milled Bi0.5Sb1.5Te3 yielded a zT over 1.5 [14]. Moreover, the development of material synthesis can also improve the mechanical properties of thermoelectric materials so as to make robust thermoelectric devices [15, 16]. To achieve the industrial production of large-scale thermoelectric materials, a suitable synthesis method also needs to be established [17]. In this chapter, we make a comprehensive summary of the synthesis methods of thermoelectric materials by highlighting the contributions to property enhancement. First, we introduce the melting methods, including zone melting, solid-reaction Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00010-2 Copyright © 2021 Elsevier Ltd. All rights reserved.

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method, arc melting, induction melting, etc. Then, we go to the progress in ballmilling technology, which can be used to form pure-phase materials by mechanical alloying and produce fine powders from ingots. Following this, we present a summary of the solution method, which is based on wet-chemical reactions. Afterward, liquid exfoliation is presented to cover the achievement in developing thermoelectric materials composed of ultrathin films. Moreover, the high-pressure synthesis method is also introduced. Finally, the methods of electrodeposition and chemical vapor deposition (CVD) to fabricate low-dimensional thermoelectric materials are introduced.

4.2

Melting methods

As a traditional method, the melting method is widely used to synthesize thermoelectric materials. For example, the commercial Bi2Te3-based thermoelectric materials are produced by the zone-melting method [18]. According to the heating mechanisms (electric resistance, voltaic arc, eddy current, etc.), melting methods can be categorized into solid-state reaction, arc melting, induction melting, levitation melting, etc. For fabricating thermoelectric materials, these methods are intentionally selected based on the features of precursors and final products.

4.2.1 Zone melting In the zone melting process, a narrow region of an ingot material is melted, and this molten zone is moved through the material. The impurities are in the melt and moved to one end of the ingot. The driving force of the movement of impurities is the segregation coefficient, namely the ratio of an impurity in the solid phase to that in the liquid phase, which is commonly less than one. Therefore, at the solid/liquid boundary, the impurities tend to diffuse to the liquid region. Finally, the impurities can be segregated at the end of the crystal [19].

4.2.2 Solid-state reaction In the solid-state reaction method, quartz tubes are the ampule to contain the precursors. The quartz tubes are pretreated through baking to remove organic residues. When reactive elements are used, the inner walls of the quartz tubes are carbon-coated. Precursors are then sealed in fused quartz tubes under a vacuum and heated to the setting temperature in a muffle furnace. After holding for a certain period, the posttreatments, such as quenching or annealing, are performed to decrease the grain sizes or introduce nanostructures/lattice imperfections into the matrix materials. The solid-state reaction involves the setting temperature, temperature-increasing rate, dwell time, quenching, annealing temperature, and time, and modifying these factors can ensure the production of pure phase and tune the nanostructures of the materials. The solid-state reaction method can tune the doping level and introduce nanostructures. For example, the highly reactive alkali metals with different ratios (from 0.1% to 1%) were successfully doped into thermoelectric materials, such as PbTe [20], PbSe [21], and SnSe [22, 23], to tune the carrier concentrations so as to enhance the electronic

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transport properties. The interstitial Cu doping in the crystal lattices of SnTe [8] and PbTe [24] was reported to enhance thermoelectric performance. Moreover, combined with the postannealing process, various lattice imperfections, such as dislocations [25, 26] and planar vacancies [27, 28], were produced in the host materials to decrease κ l. One representative example is PbTe0.7S0.3 synthesized by solid-state reaction [29]. This material often undergoes decomposition to separate into PbTe and PbS; therefore, there exist grain boundaries and phase boundaries [29]. Fig. 4.1A is the highresolution transmission electron microscopy (HRTEM) image of the small-angle grain boundary (yellow curve) between PbS and PbS, and the inset selected area electro diffraction (SAED) pattern reveals the angle of 3.4 degrees. Fig. 4.1B shows the phase boundary between PbTe and PbS. The inset SAED pattern displays the split of spots. In addition, the observed dislocations exist in these two cases. The insets of HRTEM images in Fig. 4.1A and B clearly show the dislocation, and the corresponding geometric phase analysis (GPA) [30] indicating the strong strain associated with the dislocations. In the synthesized samples, precipitates can be observed. Fig. 4.1C and D shows the plate-like and cubic nanoprecipitates. The observed dislocations due to the mismatch of grains and nanoprecipitates significantly reinforce phonon scatterings and account for a remarkably decreased κl close to the amorphous

Fig. 4.1 (A) HRTEM image of PbS/PbS grain boundary marked. (B) HRTEM image of PbTe/ PbS phase boundary. Dislocations along the boundaries are marked with green dashed circles. Insets show the enlarged images of the dislocations, GPA strain analysis, and SAED patterns. HRTEM images of (C) 0.5% K-PbTe0.7S0.3 with plate precipitates and (D) 2.5% K-PbTe0.7S0.3 with cubic precipitates. Temperature-dependent (E) κ l and (F) zT for x% K-PbTe0.7S0.3. Reproduced with permission from H.J. Wu, L.D. Zhao, F.S. Zheng, D. Wu, Y.L. Pei, X. Tong, M.G. Kanatzidis, J.Q. He, Broad temperature plateau for thermoelectric figure of merit ZT> 2 in phase-separated PbTe0.7S0.3, Nat. Commun. 5 (2014) 4515. Copyright 2014, Nature Publishing Group.

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limit, as verified in the measured κl (Fig. 4.1E). The electron transport was also significantly enhanced. Therefore, a zT of >2 has been achieved (Fig. 4.1F).

4.2.3 Arc melting Although solid-state reactions have various advantages to advance the development of thermoelectric materials, it still has drawbacks. At a high temperature, for example, over 1200°C, quartz tubes tend to crack because of the reduced strength; therefore, it is difficult to maintain the high vacuum. It is difficult to melt the reactants with very high melting points using the conventional solid-state reaction with quartz tubes as the containers. Furthermore, solid-state reactions cannot be used to directly synthesize materials with highly active metals (such as Mg), which react with the quartz at high temperature. In these situations, alternative melting methods, such as arc melting, are employed to synthesis thermoelectric materials composed of elements with very high melting points or highly reactive reactants. Prior to the arc melting process, precursor powders are mixed and cold-pressed into a pellet. Then the pellet is loaded into the arc melting apparatus under a vacuum. The direct current generates the electrical arc between the pellet and the electrode. Consequently, the pellet is melted [31]. Control of the current, cooling water, and gap between the pellet and electrode is essential to produce high-quality materials. Arc melting can fabricate large-scale materials within a short period of time. Arc temperature can reach 3000°C, enabling the synthesis of clathrates [32], half-Heuslers [33], and Si1 xGex alloys [34]. Moreover, arc melting can be used to synthesize Mg alloys. Recently, n-type Mg3Sb1.50.5xBi0.50.5xTex was synthesized by arc melting, and its thermoelectric performance was significantly enhanced by band engineering [35]. Fig. 4.2A shows the temperature-dependent S2σ of such an n-type Mg3Sb1.50.5xBi0.50.5xTex. As can be seen, Mg3Sb1.48Bi0.48Te0.04 has the maximum S2σ, which is much higher than the reported values of p-type Mg3Sb2-based alloys [36, 37]. The enhancement in S2σ is due to the high band degeneracy of 6 for the conduction band. The significantly enhanced S2σ leads to a high zT over 1.6 in Mg3Sb1.48Bi0.48Te0.04, as shown in Fig. 4.2B. Arc melting enables the cross-substitution of framework elements in type I Ba8Ga16Ge30 clathrates, which introduce ionized impurities and lattice defects into the materials to increase the ionized impurity scattering of carriers and point defect scattering of lattice phonons. As a consequence, S2σ is dramatically increased, as shown in Fig. 4.2C. In addition, κ is significantly decreased. As shown in Fig. 4.2D, an overall zT of 1.2 is achieved in Ba8Ni0.31Zn0.52Ga13.06Ge32.2.

4.2.4 Induction melting Induction melting is based on electromagnetic induction. Specifically, the highfrequency current generates a rapidly alternating magnetic field, which results in an eddy current in the material. As a consequence, the material is heated up by Joule heating [38]. Induction heating has been used to synthesize skutterudites [39], halfHeuslers [40], and clathrates [32].

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Fig. 4.2 Temperature-dependent (A) κ and (B) zT of Mg3Sb1.50.5xBi0.50.5xTex prepared by arc melting and the comparison with Mg3Sb2 [36], Mg3Sb1.8Bi0.2 [36], and Na0.006Mg2.994Sb2 [37]. Temperature-dependent (C) S2σ and (D) zT for Ba8NiyGazGe46 y z prepared by arc melting. (A and B) Reproduced with permission from J. Zhang, L. Song, S.H. Pedersen, H. Yin, L.T. Hung, B.B. Iversen, Discovery of high-performance low-cost n-type Mg3Sb2-based thermoelectric materials with multi-valley conduction bands, Nat. Commun. 8 (2017) 13901. Copyright 2017, Nature Publishing Group. (C and D) Reproduced with permission from X. Shi, J. Yang, S. Bai, J. Yang, H. Wang, M. Chi, J.R. Salvador, W. Zhang, L. Chen, W. Wong-Ng, On the design of high-efficiency thermoelectric clathrates through a systematic cross-substitution of framework elements, Adv. Funct. Mater. 20 (2010) 755–763. Copyright 2010, Wiley-VCH.

A typical example of skutterudites prepared by induction melting is BauLavYbwCo4Sb12 [39]. Fig. 4.3A shows a high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of BauLavYbwCo4Sb12 skutterudites along h111i zone-axis. Uniform and highly crystalline skutterudite frameworks are clearly shown. Fig. 4.3B shows the high-resolution HAADF-STEM

a

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Fig. 4.3 (A) HAADF-STEM image of BauLavYbwCo4Sb12 skutterudites along zone-axis. (B) HAADF-STEM image of Ba0.08La0.05Yb0.04Co4Sb12 along < 001> zone-axis. (C) Enlarged view of framed area in (B) showing the atomic configuration that agrees with the atomic model. (D) Intensity profile of the atomic column along the framed area in (B). Reproduced with permission from X. Shi, J. Yang, J.R. Salvador, M. Chi, J.Y. Cho, H. Wang, S. Bai, J. Yang, W. Zhang, L. Chen, Multiple-filled skutterudites: high thermoelectric figure of merit through separately optimizing electrical and thermal transports, J. Am. Chem. Soc. 133 (2011) 7837– 7846. Copyright 2011, American Chemical Society.

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image of Ba0.08La0.05Yb0.04Co4Sb12 along h001i zone-axis. The columns of filler atoms are clearly observed. Compared with the homogeneous intensity of Sb or Co atomic columns, the significant intensity fluctuation among the columns of atomic fillers indicates a random distribution of the fillers in the voids of the skutterudite (Fig. 4.3C and D).

4.2.5 Levitation melting In the levitation melting method, a high-frequency furnace is used, and the heat is generated by the material itself [41]. Moreover, a magnetic field (using an extra coil) is coupled with the primary induction heating mode. The advantages are no external contact to avoid contamination and the magnetic field to ensure homogeneity. Levitation melting has been successfully employed to synthesize half-Heusler alloys [42–44]. Fig. 4.4A plots κ of the FeNbSb alloys prepared by the levitation melting method. After doping with Hf or Zr, κ is dramatically reduced, originating from the

Fig. 4.4 Temperature-dependent (A) κ, (B) κ l, and (C) zT of the Hf- or Zr-doped FeNbSb halfHeusler compared with other analogs [44–47]. (D) Maximum output power and conversion efficiency of the thermoelectric device composed of the as-prepared best n-type ZrNiSn- and p-type FeNbSb-based half-Heusler alloys. Reproduced with permission from C. Fu, S. Bai, Y. Liu, Y. Tang, L. Chen, X. Zhao, T. Zhu, Realizing high figure of merit in heavy-band p-type half-Heusler thermoelectric materials, Nat. Commun. 6 (2015) 8144. Copyright 2015, Nature Publishing Group.

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decreased κ l, as shown in Fig. 4.4B. The reduction of κl is very sensitive. Even with a small ratio of dopant, κ l is significantly decreased, which is due to the strong point defect scatterings. In addition, electronic transport has been enhanced. Consequently, a record-high zT of 1.5 has been achieved. In p-type FeNb1 xHfxSb, half-Heusler thermoelectric materials have been significantly improved (Fig. 4.4C). Using the asdeveloped best p-type FeNb1 xHfxSb and n-type ZrNiSn-based alloys, the thermoelectric device was assembled. Fig. 4.4D plots the measured output power and conversion efficiency. With the thermoelectric device shown in the inset of Fig. 4.4D, a maximum output power of 8.9 W and conversion efficiency of 6.2% were achieved when temperatures of cold and hot sides were set as 336 K and 991 K, respectively.

4.2.6 Self-propagation high-temperature synthesis In the self-propagation high-temperature synthesis (SHS), precursors are mixed and cold-pressed into a cylinder. The synthesis is initiated by heating one end of the cylinder, and a combustion wave caused by exothermic reactions passes through the remaining material. In this process, the chemical reaction is localized in the combustion zone that spontaneously propagates over the material. Featured by the time efficiency, precise control of composition, and minimization of energy, SHS has been widely used to synthesize thermoelectric materials of Cu2Se [48], Bi2Te3 xSex [49], SnTe [50], Mg2Si [51, 52], skutterudites [53], BiCuSeO [54], and other oxides [55, 56]. Fig. 4.5A plots κ and κl for the n-type Zr0.5Hf0.5NiSn0.985Sb0.015 and p-type Zr0.5Hf0.5CoSb0.8Sn0.2 prepared by the SHS method. SHS process generates dense arrays of dislocations in samples alloyed with Zr and Hf. Consequently, the κ and κ l of Zn and Hf alloyed half-Heusler samples are effectively suppressed compared with the unalloyed samples and counterparts prepared by other synthesis methods. Fig. 4.5B shows the temperature-dependent zT for the n-type Zr0.5Hf0.5NiSn0.985Sb0.015 and p-type Zr0.5Hf0.5CoSb0.8Sn0.2. Compared with other half-Heusler materials, zT in samples prepared by the SHS method has been significantly enhanced. Using the as-prepared half-Heusler materials, a thermoelectric device was developed. The thermoelectric leg was double-layered with half-Heusler materials and Bi2Te3. The finite element method was used to optimize the geometry of the thermoelectric leg to maximize efficiency, as shown in Fig. 4.5C and D. The contact resistivity was also optimized (Fig. 4.5E). On this basis, the assembled thermoelectric device yields a record-high efficiency of 12.4% and output power density of 1.5 W cm2 when the cold-side and hot-side temperatures are set as 313 K and 1048 K, respectively.

4.2.7 Melt spinning In the melt-spinning method, a thin stream of molten alloy is injected onto a rotating wheel, which is internally cooled, as shown in Fig. 4.6A [63]. The heat of the melts is rapidly transferred to the wheel, which induces a fast solidification of the liquid and continuously produces thin tapes or ribbons as shown in Fig. 4.6B. The cooling rate

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Fig. 4.5 Temperature-dependent (A) κ, κ l, and (B) zT of Zr0.5Hf0.5NiSn0.985Sb0.015 and Zr0.5Hf0.5CoSb0.8Sn0.2 with and without annealing. The reported values of (Zr, Hf) NiSn-based [57–59] and (Zr, Hf) CoSb-based [33, 60–62] half-Heusler alloys are included as comparisons. (C) Contour plot of calculated ηmax as functions of thermoelectric leg height ratios. (D) Calculated ηmax and Pd_max as a function of the cross-sectional area ratio at cold side temperature of 313 K and hot side temperature of 1048 K. (E) Contact resistances of interfaces between half-Heusler and Bi2Te3. (F) The measured ηmax and Pd_max against the hot side temperature, compared with the calculated values. Reproduced with permission from Y. Xing, R. Liu, J. Liao, Q. Zhang, X. Xia, C. Wang, H. Huang, J. Chu, M. Gu, T. Zhu, C. Zhu, F. Xu, D. Yao, Y. Zeng, S. Bai, C. Uher, L. Chen, High-efficiency half-Heusler thermoelectric modules enabled by self-propagating synthesis and topologic structure optimization, Energy Environ. Sci. 12 (2019) 3390–3399. Copyright 2019, The Royal Society of Chemistry.

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Fig. 4.6 Photos of (A) the melt-spinning system and (B) melt-spun Bi2Te3 ribbons. SPS images of single-element, melt-spinning, spark-plasma-sintered Bi2Te3; (C) free surface; and (D) contact surface. (E) and (F) HRTEM images of Bi0.48Sb1.52Te3 with nanocrystals embedded in the bulk matrix (G) TEM image and (H) HRTEM images of Bi0.48Sb1.52Te3 with nanoscale modulations. (A–D) Reproduced with permission from W. Xie, S. Wang, S. Zhu, J. He, X. Tang, Q. Zhang, T. M. Tritt, High performance Bi2Te3 nanocomposites prepared by single-element-melt-spinning spark plasma sintering, J. Mater. Sci. 48 (2013) 2745–2760. Copyright 2013, Springer. (E–H) Reproduced with permission from W. Xie, J. He, H.J. Kang, X. Tang, S. Zhu, M. Laver, S. Wang, J.R.D. Copley, C.M. Brown, Q. Zhang, T.M. Tritt, Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites, Nano Lett. 10 (2010) 3283–3289. Copyright 2010, American Chemical Society.

can be as high as 104 to 107 K min1, which leads to refined grains and nanostructures in the host materials. Practically, tuning the wheel rotating speed and the ejection pressure of molten liquid can effectively adjust the nano/microstructures of the asfabricated ribbons. Melt-spinning method has been used to fabricate a wide range of thermoelectric materials, including Bi2Te3-based alloys [64–66], skutterudites [67, 68], silicides [69, 70], half-Heuslers [71], and Zintl phase alloys [72]. Interesting micro/ nanostructures are often found in these materials synthesized by melt-spinning method and lead to significantly enhanced thermoelectric performance. Fig. 4.6C and D shows the scanning electron microscopy (SEM) images of the free surface and contact surface of Bi2 xSbxTe3, respectively [66]. The free surface shows interconnected dendritic crystals of 200–500 nm wide, whereas the contact surface displays dense features. The melt-spinning-processed ribbons are consolidated by spark plasma sintering (SPS). Fig. 4.6E–H are the transmission electron microscopy (TEM) images of sintered pellets, in which there exists a large number of nanocrystals

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with size of 10–20 nm. These unique nanostructures significantly enhance phonon scattering and result in a κ l, while the coherent grain boundary ensures the transport of charge carriers. Fig. 4.7A and B shows the temperature-dependent ρ and S for Bi0.48Sb1.52Te3 prepared by melting spin, compared with the commercial ingot. As can be seen, ρ of the melting-spinning sample is similar to that of the ingot, while S of the melting-spinning sample is slightly lower than that of the ingot. Favorably, κ is much lower in a melting-spinning sample (Fig. 4.7C), which is mainly caused by the significantly decreased κ l resulting from the observed dense nanocrystals in Fig. 4.6E–H. The significant reduction in κ overwhelms the slightly decreased electronic transport properties, leading to a peak zT of 1.5, which is higher than that of ingot.

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Fig. 4.7 Thermoelectric properties of Bi0.48Sb1.52Te3 prepared by melt spinning and SPS. (A) Electrical resistivity, (B) Seebeck coefficient, (C) lattice thermal conductivity, and (D) figure of merit. Reproduced with permission from W. Xie, J. He, H.J. Kang, X. Tang, S. Zhu, M. Laver, S. Wang, J.R.D. Copley, C.M. Brown, Q. Zhang, T.M. Tritt, Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites, Nano Lett. 10 (2010) 3283–3289. Copyright 2010, American Chemical Society.

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Ball milling

Ball milling includes mechanical alloying and mechanical grinding. Mechanical alloying can synthesize pure phase materials from elemental powders driven by mechanical energy [17, 73]. Mechanical grinding can efficiently produce fine powders from ingots. Featured by cost-effectiveness and high efficiency, ball milling has been broadly used to fabricate thermoelectric materials. Moreover, ball milling has led to an enhanced thermoelectric performance in materials of Mg alloys [74, 75], half-Heuslers [33, 76, 77], and SiGe [78, 79].

4.3.1 Mechanical alloying Mechanical alloying is a dry powder processing technique in which the powders mixed with the milling balls are sealed in a container (for example, stainless steel or tungsten) under a protective atmosphere to minimize oxidation. During the milling, the collision energy between grinding balls is effectively transferred to powders, which involves cold welding, fracturing, and rewelding of powder to form the pure phase. The factors affecting the intensity of ball milling are milling speed, duration, and the ratio of powders to balls. Adjusting these parameters can fabricate highquality materials. Moreover, organic agents, for example, stearic acid or ethanol are used to adjusting the milling process. Recently, high-performance n-type Mg2Sn1 x yGexSby was fabricated by the mechanical alloying method [74]. Fig. 4.8 plots the temperature-dependent 1/σ, S, κ, and zT for these materials. As can be seen, a peak zT of 1.4 was achieved at 450 K. Considering the high zT and the cheap cost, the n-type Mg2Sn1 x yGexSby is likely to be a promising thermoelectric candidate.

4.3.2 Mechanical grinding Using ball milling to grind the ingot of Bi0.5Sb1.5Te3 can significantly decrease the grain size and introduce nanocrystals into the matrix [14]. The grain sizes are reduced to nanoscale, and the nanograins have high crystalline quality with clean grain boundaries. Moreover, there exist Sb-rich nanodots embedded in the matrix. Benefiting from the obtained nanoscale grains and the embed nanodots, phonon scattering has been significantly enhanced, leading to much lower κ in the ball milling-processed sample compared with the ingot counterpart. As a result, a zT of 1.5 was achieved at 110°C, higher than that of ingot [14].

4.4

Solution synthesis

The solution synthesis method has been widely used to synthesize thermoelectric materials because of the advantages of low synthesis temperature, small particle size, and well-controlled morphology. The most widely used solution synthesis method for

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Fig. 4.8 Thermoelectric properties of Mg2Sn1 x yGexSby prepared by ball milling mechanical alloying: (A) Electrical resistivity (1/σ), (B) S, (C) κ, and (D) zT. Reproduced with permission from W. Liu, J. Zhou, Q. Jie, Y. Li, H.S. Kim, J. Bao, G. Chen, Z Ren, New insight into the material parameter B to understand the enhanced thermoelectric performance of Mg2Sn1-x-yGexSby, Energy Environ. Sci. 9 (2015) 530–539. Copyright 2015, The Royal Society of Chemistry.

thermoelectric materials include solution synthesis under atmosphere pressure, solvothermal synthesis, and microwave-assisted solvothermal method [80].

4.4.1 Solution synthesis under atmosphere pressure Solution synthesis under atmosphere pressure was developed to synthesize ultrathin Te-rich Bi2Te3 nanowires [81], PbTe-Ag2Te nanowire heterostructure [82], and ultrathin PbTe nanowires [83]. Because of the nanoscale grain size and electron filtering effect to remove the low-energy carrier, thermoelectric performance has been enhanced in these rationally fabricated nanostructured thermoelectric materials. In addition, Bi2Te2.5Se0.5 hollow nanorods can be also synthesized by a similar method. The sintered pellet from the as-synthesized nanomaterials shows high-density pores, leading to an ultralow κ. Therefore, the thermoelectric performance was also enhanced [84]. Such a solution method was applicable to synthesize new thermoelectric materials, for example, nanorods of Bi13S18I2 + 2% BiCl3, and leads to promising thermoelectric performance [85].

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4.4.2 Conventional solvothermal synthesis Solvothermal synthesis is widely used to fabricate a wide range of nanoscale and nanostructured materials. In this process, precursors with the end-product stoichiometry are mixed in an organic solvent with reduction and template reagents. After being stirred completely, the mixture is added into a sealed autoclave, which is heated at a temperature normally between 100°C and 250°C for a period of time [86, 87]. Finally, once cooled to room temperature, the products are washed, centrifuged, and dried. One of the outstanding features of this method is that the morphology and size of products can be controlled [88, 89]. Under the high pressure and high temperature, wellcrystalline nanostructured thermoelectric materials can be fabricated [90, 91]. Using ethylene glycol as the solvent and polyvinyl pyrrolidone as the surfactant, the Tshaped Te/Bi2Te3 nanostructures were synthesized [92]. Fig. 4.9A is the TEM image of a typical T-shaped Te/Bi2Te3 nanostructure. The composition difference was examined by EDS, shown in Fig. 4.9B. The growth of such a nanostructure is driven by the crystalline relationship between Te and Bi2Te3, which is confirmed by the SAED pattern and the HRTEM (Fig. 4.9C–F). On this basis, Fig. 4.9G–I shows the atomic model to demonstrate the epitaxial growth mechanism.

4.4.3 Microwave-assisted solvothermal method The conventional solvothermal method is time consuming. To shorten the material preparation, the microwave-assisted solvothermal method only needs a few minutes to finish the synthesis due to the localized superheating mechanism of microwave irradiation. The microwave-assisted solvothermal method has been successfully used to synthesize Bi2Te3-based [6, 7], SnSe [93], and SnTe thermoelectric materials [94, 95]. Fig. 4.10A is an SEM image of the SnSe0.9Te0.1 sample synthesized by the microwave-assisted solvothermal method [93]. The sample has a plate-like morphology with an average lateral size of 10 μm and a thickness of 100 nm. Fig. 4.10B is a TEM image of a typical SnSe0.9Te0.1 nanoplate. The corresponding SAED pattern and HRTEM suggest the high-quality crystalline feature. To measure the thermoelectric properties, the powders are consolidated by SPS. From the SEM images of the fracture morphologies in Fig. 4.10E and F, the normal direction of the nanoplates is parallel to the pressing direction. The preferential orientation can enhance thermoelectric properties. Fig. 4.10G and H plots the temperature-dependent S2σ and zT for SnSe1 xTex nanoplates. A zT of 1.1 was achieved in SnSe0.9Te0.1 nanoplates-based pellet.

4.5

Liquid exfoliation of layered thermoelectric materials

Layered crystals are those that form strong chemical bonds in-plane but display weak out-of-plane bonding. This allows them to be exfoliated into so-called nanosheets. Such exfoliation leads to materials with extraordinary values of crystal surface area. Another result of exfoliation is quantum confinement of electrons in two dimensions,

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Fig. 4.9 (A) TEM image of a T-shaped Te/Bi2Te3 nanostructure, (B) EDS taken from the marked spots in (A), (C) SAED pattern taken from the junction in (A), (D) TEM image of a nanoplate broken from the T-shaped nanostructure, (E) the SAED pattern, (F) and the corresponding HRTEM. Atomic model of the T-shaped nanostructure along (G) [0001], (H) [10-10], and (I) [2-1-10] directions. Reproduced with permission from L. Cheng, Z.-G. Chen, L. Yang, G. Han, H.-Y. Xu, G.J. Snyder, G.-Q. Lu, J. Zou, T-shaped Bi2Te3-Te heteronanojunctions: epitaxial growth, structural modeling, and thermoelectric properties, J. Phys. Chem. C 117 (2013) 12458–12464. Copyright 2013, American Chemical Society.

transforming the band structure to yield new types of electronic and magnetic materials. Liquid exfoliation has been widely used to prepare the atomically thin nanosheets and can be generally classified into ion intercalation, ionic exchange, and sonication-assisted exfoliation. The ionic intercalation involves the intercalation of ions between the layers to swell the crystal and break the interlayer attraction. Afterward, the postprocessing methods, such as shear, ultrasonication, or thermal, can completely separate the layers, resulting in free-standing atomically thin nanosheets [96]. The ionic exchange is applicable for layered crystals with ions between the layers. These ions can be exchanged with other

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Fig. 4.10 Electron microscopy characterization of SnSe0.9Te0.1 nanoplates synthesized by microwave-assisted solvothermal: (A) SEM image with the inset revealing the thickness, (B) TEM image of a typical nanoplate, (C) SAED pattern, and (D) HRTEM image. SEM images of the sintered pellet demonstrating the fracture morphologies along directions of (E) in-plane and (F) out-of-plane. Temperature-dependent (G) S2σ and (H) zT for sintered SnSe1 xTex pellets. Reproduced with permission from M. Hong, Z.-G. Chen, L. Yang, T.C. Chasapis, S.D. Kang, Y. Zou, G.J. Auchterlonie, M.G. Kanatzidis, G.J. Snyder, J. Zou, Enhancing the thermoelectric performance of SnSe1-xTex nanoplates through band engineering, J. Mater. Chem. A 2017, 5, 10713–10721. Copyright 2017, The Royal Society of Chemistry.

larger ions. Then, the similar postprocessing can result in exfoliated nanosheets. As for sonication-assisted exfoliation, the layered crystal is sonicated in a solvent, yielding exfoliated thin nanosheets [97]. Liquid exfoliation has been used to fabricate thermoelectric materials composed of atomically thin nanosheets. Due to the quantum confinement effect and the nanoscale grain sizes, thermoelectric performance has been significantly enhanced. Fig. 4.11A is the TEM image of two Bi2Se3 nanosheets prepared by ion intercalation. Specifically, the Li ions were inserted into the layers of Bi2Se3 ingots. The following sonication led to ultrathin Bi2Se3 nanosheets. The HRTEM and corresponding fast Fourier transform (FFT) in Fig. 4.11B and C confirm the high crystalline quality of the obtained nanosheets. The XRD pattern in Fig. 4.11D demonstrates the preferential orientation along the c axis. AFM was used to measure the thickness. Fig. 4.11E is the AFM image of an examined nanosheet, and the obtained height profile is shown in Fig. 4.11F, which reveals the thickness to be 1 nm, equal to the thickness of the quintuple layer of Bi2Se3 crystal.

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Due to the atomically thin nanosheets with small grain size, phonon scattering has been greatly reinforced. Therefore, the corresponding κ is much lower than the Bi2Se3 ingot, shown in Fig. 4.11G. In addition, by reducing the thickness, the density of states was modified, leading to enhanced S2σ, as shown in Fig. 4.11F. The peak zT of the pellet sintered from atomically thin Bi2Se3 nanosheets was up to 0.36, much higher than that in the ingot, as shown in Fig. 4.11I.

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High-pressure synthesis techniques

Pressure is a thermodynamic variable that is as fundamental as temperature. Pressure is a useful tool both for the synthesis of new solid-state phases and for probing existing phases of scientific or technological significance. Extreme changes in chemical equilibria and material properties can allow access to a wide range of new compounds and unusual states of matter. Furthermore, many solids synthesized at high pressure can be quenched to ambient conditions where they can be thermodynamically metastable, yet remain indefinitely kinetically stable. Pressure can also induce reaction between chemical components at much lower temperatures and facilitate the synthesis of metastable phases. The high-pressure techniques are capable of tuning the structures and properties of materials resulting in the synthesis of novel materials. The most widely used highpressure techniques assist in the synthesis of equilibrium high-pressure phases that can be maintained after the release of pressure. High pressure can also modify micro- and macrostructure of material at the nano- and mesolevel, i.e., grain size, texture, morphology, defect structure, and concentration [98, 99]. Magnesium sulfide (Mg2S) has been identified as an environmentally friendly thermoelectric material. It is difficult to synthesize Mg2S with a stoichiometric ratio of 2:1 because the Mg boiling point (1363 K) is close to the melting point of Mg2S (1358 K). The use of high-pressure synthesis can control the melting and boiling point temperatures to obtain a stoichiometric Mg2S ratio without residual Mg. Moreover, calculated band structures prove that HPS realizes the convergence of the conduction band (Fig. 4.12A) and leads to enhanced electronic transport properties, as shown in Fig. 4.12B and C. Consequently, S2σ was significantly enhanced, as shown in Fig. 4.12D. After applying pressure, zT of Cr-doped PbSe increased from 0.4 to 1.7 at room temperature. A pressure-driven topological phase transition is found to enable this enhancement. Fig. 4.13A shows the calculated Fermi surface of PbSe under different pressures of 1 ambient pressure (atm), 2.6 GPa, and 4.8 GPa. At ambient pressure, the center pocket is located at the Γ L line. At 2.6 GPa, the center pocket located on the Γ  L lines disappears, which is a characteristic of the TPT. When the bulk band gap reopens, the material enters a TCI state featuring metallic properties at the surface but insulating ones in the bulk (Fig. 4.13B). Fig. 4.13C plots the temperature-dependent zT at 1 amt. The peak zT was 1.0 near 700 K. Fig. 4.13D shows the zT as a function of pressure at 300 K. Upon increasing pressure, zT increases until 2 GPa and then shoots to a peak value of 1.7 at 2.8 GPa, which is much higher than zT of 0.4 under the ambient pressure.

4.7

Electrodeposition

Electrodeposition has been extensively used to synthesize thin films for thermoelectric applications [100]. Using the template, nanowires can be fabricated by electrodeposition as well [101]. Electrodeposition can be generally classified into direct

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Fig. 4.12 (A) Calculated band structures of Mg63AlSi32 under different pressures. Temperature-dependent (B) S, (C) σ, and (D) S2σ for Mg1.97Al0.03Si prepared by high-pressure synthesis under different pressures of 0, 2, 3, 3.5, and 4 GPa. Reproduced with permission from J. Li, X. Zhang, B. Duan, Y. Cui, H. Yang, H. Wang, J. Li, X. Hu, G. Chen, P. Zhai, Pressure induced convergence of conduction bands in Al doped Mg2Si: experiment and theory, J. Mater. 5 (2019) 81–87. Copyright 2012, Elsevier.

current (DC) and pulse electrodeposition. DC electrodeposition is likely to form the dendritic structure in the thin film and lead to an inhomogeneous surface. Pulse electrodeposition can effectively address this issue. During the off (resting) period, there is sufficient time for the ions to diffuse on the electrode surface as well as for crystal formation at the alloy surface. As shown in Fig. 4.14A and B, pulsed depositions put the amorphous materials deposited during “on” time in a position to crystallize during the “off” time. From Fig. 4.14C and D, Sb2Te3 films deposited with constant voltage (DC deposition) show surfaces with large grains of a few micrometers that are inhomogeneously distributed. Films deposited in pulsed mode show a homogeneous growth at lower deposition rates and homogeneous surface with needle-like structures. By tuning the experimental conditions, electrodeposition can produce thermoelectric thin films with interesting lattice imperfections, so as to enhance phonon scatterings. In Bi2Te3 nanowires prepared by electrodeposition, dense twin structures

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Fig. 4.13 (A) Calculated Fermi surface to show the evolution of band degeneracy under pressures of 0 GPa, 2.6 GPa, and 4.8 GPa and (B) calculated energy and momentum dispersion with the local density of states on the (001) surface. (C) Temperature-dependent zT under ambient pressure and (D) zT as a function of pressure. Reproduced with permission from L.-C. Chen, P.-Q. Chen, W.-J. Li, Q. Zhang, V.V. Struzhkin, A.F. Goncharov, Z. Ren, X.-J. Chen, Enhancement of thermoelectric performance across the topological phase transition in dense lead selenide, Nat. Mater. 18 (2019) 1321–1326. Copyright 2019, Nature Publishing Group.

can be produced by changing the electrodeposition voltage. Fig. 4.15A and B are HAADF-STEM images of the twin-free and twin-containing Bi2Te3 nanowires and the inset shows the corresponding FFT images. We can clearly observe the twins. Accordingly, κl is significantly decreased in Bi2Te3 nanowires with twins, shown in Fig. 4.15C. Moreover, electrodeposition can produce nanowires containing high-density dislocations. As shown in Fig. 4.15D, the electrodeposited Bi2Te3 ySey nanowire has dense dislocations vertical to the growth direction [102]. Moreover, combining with annealing posttreatment process, dislocations were formed in Bi2Te3 nanowire, shown in Fig. 4.15E [103]. Fig. 4.15F shows the S as a function of annealing temperature. With increasing annealing temperature, the initial increase in S is caused by the existence of dislocations. When the annealing temperature is higher than 630 K, Te evaporates and degrades S [103].

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Fig. 4.14 Schematic diagram showing the growth mechanisms of thin films synthesized by (A) constant-potentiostatic electrodeposition and (B) pulse electrodeposition. SEM images of Bi2Te2.71Se0.15 film by (C) constant-potentiostatic electrodeposition and (D) pulse electrodeposition with inset showing the cross-sectional view. Reproduced with permission from J. Kim, K.H. Lee, S.W. Kim, J.-H. Lim, Potential-current coadjusted pulse electrodeposition for highly (110)-oriented Bi2Te3-xSex films, J. Alloys Compd. 787 (2019) 767–771. Copyright 2019, Elsevier.

4.8

Chemical vapor deposition

CVD is a process in which gaseous materials react in the vapor phase or on the surface of substrates and thus form solid products that are deposited on the substrates. Tuning the growth parameters such as temperature, chamber pressure, carrier gas flow rate, relative amounts of source materials, and source substrate distance can control the

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Fig. 4.15 Electrodeposited nanowires with lattice defects. HAADF-STEM images of electrodeposited (A) twin-free and (B) twin-containing Bi2Te3 nanowires. (C) Comparison of temperature-dependent κ l of twin-free and twin-containing Bi2Te3 nanowires. (D) TEM image of an electrodeposited Bi2Te3 ySey nanowire with dislocations vertical to the growth direction (110). (E) IFFT HRTEM image of a Bi2Te3 nanowire with the red frame (dark gray in print versions) indicating the edge dislocation induced by annealing and (F) the measured room temperature S of the Bi2Te3 nanowire annealed at temperatures from 423 K to 673 K. (A–C) Reproduced with permission from H.S. Shin, S.G. Jeon, J. Yu, Y.-S. Kim, H.M. Park, J.Y. Song, Twin-driven thermoelectric figure-of-merit enhancement of Bi2Te3 nanowires, Nanoscale 6 (2014), 6158–6165. (D) Reproduced with permission from P. Kumar, M. Pfeffer, N. Peranio, O. Eibl, S. B€aßler, H. Reith, K. Nielsch, Ternary, single-crystalline Bi2 (Te, Se)3 nanowires grown by electrodeposition, Acta Mater. 125 (2017) 238–245. Copyright 2014, The Royal Society of Chemistry. (E and F) Reproduced with permission from J. Lee, J. Kim, W. Moon, A. Berger, J. Lee, Enhanced Seebeck coefficients of thermoelectric Bi2Te3 nanowires as a result of an optimized annealing process, J. Phys. Chem. C 116 (2012), 19512–19516. Copyright 2012, American Chemical Society.

size, morphology orientation, and introduction of dopants or defects in the final products. CVD has been widely used to synthesize high-quality two-dimensional thin films and one-dimensional nanowires for thermoelectric applications [104]. As a representative example, thermoelectric Si0.9Ge0.1 nanowire was grown by CVD [105]. Fig. 4.16A is an HRTEM image of a Si0.9Ge0.1 nanowire grown by CVD, and the inset shows the corresponding SAED pattern [105]. Thermoelectric properties of the as-grown nanowire were measured simultaneously by the experimental setup shown in Fig. 4.16B. Specifically, the nanowire was bridged between two suspended membranes. Fig. 4.16C shows the measured zT. As can be seen, the nanowire has achieved a large improvement in zT values, experimentally 0.46 at 450 K

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Fig. 4.16 (A) HRTEM image of the Si0.9Ge0.1 nanowire grown by CVD. (B) SEM image of the microdevice with the nanowire bridged between two suspended membranes for measuring thermoelectric properties. (C) Temperature-dependent zT of Si1 xGex nanowires prepared by CVD. Reproduced with permission from E.K. Lee, L. Yin, Y. Lee, J.W. Lee, S.J. Lee, J. Lee, S.N. Cha, D. Whang, G.S. Hwang, K. Hippalgaonkar, A. Majumdar, C. Yu, B.L. Choi, J.M. Kim, K. Kim, Large thermoelectric figure-of-merits from SiGe nanowires by simultaneously measuring electrical and thermal transport properties, Nano Lett. 12 (2012) 2918–2923. Copyright 2012, American Chemical Society.

and computationally 2.2 at 800 K. The zT improvement is attributed to remarkable thermal conductivity reductions, which are thought to derive from the effective scattering of a broad range of phonons by alloying Si with Ge as well as by limiting phonon transport within the nanowire diameters. The growth of CVD can introduce various types of lattice imperfections to tune thermoelectric properties, for example, In2 xGaxO3(ZnO)n nanowires papered by CVD. Fig. 4.17A is the TEM image of the nanowires and shows a modulation in contrast along their longitudinal axis, which can be attributed to a superlattice structure. Fig. 4.17B is the Z-contrast TEM image. As can be seen, the nanowire clearly shows the presence of In-enriched layers (brightest lines) oriented perpendicular to the [002] direction. From the HRTEM in Fig. 4.17C, the In atoms sit on individual planes and + are separated by wurtzite MZnnO(n+1) slabs of varying thickness. After the introduction of nanometer-scale features (individual atomic layers and alloying), thermal and electrical measurements on single In2 xGaxO3(ZnO)n nanowires reveal a simultaneous improvement in all contributing factors to the thermoelectric figure of merit, indicating successful modification of the nanowire transport properties.

4.9

Summary

This chapter introduces the synthesis methods of thermoelectric materials. It starts with describing the different types of melting methods for synthesizing bulk thermoelectric materials in which the widely used solid-state reaction methods are the classical melting methods to synthesize high-performance thermoelectric materials by enabling the doping/alloying and rationally tuning the microstructures. Then, ball

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Fig. 4.17 Electron microscopy characterization of In2 xGaxO3(ZnO)n nanowire. (A) TEM image of the nanowires, (B) STEM image of the nanowire. (C) HRTEM showing the sandwiched layers. Temperature-dependent (D) σ, (E) S, (F) κ, and (G) zT. Reproduced with permission from S.C. Andrews, M.A. Fardy, M.C. Moore, S. Aloni, M. Zhang, V. Radmilovic, P. Yang, Atomic-level control of the thermoelectric properties in polytypoid nanowires, Chem. Sci. 2 (2011) 706–714. Copyright 2011, The Royal Society of Chemistry.

milling, the typical powder metallurgy method, is introduced. Because it is energysaving and enables the production of materials with highly reactive metals, ball milling has been widely used to fabricate thermoelectric materials. Moreover, the obtained fine grains generally lead to low thermal conductivity, securing a high figure of merit in the final products. Afterward, the mechanism of solution synthesis methods was presented. As it can well control the morphology and size of the obtained nanopowders, it has been widely used to fabricate high-performance nanostructured thermoelectric materials. The solution synthesis was followed by the exfoliation method

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to produce ultrathin films for thermoelectric applications. Furthermore, we introduce high-pressure synthesis technology. Because pressure is an important parameter in the synthesis of materials, high-pressure synthesis cannot reduce the synthesis temperature but provides additional handles to tune the microstructures and band structures. Finally, we introduce the electrodeposition and CVD methods, which can be used to fabricate thin films and nanowires for assembling thermoelectric devices. These introduced thermoelectric synthesis methods provide guides for developing thermoelectric materials.

Acknowledgments This work was financially supported by the Australian Research Council. ZGC thanks the USQ start-up grant and strategic research grant.

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[80] M. Hong, Z.-G. Chen, Y. Pei, L. Yang, J. Zou, Limit of zT enhancement in rocksalt structured chalcogenides by band convergence, Phys. Rev. B 94 (2016) 161201. [81] G. Zhang, B. Kirk, L.A. Jauregui, H. Yang, X. Xu, Y.P. Chen, Y. Wu, Rational synthesis of ultrathin n-type Bi2Te3 nanowires with enhanced thermoelectric properties, Nano Lett. 12 (2012) 56–60. [82] H. Yang, J.-H. Bahk, T. Day, A.M.S. Mohammed, G.J. Snyder, A. Shakouri, Y. Wu, Enhanced thermoelectric properties in bulk nanowire heterostructure-based nanocomposites through minority carrier blocking, Nano Lett. 15 (2015) 1349–1355. [83] S.W. Finefrock, G. Zhang, J.-H. Bahk, H. Fang, H. Yang, A. Shakouri, Y. Wu, Structure and thermoelectric properties of spark plasma sintered ultrathin PbTe nanowires, Nano Lett. 14 (2014) 3466–3473. [84] B. Xu, T. Feng, M.T. Agne, L. Zhou, X. Ruan, G.J. Snyder, Y. Wu, Highly porous thermoelectric nanocomposites with low thermal conductivity and high figure of merit from large-scale solution-synthesized Bi2Te2.5Se0.5 hollow nanostructures, Angew. Chem. Int. Ed. 56 (2017) 3546–3551. [85] B. Xu, T. Feng, M.T. Agne, Q. Tan, Z. Li, K. Imasato, L. Zhou, J.-H. Bahk, X. Ruan, G.J. Snyder, Y. Wu, Manipulating band structure through reconstruction of binary metal sulfide for high-performance thermoelectrics in solution-synthesized nanostructured Bi13S18I2, Angew. Chem. 130 (2018) 2437–2442. [86] X. Shi, A. Wu, W. Liu, R. Moshwan, Y. Wang, Z.-G. Chen, J. Zou, Polycrystalline SnSe with extraordinary thermoelectric property via nanoporous design, ACS Nano 12 (2018) 11417–11425. [87] X. Shi, A. Wu, T. Feng, K. Zheng, W. Liu, Q. Sun, M. Hong, S.T. Pantelides, Z.-G. Chen, J. Zou, High thermoelectric performance in p-type polycrystalline cd-doped SnSe achieved by a combination of cation vacancies and localized lattice engineering, Adv. Energy Mater. 9 (2019) 1803242. [88] X. Shi, Z.-G. Chen, W. Liu, L. Yang, M. Hong, R. Moshwan, L. Huang, J. Zou, Achieving high figure of merit in p-type polycrystalline Sn0.98Se via self-doping and anisotropystrengthening, Energy Storage Mater. 10 (2018) 130–138. [89] R. Moshwan, L. Yang, J. Zou, Z.-G. Chen, Eco-friendly SnTe thermoelectric materials: progress and future challenges, Adv. Funct. Mater. 27 (2017) 1703278. [90] L. Yang, Z.-G. Chen, G. Han, M. Hong, L. Huang, J. Zou, Te-doped Cu2Se nanoplates with a high average thermoelectric figure of merit, J. Mater. Chem. A 4 (2016) 9213–9219. [91] L. Yang, Z.-G. Chen, G. Han, M. Hong, Y. Zou, J. Zou, High-performance thermoelectric Cu2Se nanoplates through nanostructure engineering, Nano Energy 16 (2015) 367–374. [92] L. Cheng, Z.-G. Chen, L. Yang, G. Han, H.-Y. Xu, G.J. Snyder, G.-Q. Lu, J. Zou, T-shaped Bi2Te3-Te heteronanojunctions: epitaxial growth, structural modeling, and thermoelectric properties, J. Phys. Chem. C 117 (2013) 12458–12464. [93] M. Hong, Z.-G. Chen, L. Yang, T.C. Chasapis, S.D. Kang, Y. Zou, G.J. Auchterlonie, M.G. Kanatzidis, G.J. Snyder, J. Zou, Enhancing the thermoelectric performance of SnSe1-xTex nanoplates through band engineering, J. Mater. Chem. A 5 (2017) 10713–10721. [94] L. Wang, X. Tan, G. Liu, J. Xu, H. Shao, B. Yu, H. Jiang, S. Yue, J. Jiang, Manipulating band convergence and resonant state in thermoelectric material SnTe by Mn–In codoping, ACS Energy Lett. 2 (2017) 1203–1207. [95] L. Wang, S. Chang, S. Zheng, T. Fang, W. Cui, P.-p. Bai, L. Yue, Z.-G. Chen, Thermoelectric performance of Se/Cd codoped SnTe via microwave solvothermal method, ACS Appl. Mater. Interfaces 9 (2017) 22612–22619.

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[96] V. Nicolosi, M. Chhowalla, M.G. Kanatzidis, M.S. Strano, J.N. Coleman, Liquid exfoliation of layered materials, Science 340 (2013) 1420. [97] X. Cai, Y. Luo, B. Liu, H.-M. Cheng, Preparation of 2D material dispersions and their applications, Chem. Soc. Rev. 47 (2018) 6224–6266. [98] V.V. Brazhkin, High-pressure synthesized materials: treasures and hints, High Pressure Res. 27 (2007) 333–351. [99] M. Yang, T. Su, D. Zhou, H. Zhu, S. Li, M. Hu, Q. Hu, H. Ma, X. Jia, High-pressure synthesis and thermoelectric performance of tellurium doped with bismuth, J. Mater. Sci. 52 (2017) 10526–10532. [100] S. Bae, S. Lee, H.-S. Sohn, H.S. Lee, Synthesis and characteristics of PbTe1  xSex thin films formed via electrodeposition, Met. Mater. Int. 23 (2017) 1056–1061. [101] L. Li, S.-c. Xu, G.-h. Li, Epitaxial growth and thermoelectric measurement of Bi2Te3/Sb superlattice nanowires, Chin. J. Chem. Phys. 29 (2016) 365–368. [102] P. Kumar, M. Pfeffer, N. Peranio, O. Eibl, S. B€aßler, H. Reith, K. Nielsch, Ternary, single-crystalline Bi2 (Te, Se)3 nanowires grown by electrodeposition, Acta Mater. 125 (2017) 238–245. [103] J. Lee, J. Kim, W. Moon, A. Berger, J. Lee, Enhanced Seebeck coefficients of thermoelectric Bi2Te3 nanowires as a result of an optimized annealing process, J. Phys. Chem. C 116 (2012) 19512–19516. [104] C.J. An, Y.H. Kang, A.Y. Lee, K.-S. Jang, Y. Jeong, S.Y. Cho, Foldable thermoelectric materials: improvement of the thermoelectric performance of directly spun CNT webs by individual control of electrical and thermal conductivity, ACS Appl. Mater. Interfaces 8 (2016) 22142–22150. [105] E.K. Lee, L. Yin, Y. Lee, J.W. Lee, S.J. Lee, J. Lee, S.N. Cha, D. Whang, G.S. Hwang, K. Hippalgaonkar, A. Majumdar, C. Yu, B.L. Choi, J.M. Kim, K. Kim, Large thermoelectric figure-of-merits from SiGe nanowires by simultaneously measuring electrical and thermal transport properties, Nano Lett. 12 (2012) 2918–2923.

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Manoj K. Yadava,b and Biplab Sanyalc a National Research, Training and Innovation Center, Kathmandu, Nepal, bSt. Xavier’s College, Maitighar, Kathmandu, Nepal, cDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden

5.1

Introduction

Thermoelectric (TE) effect was discovered almost exactly two centuries ago in 1821 by Baltic German physicist Thomas Johann Seebeck. He observed the deflection of a compass needle by a closed loop formed by two wires of different metals when a temperature gradient was maintained between the two joints. Seebeck initially termed this phenomenon as “thermomagnetic effect.” The loop formed by joining wires of two different materials was called a thermocouple. The term “thermoelectric effect” was coined by Danish physicist Hans Christian Oersted, who explained the actual cause of the deflection of the magnetic needle. The carriers with varying densities in the two sections are driven by the temperature gradient leading to the flow of electric current through the loop. The electric current produces a magnetic field around it causing the deflection of a magnetic needle placed near it. The reverse phenomenon of the Seebeck effect was discovered by Jean Charles Athanase Peltier in 1834 [1]. He observed that, if an electric current is passed through the loop of a thermocouple, heat is evolved at one junction and absorbed at the other junction. This phenomenon is known as the Peltier effect. With the Seebeck effect, electricity can be produced using heat, whereas with the Peltier effect, cooling can be achieved by supplying electricity. TE devices based on these effects have various advantages, such as they do not consist of any moving parts and hence are free from wear-tear and noises. They are free from emissions and thus are environment friendly. Apart from an electricity generation purpose, TE devices based on the Seebeck effect are used for other applications as well. TE thermometers, TE purity detector of metals and alloys, and TE infrared radiation detectors are some such examples. Similarly, automobile’s seat cooling system, TE refrigerators, and the dew point hygrometer are some examples of TE devices based on the Peltier effect. Despite the fact that the TE effect is the simplest way of generating electricity, the practical use of thermoelectric generators (TEG) for large-scale electricity production is limited by its very low efficiency. Over the first century after its discovery, various combinations of materials were tried, but the efficiency remained just about 3%. The efficiency of a TEG is directly proportional to the temperature gradient between the two junctions. One of the reasons for low efficiency during the first century was the use of metals, as metals cannot maintain a large temperature gradient between

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the two junctions. With the advent of semiconductors in place of two different metals, semiconductors of two different types (p-type and n-type) were used in a thermocouple. As the power output of a single thermocouple is very small, a large number of thermocouples are connected, and such a combination is known as a thermopile. The efficiency of TEG using semiconductors started to improve, and by 1950, efficiency of about 5% was achieved. The efficiency remained around the same 5% over the next four decades. With the resurgence of new interest after 1990, many new materials were explored and the efficiency of TEG saw a remarkable jump reaching about 20% [2, 3]. Such promising improvements in efficiency encouraged various research and development (R&D) organizations around the globe. They started various projects to increase the efficiency of automobiles by utilizing waste heat using TEGs. In 1994, New Energy and Technology Development Organization (NEDO) of Japan initiated NEDO/Cardiff project with an aim to economically convert low-temperature waste heat into electrical power using TEG [4]. Likewise a US Department of Energy (DOE)-sponsored project was launched in 2004 for the development of TEG for passenger vehicles [5, 6]. The project had collaboration with BMW, Ford, and Faurecia. In the same year, the Automobile Exhaust Thermoelectric Generator (AETEG) project was launched by Clarkson University [7, 8].

5.2

Efficiency hurdles

The TE generation efficiency of a TE material is described by a dimensionless quantity, ZT called the figure of merit. It is given by the relation ZT ¼

S2 σT , k

(5.1)

where S is the Seebeck coefficient, σ is the electrical conductivity, k is the thermal conductivity of the material, and T is the absolute temperature. The thermal conductivity, k, is the sum of electronic thermal conductivity, ke, and the lattice thermal conductivity, kl. The Seebeck coefficient is also known as thermopower, and the product of square of thermopower with the electrical conductivity (i.e., S2σ) is commonly known as TE power factor. The first sight inspection of Eq. (5.1) reveals a very simple prescription for the enhancement of the figure of merit. To achieve a larger figure of merit, one has to find a TE material with a large Seebeck coefficient, large electrical conductivity, and small thermal conductivity. This optimistic prescription is further supported by the fact that there is no upper limit to values of S and σ and no lower limit to the value of thermal conductivity. Thus, in principle, there is no upper limit for the value of the figure of merit. However, this simple-looking solution has inherent complications, which will be visible after analyzing interrelations among S, σ, and k.

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The Seebeck coefficient is related to the effective mass, m*, of carrier and the carrier concentration, n, by the relation [9]: 2m kB2 T
π 2=3 , 3eħ2 3n ∗

S¼

(5.2)

where kB is the Boltzmann constant, e is the electronic charge, and ħ ¼ h=2π is the reduced Planck’s constant. The electrical conductivity, σ, is related to the carrier density n and carrier mobility μ by the relation: σ ¼ neμ:

(5.3)

Finally, the thermal conductivity, k, is the sum of electronic thermal conductivity, ke, and the lattice thermal conductivity, kl, that is, k ¼ ke + kl :

(5.4)

The insight into Eqs. (5.2)–(5.4) reveals the following conflicts among the parameters that are responsible for the value of the figure of merit.

5.2.1 Conflict between S and σ It is clear from Eq. (5.2) that the value of the Seebeck coefficient increases with the decrease in carrier concentration. However, the decrease in carrier concentration leads to a decrease in the value of electrical conductivity and thus ZT value will be adversely affected.

5.2.2 Conflict between m* and σ To have a large value for the Seebeck coefficient, we need to have carriers with larger values of effective mass m*. Again, large effective mass decreases the mobility of the carriers. According to Eq. (5.3), the decrease in the value of mobility decreases the electrical conductivity and hence results in lowering the ZT value.

5.2.3 Conflict between k and σ A material having large values for Seebeck coefficients and electrical conductivity have large thermopower but still cannot be considered a good TE material if it has thermal conductivity high enough, which greatly lowers ZT value. Thus, the lower value of k is one of the important factors for having a good TE material. Here comes a subtle hurdle because of the interrelation between the thermal

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conductivity and electrical conductivity. The electronic thermal conductivity, ke, is related to electrical conductivity by Wiedemann-Franz law ke ¼ LσT,

(5.5)

where L is the Lorentz number. Clearly, the electronic thermal conductivity increases with the increase in electrical conductivity, which ultimately leads to the increase in the value of the total thermal conductivity k according to Eq. (5.4). The large value of the total thermal conductivity generally leads to the reduction of ZT even if the TE has a large value of thermopower.

5.3

Possible routes for high ZT

It is obvious from the previous section that the optimization among the three important parameters, namely, S, σ, and k, plays a central role in the search for better TE material. To be more precise, the aim should be to achieve high TE power factor and low thermal conductivity for a TE material. Since the TE power factor is proportional to the square of the Seebeck coefficient, the main contribution of the TE power factor comes from the Seebeck coefficient. Thus, the approach further narrows down, and enhancement of the Seebeck coefficient remains the main concern for the enhancement of TE power factor. This approach is further bolstered by the fact that any increase in the value of electrical conductivity to increase the TE power factor increases the total thermal conductivity, which leads to the reduction of the ZT value.

5.4

Computational design

It is clear from these discussions that suitable choice of materials with optimal parameters is an important ingredient for the development of efficient TE materials. Here, computational materials design with the aid of ab initio electronic structure calculations plays a pivotal role. It has been firmly established that ab initio density functional theory [10]-based calculations have been very successful in reliably predicting new materials with desired properties for the last few decades. In this formalism, total energy is expressed as a functional of electron density, which with its ground state form yields ground state energy through a variational minimization procedure. The advantage of using electron density over wave functions in standard quantum chemistry methods is enormous from the point of view of tractability of the size of the systems with a large number of ions and electrons involved. However, issues with suitable forms of exchange and correlation functional exist, which sometimes limit the accuracy of the results. Nevertheless, a great body of literature exists based on ab initio density-functional theory (DFT) for studying TE materials. As the figure of merit of TEs is critically dependent on the properties of electrons and phonons, its reliable estimation depends on the accuracy of the calculations of band structure and phonon dispersion spectra. Using semiclassical Boltzmann

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transport equation (BTE), one can calculate the transport coefficients by, for example, BoltzTraP code [11]. Seebeck coefficient, electrical conductivity, and electronic thermal conductivity are calculated in this way. These quantities are calculated by very accurate determination of band structure. Moreover, advanced methods are necessary to calculate lattice thermal conductivities. This is achieved by solving BTE. The following method is used in the ShengBTE code [12], frequently used to calculate lattice thermal conductivity. In the steady state, the rate of change of phonon distribution function must vanish. This is expressed as   dfλ ∂fλ  ∂fλ  ¼  +  ¼0 dt ∂t diff ∂t scatt

(5.6)

 ∂fλ  ∂fλ ¼ rT  vλ ,  ∂t diff ∂T

(5.7)

with

fλ is the phonon distribution function and vλ is the phonon group velocity of mode λ. In BTE, the two terms represent diffusion and scattering. When rT is small, one can 0 write fλ ¼ f0 ðωλ Þ  Fλ  rT df dT . Here, f0(ωλ) is the Bose-Einstein distribution function in thermal equilibrium. The linearized form of BTE reads Fλ ¼ τ0λ ðvλ + Δλ Þ,

(5.8)

where τ0λ is the relaxation time of mode λ. Finally, it can be shown that the lattice thermal conductivity tensor can be obtained as καβ l ¼

X 1 f0 ðf0 + 1Þðħωλ Þ2 vαλ Fβλ , 2 kB T ΩN λ

(5.9)

where ωλ is the angular frequency of the phonon mode λ and Ω is the volume of the unit cell. Eq. (5.8) is solved iteratively until the relative change in the conductivity tensor reaches a small value. Let us now discuss various approaches for the optimization of the TE parameters mentioned previously.

5.4.1 Enhancing Seebeck coefficient As described in Section 5.1, the modern thermocouple consists of a combination of p-type and n-type semiconductors. Thus, we have to obtain such extrinsic semiconductors with suitable doping concentrations. The Fermi level in a semiconductor varies with the varying doping concentration. Furthermore, the value of the Seebeck coefficient strongly depends on the position of Fermi level. The value of the Seebeck coefficient is generally very high in mid-gap region, whereas it rapidly goes on

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LiBeAs DOS

20

LiMgAs

LiCdAs

LiZnAs

10 0

S

2000

0

164

136

156 146

2

S s/t

−2000 20 10 0

−1 −0.5 0

0.5

1 −1 −0.5 0

0.5 1 −1 −0.5 0 Fermi level (eV)

0.5

1 −1 −0.5 0

0.5

1

Fig. 5.1 Interrelation between thermopower, S, and TE power factor, S2σ. Taken from M.K. Yadav, B. Sanyal, J. Alloy Comp. 522 (2015) 388.

decreasing as the Fermi level moves toward the band edge (see Fig. 5.1). The high value of S in the mid-gap region is not useful for TE performance because it corresponds to very low carrier concentration with negligible electrical conductivity. The value of S just inside the band edge is important for TE performance. Thus, band engineering plays a crucial role for the optimization of the Seebeck coefficient and electrical conductivity. Fig. 5.1 shows the interrelation between thermopower and TE power factor for selected Nowotny-Juza phase half-Heusler alloys [13]. As can be seen, the value of S is very high near the mid-gap region, but TE power factor is negligible in the mid-gap region. As we move either toward valence band maximum (VBM) or toward the conduction band minimum (CBM), there is a rapid decrease in the value of S. On the other hand, the TE power factor starts to increase as we move toward the band edges. Another important point to notice in Fig. 5.1 is the value of density of states (DOS) corresponding to the maximum value of TE power factor. The power factor of LiMgAs stands out among the four compounds shown in Fig. 5.1. If we inspect its DOS, we find very rapidly rising DOS near the band edge. Such rapidly rising DOS implies flatness of the corresponding band, which further implies the high effective mass of the carrier. This results in high value for the Seebeck coefficient, which is clear from the figure as the S value corresponding to the maximum power factor is the largest for LiMgAs among the four compounds considered in Fig. 5.1. Thus, the availability of sharp and spiky DOS near the band edge is a very important characteristic of a good TE material. It should be noted that the DOS shown in Fig. 5.1 are for pure compounds. Now, to have sharp spiky DOS at band edge, one has to do band engineering. One has to find a

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Fig. 5.2 DOS of pure and O-doped ZnSe. Top: pure ZnSe, middle: 3.125 at.% O-doped ZnSe, and bottom: 6.25 at.% O-doped ZnSe. Taken from J.-H. Lee, J. Wu, J.C. Grossman, Phys. Rev. Lett. 104 (2010) 016602.

suitable impurity that, when doped into the compound, contributes to enhance the DOS near the band edge. This process of enhancing DOS at the band edge with suitable impurity is known as resonant doping. To illustrate the DOS enhancement by resonant doping, we take an example of O-doped ZnSe. Fig. 5.2 shows the DOS of pure as well as O-doped ZnSe [14]. Clearly, O doping enhances the DOS at about 1.1 eV above the CBM. For x ¼ 3.125% in ZnSe1xOx, there is about 30 times enhancement of the value of the Seebeck coefficient. The corresponding value of the power factor at this concentration has been found to be enhanced by a factor of 180 relative to the undoped case.

5.4.2 Decreasing thermal conductivity k Eq. (5.4) somehow presents a pessimistic view regarding the reduction of total thermal conductivity without compromising with the reduction of electrical conductivity. However, in the case of semiconductors, lattice contribution to thermal conductivity alone accounts for about 90% of the total thermal conductivity [15]. This fact offers optimism as we just have to figure out ways for the reduction of lattice contribution to the thermal conductivity only. The following sections present some of popular techniques for reducing the lattice thermal conductivity, kl.

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5.4.2.1 Phonon mass fluctuation scattering The core idea of the mass fluctuation scattering technique is to dope a semiconductor by substituting some concentration of one of its constituents with a relatively heavier element. The heavier dopants scatter phonons more and thus leads to the reduction of lattice thermal conductivity. Various reports based on this technique suggest substantial reduction of kl. Shen et al. [16] reported experimental study of Pd doping, at Ni sites of ZrNiSn. With 20 at.% of Pd doping, there was reduction of total thermal conductivity by about a factor of 2. The reduction in total thermal conductivity was attributed to the reduction of lattice thermal conductivity because of large phonon scattering by heavier Pd (atomic mass 106.4) than that by lighter Ni (atomic mass 58.7). In the case of Zr0.5Hf0.5 Ni0.5 Pd0.5Sn0.99 Sb0.01 (Hf [atomic mass 178.49] doped at Zr site, Pd doped at Ni site, and Sb [atomic mass 121.75] doped at Sn [atomic mass 118.71] sites) they could achieve thermal conductivity of 3.1 W m1 K1 against the room temperature thermal conductivity of ZrNiSn of 11.4 W m1 K1.

5.4.2.2 Grain boundaries This technique for the reduction of lattice thermal conductivity relies on phonon scattering by grain boundaries. The grain-to-grain phonons propagation is reduced due to scattering by grain boundaries. This method requires fabrication of a material with nanoparticles. The material so formed consists of numerous grain boundaries, which can scatter phonons resulting in the reduction of thermal conductivity. Poudel et al. [17] fabricated p-type nanocrystalline bulk BiSbTe using ball-milled nanoparticles of BiSbTe of sizes ranging up to 50 nm. The lattice thermal conductivity of the fabricated BiSbTe was reduced by a factor of 2. This resulted in the enhancement of ZT value from 1 to 1.4. Takashiri et al. [18] have shown the reduction of lattice thermal conductivity with reduction of grain size in n-type nanocrystalline bismuth telluride-based thin film. Three different thin films were fabricated with constituent nanoparticles of three different sizes. The lattice thermal conductivity was observed to decrease with a decrease in size of the constituent nanoparticles. The bulk value of lattice thermal conductivity of 0.9 W m1 K1 was reduced to 0.4, 0.28, and 0.2 W m1 K1 corresponding to constituent nanoparticle sizes of 60, 27, and 10 nm, respectively.

5.4.2.3 Superlattices Superlattices are formed by stacking thin layers of different materials, one above another. The lattice mismatch between different layers serves as a phonon scatterer. The added advantage of this approach is that the layers can even be chosen such that they not only reduce lattice thermal conductivity but also modify electronic states for better ZT [19]. Several IV–VI [20, 21] and V–VI [21, 22] superlattices have been studied for the sake of achieving better TE performance. A factor of 2.2 reduction of lattice thermal conductivity along the cross-plane direction of Bi2Te3/Sb2Te3 superlattices has been reported [23]. Likewise, a factor of 4 enhancement of ZT value has been found in IV–VI superlattices of PbTe/PbSeTe,

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mainly coming due to a reduction in lattice thermal conductivity as the TE power factor more or less remains comparable to the corresponding bulk value [20].

5.4.2.4 Dynamic cation off-centering Very recently, it has been shown [24] that inorganic halide perovskites, which are well known for their potential as high-performance solar cells, can also exhibit ultralow thermal conductivity. Also, among them, CsSnBr3xIx exhibits a reasonable value of the Seebeck coefficient and electrical transport properties and hence can be regarded as a good TE material. From experiment and theoretical calculations, it has been found that Cs has a rattling oscillatory motion and deviates from its ideal cuboctahedral geometry. This brings distortion in the structure producing a very low phonon velocity and Debye temperature. A strong coupling between acoustic and low-frequency optical phonons was revealed, which gave rise to strong phonon resonance scattering and hence very low value of lattice thermal conductivity.

5.5

2D thermoelectrics

After the successful synthesis of two-dimensional (2D) graphene from its 3D counterpart graphite, very active research field has evolved to synthesize a variety of 2D materials, which can exhibit novel properties. These include unprecedented electron transport, mechanical properties, superconductivity, magnetic long-range order, ferroelectricity, and even thermoelectricity in two dimensions. A number of 2D materials have been predicted to have significant TE performance such as graphene, MoS2, SnSe, Bi2Te3, etc. As mentioned before, the figure of merit depends crucially on the electrical conductivity, Seebeck coefficient, and electronic and lattice thermal conductivity. Determination of these quantities from ab initio theory can be really challenging, especially the calculation of lattice thermal conductivities. Recent developments of the numerical solution by solving BTE [12] have provided enormous possibilities for efficient and accurate calculations of lattice thermal conductivity from third-order anharmonic interatomic force constants, which can be extracted from phonon calculations. Very recently, a series of 2D materials with square A2B (A ¼ Cu, Ag, Au, and B ¼ S, Se) structure have been predicted [25] by evolutionary structure search algorithm and DFT calculations. These materials have unusually low lattice thermal conductivities at room temperature (Fig. 5.3) in the range 1.5–4.0 W m1 K1, which are comparable to that of 2D tellurium, that is, 2.16 and 4.08 W m1 K1, which was reported to have the lowest lattice thermal conductivity in synthesized 2D materials. It was also observed that the selenides have smaller values (with Cu2Se having the smallest values) than that of the sulfides. The reason for this can be traced to the weak interatomic bonding and large atomic masses. The extreme low values of lattice thermal conductivities bring promise to achieve 2D TEs with large figure of merit. However, the Seebeck coefficient and the electric conductivity should be calculated to confirm this.

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Fig. 5.3 Lattice thermal conductivities of A2B compounds as a function of temperature. Reproduced with permission from X. Chen, D. Wang, X. Liu, L. Li, B. Sanyal, J. Phys. Chem. Lett. 11 (2020) 2925.

Very recently, data-driven discovery of 3D and 2D TE materials has been reported [26]. This is based on a systematic search of potential TEs from the materials in JARVIS-DFT database and utilizing semiclassical transport equations, DFT calculations, and machine learning models. In this process, the Seebeck coefficients, electrical conductivities, power factors, and electronic part of thermal conductivities were calculated as a function of temperature and doping. Several compositional classes with high TE performance were identified, among which ZrBrN class of TEs exhibited very low values of lattice thermal conductivity. Finally, supervised classification machine learning models were trained for n- and p-type Seebeck coefficients and power factors to prescreen materials for advanced calculations. This route of machine learning methods seems to be one of the efficient methods to predict new TEs in a faster time scale for guiding experimentalists.

5.6

Future prospects

In spite of the fact that efficiency of TEG is still well below the efficiency of conventional generators, it has several advantages. First, it is aimed primarily at the utilization of waste heat energy from automobiles and industries. So, no extra input energy is required for the production of electricity. Second, the absence of any moving part makes it durable. This property is particularly important for applications in remote areas where frequent access for maintenance purposes is difficult. For example, for deep space missions, radio isotope-powered TEG is used because of its durability [27]. Third, it provides environment friendly clean source of energy. Fourth, the

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large-scale use of TE-based cooling systems has huge prospects to replace conventional cooling systems, thereby reducing harmful emissions. Finally, computational materials science along with machine learning algorithms will continue to play a very important role in the prediction of new TE materials. The ab initio determination of relevant quantities required for the assessment of the figure of merit will become more accurate with the use of more sophisticated electronic structure methods. In this regard, the advent of more and more powerful high-performance computational facilities will go hand in hand toward efficient materials discovery. With all these brighter sides, the future of thermoelectricity-based technologies is enormous.

References [1] Peltier, “Nouvelles exp
eriences sur la caloricit
e des courants
electrique” [New experiments on the heat effects of electric currents], Ann. Chim. Phys. (in French) 56 (1834) 371–386. [2] M.S. Dresselhaus, G. Chen, M.Y. Tang, R.G. Yang, H. Lee, D.Z. Wang, Z.F. Ren, J.P. Fleurial, P. Gogna, New directions for low-dimensional thermoelectric materials, Adv. Mater. 19 (2007) 1043. [3] G. Chen, M.S. Dresselhaus, G. Dresselhaus, J.P. Fleurial, T. Caillat, Recent developments in thermoelectric materials, Int. Mater. Rev. 48 (2003) 45. [4] D. Rowe, in: 17th International Conference on Thermoelectrics, 1998. [5] D. Crane, J. LaGrandeur, V. Jovovic, M. Ranalli, M. Adldinger, E. Poliquin, J. Dean, D. Kossakovski, B. Mazar, C. Maranville, TEG on-vehicle performance and model validation and what it means for further TEG development, J. Electron. Mater. 42 (2012) 1582. [6] J. LaGrandeur, D. Crane, S. Hung, B. Mazar, A. Eder, International Conference on Thermoelectric, 2006. [7] Z.-G. Shen, L.-L. Tian, Automotive exhaust thermoelectric generators: current status, challenges and future prospects, Energy Convers. Manag. 195 (2019) 1138. [8] J. Yang, F.R. Stabler, Automotive applications of thermoelectric materials, J. Electron. Mater. 38 (2009) 1245. [9] G.J. Snyder, E.S. Toberer, Complex thermoelectric materials, Nat. Mater. 7 (2008) 105. [10] P. Hohenberg, W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136 (1964) B864 (W. Kohn, L.J. Sham, ’Self-consistent equations including exchange and correlation effects, Phys. Rev. 140 (1965) A1133). [11] G.K.H. Madsen, D.J. Singh, BoltzTraP. A code for calculating band-structure dependent quantities, Comp. Phys. Comm. 175 (2006) 67. [12] W. Li, J. Carrete, N.A. Katcho, N. Mingo, ShengBTE: a solver of the Boltzmann transport equation for phonons, Comp. Phys. Commun. 185 (2014) 1747. [13] M.K. Yadav, B. Sanyal, First principles study of thermoelectric properties of Li-based half-Heusler alloys, J. Alloy Comp. 522 (2015) 388. [14] J.-H. Lee, J. Wu, J.C. Grossman, Enhancing the thermoelectric power factor with highly mismatched isoelectronic doping, Phys. Rev. Lett. 104 (2010) 016602. [15] S. Lv, Z. Qian, D. Hu, X. Li, W. He, A comprehensive review of strategies and approaches for enhancing the performance of thermoelectric module, Energies 13 (2020) 3142. [16] Q. Shen, L. Chen, T. Goto, T. Hirai, J. Yang, G.P. Meisner, G. Uher, Effects of partial substitution of Ni by Pd on the thermoelectric properties of ZrNiSn-based half-Heusler compounds, App. Phys. Lett. 79 (2001) 4165.

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[17] B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M.S. Dresselhaus, G. Chen, Z. Ren, High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys, Science 320 (2009) 634. [18] M. Takashiri, K. Miyazaki, S. Tanaka, J. Kurosaki, D. Nagai, H. Tsukamot, Effect of grain size on thermoelectric properties of nn-type nanocrystalline bismuth-telluride based thin films, J. Appl. Phys. 104 (2008) 084302. [19] H. B€ottner, G. Chen, R. Venkatasubramanian, Aspects of thin-film superlattice thermoelectric materials, devices, and applications, MRS Bull. 31 (2006) 211. [20] T.C. Harman, P. Taylor, M.P. Walsh, B.E. LaForge, Quantum dot superlattice thermoelectric materials and devices, Science 297 (2002) 2229. [21] H. Beyer, A. Lambrecht, E. Wagner, G. Bauer, H. B€ottner, J. Nurnus, All-inorganic halide perovskites as potential thermoelectric materials: dynamic cation off-centering induces ultralow thermal conductivity, Phys. E 13 (2002) 965. [22] R. Venkatasubramanian, T. Colpitts, B. O’Quinn, M. Lamvik, N. El-Masry, High thermoelectric figure of merit ZT in PbTe and Bi2Te3-based superlattices by a reduction of the thermal conductivity, Appl. Phys. Lett. 75 (1999) 1104. [23] R. Venkatasubramanian, E. Siivola, T. Colpitts, B. O’Quinn, Low-temperature organometallic epitaxy and its application to superlattice structures in thermoelectrics, Nature 413 (2001) 597. [24] H. Xie, S. Hao, J. Bao, T.J. Slade, G.J. Snyder, C. Wolverton, M.G. Kanatzidis, Thin-film thermoelectric devices with high room-temperature figures of merit, J. Am. Chem. Soc. 142 (2020) 9553. [25] X. Chen, D. Wang, X. Liu, L. Li, B. Sanyal, Two-dimensional square-A2B (A ¼ Cu, Ag, Au, and B ¼ S, Se): auxetic semiconductors with high carrier mobilities and unusually low lattice thermal conductivities, J. Phys. Chem. Lett. 11 (2020) 2925. [26] K. Choudhary, K.F. Garrity, F. Tavazza, Data-driven discovery of 3D and 2D thermoelectric materials, J. Phys. Condens. Mat. 32 (2020) 475501. [27] C.B. Vining, An inconvenient truth about thermoelectrics, Nat. Mater. (Commentary) 8 (2009) 83.

Strategies for improving efficiency of thermoelectric materials

6

Prafulla K. Jha Department of Physics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, India

6.1

Introduction

A sparkling glimpse of the thermoelectric (TE) effect was observed during the early years of the 19th century when Estonian-German physicist Thomas Johann Seebeck submitted his observations to the Prussian Academy of Sciences. Seebeck for the very first time observed that the needle of a magnetic compass deflects when a junction of two dissimilar metals or semiconductors were kept at different temperatures [1]; he named this effect thermomagnetism, and the phenomenon was further explained by Hans Christian Oersted who discovered electromagnetism [2]. The term “thermoelectricity,” originally coined by Oersted, refers to the peculiar way of utilizing heat energy for the generation of electric energy and vice-versa. Three major effects, namely Seebeck effect, Peltier effect, and Thompson effect, are variants of thermoelectricity, amongst which we are going to discuss the conversion of heat, i.e., thermal energy to electric energy, also referred to as the Seebeck effect. This technique has been studied extensively by theoreticians and experimentalists for many years to optimize thermal-to-electric power conversion efficiency (PCE). The phrase “Necessity is the Mother of Invention” is most appropriate for the present scenario of energy crises that needs attention and a clear perspective to build suitable and sustainable alternatives. As our aim is not simply to design or develop materials for energy harvesting/ generating/storing purpose, but to develop materials in an ecofriendly manner with nonhazardous properties. Apart from many other energy-generation techniques, this technique was observed during the early years of the 19th century; however, the materials for TE application have been developed and investigated more furiously in the recent past and immense efforts are being made by researchers/scientists to achieve the highest possible TE efficiency. In the present chapter, we will have a brief discussion on the TE effect followed by the parameters on which TE efficiency depends and, diverse ways that are being utilized today to tailor the TE properties for achieving peak efficiency. In principle, in TE materials, an electric potential is created due to temperature gradient and hence the material is useful for power generation. The TE converter converts a part of the low-grade waste heat generated by engines, furnaces, gas pipes, etc. The TE efficiency, also defined as the TE figure of merit (FOM), expressed as zT, depends on macroscopic parameters like Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ), and tailoring the interplay between these three Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00003-5 Copyright © 2021 Elsevier Ltd. All rights reserved.

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parameters through various strategies can yield surprising results. Thermal conductivity κ contains contributions from electrons (κ ele) and phonons (κph). 

 S2 σ zT ¼ T κele + κph

(1)

Until the early 1990s of the 20th century, the benchmark of attaining zT more than unity was seems to be impossible; as the TE parameters S, σ, and κele are dependent on each other via a complex relation and, thus, modulation in one of the parameters causes a change in the others, leaving no room to manipulate the overall efficiency zT through tailoring these three parameters; this leads to a conclusion that only the parameter κ ph could be manipulated/reduced independently so as to tailor the FOM in a nontedious way. It is clear from Eq. (1) that, to reach a high FOM, a large Seebeck coefficient S, a high electrical conductivity σ, and a low thermal conductivity κ are required. Larger FOM means a higher energy conversion efficiency, which achieves its thermodynamic limit of Carnot efficiency when zT is infinite. In addition, high electrical conductivity (σ) comes together with high thermal conductivity (κ ele). The electric conductivity observed in the case of narrow band gap materials is quite high due to enhanced carrier mobilities. The energy band gap that plays a key role in tailoring electronic transport properties can be further tuned by varying chemical composition [3–6]. Furthermore, to reduce the thermal conductivity, elements with larger atomic mass are a natural choice due to their ability to scatter carriers more effectively with lower vibrational energy. The grain boundaries and formation of alloys also dramatically enhance the phonon scattering and hence thermal conductivity [7]. Various studies reported in early 1990s show that, apart from reduction in κph, it is also necessary to decouple the Seebeck coefficient and electric/electronic conductivity for attaining optimal zT and, in this regard, many researchers have elaborated distinct techniques that give total control over TE materials’ properties to achieve desired outcomes. One of the best techniques for achieving this goal is nanostructuring the material, which was first proposed by Hicks and Dresselhaus [8], who predicted that, through reducing the dimension of the material, one can impose confinement on charge carriers, and high TE efficiency can be achieved. Through the nanostructuring technique, one can finely tune the TE transport through the material by modifying the microscopic parameters like electronic transport, carrier relaxation times, and phonon scattering channels [9]. The carrier mobility and relaxation times solely depend on the dimensions, chemical composition, and phase of the material, hence providing an opportunity to manipulate the electronic and thermal conduction, which in turn contributes to the TE efficiency. Apart from nanostructuring, modifying the chemical composition of the material through injecting foreign dopant element/s in the host material or creation of defects have been viewed as promising techniques for tailoring TE properties, together with improving other important aspects like melting temperature, mechanical strength, corrosion resistance, etc. [10]. The previously mentioned ways help in manipulating the TE performance of the material by either modulating the electronic transport or by playing with the thermal transport. However, to

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simultaneously achieve a reduction in thermal conductivity with an enhancement in the power factor, an approach called “phonon-glass-electron-crystal” (PGEC) was introduced by Slack in 1999 [11, 12]. The PGEC materials usually possess finely aligned electronic dispersion similar to that of a classical semiconductor, but the phonon-related properties, i.e., thermal properties are akin to the amorphous glass-like materials. The glass materials, due to their largely disordered geometry, cause immense enhancement in phonon scattering, which is responsible for their ultralow thermal conductivity. Similar to disordered materials, the glass-like improved scattering channels can be achieved in crystalline materials by means of introducing defects in the lattice [13–15]. The defected crystals possess broken symmetry that aid in manipulating conduction of phonons within the host material [16, 17]. Although there have been many diverse ways through which one can play with the material parameters and tailor the FOM, in the present chapter, we have focused on the four major strategies/techniques for manipulating the macroscopic and microscopic parameters contributing to TE transport for enhancing thermal-to-electric PCE.

6.2

Strategies for improving thermoelectric efficiency

There are several methods/techniques through which the TE properties of a TE material can be tuned. However, tailoring one of the parameters should not manipulate the complementary parameters, as this might cause compensation of overall TE efficiency resulting in no enhancement in zT. The four major techniques that have been realized to impose a huge effect on the transport parameters via decoupling the electronic and phonon dependent transport parameters are: 2.1. 2.2. 2.3. 2.4.

Nanostructuring (includes zero-, one-, and two-dimensional nanomaterials) Alloying/chemical doping Phase engineering Defect creation These techniques can directly modify the electron transport properties of the material and/or the phonon lifetimes, which also depend on the phonon scattering mechanism and electron-phonon coupling strengths or modulation in electronic and phonon parameters simultaneously, as the fine tuning of the TE FOM (zT) needs conduction of charge carriers and phonons to be tuned to achieve desired efficiency. The electronic dispersion curves or the band structures of the material indicate the pathway of the charge carriers through which electronic conduction takes place, and the phonon dispersion curve or the vibrational spectra reveals the vibrational frequencies of the acoustic and optic phonon modes together with a spatial explicit resolution to the phonon group velocity and phonon lifetimes along the high-symmetry path of the Brillouin zone. The refinement of these two major conductions can yield tremendous results. As far as the electronic nature of the material is concerned, the semiconductors win the race, defeating semimetals and metals aside; the reason being their spatial charge carrier density and electronic and phonon dispersion curves that govern electron and phonon transport through them. This helps to tune the particular TE parameter without compromising other important properties of the materials [18–20]. When comparing the electronic dispersion curves of the semiconductors with that of metals or semimetals, it can be clearly observed that the semiconductors like PbTe,

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Bi2Te3, PbSe, etc. possess very narrow electronic band gaps [18–22]. Also, as far as the curvature of the dispersion is concerned, the term valley degeneracy (that defines the number of degenerate energy levels within the conduction band minima [CBM] and/or valence band maxima [VBM] regimes) owns the crown for enhancing the carrier mobility. The methods like band convergence [23, 24] and nestification [25] are mostly utilized for increasing the degeneracy that at the end, results in significantly reduced carrier effective masses [26]. These techniques have been proven to successfully decouple the critical connection between the electronic and thermal transport properties.

6.2.1 Nanostructuring The word nano refers to one-billionth part of a dimension of any material when measured in SI units. The reduction of the dimensional length is also referred as nanostructuring or dimensional confinement. The term confinement has been introduced for an elementary particle responsible for the electric and electronic conductions, i.e., the electron (hole). When electron motion is confined in any one of the dimensions of the material, then the material is said to behave as a nanomaterial. In other words, when at least one of the characteristic lengths of the material dimension is comparable to the effective de-Broglie wavelength of the charge carrier(s), the material is said to be quantum mechanically confined, or the motion of the charge carrier/s in certain direction/s is restricted, as in case of a particle trapped in a potential well. In this case, the electronic dispersion spectra of the material would be drastically different from that of the bulk counterpart; the effect causing this modulation is known as the quantum size effect. If the number of dimensions confined in a material are three, two, or one, then the respective nanomaterials can be referred to as zerodimensional (0D), one-dimensional (1D), or two-dimensional (2D) nanostructure/s. Reduction in material dimension directly affects the Seebeck coefficient of the material, and enhancement in the Seebeck coefficient can be achieved by means of improving the electronic density of states. As can be observed from the following Mott equation, the Seebeck coefficient depends on the energy derivative of electrical conductivity that, in turn, depends on the density of states and Fermi function [27].     π 2 KB dlnðσ ðEÞÞ π 2 KB 1 dnðEÞ 1 dμðEÞ S¼ + KB T KB T ¼ dE n dE μ dE E¼EF 3q 3q E¼EF

(2)

Hence, for the improvement of the Seebeck coefficient, either of the two major factors needs to be engineered. One is the carrier mobility μ(E) that can be tailored by controlling the scattering mechanism or by enhancing the local density of states n(E). For nanostructured materials, the efficient way of improving S is found to be modification in the local density of states near the Fermi level. The enhancement in Seebeck coefficient subjected to the quantum confinement effect has been reported theoretically as the density of states in low-dimensional materials get significantly enhanced on reduction in characteristic length of the material. The enhancement of Seebeck coefficient directly depends on the material’s dimension, as can be observed from the study reported on IV–VI compound GeSe [28]. GeSe exhibits a semiconducting nature with an indirect

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band gap of 0.41 eV in its bulk phase, while shifting of band energies is observed due to a reduction of dimensions leading to spatial charge confinement. Thus, the band nature of 2D and 1D GeSe is observed to be direct in nature with band gap magnitude of 1.19 and 1.65 eV, respectively (see Fig. 6.1). The enhancement in Seebeck coefficient is about 1.86 times its bulk counterpart with a carrier concentration of 1019 cm3 at 300 K (see Fig. 6.2). Apart from the conventional chalcogenide-based materials PbTe [20], PbSe [20], GeTe [29], GeSe [28], Bi2Te3 [30], etc., the effect of nanostructuring on the TE properties has also been studied for III-V materials [31–34]. Mingo et al. [31] systematically studied TE properties of different III-V nanowires (NWs; InP, InAs, InSb, and GaAs), and found that, out of all four, InSb NW with a lower diameter stands out as a better candidate for TE application owing to its improved FOM. A theoretical investigation by Gireesan et al. [32] shows that the thermal conductivity of GaP NWs exceeds the bulk magnitude on reduction of NW diameter to 1–2 nm. In the case of GaAs, a report by Xiaolong Zou et al. [33] suggest 100-fold enhancement in TE FOM compared with its bulk counterpart. The root cause of the difference in the thermal conductivity trends of the two different III–V compounds could be attributed to the difference in the NW dimensions, crystal geometry/phase, and the theoretical approaches utilized for investigation. Boron nitride (BN), being a suprahard material, was also investigated under nanoregime for its role in TE transport devices [34]. All of these studies support the giant modulation due to confinement proposed by Dresselhaus [8]. Furthermore, under reduced dimensions, the surface atoms in nanostructured materials are prone to become more reactive due to their unsatisfied electronic configuration, and the untreated surfaces of nanostructured materials give rise to dangling bonds that result in the presence of pseudoelectronic edge states causing incorrect prediction of electronic properties [35–37]. To overcome these side effects, usually the surfaces of the nanosheets and nanowires are treated via passivating the surface through

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Fig. 6.1 Dimension confinement-dependent electronic band structure and density of states of GeSe [28].

Fig. 6.2 Carrier concentration-dependent variation in the thermoelectric parameters of 1D GeSe [28].

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suitable adatoms or molecules. The clear effect on modulation of the properties of SiGe monolayer subjected to passivation through distinct halogen adatoms is observed in a report by Sharma et al. [35]. The phonon dispersion curve that validates the dynamical stability of the system is depicted for SiGe monolayer under pristine and fluorine passivated conditions (see Fig. 6.3). The authors observed that the SiGe monolayer retains its dynamic stability under fluorine passivation but becomes unstable for chlorinated and brominated surfaces. It is noteworthy that the peak magnitude of zT increases to 0.81 (at 700 K) from 0.23 (at 450 K) after F2 passivation of SiGe monolayer (see Fig. 6.4). This remarkable enhancement was subjected to a dramatic reduction in the lattice thermal conductivity from 1.34 W/mK to 0.32 W/mK on incorporation of fluorine [35]. The enhancement of FOM via reduction in thermal conductivity and improvement in thermopower was observed for a few of the notable TE

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Fig. 6.4 Temperature-dependent lattice thermal conductivity and FOM of pristine and fluorinated SiGe monolayer [35].

materials, i.e., Bi2Te3, CoSb3, and Mg3Sb2 [38, 39]. These reports show that imposing quantum confinement on these materials results in reduction in the thermal conductivity. The enhancement in the low-energy phonon density of states and modified nature of the phonons under confined dimensions were found to be major causes for reduction in phonon group velocity and thermal conductivity [38]. In the case of Mg3Sb2, the zT attains 2.5 magnitude at 900 K under two-dimensional configuration (see Fig. 6.5) leaving traditional TE materials behind [39].

6.2.2 Chemical doping/alloying The intrinsic electronic transport properties of a material solely depend on its electronic configuration and orbital hybridization [11]. By modulating the chemical composition via changing stoichiometry or by introducing dopants in the host material, one can easily manipulate physical and chemical properties of any material, as we can observe in the case of steel, which is nothing but an alloyed form of iron. Yet its electric, electronic, and thermal properties are not alike; moreover, alloying the iron improves its corrosion resistance and mechanical properties [40, 41]. Similar methods can be utilized for tailoring the microscopic parameters like electron and phonon conductions by engineering their lifetimes and electron-phonon coupling strengths. As discussed in the Introduction, semiconducting materials are found to be more efficient in achieving TE FOM, even more than unity in some cases [3–5, 42]. In this regard, these materials can be further classified on the basis of the density of the dopants. In one type of material in which the doping concentration is moderate, the dopant species show less interaction and the contributions can be found in the internals of the electronic bands with the Fermi level lying within the forbidden gap regime, which is a nondegenerate semiconductor. However, the type of material is a degenerate semiconductor in which the dopant level is quite high, and dopant species are found highly interactive causing a shift of the Fermi level inside the VBM or the CBM. Furthermore, the contribution of the dopant species can be observed in the form

Fig. 6.5 Thermoelectric figure of merit zT of Mg3Sb2 under bulk and confined configurations [39].

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of individual bands in the electronic dispersion curve rather than in the form of sub-bands in the case of nondegenerate semiconductors [43]. The constituent elements of the material also individually contribute to the overall TE performance. As observed from the literature, almost all good TE materials are a combination of heavy elements like Pb, Mg, Pd, Bi, Sb, Te, Se, etc. [44]. The reason can be the spatial electronic configuration of the compounds that give the desired electronic dispersion and band gap, and second most important factor being the mass of the heavy elements that not only reduce the atomic vibrations but causes an enhancement in carrier scattering time, which ultimately leads to a reduction in lattice thermal conductivity [44]. Comparing the group of chalcogenides, Te being heavier wins the race and gives the optimum performance due to enhanced power factor and reduced thermal conductivity [44]. Apart from the macroscopic parameter, i.e., electronic band gap, the minute parameters like orbital hybridization, valley degeneracy, dispersion curvature, etc. also play a dramatic role in fine-tuning the power factor [45]. Te-based TE materials, compared with the sibling chalcogenides, possess enhanced power factors [44]; the reason behind this is the strongly hybridized orbitals that cause high valley degeneracy, and thus enhanced Seebeck coefficient and electrical conductivities [46]. The literature reveals numerous studies on the effect of doping diverse elements in one of the notable TE materials, Bi2Te3 [47]. According to Srashti et al. [47], five-fold enhancement in the Seebeck coefficient and six- to nine-fold enhancement in power factor was achieved by doping Ag in Bi2Te3 at annealing temperatures of 573 and 773 K, respectively (see Fig. 6.6). Furthermore, incorporating Sb in Bi2Te3 through hot-forging method with Bi0.5Sb1.5Te3 stoichiometry showed enhancement of 65% in power factor under nanostructured configuration that resulted in a 50% increase in FOM with zT magnitude reaching 1.5 [49]. It is surprising that the improvement in the power factor of the system was not because of electrical conductivity σ but was primarily due to giant enhancement in thermopower S and remarkable reduction in electrical conductivity of the system. The reason behind this unusual behavior is the successful decoupling of the interrelated complex parameters S, σ, and κele, which in principle is a crucial task. This can be done by manipulating the correlation between them via hot-forge method, which causes the introduction of point and planar defects when hot-forging the material. The defects cause a reduction in the electric and electronic conduction that, in turn, result in enhancement of the power factor [49]. These results are more significant as the enhancement in the power factor and FOM is achieved near room temperature (320 K), which in other reported cases is observed at elevated temperatures [47]. Another notable material, Mg3Sb2, has also been investigated under doped conditions to understand the dopant-dependent modulation in the TE performance in the system [39, 51]. Wang et al. [51] studied the effect of Ag doping on the TE properties of the Mg3Sb2 using first principles-based density-functional theory (DFT) calculations, and they found a reduction in electronic band gap with introduction of double transport mechanism at thermal excitation temperature, i.e., at a certain temperature, conduction is governed via both metallic and semiconducting transport mechanisms that causes a reduction in electrical resistivity and an enhancement in TE power factor. Zhang et al. [52] suggested that the Bi doping is also possible in Mg3Sb2 for enhancing thermoelectricity. A recent study on BiCuSeO shows that the doping of light element

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T

Tf3 Ta2

Tf4 Ta1 L

Fig. 6.7 Thermoelectric profiles of BiCuSeO compared with different materials [48].

Li with magnetic codoping of Mn ions in BiCuSeO increases carrier mobility and hence resulted in an enhancement of Seebeck coefficient and power factors [48]. The Mn codoping causes a reduction in the thermal conductivity as low as 0.5 W/mK at 873 K (see Fig. 6.7) [48]. Apart from traditional TE materials, the Si/Ge alloy has also been investigated with great interest owing to its remarkable magnitude of FOM [53, 54]. As we know, neither silicon nor germanium under their pristine configuration possess significant TE FOM, but their alloy shows giant enhancement in power factor and markedly reduced thermal conductivity.

6.2.3 Phase engineering Crystals in material science have secured central attraction owing to their symmetric and periodic arrangements of atoms with diverse designs that result in different crystal phases. The conduction of electrons and phonons can also be manipulated by engineering the crystal phase of the material. As observed in the case of conventional III–V semiconducting materials, in their bulk configuration most of them crystalize in a cubic zincblende structure, while imposing quantum confinement via reduction in characteristic length of at least one of the dimensions causes them to possess Wurtzite phase with hexagonal symmetry [55]. The report on TE properties of the selected III–V materials show phase-dependent diversity in TE properties owing to the difference in their atomic arrangement and electronic configurations that result in different electron and phonon dispersion curves [50]. Furthermore, in the case of dominating TE materials like Bi2Te3 [47, 49] with distinct stoichiometry than the simple BiTe [56], crystalizes in the Zintl phase, it is evident from the reported literature that, even having same constituent atomic species, the Zintl Bi2Te3 stands out as a suitable TE material. Si/Ge [53, 54]-based alloys that usually possess hexagonal symmetry, PbTe [57] with cubic rock-salt phase, and GeTe [29] with rhombohedral phase have been reported to possess significant magnitudes of TE FOM (zT), but the major issue in these practically utilized materials is their toxicity that affects environment and ecology. Thus, phase engineering has been successfully applied to utilize nontoxic and ecofriendly materials for TE devices via tuning the electronic and phonon

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transport [50]. As the present chapter is more focused on combining different aspects for tuning FOM, we will not be discussing nontoxicity dependent studies. In the case of reported III–V group materials, gallium pnictides (GaX; X ¼ P, As, Sb), the dynamic stability is confirmed via phonon dispersion curves (see Fig. 6.8), and the phase-dependent TE responses can be viewed in Figs. 6.9, 6.10, and 6.11. As can be observed, the vibrational and TE trends follow classic nature with a remarkable difference in the magnitude owing to a difference in their crystal phases. Similar difference has been also observed in the TE profiles of the IV–VI compound GeTe, which crystalizes in different phases at different pressures and temperatures [29]. The R3m phase out of R3m, Fm3m, and pm3m phases of GeTe is found to be dynamically stable at ambient conditions [29]. However, the remaining two phases, Fm3m and Pm3m, are found stable at high pressures of 3.1 and 33 GPa, respectively (see Fig. 6.12). The electronic band gap reduces with pressure in the case of Pm3m phase transiting to a metallic nature. As far as thermal conductivity is concerned, the Fm3m phase of GeTe possesses the lowest magnitude amongst the three phases (see Fig. 6.14). Figs. 6.13 and 6.14 show a variation of TE parameters like Seebeck coefficient, electric/electronic conductivity, zTe, lattice/phonon conductivity, group velocity, and overall FOM zT of GeTe in three different phases. As can be observed from these figures, the lattice thermal conductivity for Pm3m phase is superior to Fm3m and R3m phases, whereas the temperature-dependent profiles of zT show reverse trend

Fig. 6.8 Phase-dependent phonon dispersion curves of III-V compounds GaX (X ¼ P, As, and Sb); (ZB ¼ Zincblende, WZ-Wurtzite) [50].

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GaP ZB GaAs ZB GaSb ZB

10

(D)

200

400

600

800 1000 1200 1400

Temperature T (K)

Fig. 6.9 Thermoelectric parameters of III–V compounds in ZB phase [50].

with R3m phase possessing highest magnitude of zT at an elevated temperature. The Fm3m phase shows R3m-like trend of zT, while the Pm3m phase shows least and insignificant magnitude of zT [29].

6.2.4 Defect creation Crystalline materials, being the heart of material science, have been studied and utilized for numerous applications, yet amorphous materials that possess glasslike characteristics have also gained a considerable amount of attention for thermal management-based applications. However, to achieve semiconducting crystal-like electronic properties with glass-like thermal transport properties, a unique combination was introduced by G. A. Slack for the first time in 1999; the approach is known as PGEC [11, 12]. Materials with a reduced thermal conductivity and enhanced electronic transport properties have been grouped with these kinds of materials; one such example is the Skutterudite, which is one type of natural mineral occurring in Skutterud, Norway. The materials with Skutterudite-like crystal structure tend to accommodate guest atoms within the voids of the lattice, and the guest atoms can actually rattle through the lattice effectively causing increased phonon scattering that ultimately aid in reducing thermal conductivity of the material [11]. Apart from Skutterudites, the same task can be achieved by means of creating defects in the host lattice. The creation of defects induces asymmetry in the crystalline host that results in

Strategies for improving efficiency of thermoelectric materials

131

350

s x 105 (W–1 m–1)

250 200 150 GaP WZ GaAs WZ GaSb WZ

100 50 0

(A) Power factor S2 s (arb. unit)

16

300

400

600

800

1000

1200

Temperature T (K)

8 GaP WZ GaAs WZ GaSb WZ

4

200

(B)

400

600

800

1000

1200

Temperature T (K)

10

0.006

8

0.005 0.004 0.003 0.002

GaP WZ GaAs WZ GaSb WZ

0.001 200

400

600

800

Temperature T (K)

1000

6 4 GaP WZ GaAs WZ GaSb WZ

2

0.000

(C)

12

0 200

Ke(W/mK)

Seebeck coefficient S (mV/K)

20 400

1200

0

(D)

200

400

600

800

1000

1200

Temperature T (K)

Fig. 6.10 Thermoelectric parameters of III–V compounds in WZ phase [50].

improved phonon scattering rates due to a greater number of scattering channels created due to defected lattice and reduced thermal conductivity [11]. Considering the conventional material Bi2Te3, the classical molecular dynamics simulations reveal that the reduction in κph can be achieved by introducing point defects [38]. The authors claim 80% reduction in lattice thermal conductivity κph due to Bi antisite defect, which is significantly high. Apart from the notable Bi2Te3, a novel Zintl compound Mg3Sb2 has also developed significant interest amongst the research community owing to its multiple advantages like narrow energy gap, optimum effective mass, and remarkable FOM [58–64]. Besides the effect of doping [58], this compound was also investigated under defected conditions [58] to understand the role of defects in modulating the TE transport through the system. A report by Mao et al. [58] suggests that the introduction of point defects via optimizing synthesis parameters like hot-pressing temperature and holding time resulted in significant enhancements in the carrier mobility and power factor. It is noteworthy from the reported literature that even tiny amounts of defects can aid in realizing high FOM in TE materials via modulating the electron and phonon scattering rates.

6.3

Conclusive remarks and future outlook

In this chapter, we discussed the occurrence of TE effect by quoting a brief history followed by a description on the efficient materials utilized for TE devices with four major ways to improve overall TE FOM (zT) of the material/s. As observed from the

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Fig. 6.11 Phase-dependent overall thermoelectric figure of merit (zT) of III–V compounds in ZB and WZ phases [50].

literature review, out of the four different ways to engineer electronic and thermal (phonon) transport, the nanostructuring way has emerged as an efficient way to achieving the desired performance of TE materials due to interference of quantum mechanical confinement effects that govern and modify the transport properties of the materials in a crisp manner. However, the complex relation between S, σ, and κ makes the independent manipulation of one of the parameters a crucial step. Hence, to build a strategy that can manipulate the interplay between these parameters that govern the transport properties, we need to overlap techniques that can give access to independent manipulation. As discussed in one of the subsections, the decoupling of the interrelated TE parameters is a crucial challenge, while fusing two techniques, i.e., introduction of doping/alloying/defects with nanostructuring the materials has been proven to be a superior pathway for designing TE materials with tailor-made properties. Along with many examples, Bi2Te3 being one of the cases, the Sb doping

Fig. 6.12 Phase-dependent phonon dispersion curves of GeTe along high-symmetry points of Brillouin zone [29].

Fig. 6.13 Phase-dependent thermoelectric properties of IV-VI compound GeTe [29].

Fig. 6.14 Lattice thermal conductivity, phonon group velocity, and figure of merit (zT) of GeTe for R2m, Fm3m, and Pm3m phases [29].

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that introduced nanostructured Bi2Te3 is reported to show surprising results with smoothly decoupled TE parameters that result in optimized peak magnitude of FOM zT. On the other hand, the Zintl compound Mg3Sb2 has been realized as a competitor for other chalcogenide-based conventional TE materials. Apart from an enhancement of the overall efficiency, it is desired to also give weightage to the design and development of efficient TE materials with nontoxic/nonhazardous properties that can secure the environment through ecofriendly interactions. We believe that the present chapter elaborates the synergetic pathways to precisely tailor the TE properties of the material/s and would serve the purpose of giving fruitful insights into the manipulation of the transport mechanism to upcoming researchers.

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Kulwinder Kaura, Enamullahb, Shakeel Ahmad Khandayc, Jaspal Singhd, and Shobhna Dhimana a Department of Applied Sciences, Punjab Engineering College (Deemed to be University), Chandigarh, India, bDepartment of Physics, School of Applied Sciences, University of Science and Technology, Meghalaya, India, cDepartment of Physics, National Taiwan University- Taipei, Taipei, Taiwan, dDepartment of Physics, Mata Sundri University Girls College, New Delhi, India

7.1

Traditional thermoelectric materials

In general, the materials used to synthesize thermoelectric (TE) devices are semicon2 ducting [1]. It is well known that the intrinsic figure of merit (zT ¼ S kσT ) is the central parameter in designing TE materials. The intrinsic zT is calculated from various transport parameters such as Seebeck coefficient (S), electrical conductivity (σ), and total thermal conductivity (k) (due to electrons, κ el and phonons, κ l). The essential requirement to acquire high value of zT corresponding to a particular material is that the material should simultaneously exhibit high power factor (i.e., S2σ) and low lattice thermal conductivity. In earlier days, metals were used for TE applications due to their good electrical conductivity, but the corresponding zT values were very low since metals also exhibit large thermal conductivity (especially due to electrons). On the other hand, insulators reveal a large Seebeck coefficient but have very low electrical conductivity. Hence, a third type of material, semiconductors, in which electrical conductivity and Seebeck coefficient lie between conductors/metals and insulators, are utilized for TE applications. A comparison among the average values of transport coefficients (i.e., S, σ, κ, and Z) of metals, semiconductors, and insulators are shown in Table 7.1. From Table 7.1, it is obvious that, in semiconductors, the transport coefficient, particularly S(σ), is higher (lower) than metals and lower (higher) than insulators. However, the average value of Z is much higher than both the metals and insulators. Therefore, in general, semiconducting materials are used for TE purposes. Although recent progress shows significant development toward high temperature TE material, finding promising candidates is still a difficult task, especially at room temperature. High temperature TE materials are used for power generation devices utilized in the automobile industry, power plants, industrial processes, etc. As we know, traditional TE materials are mostly based upon bismuth telluride and lead chalcogenides, but the presence of toxic elements limits their commercial use. In general, the nontoxic alternatives in their pure and defect-induced states are the best substitutes Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00009-6 Copyright © 2021 Elsevier Ltd. All rights reserved.

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Table 7.1 The average comparison among the transport coefficients (σ, κ el(l), Z) of metals, semiconductors, and insulators at 300 K [1]. Transport coefficients

Metals

Semiconductors

Insulators

S σ κ 5 κel +κl Z

5 (μVK1) 106 (Ω1 cm1) κel 3  106 (K1)

200 (μVK1) 103 (Ω1 cm1)  κl 2  103 (K1)

1000 (μVK1) 1012 (Ω1 cm1)  κl 5  1017 (K1)

for TE applications, for example, complex chalcogenides [2, 3], emerging inorganic compounds (e.g., oxide-based materials) [4], intermetallic compounds (e.g., Heusler alloys [5] and Zintl-phase compounds [6]), skutterudites [7, 8], organic polymers, and quasicrystals [9]. A schematic plot representing the various materials used for TE applications is shown in Fig. 7.1. Following the plot, it reveals that most of the TE materials are based upon Bi2Te3, PbTe, Si-Ge alloys, inorganic compounds, and Heusler alloys. A brief discussion of the TE materials follows. Most traditional state-of-the-art TE materials are based upon lead chalcogenide, PbX (X ¼ S, Se, and Te) (and its relative alloys, PbTe1 xSex); bismuth telluride, Bi2Te3 (and its relative alloys, BixSb2 xTe3); and Silicon-Germanium alloys, Si1 xGex having zT > 1 at their optimal temperatures (>300 K) [11, 12]. However, the presence of toxic elements such as Te and Pb in Bi2Te3 and PbTe make them less attractive for large-scale production. Hence the nontoxic and environmentally friendly alternatives have become attractive in recent years. Moreover, the thermal stability of

Fig. 7.1 Comparison of various materials used for thermoelectric application [10].

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141

Bi2Te3 is low (melting temperature 586°C) and the maximum TE performance occurs at 150°C. Among the lead chalcogenides, PbTe is the most classic TE material used for power generation since 1950 and has been used for several NASA space missions. PbTe is a direct band gap (0.32 eV) semiconductor, which crystallizes in a rock salt structure with a melting point of 1200 K [13]. It was found that alloying PbTe with SnTe exhibits better TE performance. A few years later, a band inversion model for Pb-doped SnTe (i.e., PbxSn1 xTe) was proposed where a topological phase (TP) transition arises due to the relativistic quantum effect called spin-orbit coupling. Due to the TP transition, the material induces characteristics like Dirac semimetal. Dirac semimetals possess linear electronic band dispersion, i.e., the relation between energy and momentum is linear in which the quasiparticles behave like relativistic particles. It has been proposed that Dirac semimetals might be a good TE material because of the presence of heavy fermions at the band edges [14]. In the preceding year, Chen et al. induced Dirac semimetal characteristics in Cr-doped PbSe from the lattice parameter compression (or high pressure). This pressure-induced TP transition in Cr-doped PbSe produced a zT value of about 1.7 at 300 K, in the record territory of all known TE materials [15]. In the recent experimental study, an average zT of 1.0 between 300 and 673 K was obtained for copper chalcogenide (AgCu)0.995Te0.9Se0.1 system [16]. This compound surprisingly shows lower lattice thermal conductivity (0.4 W m1 K1) and a good power factor (13.8 μW cm1 K2) simultaneously near room temperature. The oxide-based TE materials depict lower zT compared with the state-of-the-art TE materials such as telluride-based compounds but with much higher chemical and thermal stability, allowing high operating temperatures and large temperature gradients [4]. Such compounds are very convenient for high temperature applications. Along with lower electrical and moderate thermal conductivity, these materials also exhibit a high Seebeck coefficient. However, these parameters can be tuned for high zT by various means such as doping, nanostructuring, and defect engineering. For example, p-type oxides such as Ca3Co4O9, NaxCoO2, and Bi2Ca2Co2O9 with different dopants (e.g., Cr, Sm, Tb, K, Cd, Sr, Na, W, La, Fe) give zT and power factor, S2σ (μW cm1 K2) ranging between 0.16 to 0.73 and 2.4 to 11.5, respectively, at 1000 K. Whereas, n-type oxides such as ZnO, SrTiO3, CaMnO3, and In2O3 with various dopants (e.g., Al, Ni, Ga, La, Nb, Gd, W, Y, Sn, Ge, Mn, Zn) give zT and S2σ (μW cm1 K2) ranging between 0.06 to 0.45 and 2.0 to 12.0, respectively, in the temperature range 773 K to 1200 K [17]. The Zintl-phase compounds come from the group of high-melting intermetallic compounds characterized by the ionic structure having “electron crystal-phonon glass”-like characteristics. The general composition of Zintl-phase compound is XaYZb, where X is the electropositive elements (mostly from alkaline and alkaline-earth metals), Z is the electronegative element, Y belongs to the transition metals (such as Zn, Cd, and Mn), and a (or b) denotes the number of particular elements in the composition. It was found in 2005 that Zintl-phase compounds exhibit good TE properties. Due to “phonon glass“-like characteristics, these compounds show a very low thermal conductivity even in its pristine form, which is one of the prerequisites for TE materials. For example, TlXTe2 (X ¼ Ga, In) compound shows

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the lattice thermal conductivity of 0.5 W/mK at 300 K [6], which is comparatively lower than the traditional TE materials such as Bi2Te3 (1.4 W/mK at 300 K) and PbTe (1.7–2.2 W/mK) [18, 19]. Due to the electronic structure, in 0D (2D) compounds, the carrier mobility and carrier concentration are low (high) and high (low), respectively. It has been found that p-type Zintl-phase compound (e.g., Yb15MnSb11, Sr14MnBi11, Eu11Cd6Sb12, Ga5In2Sb6, CaZn2Sb2, EuZn2Sb2, YbCd2Sb2, CaMg2Bi2, etc.) with different dopants (such as Al, Sc, Y, Zn, As, Na, Mn, Cd, Mg, Yb, Ca) give zT and power factor, S2σ (μWcm1 K2) ranging between 0.4 to 1.28 and 4.13 to 22.5, respectively, in the temperature range 650–1200 K. Whereas, the n-type Zintl-phase compound (Mg3Sb2) with various dopants (such as Nb, Mn, and Te) give zT and S2σ (μW cm1 K2) ranging between 0.61 to 1.71 and 9.16 to 20.02, respectively, at 700 K [17]. The other intermetallic compounds such as Heusler alloys recently attracted scientific attention in TE research due to the tunable electronic band structures and thermal and mechanical stabilities [5, 20, 21]. Heusler alloys exist in two types of chemical compositions, XYZ (or 1:1:1 ratio, often known as half-Heusler) and X2YZ (2:1:1 ratio, known as full-Heusler). The symbols X and Y represent the transition metal, and Z belongs to the main group (or p-block) elements. In general, half-Heusler and full-Heusler alloys crystallize in cubic phase having C1b and Fm-3 m space groups, respectively. Full-Heusler alloy consists of four interpenetrating sublattices, each of which are occupied by the constituent atoms. The corresponding Wyckoff positions are 4a(0,0,0), 4b(1/2,1/2,1/2), 4c(1/4,1/4,1/4), and 4d(3/4,3/4,3/4). On the other hand, half-Heusler alloy consists of three interpenetrating FCC sublattices, where the constituent atoms occupy 4a(0,0,0), 4b(1/2,1/2,1/2), and 4c(1/4,1/4,1/4) Wyckoff sites. In general, the 18 [24] valence electron half- (full-) Heusler compounds exhibit semiconducting behavior, which is also referred to as the Slater-Pauling rule. Considering the electronic structure of Heusler alloys near the Fermi level, which is mostly contributed by the transition metals, give high electronic density of states (DOS) and consequently lead to the large Seebeck coefficients and electrical conductivity. Kaur et al. [22–29] have calculated the TE properties of different half-Heusler compounds using Density functional theory. A recent computational study reveals the high value of zT > 0.7 obtained in pristine half- and full-Heusler semiconductors [30, 31]. It has been found that the state-of-the-art p-type half-Heusler compounds (e.g., ZrNiSn, ZrCoBi, ZrCoSb, FeNbSn, etc.) with different dopants (e.g., Sb, Sn, Hf, Ti, Zr, etc.) give the zT and power factor (μW cm1 K2) ranging between 0.7 to 1.45 and 28 to 51, respectively, in the temperature range 973 to 1200 K [17]. Whereas, the n-type half-Heusler compounds (e.g., TiNiSn, ZrNiSn, HfNiSn, NbCoSb, TiCoSb, ZrCoSb) with various dopants (e.g., Zr, Hf, Sn, Sb, Fe, Nb, etc.) give zT and power factor (μW cm1 K2) ranging between 0.4 to 1.5 and 21 to 62, respectively, in the temperature range 775 to 1173 K [17]. Comparatively, fullHeusler alloys are less explored than the half-Heusler alloys. A recent study also reveals that full-Heusler semiconductors are also significant for TEs [32]. On the basis of the previous discussion, one can see that both n- and p-type Heusler alloys are promising for TE applications. The other promising TE materials are Si-Ge alloys, which show high thermal stability up to 1200–1300 K. It has been found that silicon exhibits a very large thermal

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conductivity (148 W/mK); however, the introduction of Ge atoms in nanostructured Si-Ge alloys enhance the phonon scattering rate due to which thermal conductivity reduces to 2–5 W/mK and enhances zT > 1 [10]. The nanostructure approach is one of the common strategies to enhance the TE properties. It has been reported that n-type Si-Ge alloys with different dopants (e.g., P and Sb) give zT and power factor (μW cm1 K2) ranging n between 0.61 to 1.78 and 18.5 to 35.27, respectively, in the temperature range 1073–1173 K. Whereas, p-type Si-Ge alloys with various dopants (e.g., B and Ga) give zT and S2σ (μW cm1 K2) ranging between 0.53 to 1.82 and 15.5 to 39.05, respectively, at 1073 K [17]. The primary focus of nanostructuring is to reduce the lattice thermal conductivity. Thus, we have found that a nanostructuring approach provides zT value >1.7(>1.8) for n(p)-type Si-Ge alloys. For cooling applications, Bi2Te3 is a state-of-the-art TE material. Like PbTe, Bi2Te3 is also a narrow band gap (0.16 eV) semiconductor with a melting point of 858 K [33]. Doping with the transition metals (e.g., Co, Cu, Ag, and Cd) enhances zT value to 1.4 at 425 K [34]. Popularity of TE materials also depends upon its commercial cost. A comparison between the TE materials are given in the Table 7.2. It is clear that the chalcogenidebased materials show highest figure of merit among all others but with comparatively higher material cost. It should be noted that the efficiency of TE devices depend upon some other additional properties such as contact resistivity and the variation of TE properties in an applied temperature gradient. It has been emphasized for TE devices, the average properties such as average zT, within the respective temperature range are the key parameters instead of their peak values [36–38].

7.2

Conductivity and thermoelectric potential depending on carrier density

Keeping in view the performance measuring indicators such as Seebeck coefficient and electrical and thermal conductivity, the figure of merit (zT) plays a critical role. Recently, the artificial layers of Bi2Te3 and Sb2Te3 displayed the largest values of Table 7.2 Comparison of average cost ($/kg) of different families of thermoelectric materials [35]. TE materials

 zTmax

Temperature (°C)

Average material cost ($/kg)

Cobalt oxide Clathrate SiGe Chalcogenide Half-Heusler Skutterudite Silicide

1.4 1.4 0.86 2.27 1.42 1.5 0.93

727 727 727 727 427 427 727

345 5310 6033 730 1988 562 151

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zT ¼ 2.4 at room temperature [39]; in SnSe, zT reached a maximum of 2.6 [40], and in p-type PbTe-SrTe, zT ¼ 2.5 [41]. But, the nanostructuring in Heusler-based TE materials in 2019 was the key toward successful attempts in increasing the zT up to 5 or 6 in metastable Fe2V0.8W0.2Al [42]. The same dimensionless parameter zT governs the efficiency of a TE module, where an intricate tradeoff is to be maintained among these coefficients. This can be achieved by either decreasing k and keeping the S or σ at the constant level or vice versa. But the principles of basic physics doesn’t allow it without disturbing this tradeoff. The possible understanding can be seen in Fig. 7.2 [32]. The electrical conductivity (σ) can be described as the production of electron current when a certain force (e.g., electric field) makes the electrons move. This is related to ohms law, where the measurement is taken in terms of electrical resistivity (ρ) given by the inverse of electrical conductivity σ ¼ 1/ρ. In metals, we normally contemplate one type of charge-carrying species (electrons), but in semiconductors or semimetals there are multiple charge-resonant species such as electrons and holes (or electrons in multiple bands), or in polar molecules, we have ions and thus the total conductivity needs to be summed up in terms of individual conductivities. The simple model can be thought of interconnected parallel resistors. For example, if we have only electrons and holes as carriers, then σ total ¼ σ e + σ h. At the same time, it is to be maintained that, in anisotropic materials, these entities are not scalar but have tensor characteristics. In classical Matthiessen’s Rule and semiclassical Drude Model, we simply introduce defect/boundary/impurities-induced electronic scattering or the density of charge carriers, charge of carries, and their drift mobility [43–45]. Here, mobility is linked to effective mass of electrons or holes and the scattering time (τ) is introduced inevitably. Handling with advanced methods of Quantum Mechanics and Boltzmann Transport Theory, the electron transport is determined by the electron group velocity and DOS. This rules out the precise definition by classical concepts of mobility and effective mass. The electrons in semiconductors move substantially faster when the temperature is increased, and the classical Equipartition Theorem of kinetic energy is approximately followed (1/2 mv2  kBT). This however is linked to the scattering rate, which is determined by relaxation time constant (τ). So, this time constant plays a vital role in

Fig. 7.2 Seebeck coefficient (S), Conductivity (σ), power factor (S2σ), thermal conductivity (k), and zT plotted w.r.t the carrier concentration [32].

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thermal (phonon) and electronic (electrons) scattering and thereby decides the conductivities in general. Now focusing on the heat transport of electrons rather than charge, a contribution toward the thermal conductivity reduces the zT. Within the limits of finest approximation, the total thermal conductivity of a semiconductor can be summed up in terms of thermal conductivity from the free electrons (or holes) κ el and the phonon (atomic vibrations) thermal conductivity, often called lattice thermal conductivity (κ l) (κtotal ¼ κ el + κl). This electronic thermal conductivity can be derived from the same transport function defined in transport theory that also determines the Seebeck coefficient and electrical resistivity. For a single carrier (electron or hole charge carriers)type system, κe is sufficiently determined by the Wiedemann-Franz law κ el ¼ LσT, where L is the Lorenz factor. (Note that the bipolar charge transport plays a vital role and affects the TE properties as well [32, 46].) Lorenz factor L chiefly depends on the location of the Fermi Level (in a single band system) like that of the Seebeck coefficient (S), which in turn decides the estimation of L at any temperature. To enhance the zT, lattice or phonon thermal conductivity minimization provides a good opportunity. This can be achieved by increasing the phonon scattering, which is likely attained by incorporating disorder, heavy atoms, grain boundaries, and large unit cells, or slowing the movement of phonons so they can transport less heat. Taking into consideration the classical picture of heat transport by phonons, the thermal conductivity can be comprised of the velocity and phonon scattering time, heat capacity, Debye temperature, etc. provided the Umklapp Scattering, i.e., point defect scattering effects are ignored in general [47–51]. Another factor that needs to be balanced for maximum output of conductivities is carrier concentration (n). Keeping in view the increase in conductivity with carrier concentration, the Seebeck coefficient (S) tends to decrease opposite of TE. The former being proportional to (n), while the latter is proportional to ln(n) results in the optimization of the carrier concentration to reproduce the maximum of power factor S2σ. Or we can say that the small Seebeck coefficient is observed in conventional metal, while very low conductivity is observed in conventional semiconductors. Hence, the optimization of typical carrier concentration is assessed to be 1019–1020 cm3, which comes out to be the carrier concentration of conventional degenerate semiconductors. Therefore, the only way to maximize the conductivity is to keep the carrier concentration at its optimum value, and enhancement in the mobility is a must. The advanced TE materials in fact are high-mobility semiconductors. In the case of degenerate semiconductors, the lattice thermal conductivity predominates the electronic thermal conductivity. The electron contribution of thermal conductivity is simply assessed from the conductivity through the Wiedemann-Franz law. At room temperature, the typical TE materials have a conductivity value of about 500–1000 S cm1, which corresponds to kel ¼ 0.4–0.8 W mK1. Plausible TE materials display a low thermal conductivity of 2–3 W mK1; consequently, it has been an essential subject of how the lattice thermal conductivity can be reduced [52]. Recently, various attempts have been made to reduce the lattice thermal conductivity by nanostructuring the bulk materials and inducing strong phonon anharmonicity in 2D materials [53, 54]. Hence, the various factors discussed earlier need to be taken into consideration while attempting to increase the

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thermopower of any material, and it is obvious that different materials react differently to these strategies. Thus, we can say that there is no universal strategy to alter the conductivity of a material for better performance, and still the progress in such tactics needs to be considered in the future.

7.3

Challenges to enhance the thermopower and figure of merit

A device made with the TE materials generate electricity from a temperature gradient (i.e., thermal energy or heat). The TE device is designed on the basis of conversion efficiency. The maximum TE conversion efficiency (ηmax) of a TE device depends upon the value of zT as given by the following relation: pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 + ZT  1 ηmax ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi TC 1 + ZT + TH

(7.1)

Higher value of zT leads to high TE conversion efficiency. For practical application, the Carnot efficiency of a TE device should be 15%, which is possible only if the average zT  1.5. High conversion efficiency of TE material is limited due to the interdependence of transport coefficients. However, achieving high zT is a very challenging task due to the intercorrelated transport coefficients (as described later). A conventional way of thinking to enhance zT is to increase the power factor (S2σ) and simultaneously decrease the thermal conductivity. However, this is not an easy task to execute. According to the Wiedemann-Franz law, κel increases with increase in σ, which consequently affects zT. The relation between electronic mobility (μ) and carrier concentration (n) is σ ¼ eμn, where e is the electronic charge that shows high value of neither n nor μ nor both are required to get a higher value of σ; however, this also leads to higher κ el. The drift velocity of charge carrier per unit electric field defines carrier mobility. In classical approximation, μ is determined by the carrier’s inertial effective mass (m*) and the scattering time as: μ¼

eτ m∗

(7.2)

It is evident from this equation that heavy carriers have low group velocity and therefore have low mobility. Moreover, charge carriers encounter a number of scattering sources (e.g., lattice vibration, crystal defects, grain boundaries, etc.), which reduce carrier mobility. Furthermore, enhancing carrier concentration negatively affects the Seebeck coefficient. In view of constant scattering time approximation, the thermopower of S can be expressed by the following relation: S¼

  4π 2 kB2 4π 2=3 ∗ m T eh2 3n

(7.3)

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where kB, h, n, m*, and T represent Boltzmann constant, Plank constant, carrier concentration, effective mass of the charge carrier, and absolute temperature, respectively. Eq. 7.3 clearly shows that S is directly and inversely proportional to m* and n, respectively. The effective mass is related to the dispersion relation (E vs. k) i.e., an electronic band structure-dependent quantity, given by the following relation: 1 1 d2 E ¼ 2 2 m∗ ђ dk

(7.4)

which shows that the effective mass depends upon the curvature of the electronic bands. Flat electronic bands give high effective mass and consequently leads to high S. However, this also leads to lower carrier mobility and consequently lower electrical conductivity. Hence, optimizing the power factor (i.e., S2σ) is a challenging task. In semiconductors, thermal conductivity due to phonons is dominated over thermal conductivity due to electrons. Hence, reduction in κ l ultimately enhances TE performance. However, there is another kind of thermal conductivity that arises in semiconductors due to the bipolar effect, the so-called bipolar thermal conductivity (κ bp) [14], e.g., in a doped semiconducting system, majority and minority charge carriers increase the total κ. Apart from this, the bipolar effect also effectively suppresses the Seebeck coefficient, because both the charge carriers contribute with opposite effects. Bipolar thermal conductivity is related to the band gap (ΔEg) and temperature (T) as follows [55]: 

ΔEg kbp ¼ exp 2kB T

 (7.5)

Eq. (7.5) clearly reveals that an increase in temperature enhances κbp and eventually limits zT for intermediate or higher temperatures [56]. However, increasing ΔEg suppress κ bp due to the reduction in thermally excited minority charge carriers at higher temperature. Moreover, Hong et al. [56] investigated that κ bp can be reduced by hierarchical nanostructures Bi2Te3/Te by introducing an extra energy offset between conduction and valance bands, which arises due to the band gap difference between Bi2Te3 (0.15 eV) and Te (0.33 eV) and eventually enhances zT. Hence, from the previous discussion, we have seen that any effort to increase either power factor or reduce thermal conductivity has its own countereffect, hence, optimization is necessary. There are various traditional ways to optimize/enhance zT, such as doping and alloying, which optimize the carrier concentration to enhance the electrical conductivity [32, 57]. Moreover, nanostructuring significantly reduces the thermal conductivity due to the increase of boundary scattering [58]. This technique successfully leads to high zT of 2.2 in PbTe/SrTe and AgPbmSbTe2+ m [59, 60]. A brief summary of various ways to optimize different transport coefficients to enhance zT follows. One of the oldest [61] and most significant ways to increase figure of merit is by alloying to form solid solutions such as Pb1 xSnxTe1 ySey or Bi2(1 x)Sb2(1 x) Te3(1 y)Se3y. The motive of this approach is to enhance the scattering rate of phonons due to the presence of the mass difference of the constituent atoms, which consequently leads to a decrease in lattice thermal conductivity. In this approach,

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the long-range order/periodicity of the lattice is preserved, but there exist intense short-range perturbations. The charge carriers, i.e., electrons are essentially unaffected by these perturbations, whereas, on the other hand, phonons are strongly scattered by these local distortions in atomic mass and size. The decrease in κ l ultimately enhances the zT value. Another commonly adopted method to increase zT is to reduce thermal conductivity due to phonons. This can be achieved by increasing the scattering rate of phonons by various mechanisms such as external doping (which induces the mass fluctuation in the crystal), grain boundary, and interfaces. For example, in one of the most studied half-Heusler compounds, (Zr,Hf)NiSn, the maximum zT is obtained 0.2–0.3 in the pristine (or without doping) form [62]. However, doping with various transition metals such as Ti, Ni, and Co enhances zT up to 0.7–1.5 [62–64]. Another example is the peak value of zT is 1.5 obtained at 1200 K in Hf-doped FeNbSb compound [65]. The key reason for not getting a high zT in ideal crystal is high values of κ, which have been suppressed by doping effect. Another promising property, so-called “phonon-glass electron-crystal (PGEC)”, is used for the reduction of thermal conductivity. The PGEC complex crystal structure provides a favorable environment for the conduction of charge carriers (electrons) and becomes unfavorable for the conduction of phonons. A cage-type structure is found in the corresponding PGEC complex such as in skutterudites, clathrates, Zintl-phase compounds, half-Heusler alloys, and β-Zn4Sb3 alloys that allow the external/host atom to rattle inside the voids and consequently reduce lattice thermal conductivity [66]. The intrinsic defects such as vacancies also cause a reduction in lattice thermal conductivity, which act as ideal scattering sites. For example, rare-earth chalcogenides with Th3P4 structure such as La3 xTe4 show relatively low thermal conductivity [1]. Most of the approaches to enhancing zT involve reducing the thermal conductivity, especially due to phonons (e.g., doping, nan structuring, etc.). In the case of semiconductors, it has been reported that the lower limit of lattice thermal conductivity is 0.2 W/mK [67]. Due to this lower limit, one can think to reduce κ el rather κl. This can be done by the spike (or Dirac-delta)-type distribution of carriers within a narrow spreading energy range near the Fermi level. In this scenario, κel can be minimized without decreasing electrical conductivity. This kind of distribution leads to high effective mass, which enhances the Seebeck coefficient and consequently increases zT [67]. In most of the cases, TE material itself shows high thermal conductivity. Due to which, in last few years, the scientific community has started considering those materials that intrinsically have lower lattice thermal conductivity. However, this is also a challenging task to find such materials. Electronic band convergence is another efficient way to enhance thermopower, which eventually boosts zT. The band convergence is related to the band effective mass as [68]: m∗ ¼ NV m∗b 2=3

(7.6)

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Where m*b is the effective mass corresponding to a single valley. From this equation, one can see Nv can increase m*, but at the same time μ should be unaffected. Band convergence can be increased when multiple electronic bands converge via suitable doping, pressure effect, or changing the crystal symmetry [68]. High effective mass and high carrier mobility are the prerequisites for designing TE materials. It has been reported that, in the case of binary semiconductors, low effective mass and high carrier mobility are found in covalent (bond) compounds with small differences in electronegativity between the constituent elements (e.g., IrSb3 compound, μ ¼ 1320 cm2/(V-s) and m* ¼ 0.17 me at 300 K). On the other hand, high effective mass and low carrier mobility are found in ionic compounds (e.g., FexCr3 xSe4 compound, μ ¼ 0.1 cm2/(V-s), m* ¼ 4 me at 300 K) [60, 65, 69, 70]. As per the earlier discussion (see Eq. 7.2), we have seen that an increase in μ leads to the reduction of m* and vice versa. Hence, there should be bridging materials that optimize these parameters (i.e., m* and μ) efficiently. This also means that the materials should possess both ionic and covalent characteristics. These kinds of materials are Zintl-phase compounds and Heusler alloys. Due to the interdependence of the transport coefficients, improving TE performance is a tedious task especially in bulk material. Due to that, research on TE materials was nearly frozen for three decades after 1960. In 1993, Dresselhaus et al. theoretically found that low dimensional materials can have higher zT than their bulk analogs due to their lower κ and quantum confinement effects. Their work attracts the scientific attention back toward thermoelectricity. The highest value of zT  3.6 at 580 K was found in Pb0.98Te0.02/PbTe quantum-dot superlattices grown by molecular beam epitaxy [71].

7.4

Doping of traditional thermoelectric materials

As we know, TE materials are facing the challenge of low conversion efficiency, which causes their less practical use. This limitation can be removed only by improving their figure of merit (zT), even when the zT for some of the TE compounds, i.e., CoSb3 and Bi2Te3 approaches 1.3 and 1.41, respectively, at 300 K temperature [72–74] and are regarded as the state of art TE materials. But until that day, researchers have a dream to reach zT ¼ 1 for most of the compounds. Along with the many other methods, i.e., Mechanical Stress, Nanostructures, Quantum Dots, and Doping are also efficient ways to enhance the energy conversion performance. In 1956, Ioffe and his team announced that the ratio (σ/κ) can be increased if the TE material is doped with an isomorphous element [61], which increases the figure of merit. The main focus of doping in a bulk material is to vary the lattice thermal conductivity (kl) without affecting its electrical conductivity (ke). It has been observed that the good TE materials with a very high zT are the heavily doped semiconductors with low thermal conductivity. There are significant effects of doping on the TE parameters: 1. The predominant effect of doping has been observed on the electrical conductivity, thermal conductivity, and the Seebeck coefficient. However, other parameters like carrier density, mobility, effective mass, and the band structure are also affected by proper doping.

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2. It causes an optimum carrier density for the enhanced electrical conductivity and Seebeck coefficient at the given temperature, which results in an optimum power factor and hence the maximum zT. 3. The dopant elements cause the point defects that can influence the carrier density of a material. 4. The doping induced the convergence of conduction or valence bands to the increased valley of degeneracy, which can increase the electrical conductivity while maintaining the Seebeck coefficient hence the power factor will rise. 5. The atomic scale is influenced by doping, which results in point defects in the crystal lattice. These defects effectively delay the phonon propagation when the lattice mismatch between the host and the dopant is sufficient, which causes a reduction in lattice thermal conductivity and hence influences zT.

Therefore, doping is needed to prove the TEs on practical heights without altering their crystal structures and the mechanical properties.

7.5

Effect of doping in traditional thermoelectric materials

In recent years, doping of traditional TE materials results in wonderful improvement in enhancing zT as well as the better designing and operation of TE modules. Doping of suitable elements in the required ratio does not alter the mechanical and phonon properties of the compounds. The amazing effects of doping on TE performance are discussed as follows. The TE properties of the chemically doped FeGa3 has been reported by N. Haldolaarachchige et al. [75], where the doped compound Fe0.99Co0.01 (Ga0.997Ge0.003)3 shows zT ¼ 1.3  102 at 390 K that is about five times that of the pure compound. The alloy Bi(2 x)GaxTe2.7Se0.3 (x ¼ 0, 0.04, 0.08, 0.12) fabricated by vacuum melting and hot pressing technique results in a maximum zT ¼ 0.82 at 400 K for the composition x ¼ 0.04 [76]. The enhancement in the TE properties of Cu2Se by the doping of Te has been reported by Yong-Bin Zhu et al. [77] in which the effect of Te content (x) has been studied for the series of Cu2Se1 xTex (x ¼ 0, 0.02, 0.04, 0.06, and 0.08) that are prepared by mechanical alloying and spark plasma sintering. Finally, it was found that the maximum value of zT ¼ 1.25 is achieved for Cu2Se0.98Te0.02 at 773 K that is due to decreasing the thermal conductivity of the bulk compound. Na doping in BiCuSeO oxyselenides in the series of compounds Bi1 xNaxCuSeO (0.0  x  0.02) have been investigated in the temperature range of 300–923 K. It results in an increase to the carrier concentration, reduces the thermal conductivity, and leads to zT of 0.91 at 923 K for the doped compound Bi0.985Na0.015CuSeO, i.e., twice the bulk BiCuSeO compound [78]. The TE performance of Bi2Te3 also depends on its composition, such that corresponding to 60 atomic present Te is p-type and, as the concentration of Te increases, the compound Bi2Te3 becomes the n-type. The maximum zT of p-type

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and n-type Bi2Te3 crystalline material at room temperature are 0.75 and 0.86, respectively [79]. Doping of Cs in Bi2Te3 forms the compound CsBi4Te6 that lowers only thermal conductivity without causing too much degradation of electronic properties due to the suitable tuning of carrier concentration and thermal conduction. This compound exhibits a high TE zT of 0.8 at 225 K that is even below room temperature [3]. E.A. Skrabek et al. [66] reported that the p-type alloy (GeTe)0.85(AgSbTe2)0.15, also known as the TAGS, has zT about 1.2 at 400 K for the long life and reliable TE applications. The heavily La-doped SrTiO3 has been found with remarkable power factor of 3.6  103 W/mK2 at room temperature [80] that is comparable to that of the state of art TE material Bi2Te3. There is also an effect of doping on the p-type layered cobaltites, such that the zT of NaxCoO2 by the doping of Ag, Au and K, Sr, Y, Nd, Sm, Yb groups is 0.4 and 0.5, respectively [17, 81]. A similar improvement in the figure of merit has been observed in the n-type oxides, e.g., zT of In2O3 is 0.08 for the dopant elements Sn and Al [82], whereas it increased to 0.15 by the doping of Ge, Mn, Zn elements [82]. The effect on figure of merit of the p-type half-Hesuler compound FeNbSb is recently reported by Mario Wolf et al. in 2019 [17], which results when Nb is substituted by Ti or Hf to form FeNb0.88Hf0.12Sb, FeNb0.86Zr0.14Sb, and FeNb0.95Ti0.05Sb, then the resulting figure of merit is 1.45 (1200 K), 0.80 (1050 K), and 0.70 (973 K), respectively. When the p-type half-Heusler XCoSb is doped either by X ¼ Zr or Hf, then it shows n-type behavior and (Zr0.4Hf0.6)0.88Nb0.12CoSb shows the figure of merit zT ¼ 0.99 at room temperature, which was described by Liu et al. [83] in 2018. Eyob K Chere [84] and his coworkers reported that Na doping in polycrystalline SnSe effectively increases the carrier concentration to 2.7  1019 cm3 that finally shows a peak of zT of 0.8 at 773 K. There is a 30% increase in the TE figure of merit of nickel-doped tetrahedrite Cu12Sb4S13 with the addition of Zn. They also described the mechanism of doping that causes the tuning of Fermi energy level that results in optimizing the Seebeck coefficient and a significant reduction in both of the electronic and lattice thermal conductivity [85]. The effect of Bi as a dopant on the TE properties of Mg2Si are investigated as Mg2Si1 xBix (x ¼ 0.125, 0.25, 0.375, 0.5) by Kulwinder Kaur and Ranjan Kumar [86], who explored that Bi affects all the TE properties as well as the carrier concentration, and there is a maximum zT of 0.67 for x ¼ 0.125 at 1200 K temperature.

7.6

Nanostructured traditional thermoelectric materials

Dimensionality plays an important role in controlling the properties of materials. There is a marked change in the DOS when the dimension of the materials decreases and approaches the nanometer scale (Fig. 7.3). In the scientific community,

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researchers are trying to improve the TE efficiency of TE devices. They are finding different ways with which they can enhance the zT of TE materials. On the basis of dimensionality, the new strategy to enhance zT was first discovered by Hicks and Dresselhaus [87,88]. They showed significant enhancement in zT of quantum wire (1D) or quantum well (2D) of Bi2Te3 with theoretical calculation (Fig. 7.4). zT can be monotonically improved with a decrease in diameter of quantum wire or thickness of quantum well. There are two distinct approaches with which the TE properties can be boosted in low dimensional TE materials. 1. The power factor (S2σ) increases due to the quantum confinement effect. The DOS near the Fermi level increased, which enhanced the Seebeck coefficient (S). 2. The phonon scattering increases due to the presence of surface and interfaces, which results in a decrease in lattice thermal conductivity.

The value of the Seebeck coefficient (S) depends upon the energy derivative of energy-dependent electrical conductivity (σ ¼ n(E)eμ(E)) present at the Fermi level Ef [91] with n(E) ¼ g(E)f(E) where g(E), f(E), e, and μ(E) correspond to the DOS per unit energy and per unit volume, Fermi function, carrier charge, and mobility, respectively.

Fig. 7.3 Schematic illustration of electronic DOS as a function of energy of (A) a bulk material (3D), (B) quantum well (2D), (C) nanowire or nanotube (1D), and (D) a quantum dot (0D) [89,90].

Fig. 7.4 (A) Variation of zT as the function of the layer thickness in Quantum Well. (B) Variation of zT with diameter in Quantum Wire [87,88,90].

Traditional thermoelectric materials and challenges

(     π 2 kb2 ln ðσ ðEÞ π 2 kb2 1 dnðEÞ 1 dμðEÞ + T d T S¼ ¼ dE n dE μ dE E¼Ef 3e 3e E¼Ef

153

(7.7)

On the basis of Eq. (7.7), S can be enhanced by two mechanisms: (a) To increase the energy dependence of μ(E) by scattering mechanism, which strongly depends upon the energy of the charge carrier. (b) To increase the energy dependence of n(E) by a local increase in g(E).

In low dimensional materials, the enhancement in the Seebeck coefficient is observed due to the second mechanism. For a degenerate semiconductor, this concept can be explored in terms of DOS effective mass (m∗d) [91]: S¼

8π 2 kb2 ∗ h π i2=3 Tmd 3n 3eh2 

(7.8)

3=2 gðEÞђ3 π 2 pffiffiffiffiffiffi . 2E Due to the quantum confinement effect, there is a strong modification observed in phonon group velocity [92,93]. When the dimensions of the materials decrease, the interfaces or surface scattering gain significant attention [94,95]. Due to the presence of interfaces and surfaces, the phonon effectively scattered the phonon because it has a large mean free path (mpf). Thus, the lattice thermal conductivity decreases. It has been observed that zT can be improved with the reduction of lattice thermal conductivity in different types of nanostructure materials [39,96–125]. The improvement in the Seebeck coefficient has been massively studied in low dimensional materials, e.g., Quantum wire (1D) [120,121,126–129] and Quantum Well superlattice (2D) [96,107,118,130–140]. Here, some representative examples are reported. Herman et al. [134] prepared the multiple quantum well (MQWs) of Pb1 xEuxTe/ ˚ . He observed that the Seebeck coefficient of MQWs was PbTe having width 20 A higher than the bulk. Hicks et al. [135] found that, in Pb1 xEuxTe/PbTe, the Seebeck coefficient enhanced by a factor 3 from the bulk with a decrease in the thickness of ˚. the well from 55 to 17 A Harman et al. [138] reported the TE parameters of quantum dot superlattice (QDS) of PbTe1 xSex/PbTe and observed a higher value of Seebeck coefficient in QDS than their bulk counterpart. Ohta et al. [131] reported that, by decreasing the thickness of quantum well to only one unit cell layer, the Seebeck coefficients of SrTiO3 superlattice is five times greater than bulk. Boukai et al. [120] showed that Si nanowire has a large value of Seebeck coefficient compared with bulk Si. Wang et al. [37] observed that the value of the Seebeck coefficient increases by varying the nanocrystal size of PbSe nanocrystal superlattice. where m∗d ¼

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Zuev et al. [126] reported that, in Sb2Te3 nanowire, the Seebeck coefficient shows enhancement from 81 to 111 μV/K when the diameter of the wire changes from 95 to 22 nm. Shimizu et al. [141] fabricated the electric double layer transistor based on singlewall carbon nanotube film, and the results show that there is an enhancement in the Seebeck coefficient by tuning the gate bias voltage. Saito et al. [142] also showed similar results in black phosphorus. Yao [122] found that the thermal conductivity of AlAs/GaAs superlattice decreases with layer thickness. A similar trend in the reduction of in-plane thermal conductivity is observed in PbTe/PbSe0.2Te0.8 superlattice [99]. The value of in-plane thermal conductivity Ge/Si quantum dot superlattice is 305 W/mK, which is much lower than that of bulk Si [97]. Boukai et al. [120] showed that the thermal conductivity of Si wire decreases as the diameter of nanowire decreases. Same trends were observed in PbTe nanowire [102,104] and Bi single crystalline nanowire [124]. Gayatri Kesker et al. [143] showed significant improvement of zT with bismuth nanotube and nanowire and noticed that the thermal conductivity is five times less than that of Bi powder. In Si0.8Ge0.2 alloy, the lattice thermal conductivity is low compared with the crystalline alloy due to the heavy point defect, but the value of zT did not increase due to a proportional decrease in electrical conductivity. A similar trend was observed in Si/Ge superlattice, and in SiyGe1 y/SixGe1 x superlattice, the reduction in thermal conductivity did not enhance zT [123]. Bi2Te3/Sb2Te3 superlattice has less thermal conductivity than solid solution alloy [144]. In two-dimensional materials, graphene exfoliated from bulk graphite [145,146] became an interesting topic in the scientific community due to its wonderful physical and chemical properties. Graphene has unique optical, electrical, catalytic, and mechanical properties. Due to high electron mobility [147], graphene has an ultrahigh electrical conductivity (106 S/m) at room temperature. The value of thermal conductivity is 4840–5300 W/mK [148] at room temperature, and the maximum value of the Seebeck coefficient is 80 mV/K [149–151]. Transition metal dichalcogenides (TMDCs) are a novel class of layered materials, i.e., MX2 (M ¼ Mo, W, Ti and X ¼ S, Se, Te) have received large attention in scientific research due to their outstanding chemical stability, semiconducting nature, and physical and mechanical properties. TMDCs attain a high value of Seebeck coefficient. Considering MoS2 as a reference material, the TE properties of TMDCs are given in Fig. 7.5. The TE parameters along in-plane direction of MoS2 multilayers are calculated at 300 K (Fig. 7.5A–C). The results indicate that the Seebeck coefficient is not affected too much by altering the layer number. But the electrical conductivity shows strong dependence on the layer thickness (Fig. 7.5B). Significant enhancement is observed in electrical conductivity and power factor due to valley degeneracy at the valence band edge [152]. In Fig. 7.5D–F, the layer structure has a large value of zT compared with bulk. Experimentally, it has been proven that the TE properties can be enhanced by

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155

Fig. 7.5 Variation of (A) Seebeck coefficient, (B) electrical conductivity, and (C) power factor with thickness and chemical potential of p-type MoS2 at 300 K [152]. Variation of zT of (D) MoSe2, (E) WS2, (F) and WSe2 for bulk, one layer, two layers, three layers, and four layers with reduced Fermi energy F. zT of n-type (p-type) is plotted with solid line (broken line) [153].

applying pressure and an external electric field. Buscema et al. [154] observed that, in the presence of an external electric field, there is a large tunability in Seebeck coefficient between 4  102 and 1  105 μV/K in the MoS2 monolayer. Wu et al. [155] found that, by adjusting the backgate voltage, the Seebeck coefficient of MoS2 attains maximum value of 30 mV/K. Hippalgaonkar [156] measured the TE properties of an exfoliated 2D MoS2 flake with different thicknesses. The bilayer MoS2 has the highest power factor (8.5 mW m/K2) as the gate voltage approaches 104 V at n ¼ 1.06  1013 cm2 concentration. The thermal conductivity of a few layers of MoS2 is 52 W/mK [157]. Yan et al. [158] measured the thermal conductivity of exfoliated MoS2 monolayer that was found to be 34.5 W/mK. Using Raman spectroscopy, Taube et al. [159] measured the temperature-dependent thermal conductivity of MoS2 monolayer grown on SiO2/Si substrate and observed that the thermal conductivity decreases with an increase in temperature, and the value decreases from 62.2 to 7.45 W/mK as the temperature increases from 300 to 450 K. Two-dimensional materials based on group IV–VI A elements have gained much attention in the research of TE community. Materials such as Sn(S, Se, Te), Ge(S, Se, Te), Pb(S, Se, Te), Sn(Se, S)2, and their alloys have been widely explored for TE applications such as power generators, TE sensors, and cooling devices [160,161]. Cheng [162] found that bismuth monolayer has a promising TE efficiency. In few layers of black phosphorene, the observed Seebeck coefficient is 510 μV/K, which shows in-plane anisotropic behavior in conductivity and Seebeck coefficient due to its puckered structure.

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Newly designed 2D materials contain transition nitrides and carbides. MXenes shows either semiconducting or metallic properties based on its surface functionalization [163]. 2D materials of Max phase can be defined as Mn+1AXn where n ¼ 1, 2, or 3; M represents transition elements (Sc, Ti, V, Cr, Zr, Nb, Ta, Hf); A is the element from groups 13–16 (Pb, Al, Si, S, P, Ge, Ga, As, In, Tl); and X corresponds to nitrogen or carbon. MXenes are high temperature TE materials. Kumar et al. [164] reported that, with the functionalization of MXene by O, F and OH group can alter the electronic band structure and also improve the TE performance. The value of the Seebeck coefficient of Sc2C(OH)2 is 372 μV/K, but Sc2CX2 (X ¼ O, F) have Seebeck coefficients more than 1000 μV/K at room temperature. The lattice thermal conductivity of Sc2Co2, Sc2CF2, and Sc2C(OH)2 is 59, 36, and 10 Wm/K, respectively.

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Manish K. Kashyapa,b and Renu Singlab a School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India, bDepartment of Physics, Kurukshetra University, Kurukshetra, Haryana, India

8.1

Introduction

After World War II in the wake of cumulative carbon dioxide emission crises and balancing the overall global needs of electricity, including those related to supply, price, and pollution associated with the traditional sources, the international community has been seriously looking for an alternative solution that must be economic and environment friendly. Ioffe [1] presented a solution by introducing the first thermoelectric generator (TEG) and cooler based on doped bismuth telluride (BiTe). Thermoelectric (TE) materials are the semiconductors/insulators that lead to the direct conversion of temperature differences to electric voltages and vice versa. Since then, TE materials seem to be most promising in a vast number of applications because the fabrication of most devices depends upon BiTe and similar chemical compounds. They have value in automotive waste heat power generation, space power production, energy storage, and utilization of solar energy due to their high reliability and intelligibility. Practically speaking, nearly all space trials sent beyond Mars have had a specific type of radioactive heat-powered TEG, which avails itself the heat released by radioactive decay to produce power. These probes have been working successfully for more than two decades, proving the incredibility and strength of these TE materials. The uses of TE cooling include temperature control for semiconductor lasers, seat coolers in high-end cars, and solid-state coolers in compact refrigerators. Also, in many developing countries, the use of fossil fuels is still a problem to tackle. In this critical situation, the combustion efficiency of wood stoves can be improved to a great extent using these materials. Furthermore, they reduce the harmful smoke output and the amount of wood required to do so. They are highly capable of generating power from the sun by employing solar energy to build a temperature gradient across them, popularly known as solar thermal energy conversion. This shows their immense potential in the industrial market, but they still have some engineering challenges in the form of low efficiency relative to mechanical cycles. The performance of a TE material is characterized by a dimensionless figure of merit (zT) that requires high electrical conductivity, high thermopower, and low thermal conductivity. Even after several decades of searching for better alternatives of BiTe, the researchers could not find any new material with improved TE performance up to the 20th century. Howbeit, Dresselhouse et al. [2] brought out nanostructured TE materials where the Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00007-2 Copyright © 2021 Elsevier Ltd. All rights reserved.

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quantum confinement expands the thermal power while countless grain boundaries secure a feeble thermal conductivity. These quantum materials gathered huge excitement [3] and, at present, the TE materials consist of compounds of different chemical compositions and structures including oxides, Zintl phase materials, hybrid compounds, metal chalcogenides, skutterudite antimonides, half-Heusler compounds, manganese silicide, etc. However, this chapter does not cover all of the important aspects regarding modern TE materials but particularly highlights the significant contributions of eminent scholars. This, nevertheless, provides state-of-the-art advanced TE materials and a range of their specific figures of merits that might be fruitful for readers to enhance their knowledge and understanding regarding this phenomenal area. It is intended that this chapter will motivate researchers, material scientists, and engineers to further explore modern applications and material development in TEs.

8.2

Oxides-based thermoelectric materials

Since the last two decades, oxide materials have been established to be very promising as TE materials with the increase in zT almost by 10-fold than conventional BiTe and PbTe. In this way, they brought new excitement and a revolution in this leading area of TE research. Here, we discuss in brief the following versatile substances that fall in the wide category of the landscape of oxide-based TE materials: l

l

l

l

High mobility oxides Layered cobalt oxides Perovskite-based oxides ZnO-based oxides

8.2.1 High mobility oxides At the end of the 20th century, various researchers started exploring the worth of oxides in TE devices. The first member of this family was complex In2O3-SnO2, which is known as Indium-Tin-Oxide (ITO). Initially, it was one of the most conductive oxides and proved highly efficient in industry. Ohtaki et al. [4] found its thermal conductivity as low as 1.7 Wm
1 K
1 at room temperature, which goes to 3.1 W m
1 K
1 at 1023 K with zT ¼ 0.4  10
4 at 1273 K. However, being most conductive and mobile, a very low value of zT compared with other nonoxide TE materials limits its worth to a great extent. Many distinct efforts were made by researchers to improve its zT. Furthermore, they reported that zT can be modified by increasing temperature, predicting a possibility of heat-resistant oxide semiconductors for high temperature TE power generation [4]. B
erardan et al. [5] studied that zT can be improved from 0.06 to 0.45 at 1273 K by replacing In with Ge in In2O3 (In1.8Ge0.2O3). This substitution leads to an increase/decrease in electrical/thermal conductivity, resulting in an appreciable increase in TE performance.

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8.2.2 Layered cobalt oxides This class of oxides mainly includes metal oxides such as high Curie temperature (TC) Cuprate superconductors having layered structures. In these layered structures, scattering of phonons takes place at the interfaces that leads to a significant reduction in their thermal conductivity. The large value of Seebeck coefficient in NaCo2O4 [6, 7] aroused excitement toward these layered oxides. In NaCo2O4, CoO2 and Na layers are stacked alternately with each other along c-axis. Its phenomenal TE performance is attributed to the fact that it has quite high thermal power, high carrier concentration, and feeble thermal conductivity compared with that of glass-like materials. This large thermal power originates as a result of strongly correlated electrons by means of a fluctuation in spin. Due to these remarkable features, researchers further explored these cobalt oxides. By replacing Na in NaCo2O4 with Ca/BiSr, the resultant materials Ca3Co4O9 and Bi2Sr2Co2Oy appeared to be more feasible TE material. The TE properties of these oxides in the form of single crystals ranging from 50 to 200 mm width revealed the largest zT ¼ 1.2–2.7 for Ca at 873 K and zT > 1.1 for BiSr at 1000 K [8, 9]. In this regard, the zT that crosses even unity for these in-plane single crystals of cobalt oxides serves as a breakthrough in all TE applications.

8.2.3 Perovskite-based oxides The conduction electrons are highly localized in the ionic crystals as they can polarize the crystal lattice due to strong lattice-electron interactions. This leads to the distortion in lattice, and such conduction electrons are known as small polarons. These electrons follow by a hopping mechanism, and their mobility is much lower in comparison to the electrons in the conduction band. The main condition to undergo hopping mechanism is that the polarons must have carrier mobility less than 1–0.1 cm2/Vs. The first perovskite oxide based upon this hopping conduction mechanism, La1
xSrxCrO3, appeared to be highly capable as an interconnector in solid fuel cells. It has long thermal duration, high conductivity, and better TE performance (zT ¼ 0.14 at 1600 K) [10]. The next perovskite in this category is CaMnO3, having similar conduction mechanism and, upon replacing Ca sites with Ba, an enhanced TE performance with power factor (PF) of about 2–3.5  10
4 W/m K2 and zT ¼ 0.16 at 1173 K can be obtained. Also, strontium titanate (SrTiO3) forms cubic perovskite structure at room temperature and seems a nice TE material without undergoing hopping conduction mechanism. It is basically an insulator having a vacant conduction band that comprises of only 3d orbitals of Ti and completely filled valance band in which contribution arises only from 2p orbitals of O. Despite being an insulator, it has high electrical conductivity because heating effects in the atmosphere cause oxygen vacancies, and some electrons are injected into the conduction band. However, it has one limitation; its thermal conductivity is high due to the presence of a simple structure consisting of light elements that limits zT only to 0.1–0.2. Later, zT was increased up to 0.37 at 1000 K by doping Nb into SrTiO3 [11].

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8.2.4 ZnO-based oxides The carrier mobility in oxides can be further increased by reducing the ionic nature of metal-oxygen bonds. ZnO, the earth-abundant compound, is a direct band gap semiconductor with band gap of 3.2–3.5 eV. The electronegativity of Zn is higher as compared with other transition metals, resulting in low polarization of ZnO bonds. ZnO is highly efficient in various applications such as photodetectors, transparent electrodes, and thin film transistors [12, 13]. It was reported that Al doping in ZnO [6] leads to significant zT even at room temperature (Fig. 8.1). However, high thermal conductivity of ZnO limits its worth and is quite challenging. Nevertheless, oxide TE modules are highly attractive as they can use traditional ceramic processes, are nontoxic and cheap, can be utilized either directly or in combustion flames at high temperature, and have a long lifetime. But they also have some limitations. While some oxides have attained zT ¼ 1 in single crystal form, the performance of practical bulk oxide materials are still not satisfactory.

8.3

Zintl phase-based thermoelectric materials

The designing of a TE material is a quite tedious task as high zT requires variations in all thermodynamical, electrical, as well as thermal transport properties at once.

Fig. 8.1 Variation of zT with temperature for Zn1
x,1
yAlxGayO. Adapted from M. Ohtaki, Recent aspects of oxide thermoelectric materials for power generation from mid-to-high temperature heat source, J. Ceram. Soc. Jpn. 119 (11) (2011) 770–775 with permission from Springer Nature.

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Various researchers reported that this unique mixture of properties can be attained by envisioning a complex material with diverse components providing distinct functions [14, 15]. The structure of this complex TE material would have basically two regions. One of the regions is composed of a compound semiconductor having high mobility that forms the “electron-crystal” electronic structure, and the remaining region consists of a phonon-inhibiting structure that acts as the “phonon-glass”. Also, the phonon-glass region would be suitable for doping without disturbing the electroncrystal region [16]. Zintl phase materials are most appropriate candidates for this concept of envisioning two diverse components to obtain TE materials with high zT as they can easily tailor the required properties of “electron-crystal, phonon-glass". Zintl phases are mainly composed of cations that donate electrons to anions and form bonds. Thus, Zintl phases must have both ionic and covalent character. In other words, Zintl phases are mainly polar intermetallics with a small difference in electronegativity between anions and cations compared with ionic compounds. The most potential member of this family is CaxYb1
xZn2Sb2. It contains precise anionic Zn-Sb sheets. As a result of a small electronegativity difference between Zn and Sb, the bonding among Zn-Sb sheets is covalent. Also, CaZn2Sb2 is a semiconductor with feeble band gap of about 0.25 eV, and the presence of cation (Yb) turns it into a p-type semiconductor having transport properties similar to metals [17]. In this way, the electronic crystal in the resultant compound comes from the Zn2Sb2 framework, while alloying of Ca and Yb on cation site decreases the thermal conductivity by lowering its phonon contribution. The thermal conductivity reduces to such an extent that zT of the resultant compound attains an appreciable value (>1). The next popular member of this family with high zT is Zn4Sb3 having a complex Zn13Sb10 structure [18]. It has two different kinds of Sb atoms such as isolated nonbonded Sb3
anion and Sb-Sb dumbbells bonded in the state of [Sb2]4
(Fig. 8.2). In the Zintl formalism, there exists 6 isolated Sb3
anions, 2 dumbbells bonded [Sb2]4
, and 13 Zn2+ cations.

Fig. 8.2 Structural view of Zn4Sb3 along with electron density maps. In these maps, interstitial Zn atoms are clearly visible. Adapted from S.M. Kauzlarich, S.R. Brown, G.J. Snyder, Zintl phases for thermoelectric devices, Dalton Trans. 21 (2007) 2099–2107 with permission from Royal Society of Chemistry.

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The high zT in Zn4Sb3 is due to the presence of Zn at the interstitial site that results in decreasing lattice thermal conductivity. Furthermore, binary Zintl compounds, having cations from Group I or II, also seem to be highly efficient for TE devices due to significant phonon–glass qualities. Structure like A11Sb10 belongs to this binary Zintl form. Like Zn4Sb3, it has 44 A2+ cations with 8 [Sb2]4
dumbbells, 2 [Sb4]4
, and 16 Sb3
anions in each unit cell [19]. Surely, lattice thermal conductivity of this complex structure is quite low, suggesting an appreciable TE performance. However, in contrast to Zn4Sb3, it is bipolar having conduction due to both electrons and holes, which compensates the decrease in thermal conductivity and gives rise to low zT. The latest discovered compounds in this category have general formula, A14MPn11 (A ¼ 2 + cation, M ¼ Metal, Pn ¼ P, As, Sb, Bi), and the structure for the same is shown in Fig. 8.3. Among these, Yb14MnSb11 has emerged to be one of the most efficient TE materials [20–22]. It validates the perfect consolidation of electron-crystal and phonon-glass properties. It is made up of multiple anions such as the structure composed of tetrahedra [MnSb4]9
, polyatomic [Sb3]7
, and isolated Sb3
anions (Fig. 8.3). Also, Yb acts as a cation in state Yb2+. In addition, it must have high melting point due to strong bonding between these anions and cations, giving

Fig. 8.3 Structural view of A14MPn11 (A ¼ 2+ cation, M ¼ Metal, Pn ¼ P, As, Sb, Bi). MPn4 polyhedra and Pn3 unit are depicted. The gold/blue/red sphere (light/dark/medium gray in print versions) represents the A/Pn/M atom. Adapted from S.M. Kauzlarich, S.R. Brown, G.J. Snyder, Zintl phases for thermoelectric devices, Dalton Trans. 21 (2007) 2099–2107 with permission from Royal Society of Chemistry.

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incentive for stable TE properties at high temperature. It is crystal clear that this structure is indeed more complex than CaZn2Sb2 and has many more attributes and potentials for the fine tuning of zT. In a nutshell, Zintl formalism requires a proper complex structure suitable for electron-crystal and phonon-glass properties that results in remarkably high zT. They adjoin the different regions of cations and anions, which results in an appropriate tuning of electronic properties and introduction of disorders. These disorders lead to low lattice thermal conductivity, necessary for high zT. A proper knowledge related to the bonding mechanism and relation with the transport properties may give rise to a focused approach for the search of new materials in this area.

8.4

Hybrid thermoelectric materials

Hybrid TE materials have gathered wide attention during the past decade due to the increased requirements for the energy sector to fulfill the needs of a rapidly growing population over the globe. Organic and hybrid TE materials are feasible to extract electricity from waste heat at moderate temperatures. In the practical situation, the waste heat energy generated from the burning of fossil fuels is released at temperatures 1). They possess quite high mechanical strength. They have an appreciable electron transport property and are generally stable.

The costs of various TE materials are shown in Fig. 8.8, which clearly tells the economical availability of skutterudites [73]. The skutterudite antimonides offer a wide range of physical properties such as Kondo scattering, hopping conductivity, longrange ferromagnetic order, impressive crystal-filed splitting, and high superconductivity. CoSb3 is a magnetic semiconductor with a feeble band gap of about 0.2 eV that has both mobility and effective mass high. When combined with rare earth element to form skutterudites, zT is only 0.8. However, there are certain ways by which this zT can be enhanced. It can be done either by substituting proper dopant at Co and Sb sites or by filling the levels of rare earth elements in 2a state [74]. This type of substitution or filling leads to an alteration in electronic DOS, which in turn increases the electrical conductivity and gives rise to a large Seebeck coefficient. The first member of the filled skutterudite family comes from LaFe4Sb12 antimonides [75] whose structure is depicted in Fig. 8.9. As lanthanum atoms are very heavy, their anisotropic displacement parameters are also very large, which corresponds to long interactions between Ln and Sb atoms known as rattling effects. These rattling effects lead to a decrease in thermal conductivity and provide decent zT. After that, various ventures were triggered across the globe to enhance the filling of these levels in skutterudite antimonides. High Temperature High Pressure Sintering

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Fig. 8.9 Cubic crystal structure representation of LaFe4Sb12 (left) and the coordination polyhedron of La atom along with the LaSb12 icosahedron (right). Adapted from H. Kleinke, New bulk materials for thermoelectric power generation: clathrates and complex antimonides, Chem. Mater. 22 (2010) 604–611 with permission from American Chemical Society (ACS).

(HTHP) technique seems to fulfill this purpose [75–81]. By using the HTHP technique, zT of simple and melted RyCo4Sb12 (R ¼ Nd, Ca, Sm, Ce, Gd, Yb, and Dy) escalates up to 1.3. In a similar way, Tomida et al. [80] synthesized La-filled n-type skutterudite with modest zT of about 1.0 at 773 K. The thickness, diameter, and weight of the sample prepared were 21 mm, 200 mm, and 5 kg, respectively. The second technique that leads in this era are nano- or mesocomposites with increased grain boundary scattering. The nanocomposites of Bi0.4Sb1.6Te3 when embedded in Ybfilled CoSb3 gives zT ¼ 0.96 at 650 K [82]. However, when the same compound is embedded with WTe2 mesocomposites, zT falls drastically and becomes 0.78 at 575 K [83]. Later, the next technique that adds to this area was the hydrothermal method based on encapsulated and evacuated heating. Kruszewski et al. [84] produced Co1
x
yNixFeySb3 by making use of this technique and reported enhancement by 0.68 in zT in contrast to CoSb3 prepared simply without this technique. Some more techniques such as pulse plasma sintering and nanostructures synthesis at high pressure were used that bring zT inthe range of 0.8–0.9 at 750 K [85–87]. In addition, many other methods were adopted to further enhance the zT of these skutterudites. It was found that zT of single-filled n-type YbyCo4Sb12 can be varied in a range from 0.7 to 1.5 depending upon distinct synthesis methods such as combination of traditional annealing methods with ball milling, spinning melt with cyclic thermal loading, and spark plasma sintering (SPS) [88–92]. Also, like single-filled skutterudites, double and multiple filling lead to even more increment in zT. This may be due to the variations in the masses and resonant frequencies of the fillers modifying the phonon scattering to a greater extent and thus decreasing the thermal conductivity by manifold [93]. The

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various p-type double-filler skutterudites that fall in this category have zT in a range of 0.81–1.02 [94–98]. La0.68Ce0.22Fe3.5Co0.5Sb12 has the highest zT (1.15) among all known double-filled skutterudite so far [99]. Matsubara and Ashi [100] made an excellent attempt to modify the zT further. They compensated the extra carriers produced as a result of filler addition by substituting Fe and Co in R0.4B0.1Yb0.2Al0.1. Now the resultant compound R0.4B0.3Co4
xFexSb12 provided an improved TE performance with zT ¼ 1.5. Just like inverse clathrates, there exists a class of inverse-filled skutterudite having electronegative atom as guest with inverse polarity. The guest and host atoms interact through strong covalent bond resulting in the formation of cluster vibrations. These vibrations highly influence the lattice parameters, and substitution leads to originating the point defects that, in turn, reduce the thermal conductivity [101]. S0.28Co4 Sb11.11Te0.73 is the most important inverse-filler skutterudite with exceptional zT > 1.5 at 850 K [102]. Also, bromine and iodine were used as fillers in this. On the basis of these results, we can say that skutterudite antimonides can be highly efficient for power generation. Recently, these filled skutterudites are being explored by the National Aeronautics and Space Administration (NASA) and automobile industries for the generation of power in spacecrafts and vehicles.

8.7

Half-Heusler compounds

The Heusler compounds were discovered by German mining engineer Friedrich Heusler in 1903 and named after him [102]. Heusler compounds [103] are ternary intermetallics with a composition of X2YZ (full-Heusler) or XYZ (half-Heusler), where X and Y are transition metals (TMs)/rare earths (REs) and Z is an sp-element existing in face-centered cubic crystal structure. The half-Heusler (XYZ) compounds contain two different TMs/REs (X and Y) and crystallize in the cubic MgAgAs-type or C1b-type structure (space group: F43m). The unit cell of C1b-type structure contains three atoms as a basis with X/Y/Z present at 4a (000)/4b (½,½,½)/4c (¼,¼,¼) site, along with a void at 4d (¾,¾,¾) site and three interpenetrating face-centered-cubic (fcc) sublattices as depicted in Fig. 8.10. NiMnSb was the first half-metallic (HM) half-Heusler alloy to be predicted by de Groot et al. [104] The half-Heusler compounds containing 18 valence electrons are generally stable due to the presence of occupied bonding states only [105] and exhibit semiconducting behavior satisfying the Slater Pauling rule [106]. The final compounds with three different constituents may be semiconducting (e.g., ZrNiSn with band gap of 0.5 eV [107]), semimetallic (e.g., (Zr,Hf)CoSb compound [108]), or half-metallic (e.g., NiCrSi [109]). These compounds with narrow band gap are efficient TE materials and can yield higher PF compared with others [105,110,111]. The DOS in these materials remains present in the vicinity of Fermi level due to the d-d orbitals overlapping, which results in high electrical conductivities and large Seebeck coefficients [112]. The half-Heusler TE compounds have been in the limelight for the last two decades due to their excellent mechanical strength, thermal stability, and significant zT for medium to high temperature range, which is beneficial for use in most industrial waste heat sources. For the next generation TE technology, the TE materials must possess zT > 1. To show the TE potential of half-Heusler alloys, Berland et al. [113]

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Fig. 8.10 Unit cell representation of half-Heusler compound in C1b-type structure (space group: F43m).

compiled a comprehensive list of all 30 related stable compounds with optimal zT at T ¼ 800 K as depicted in Fig. 8.11 along with the corresponding PF and thermal conductivity. Through their DFT calculations, they showed high zT is a result of high PF (e.g., n-doped TiIrAs and p-doped ZrCoSb) or low thermal conductivity (e.g., n-doped ZrRhBi). Depending upon the constituent elements, the effective

Fig. 8.11 Optimal zT values (thin black bar) for 30 stable half-Heusler compounds at T ¼ 800 K based on DFT calculations. The corresponding values of PF times temperature (ƤT), phonon (electric) part of thermal conductivity κ l (κ e) are shown in red and yellow (blue) bars (medium and light gray (dark gray) in print versions), respectively. The upper/lower panel gives the results for n-/p-doping. Adapted from K. Berland, N. Shulumba, O. Hellman, C. Persson, O.M. Løvvik, Thermoelectric transport trends in group 4 half-Heusler alloys, J. Appl. Phys. 126 (2019) 145102 with permission from AIP Publishing.

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half-Heusler compounds with optimum TE performance can be divided into the following two main categories: (i) Ternary half-Heusler compounds (ii) Double Heusler compounds

8.7.1 Ternary half-Heusler compounds Half-Heusler compounds with the composition XYZ (X,Y ¼ TM/RE) and sp-element Z ¼ Sn/Sb are important TE materials owing to their high TE performance and robust mechanical properties. Initially, many half-Heusler compounds with composition XNiSn (X ¼ Hf, Ti, Zr) were found to exhibit semiconducting nature (band gaps in the range 0.1–0.2 eV) along with the value of the Seeback coefficient as large as
200 to
400 μV/K at room temperature [114–117]. In 1995, Slack [118] intimated that the best TE material is one that can behave as a “phonon-glass, electron-crystal.” In other words, it should have thermal properties resembling glass and the electronic properties of a crystal. In particular, XNiSn (X ¼ Hf, Ti, Zr) compounds were investigated by many researchers due to their thermal stability and mass producibility [119,120]. But their zT values were low in the pristine form. Furthermore, it is well known that intrinsic disorders in these compounds bring drastic change in their TE properties; therefore, materials scientists made significant efforts to enhance the zT and reduce the lattice thermal conductivity of half-Heulser alloys for establishing their potential in TE devices. In this direction, Chen et al. [121] investigated TE properties of n-type (Hf,Zr)NiSn half-Heusler compounds via annealing the samples near to the melting point. This led to a reduction in lattice strain and thus to the structural disorder with a significant improvement in zT, which comes out to be 1.2 without the need of nanostructures. This increase is due to a decrease of charge carrier density. Chauhan et al. [122] demonstrated the defect engineering in nonstoichiometric half-Heusler alloys to obtain zT  1 at 873 K for both n-type Zr0.5Hf0.5Ni1 xSn and p-type Zr0.5Hf0.5Co1 x Sb0.8Sn0.2 (x ¼ 0.04) compounds. This enhanced value of zT results in high conversion efficiency of 9% and large output power density 9 W cm2 in both types of half-Heusler compounds. Later, to improve TE performance, Polycrystalline ZrNi1+ xSn (x ¼ 0–0.1) half-Heusler alloys were synthesized under an argon atmosphere using arc melting of highly pure Zr, Ni, and Sn samples by Chauhan et al. [123] They achieved zT ¼ 1.1 for ZrNi1.03Sn compound at 873 K and observed that, with extra ultralow Ni doping in ZrNiSn, both full-Heusler precipitates and Ni-induced defects came into existence in the half-Heusler matrix. The localized vibrational modes of Ni antisite defects and full-Heusler precipitates scatter the phonons carrying heat and thus results in a significant decrease of thermal conductivity. Gautier et al. [124] reported ZrNiPb, which is equivalent to ZrNiSn, also as a stable half-Heusler compound. Therefore, it is expected to have comparable electrical properties with the latter. However, due to much heavier mass of Pb compared with Sn, lower thermal conductivity is expected from ZrNiPb, which can lead to better TE response. Mao et al. [125] investigated TE properties of ZrNiPb-based materials and showed that high PF of 50 μW cm
1 K
2 can be obtained in n-type ZrNiPb

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by proper tuning the carrier concentration via Bi doping. Additionally, Sn substitution at the Pb site significantly reduces the lattice thermal conductivity and maintains the PF almost unchanged, which leads to enhancement of zT effectively from 0.55 to 0.75. FeNbSb-based half-Heusler compounds have been recently identified as promising high-temperature TE materials with zT > 1, but their thermal conductivity is relatively high [126–128]. Alloying Ta at the Nb site reduces the thermal conductivity due to large mass fluctuation between them, which results in effective phonons scattering. The resultant (Nb1
xTax)0.8Ti0.2FeSb compounds were synthesized by levitation melting and SPS by Yu et al. [129]. Since Nb and Ta have similar atomic sizes, the solid solutions of their mixture exhibit almost similar electrical response. The zT value of 1.6 was obtained at x ¼ 0.36 and 0.4 for T ¼ 1200 K with reduced thermal conductivity. The TaFeSb-based half-Heusler compounds were synthesized by two steps: ball milling and hot-pressed (HP) technique. The zT value of 1.52 at 973 K and an average zT value of 0.93 over the temperature range of 300–973 K was found for p-type Ta0.74V0.1Ti0.16FeSb. In this case, via maintaining the temperature difference across the cold and hot sides as 656 K, a conversion efficiency of 11.4% was successfully obtained [130]. Xue et al. [131] proved that the LaPtSb compound can exhibit good TE properties on the basis of first-principles calculations combined with semiclassical Boltzmann theory and deformation potential theory. At room temperature, the lattice thermal conductivity and calculated zT value of LaPtSb were obtained as 1.72 W m
1 K
1 and 2.2, respectively, via fine tuning the carrier concentration. The behavior of zT with respect to p- and n-type carrier concentrations is shown for LaPtSb in Fig. 8.12. It is worth mentioning here that the reported zT value exceeds those of many good TE materials, in particular the typical (Ti, Zr, and Hf) NiSn-based and (Ti, Zr, and Hf)

Fig. 8.12 zT response of LaPtSb as a function of p- and n-type carrier concentrations at room temperature. Adapted from Q.Y. Xue, H.J. Liu, D.D. Fan, L. Cheng, B.Y. Zhao, J. Shi, LaPtSb: a half-Heusler compound with high thermoelectric performance, Phys. Chem. Chem. Phys. 18(27) (2016) 17912–17916 with permission from Royal Society of Chemistry.

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CoSb-based half-Heusler compounds. Although rare earth-based half-Heusler compounds such as YMSb (M ¼ Ni, Pd, Pt), ErPdX (X ¼ Sb, Bi), PtYSb, and YNiBi [132–134] have been experimentally reported for TE properties, the experimental realization of LaPtSb is still pending.

8.7.2 Double-Heusler compounds The half-Heusler compounds with 18 valence electrons [135] are acknowledged to be suitable for TE applications, whereas 17- and 19-electron compounds are not suitable as TE materials. Later, contrarily, it was found that 19-electron VCoSb/NbCoSb compounds [136,137] can show zT ¼ 0.5/0.4 at 700°C, although a pure phase of the same cannot be obtained. Although zT value is still lower than that of the traditional TE halfHeusler compounds, it was established that valence electron counts of 18 are not required for half-Heuslers to show TE performance. On the other hand, for 17-electron half-Heuslers (e.g., TiFeSb), the zT values have not been found to be more than 0.1 [138,139]. Fig. 8.13A depicts possible half-Heusler compounds made from a variety of special elements from the periodic table [140]. The new half-Heusler compounds can be realized in quaternary phase (X2Y0 Y00 Z2, where Y0 , Y00 are aliovalent); the unit cell representation of such a compound, in general, is shown in Fig. 8.13B, e.g. the aliovalent substitution of Fe and Ni at Y-site results in Ti2FeNiSb2 compound (Fig. 8.13C), which can give rise to a unique valence balanced composition with 18 electrons and stable resultant quaternary compound [140]. These types of aliovalently substituted compounds are named double half-Heuslers. The Ti2FeNiSb2 compound was also synthesized, and its thermal conductivity was found to be significantly lower than TiCoSb, thus, double half-Heusler compounds provide a new front for TE efficiency improvement compared with their ternary analogue. Wang et al. [141] studied TE properties in p-Type double half-Heusler Ti2
yHfy FeNiSb2
xSnx compounds. They considered Ti2FeNiSb2 as the host material in these compounds, which is a combination of TiFeSb and TiNiSb half-Heusler compounds with 17- and 19-electron configurations, respectively. It possesses lower intrinsic thermal conductivity due to the presence of phonons with smaller group velocity and disordered scattering by Fe/Ni. Furthermore, upon alloying it with Hf2FeNiSb2 and introducing Sn doping on the Sb site, a series of Ti2FeNiSb2
xSnx (x ¼ 0.2, 0.3, 0.4, and 0.5) samples were tested for TE performance. They found peak zT for Ti1.6Hf0.4FeNiSb1.7Sn0.3 as 0.52 at T ¼ 923 K, which indicates the potential of these double half-Heusler compounds in TE applications. The work is in the preliminary stage, and a lot of breakthroughs are expected in this area.

8.8

Manganese silicide

Most of the notable TE materials [142–145] with excellent TE performance are hard to commercialize economically and effectively due to the presence of costly, rare, and toxic elements like Bi, Te, Se, and Pb. On the other hand, silicide-based materials can

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Fig. 8.13 Visualization of new double half-Heusler alloys: (A) The choice of constituent atoms X, Y, and Z are shown by violet, red, and green colors (medium, dark, and light gray in print versions), respectively. (B) Unit cell with general formula X2Y0 Y00 Z2 having equal occupancy on Y-site (in half-orange and half-magenta colors; light and dark gray in print versions) to have 18-electron configuration or net valence, NV ¼ 0). (C) Example of pseudoternary TiFexCoyNi1
x
ySb compounds with Ti2FeNiSb2 (x ¼ 1/2, y ¼ 0) having NV ¼ 0. The other related single alloys TiFeSb, TiNiSb, and TiCoSb with NV ¼
1, 1, and 0, respectively, are shown at the vertices of the triangle. Adapted from S. Anand, M. Wood, Y. Xia, C. Wolverton, G.J. Snyder, Double Half-Heuslers, Joule 3 (5) (2019) 1226–1238 with permission from Elsevier.

be potential candidates showing TE response for automotive TE generators due to their low cost and nontoxicity [146]. The first report on silicides as potential materials for TEs was given by Nikitin [147] in 1958; after that, researchers started to explore new silicide materials for mid- and high-temperature TE applications. Magnesium silicide (Mg2Si) along with higher analogues of manganese silicide (HMS) are famous p- and n-type silicide-based TE materials. Unlike Mg2Si, a HMS

Beyond 3D-traditional materials thermoelectric materials

183

Fig. 8.14 Unit cell of higher manganese silicide (HMS) composed of two different Mn and Si sublattices. The c-axis varies with the number of Mn and Si atoms in HMS. Adapted from W.-D. Liu, Z.-G. Chen, J. Zou, Eco-friendly higher manganese silicide thermoelectric materials: progress and future challenges, Adv. Energy Mater. 8 (2018) 1800056 with permission from John Wiley and Sons.

material has complicated tetragonal structure (Si/Mn sublattices appear as chimneys/ ladders) in which a- and b-axis are identical and c-axis lengths are incommensurate, known as a Nowotny Chimney Ladder (NCL) structure [148]. However, on the basis of Si-to-Mn atomic ratio, HMS materials exist in a variety of compositions such as Mn4Si7 [149], Mn7Si12 [150], Mn11Si19 [152], Mn15Si26 [153], and Mn27Si47 [154] and have NCL structures with various stoichiometry [149]. The unit cells of various HMS materials are depicted in Fig. 8.14 [155]. Although space groups and atomic compositions of these materials are distinct, they still contain similar tetragonal unit cells comprising of Mn sublattices. These sublattices are identical to β-Sn (chimney) structure and penetrating helical-like Si sublattices similar to ladder. [149, 156] Also, c-axis basically follows the rule: c ¼ n  cMn ¼ m  cSi, where n/m is the number of Si/Mn sublattices of MnnSi2n
m [149]. The zT of HMS, even after doping in the sites at Mn and Si, remains low. But it is possible to increase TE performance of HMS materials via manipulating their electronic and thermal properties using nanocomposite engineering technology [157]. Ball milling is proven to be highly efficient in reducing the size of HMS grain or to directly synthesize HMS crystals of nanodimensions [158, 159]. Truong et al. [160] synthesized high-purity HMS through wet ball milling and reactive sintering and found a reduction in lattice thermal conductivity from  2.7 to  2W m
1 K
1, with a simultaneous enhancement in peak zT to 0.55 at 850 K. Miyazaki [161] fabricated partially substituted (Mn1
xMx)Si1.74 samples with M ¼ V, Ta, Fe, Nb, Cr, Mo, Re, Co, Rh, W, Ir, and Ru and confirmed the solid solution formation at x > 0.03 for the M ¼ Fe, Cr, V, Ru, and Co samples. Among these, the highest electrical conductivity and phenomenal lower thermal conductivity was found for samples in which V was substituted. The enhanced PF of 2.4 mW K
2 m
1 at 800 K

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was recorded for the melt-grown sample (x ¼ 0.02), which almost doubled compared with x ¼ 0 sample. The highest zT (¼0.6) for x ¼ 0.02 sample at 800 K was achieved for V-substitution [162]. The Cr-substituted samples also showed zT comparable to that for V-substitution. But such a high value of zT was not observed in the other melt-grown type samples due to the generation of microcracks on cooling [161]. Li et al. [157] synthesized Te nanowires (35 nm in diameter and 8 μm in length) with the help ofa method based on chemical solution phase and then embedded them in HMS to form MnTe/HMS nano/bulk structures. For the resultant structure, they achieved significant enhancement in zT value (71%) from 0.41 to 0.70 at 823 K. They argued that some nanotubes and quantum dots of Te or other nanostructures should also be tested to further enhance the TE performance. Bennet et al. [163] explained that the dislocations were widely used to scatter the phonons and thus lower the lattice thermal conductivity. In this direction, Gao et al. [164] explained that the shock compression may lead to dense dislocations in HMS materials. They achieved very low lattice thermal conductivity of 1.5 W m
1 K
1 in such samples with an increment in maximum zT by 47% to 1.0. This value of zT is more than that of many HMS materials. Their study demonstrated that the shock compression method can be advantageous for designing novel TE materials with optimum value of zT. Ghodke et al. [165] reported the transport properties of Resubstituted Mn30.4Re6Si63.6 HMS compound upon considering the influence of the grain boundary density on them. They took the advantage of the nanostructuring and heavy-element (Rhenium (Re)) substitution to greatly scatter the phonon conduction. They succeeded in lowering the thermal conductivity to 1.27 W m
1 K
1 (34%) by partial substitution of Re for Mn and nanostructuring, along with an improvement in PF (2.29 mW m
1 K
2 at 873 K). As a result, they achieved the highest zT ¼ 1.15 at 873 K for the HMS-based alloy. In a nutshell, the HMS materials made from naturally occurring elements have an effective TE performance for a temperature range of 700 to 900 K. The embedding nanoparticles, doping with foreign elements, and preventing the MnSi phase from forming in HMS can further improve their TE performance.

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Organic semiconductors and polymers

9

S.K. Tripathi and Ravneet Kaur Centre for Advanced Studies in Physics, Department of Physics, Panjab University, Chandigarh, India

9.1

Organic semiconductors

The era of electronic development due to the invention of transistors using Si or Ge dominated the previously metal-based electronics. The solid-state devices began to shape the microelectronics industry by replacing vacuum tube-based devices. The beginning of the 21st century marked the presence of a new electronic revolution by exploring a new material known as “organic semiconductors.” It was earlier known in the study of molecular crystals but was not well explored. In the early 1920s, the first reports on anthracene’s dark photoconductivity were brought up. In the 1960s, Bernanose [1] reported the discovery of electroluminescence. From the period of 1950 to 1980, major research was focused on naphthalene and anthracene. Later, Pope [2] in 1963 and Helfrich and Schneider [3, 4] in 1965 reported electroluminescence of anthracene crystal. There were several drawbacks in such molecular crystals for their practical use in day to day life. One such major drawback was the high operating voltage. It was dependent on the crystal size, which was reported to be in the micrometer to millimeter range. Later, the deposition of films of 100-nm size was achieved from spin-coated polymers and amorphous vacuum-deposited molecules that began to operate at low voltages. In 2000, the successful study of conjugated polymers (organic semiconductors) received the Nobel Prize in chemistry [5]. It also initiated the fabrication of first applications using conducting polymers, i.e., photoreceptors in electrophotography or conductive coatings. In the 1980s, there were reports of the first thin film transistor fabrication using conjugated polymers and oligomers. It took 15 years for researchers to develop the commercial use of organic semiconductors through the organic light-emitting diodes (OLEDs). Other applications such as organic field-effect transistors (OFETs) or organic photovoltaic cells (OPVCs) are still being studied. As the name suggests, organic semiconductors are defined as a class of materials with semiconducting properties along with benefits of chemical and mechanical organic compounds (e.g., plastics). They have basic insulating properties, but upon injection of charges through doping, electrodes material, or by photoexcitation, they behave as semiconductors. The rise of semiconductivity depends upon material whether it is a single molecule or exists in short-chain of molecules or long-chain Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00002-3 Copyright © 2021 Elsevier Ltd. All rights reserved.

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polymeric chains. Fullerenes and its derivatives are included in large molecules, whereas pentacene, anthracene, and rubrene come under the category of small molecules. The modification is done using chemical synthesis to alter the electronic and optical properties such as absorption and emission of light as well as the ability to conduct electricity. Based on the properties, the production of several semiconducting applications via vacuum deposition and solution processing techniques is possible such as solar cells, flexible displays, and lighting panels. The most commercial example of an organic semiconductor application is xerographic machines. The second most used in day-to-day applications is OLEDs employed in smartphones (Galaxy series of Samsung) and lighting panels (from Osram). Thus, the large technological industry is constantly working toward future development exploiting organic semiconductors. Why organic semiconductors? l

l

l

l

l

They are cheaper, transparent, lightweight, and environment friendly. They consume low energy as they can be easily processed at low temperatures. The electrical properties of semiconductors along with mechanical properties of plastics make them good candidates for electronic and optoelectronic devices. Tuning the optical properties to high absorption and luminescence makes them flexible to use as thin active layers and substrates. The versatility in solution-based processing by spin coating, blade coating, inkjet printing, and role-to-role processing makes it advantageous to use.

There are a few drawbacks of organic semiconductors. They are not stable for long terms. The mobility of charge carriers is low, which affects the efficiency of devices. This occurs due to weak Van der Waals couplings forcing the charge carriers for the hopping process. Organic semiconductors: Organic semiconductors are comprised of carbon, hydrogen with oxygen, sulfur, and nitrogen with a few heteroatoms. Understanding the difference in the nature of organic and inorganic materials is important. In inorganic semiconductors (traditionally Si, Ge, or GaAs), the delocalization of electronic states takes place due to strong couplings and long-range order of atoms. This delocalization creates a valence band (VB) and conduction band (CB) having low band gaps such as 0.6 eV for Ge, 1.4 eV for GaAs, and 1.1 eV for Si. At room temperature, the generation of free carriers in CB takes place, which creates holes in the VB. This occurs due to thermal excitation from the VB to CB. This process transporting free carriers can be described by wave vector space, Bloch functions, or dispersion relations in quantum mechanical terms. The charge carrier concentration can be calculated using the relation: N ¼ Neff eEg =2kT

(9.1)

where Eg is band gap and Neff is an effective density of VB or CB states. While in organic semiconductors, hopping transport describes the motion of carriers due to the presence of defects that can be chemical or structural. This process

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takes place from site to site based on the phonon-assisted tunneling mechanism. Miller-Abraham equation describes most of the hopping models. The probability absorbing phonon for hopping from i to j localized state at νo frequency is described as [6]:


 Ej  Ei exp 2αRij  ωij ¼ νo ; Ej  Ei  0 kB T   : exp 2αRij ;Ej  Ei  0 8
90°) nature of the material [17]. The factor is very important to calculate before its use in various applications requiring self-cleaning of surfaces such as smart windows, waterproof textiles, automotive industry, fingerprint surfaces, electronic and optical devices, drug delivery, microfluidics, etc.

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9.1.3 Synthesis methods 9.1.3.1 Drop casting This is the simplest method for the fabrication of thin films. An organic semiconductor is dissolved in a solvent. Then, the solution is poured onto the substrate. A thin film is formed after the evaporation of the solvent from the substrate surface [18]. But the method lacks in forming homogeneous film thickness with less surface roughness. The orientation of deposited film is toward the evaporation direction of the solvent. The concentration gradient defining the driving force for equal surface alignment of molecules is established during evaporation. The homogeneity of the film can be improved during the dry process by a mixed solvent system inducing convective and Marangoni flows.

9.1.3.2 Spin coating Thin films prepared by this method are uniform and thin. This is the preferred method for solution-based deposition. In the spin-coating technique, a substrate placed under the vacuum condition is rotated at high speed after pouring an excess amount of material on the substrate, which is illustrated in Fig. 9.4A. The thickness of the film can be controlled by varying the RPM or concentration of the solution. Higher the concentration, the thicker it will be, while higher RPM means the thickness will be less. The uniformity of films depends on the volatility of the solvent used. The sensitivity of the spin-coating method depends on the airflow velocity, humidity, temperature, and heat transfer. The effect of spin-coating condition as well as electronic properties on thin film was studied for poly (2-methoxy-5-(20 -ethyl-hexyloxy)-1,4-phonylex vinylene) (MEH-PPV) to control the aggregation [19]. It was found that aggregation was a result of a change of properties and short-range interchain attraction forces. Therefore, the aggregate formation increases with increasing concentration because of the significant interchain forces in the polymer. Angular velocity decides the morphology of film in a spin-coated method when cohesive forces become comparable to the centrifugal force of the solution.

Fig. 9.4 (A) Spin-coating technique. (B) Screen-printing technique.

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9.1.3.3 Solvent vapor annealing (SVA) This is a technique that maintains the equilibrium of film morphology at room temperature. This method is preferred for sensitive organic material having strong intermolecular interactions. It requires equilibrium between vapor and liquid of a solvent when the sample is placed in the vessel. All the molecular interactions (i.e., molecule and substrate, molecule and solvent, molecule and molecule, solvent and substrate) on a surface by the solution need to be considered. In fact, the mobility is increased by SVA during conjugation of macromolecules of a polymeric chain, which further modifies the morphology maintaining the equilibrium. After attaining the desired morphology, the prevention of other changes is done by freezing the system immediately. The film is exposed to an atmosphere of solvent in the SVA technique. Under these conditions, the film is swelled by solvent take-up, due to which an increase in mobility is observed. Nanoscopic needles of perylene in THF subjected via SVA gave an aspect ratio above 103 on forming long fibers [20].

9.1.3.4 Dip coating This method follows the procedure of dipping the substrate into the material solution with simultaneous withdrawing at a particular speed. It was first used to coat glasses with an antireflection layer. The thickness depends on the speed of withdrawing, the evaporation rate of solvent, and the concentration of the prepared solution. Dipping rate and boiling point are parameters to be considered for film formation for the determination of alignment of direction of molecules. The organic semiconductor assembly of heteroacenes with fused thiophene units for FET applications fabricated by dipcoating technique was studied. A similar study of thiophene rings showed μ of 102 cm2/V s when used as FETs [21]. This implied that crystalline domain size was increased reducing the grain boundaries. There was also the orientation of charge carrier paths between the drain and source electrodes. Several mm2 domains have already been obtained by the method of dip-coating FETs of CBT-BTZ fabricated using spin coating that reached mobility (μ) of 0.6 cm2/V s, while the fabrication of the same devices using dip coating increased the μ to 1.4 cm2/V s [22]. This process provides long-range orientation and highly ordered structure having an edge on the arranged surface as observed in small oligomers and polymers. The increased mobility may be due to decreased grain boundaries, chain alignment toward the directive of fast carrier transport, and crystal structure. Perfect quasiarrangement across electrodes favored the migration of changes in layers deposited by dip coating.

9.1.3.5 Longmuir-Blodgett (LB) technique The alignment of CP and small molecular SC can be done by LB. This method involves the formation of thin film by spreading the solution on the interface of air and water. The ordered structure of the film is obtained by compression of the film. This method is found advantageous in terms of attaining precise thickness and a higher degree of order. Due to the unstable arrangement of the polymer at the interface, aggregates were formed in an attempt to deposit poly (akylthiophenes) films. This

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failure was overcome by mixing of fatty acids such as stearic acid with a poly (akylthiophenes), which deposited a stable monolayer. The irregular side chains in P3HT (regiorandom) presence of fatty acids that were nonconductive resulted in less mobility of 107–104 cm2/V s. Later, regioregular P3HT FET fabricated using the LB technique showed μ of 2  102 cm2/V s [23]. This is the first technique that deposited thin films of discotic liquid crystals.

9.1.3.6 Vapor deposition The vapor deposition technique is divided into two categories, i.e., physical vapor deposition (PVD) and chemical vapor deposition (CVD). In PVD, a material is sublimed at high or ultra-vacuum conditions, while in CVD, decomposition of chemicals and vapor reaction takes place on the heated surface of the substrate. The PVD method requires constant good vacuum conditions. In this method, the material is placed in a quartz crucible or a metal boat made of a material that resists between 200°C and 800°C. The substrate is placed at about 10–50 cm above the boat containing material. The material is heated at its melting point under vacuum conditions and is deposited on the substrate. The film deposited is thin and uniform. CVD helps in the growth of thin films with varying physical and chemical properties at different conditions such as substrate material, temperature, and composition of gases. They produce a film of high uniformity, good throwing power, and low porosity. It is a process in which a wafer is exposed by various precursors that react on the surface to produce uniform films along with the removal of volatile by-products under the flow of a mixture of gases in the reaction chamber.

9.1.3.7 Oxidative polymerization It is a technique in which two hydrogen atoms are abstracted from a monomer. This method of giving a polymer is classified as polycondensation. It is considered as the cleanest method. It consists of mainly aromatic compounds based on monomers. These monomers have high oxidation tendencies and properties of an electron donor inherited in thiophenols, amines, etc. The potential applied led to the oxidation of monomers, which initiates the polymer growth due to the generation of action radicals in monomers [24].

9.1.3.8 Inkjet printing The materials required for inkjet printing should have properties like sufficient solvent evaporation rate, solubility, and surface tension to eject the ink out of the nozzle. The ejection of the ink causes spreading on the substrate followed by the process of drying as the solvent evaporates. The schematic of one such process is shown in Fig. 9.4B. The organic semiconductor films require uniform morphology with less ring stain caused by outward convective flow for inkjet printing; also crystallinity of the structure plays an important role in the fabrication of OFETS using inject printing. These factors can be controlled by using a suitable solvent, considering the exact concentration of ink and substrate wettability. The deposition of semiconductor layer OFETS by

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this method using organic semiconductor inks gave better results than the layers deposited by spin coating. The reports of enhanced properties of jetting by the blend of insulating polymer with organic semiconductors are present. In fact, the blending improved the OFETS, device stability, and jetting efficiency; reduced the cost of materials; and improved the uniformity [25].

9.2

Conjugated polymers

Polymers are composed of many repeating monomers units of a macromolecule, i.e., at least 100 units for organic semiconductor. A chain of only 200 monomer units is known as oligomer, while a molecule with 20–100 repeating units is classified as long oligomer/short polymer. The various defined arrangements are homopolymers, chain polymers, and copolymers. A commercially used organic semiconductor polymer consists of 200 to 400 repeated units, e.g., PPV derivatives and polyfluorenes. (a) Homopolymers: They consist of all identical repeating monomer units. (b) Copolymers: They consist of different repeating monomer units joined together. They are further classified as alternating polymers (ABABABAB….), statistical copolymers (ABBAABABBBAABAA….) and diblock polymers (AAAAAAAABBBBBBBBBB....). (c) Chain-polymers: In main chain polymers, the backbone is formed by the repeating unit’s relevant part, while in side-chain polymers, an electronically inert molecular section forms the polymer backbone.

Conjugated polymers, having semiconducting properties, comprise of alternate single and double loads like aromatic and heteroaromatic ring structures, whereas side-chain polymers can easily dissolve in organic solvents and they also maintain a distance in polymer chain after deposition controlling the degree of electronic interaction. The long chain of polymers formed by chemically coupled conjugated monomers leads to the splitting of П-П* orbitals in energy levels through the interaction of orbitals. HOMO borders the VB that emerges from П orbital, while LUMO borders the CB formed by П* orbital. The σ bonds are responsible for preserving the linear chain in the molecular structure, while П orbitals lead to the delocalization of an electric charge along the chain as it freely undergoes electronic and optical interactions. The luminescence efficiency, carrier generation, and mobility are dependent on interchain interactions for their use in OLEDs [26], solar cells [27], and OFETS [28]. The spin-coating technique or printing technique is used to process conjugated polymers. In 1997, G. Alan et al. invented conducting polymers [29]. The first series of conducting polymers include PAC, PANI, and PPY. Various conducting polymers are listed in Table 9.1. Here, the delocalization of π electrons takes place that claims conjugation in the conductor’s polymer, increasing the conductivity [30]. The conductivity depends on various parameters such as type of doping material, degree of doping, structure, temperature, as well as density of charge carriers. The doping of polymer optimizes the thermoelectric (TE) performance by increasing the conductivity. Thus, there is the existence of new electronic states in the polymer band gap on doping.

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Table 9.1 List of various conducting polymers and their electrical conductivity.

Polymer

Abbreviation

Doping

Polyacetylene

(PAC)

Polyaniline Polypyrrole Polythiophene Poly(3-alkylthiophene) Poly(p-phenylene)

(PANI) (PPy) (PTh) (P3AT) (PPP)

Poly(p-phenylenevinylene) Poly-p-phenylene-sulphide Poly(2,5-thienylenevinylene) Poly (3,4ethylenedioxythiophene) Poly(3-alkylthiophene) Polyisothianaphthene Polyazulene Polyfuran

(PPV) (PPS) (PTV) (PEDT, PEDOT) (PAT) (PITN) (PAZ) (PFu)

I2, Br2, Li, Na, AsF5 HCl  BF 4 , ClO4  BF4 , ClO 4  BF 4 , ClO4 Li, Na, AsF5 AsF5 AsF5 AsF5 – –  BF 4 , ClO4  BF , ClO 4 4  BF4 , ClO 4

Electrical conductivity (S cm21) 1000–105

30–200 100–7500 10–1000 1000–10,000 100–1000 3000–10,000 3–500 2700 300 1000–105 50 1 100

The emission wavelength of the polymer can be controlled by the conjugation length of the polymer chain. It increases as the gap between HOMO and LUMO decreases. This concept is highly useful in fabricating organic lasers. The three sp2-hybridized organic materials are formed by combining one 2s orbital and two 2p orbitals. This carbon atom’s sp2 orbitals overlap producing strong π and π* molecular bonds. The increase in sp2-hybridized C bonds forms an alternate single and double bond, i.e., conjugated system with no attribution of electrons to CdC bond. This causes delocalization in wave function, which increases the conductivity of organic materials. The chain length and molecular weight of polymer are important characteristics influencing the solubility and viscosity. Nanostructures strongly link the electronic and mechanical properties for the development of materials having varied molecular weights. The chain length is increased until the polymer reaches the molecular weight where solubility vanishes when monomers are joined to form a polymer. The poly dispersity index (PDI) defines the chain length distribution by the ratio of weight average to number average of molecular weights [31], i.e.: PDI ¼

MW MN

(9.9)

208

9.3

Thermoelectricity and Advanced Thermoelectric Materials

Thermoelectric plastics

TE plastics define a class of materials based on polymers that are able to convert heat to electricity or vice versa. TE devices fabricated using inorganic materials are expensive and contain toxic elements such as lead, tellurium, and antimony, which restricts its applications to expensive watches harvesting body heat, arctic lights, generators, etc. Contrary to this, the low thermal conductivity, good flexibility, lightweight, nontoxicity, and easy solution processing make organic materials appealing for their use in TE devices. The TE materials are used to transform waste heat from systems to electric power. They consist of elements present in abundance, i.e., carbon, sulfur, oxygen, and nitrogen. A large amount of energy is lost from automobiles so, to attain global sustainability, we need materials with high TE performance without the emission of CO2 gases. The various devices manufactured based on TE plastics help to recover wasted heat in industries up to 200°C, i.e., done by the cladding of pipes, chimneys, and power cables. The main building blocks of TE plastics consists of organic semiconductor, especially conjugated polymers, conductive fillers, dopant counterion, and insulating polymers as shown in Fig. 9.5 Therefore, organic thermoelectric materials (OTEs) gained attraction due to the presence of no toxicity, which in such materials is defined in terms of power factor (PF) [32]: PF ¼ S2 σ where S is Seeback coefficient and σ is the electrical conductivity.

Fig. 9.5 Building blocks of thermoelectric plastics.

(9.10)

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209

Such materials should be good enough to conduct electricity with poor conduction of heat. The performance of TE materials is judged by a dimensionless quantity zT defined as [33]: zT ¼

S2 σT k

(9.11)

where z is the figure of merit, T is the temperature, and k is the thermal conductivity. Materials with high z are useful for their applications as power generators, thermal sensors, coolers, etc. They can be used in aerospace, manufacturing, military applications, chemical process, and power plant and transportation industries due to high degree of hot gas exhaust. Nowadays, they are even used for energy conversion in solar cells. If the zT lies between 3 and 4, then it is supposed that there is a conversion of >40% waste heat to electrical energy by TE generators. Mostly, OTEs are π-conjugated polymer and small molecules such as PANI, PEDOT, PAC, PPY, polythiophene, fullerene, pentacene, etc. The low PF in organic materials compared with inorganic materials makes them efficient. The problem of balancing electrical conductivity in organic materials, which is similar to inorganic, by doping chemistry is still under research. Studies on some dopants such as camphor sulphonic acid (CSA), I2, and FeCl3 added to conducting polymer are already reported that helped to control the oxidation level. Recently, thermal conductivity in organic TE materials is 0.1 by Zhu et al. [62]. The formation of polymer composites with inorganic materials (including carbon nanotubes) emerged as a new approach to obtain air-stable OTE materials of n-type. Wan et al. [63] used the process of solvent exchange and electrochemical intercalation to prepare flexible n-type TE materials, i.e., TiS2[(HA)0.08(H2O)0.22(DMSO)0.03], where TiS2 acts as electrochemical cell, and HA (hexylammonium) chloride in DMSO (dimethylsulfoxide). Wu et al. [64] fabricated n-type DETA-CaH2-SWCNT by doping of SWCNT (p-type) with DETA (diethylenetriaminine) and treated them by CaH2. It showed 27 μW/mK1 PF values. Furthermore, the fabrication of TE film of organic/ inorganic hybrid was prepared by inkjet printing as reported by Ferhat et al. Briefly, V2O5.nH2O (vanadium pentoxide) experienced insertion of PEDOT molecules through in situ oxidation polymerization to increase carrier concentration. They adapted (PEDOT)xV2O5 hybrid to inkjet printing. The metal-organic coordination polymers are repeated units of coordination complexes, although, the research based on coordination polymer was limited to electrical conductivity, porosity, nonlinear optics, catalysis, luminescence areas, etc. The TE properties of poly(M-ett), where M is a metal and ett is ethenetetrathiolate, as studied by Zhu et al. [62] brought coordination polymers to the forefront. Due to the dependence of polarity on metal and its record-breaking performance of n-type OTE, poly (M-ett) exhibited its potential for use in the OTE field. The construction of TE composites can be employed using conducting as well as nonconducting polymers. The nonconducting polymer tends to improvise processibility and results in the decrement of thermal conductivity, while the TE effect’s charge transfer is accompanied through conducting polymer. The interfacial barrier helps in filtering low energy carriers due to which large Seeback coefficient is observed. The most efficient organic component is PEDOT:PSS that constructs organic TE

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Table 9.2 Some n-type organic thermoelectric materials.

Compound Poly[Nax(Ni-ett)] Poly[Kx(Ni-ett)] Poly[Nax(Cu-ett)] N-DMBI-doped P (FBDOPV-2T-C12) P(gNDI-gT2) P(PzDPP-CT2) P(TDPP-CT2) NiETT Na[NiETT] N-DMBI-doped TEG-N2200 TDAE-doped P (NDI2OD-Tz2) N-DMBI-doped PTEG-1 IDTT-CN/SWNT NPC14

Seebeck coefficient [μV K21]

Electrical conductivity [S cm21]

Power factor [μW m21 K22]

Ref.

   267

1.22 1.12 1.03 4.2  102

27.62 25.85 27.72 0.30

[62] [62] [62] [66]

190 – – 40 75 –

0.3 8.4 0.39 0.04 40 –

0.41 57.3 9.3 – – 0.4

[67] [68] [68] [69] [69] [70]

–

–

1.5

[71]

2.05 – 0.002

284 2500 0.27

16.7 212.8 0.0027

[72] [73] [74]

composites. In addition, small molecular organic semiconductors also have much potential to be used in OTE applications, for example, polydopamine (PDA), C60, pentacene, and dinaphtho [2,3-b,20 ,30 -f] thieno [3,2-b] thiophene (DNTT) [65]. The organic conductors that are crystalline in nature have found novel functionality as electrodes, and TE conversions along with structure-property relation are being investigated. They possess higher conductivity of about one or two orders of magnitude making their performance superior in the field of TE carrying along with the difficulty of optimization by tuning carrier concentration, for example, tetrathiafulvalene-tetracyanoquinodimethane (TTT-TCNQ) (Table 9.2).

9.8

Effect of molecule structure on TE properties

The structure of TE materials should be such that it leads to a large Seeback coefficient (S), low thermal conductivity (k), and high electrical conductivity (σ). The high value of σ helps in the reduction of Joule heating, while the low value of k helps in the prevention of thermal shorting, which can be possibly achieved through chemical functionalization [75]. The clathrates, complex Zintl, and skutterudites are systems having low k value with properties of promising TE materials [76]. The cages present are filled by the guest atoms as they tend to interact by acting as rattlers within the

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framework, which in turn decreases k value. The presence of defects and the substitution sites may also be responsible for decreasing k values in the framework of clathrates [77]. Skutterudite structures have voids present to be filled by guest atoms that interact with scattered phonons and other elements. This interaction results in lower k value. In addition, the grain boundaries, as well as mass differences carried by chemical substitutions, play an effective role to decrease lattice k values. The complex structure with heavy complex Zintl causes the lower value of k [78]. The molecular structure is also affected by the contact chemistry and length of molecular junctions, due to which TE properties also vary as reported by Tan et al. [79]. The study of the relationship of structure-property at molecular junctions is very important to determine transport properties. The thermopower was found to be positive, and it increases as the length of the molecule increases in thiol-terminate junctions. Mai et al. [80] observed that the side chain of conjugated polyelectrolytes when shortened results in an increase of the doping level and crystallinity. This modulated electrical conductivity by the edge of molecular orientation. Therefore, the modification in molecular structural and TE properties can exist by chemically modifying side chains. The relation between structure and thermopower depends on various factors such as length, interface effects, substitutional effects, quantum interference, Peltier cooling effect, and molecular gating in TE junctions. The Seeback coefficient (S) and length (n) are correlated linearly using the equation [81]: S ¼ SC + n∗βS

(9.16)

where n is molecular length (A˚), βS is the rate at which thermopower changes (μV (Kn1)), and SC is hypothetical junction’s thermopower at n ¼ 0. So far, the molecular backbones such as C60 fullerene, DNA, n-alkane, phenylene, and thiophene have been investigated. The substitutional effect at the molecular junction by chemical functionalization of molecules through covalent and noncovalent bonds played an important role in the thermopower of the junction. It was found that S depends on molecular orbital energy and Fermi level energy, i.e., △ E ¼ EMO  EF and is manipulated by adding electrondonating or withdrawing groups into the molecular backbone. The quantum interference arises when the electron wave function passes through the junction after experiencing multiple scatterings from defects. The molecular gating modulates the tunneling of charges in three-terminal devices containing a single molecule. The controlled gate voltage brought a change of △ E in transmission function (T(E)), which is confirmed from Lorentzian-shaped transmission function (T(E, VG)) [81]: T ðE, VG Þ ¼

4Γ 2 4Γ + ðE  ðEO  αVG ÞÞ2 2

(9.17)

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Thermoelectricity and Advanced Thermoelectric Materials

where EO is energy separated with respect to EF of transport orbital, Γ is broadening of orbital due to electrodes contact, and α is gate coupling effectiveness. Furthermore, Landauer formula defined the thermopower Sjunction(VG) at applied gate voltage [81]:  π 2 kB 2 T d ln ðT ðE, VG ÞÞ Sjunction ðVG Þ ¼  3e dE E¼EF

(9.18)

where e is the electronic charge, T is the temperature at ambient conditions of junction, and kB is Boltzmann constant.

9.9

Carrier density and mobility test

The ionic molecular states are considered during electron or hole transport. A hole is created when an electron is removed from neutral molecule M creating M+ radical cation. The M radical ions produced by removal of electrons moves from one molecule to another causing stabilization in the solid by polarization energies. The polarization energies are needed to be considered in the case of organic solids. The distribution of transport sites by Gaussian DOS is represented in Fig. 9.10. The transport mechanisms and degree of order in organic semiconductors are explained based on band or hopping transport. At low temperatures, the delocalization of electrons becomes weak reducing the bandwidth in molecular crystals, which are highly purified. This is the case when a band transport exists. At room temperature, mobility (μ) lies in the range of 1 to 10 cm2/V s, but in-band transport power law is followed at low temperatures, i.e.: μ∝ T n ; n ¼ 1,…, 3

(9.19)

While in the case of hopping transport, amorphous organic solids have lesser μ values (i.e., 103 cm2/Vs). In this case, temperature dependence is considered to calculate activation energies lying between 0.4–0.5 eV. Here, the dependence of μ on applied field E is considered and is given by relation [82]: !
 △E β√F μðF, T Þ∝ exp exp kT kT

Fig. 9.10 Energy levels showing the distribution of transport sites.

(9.20)

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221

This is further defined as: 

2σ μðF, T Þ∝ exp  3kT

2 !


h i 

σ 2  Σ2 √F exp c kT

(9.21)

where σ is disorder parameter (80–120 meV range). Many processes are involved in charge transportation in conjugated polymers: (i) Conduction takes place at the polymer backbone. (ii) Interchain interactions cause the hopping process. (iii) The occurrence of thermal effect between conducting regions.

The charge carriers that transport inside the sample when the electric field is applied relates the charge carrier velocity (v) to electric field strength (F) by: v ¼ μF

(9.22)

Here, μ is the constant known as drift mobility. It defines the distance of transportation of charge carriers per second under the applied field. The factor μ depends on the type of charge carriers, molecular structures, and morphologies. The well-known Hall Effect measurements, as well as conductivity measurements, are done to determine large mobility, but these techniques cannot be used for low mobility polymers and highly resistive materials. For such materials, different approaches are used like Time of Flight (TOF) technique, steady-state trap-free space charge limited current method (steady-state TF-SCLC), dark injection SCLC method, pulse radiolysis time-resolved microwave (PRTRM) conductivity, and transient electroluminescence technique.

9.9.1 Time of flight (TOF) method This method has been widely used for organic disordered structures to measure mobility. It measures the carrier transit time (τ), which is defined as the time required for a photogenerated charge carrier to drift from one electrode to another electrode through pulse light irradiation under applied field. One of the electrodes in the sandwiched structure is transparent. It has the advantage of independent study of hole and electron mobilities. The transit time (τ) is related to velocity and sample thickness as: τ¼

d v

(9.23)

And mobility is calculated using the relation: μ¼

d2 vτ

(9.24)

The mobility of materials having larger carrier density could not be calculated using the TOF method as the drifting of charge carriers is affected by the diffused charge carrier on applying an electric field.

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9.9.2 Steady-state trap-free space charge limited current (TF-SCLC) method This method measures carrier drift mobility by analyzing the characteristics of current density (J) vs. Voltage (V) taken in the dark and is found to be ohmic in nature at low voltages. The space-charge limited effect is observed at high voltages as the charge carriers are injected from one electrode. At low voltage, space charge limited current (J) is calculated using the Mott-Gurney equation [83]: 9 V2 9 1 J ¼ εμ 3 θ ¼ εμ F2 θ 8 d 8 d

(9.25)

where ε is permittivity and d is the sample thickness. θ defines the ratio of the number density of free carriers to the total number of charge carriers present. Under SCLC condition, J ∝ F2, which depends on sample thickness. When θ ¼ 1, it implies J to be trapping free SCLC. In the DI-SCLC method, the step voltage is applied to the sandwiched structure forming an ohmic contact with one of the electrodes. The relation between space charge transit time τp and τo, i.e., steady-state SCLC is given as: τp  0:78τo

(9.26)

And mobility is related as: μ¼

d2 d2  0:78∗ vτo vτp

(9.27)

9.9.3 Field-effect transistor mobility Organic semiconductor-based FETs are found to be successful in replacing earlier Sibased transistor quality. The emergence of OFETs helped to reduce the cost as well as the switching speed needed in the transistor-based application. OFETs are basically devices consisting of three terminals: source, drain, and gate (Fig. 9.11A). The applied gate voltage controls the density of charge carriers between the source (S) and drain (D) across a thin dielectric. The drain current Id can be calculated using the relation [84]: ID ¼

W Ci μðVG  VT ÞVD ; Linear region L

(9.28)

W Ci μðVG  VT Þ2 ; Saturation length 2L

(9.29)

And: ID ¼

Organic semiconductors and polymers

223

Fig. 9.11 (A) Schematic of organic field-effect transistor (OFETs). (B) Various OFETs device structures.

where W is channel width, L is channel length, Ci capacitance of insulator, and VT is the threshold voltage. Tsumura et al. in 1986 successfully fabricated the fruit OLEDs using polythiophene as an organic layer on the SiO2 dielectric layer. It showed the mobility of carriers to reach 105 cm2/V s with 100–1000 value of the on-off ratio [85]. The modification in the organic layer of OFETs led to 1 cm2/V s value of its mobility reaching 10 as the on-off ratio [86]. The addition of polymer between the inorganic layer and organic semiconductor helped to overcome the issue of interface charge trapping. The OFETs performance depends on various parameters such as smaller channel length (L), the high dielectric constant of an insulator, and higher mobility. Therefore, a highly ordered structured film of organic semiconductor is needed. The device structure of OFETs can be bottom contact (BC)/bottom gate (BG); top contact (TC)/bottom gate (BG); bottom contact (BC)/top gate (TG); and bottom contact (BC)/top gate (TG), as shown in Fig. 9.11B. These structures vary depending on the semiconductor and insulator interface quality in comparison to its trap states and morphology. It also depends on the charge injection position at the interface. In OFETs, charge transport in different structures is described as: l

l

l

BC/BG: Direct injection of charges takes place from source electrode to interface. TC/BG: Injection of charges is done in the bulk of undoped SC due to which they travel several tenths of a nanometer (i.e., can travel from 10 to 100 nm) to reach the SC/insulation interfaces. BG/TG: The injection process is the same as TC/BG.

Inorganic semiconductor-based FETs operate in depletion mode, whereas organic semiconductor FETs operate in accumulation mode. In OFETs, accumulation of

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charges takes place by varying VG to modulate transistor current to prevail the generation of intrinsic charges that are absent in the large band gap of an undoped organic semiconductor. The performance of FETs can be evaluated from two main parameters, i.e., on-off ratio and the switching frequency. Both the parameters depend linearly upon the charge mobility. (i) On-off ratio: It describes the performance based on signal-to-noise ratio. If the on-off ratio is high, the signal-to-noise ratio of the signal is good. It can be described as:   Id Vg ¼ VD ¼ V  Ron=off ¼  Id Vg ¼ 0, VD ¼ V

(9.30)

where V is the required voltage. Its maximum value has been achieved from 104–108 for different materials [87]. (ii) Switching frequency: It is defined as the maximum frequency F0 required by the OFET to operate. RC time controls the operating frequency where R is the device resistance, which in turn determines the charge carrier mobility. It can be estimated using the relation [88]: F0 ¼

1 μVd 2π L2

(9.31)

where L is channel length, μ is the carrier mobility, and Vd is given by VL μ , where V is the carrier velocity. The performance of OFETs can be improved by choosing suitable electrodes for source and drain, dielectric Gate insulation, modifying charge transport properties, and polarity of OFETs.

9.9.4 Pulse radiolysis time-resolved microwave conductivity (PRTRM) method In this method, the low free carrier density is created by exciting the sample with a pulse containing highly energetic electrons. The varied electrical conductivity (△ σ) is frequency-dependent and is expressed as [89]: △σ ¼ eΣμ Neh

(9.32)

where Σμ is total mobility of electrons and holes and Neh is the density of electronhole pairs generated. Neh is defined as the ratio of energy transferred to the energy required for the creation of e–h pairs, which is again multiplied by probability accounting mechanism of charge recombination during the duration of the pulse. It is the technique that is contact-free and remains unaffected by space-charge effects. It can be applied to single polymeric chains as well as bulk materials. They provide high AC mobility at low fields of the bulk, for example, polythienylenevinylene gives the value of electron and hole mobilities as 0.23 cm2/V s and 0.38 cm2/Vs and

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polyparaphenylenevinylene provide values 0.15 cm2/V s and 0.06 cm2/V s. The charge mobilities in the polymer are limited due to interchain transport reaching 0.1 cm2/V s value [90].

9.10

Challenge in organic semiconductor thermoelectric materials

During the past decades, OTE materials have shown immense potential to harvest wasted heat energy via green energy conversion. In spite of the tremendous growth of inorganic TE materials, they are still limited in their application partly due to the presence of intrinsic defects. Therefore, the need for organic polymer-based TE devices arises because they are easily processable, nontoxic, flexible, and even exhibit low thermal conductivity. This field of research is at an early stage despite significant progress. The commercial use and production of OTE materials are restricted because of too low TE efficiencies achieved. A lot of work needs to be done to achieve TE materials with high efficiency, which can make use of wearable green energy generators. Particularly, the optimization of Seeback coefficient and thermal and electrical conductivity by adjusting the interactions to understand the structure-property relation is highly required. The development of more n-type OTE materials is needed to gain green energy from the materials. They may exist as unique materials to be used in future wearable electronics. A formidable challenge in material science and engineering is to unlock components to create organic TE plastics by understanding the relation of structure and property. The synthetic efforts require the modification of conjugated polymer’s structure and its doping. The proper analysis of side-chain solubilization, the molecular weight of polymers, polarity, the conformation of the chain, and energy levels can open up ways to address molecular dopants’ poor miscibility as well as low doping efficiency. The separation of the doping step and solidification is still a strong limitation in some of the conjugated polymers. The processing schemes need to be developed for creating a nanostructure that is well defined following the process of controlled doping, which will help to explore intrinsic parameters. The enhancement of performance in composite TEs is a great challenge to be explored in comparison to inorganic TE materials. Preparation techniques should consider strong interfacial interactions, i.e., ionic, covalent, and hydrogen bonds in addition to П-П interactions. Moreover, it should involve interfaces that provide thermal insulation, a network that has high electrical conductivity, and should decouple the TE parameters for better TE performance. In view of future prospects of TE performance, fabrication and molecular designs of monomers, polymers and multiphase composite systems should be explored in valuable ways. The molecular-level TE mechanisms should be strengthened for organic/inorganic TE composites. For flexible TE materials, the carriers in conductive polymers need to be delocalized. The conductive polymers have localized carriers, which cause interand intrahopping transport only in a limited portion. Theoretically, the prediction

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of the relation between S2σ and n in conductive polymers fails by designed models of TE semiconductors that are crystalline in nature. The effects of optimization of fillers affecting the transport of carriers at the interface should be introduced. The S2σ can be optimized when the Fermi level of filler and conductive polymer matches by modulating the interfacial energy filtering effect.

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Ajay K. Kushwahaa, Hemen Kalitab, Siddhartha Sumana, Aditya Bhardwaja, and Rajesh Ghoshb a Department of Metallurgy Engineering and Materials Science, IIT Indore, Indore, Madhya Pradesh, India, bDepartment of Physics, Gauhati University, Guwahati, Assam, India

10.1

Introduction

Energy is the primary requirement of the modern world. Conventional energy resources are limited and often lead to environmental issues. Therefore, nonconventional energy resources have received tremendous attention in the last few decades to provide clean and environment-friendly energy. Hence, advancement in renewable energy sources, i.e., solar energy, wind energy, fuel cells, biomass, thermoelectric (TE), etc. has taken center stage. Amid all these, TE devices that convert heat energy into electrical energy have shown good promise [1]. The generated electricity in TE devices can be used immediately or stored in batteries for future use. TE devices have exceptional properties such as less noise, high stability, and durability, which makes them an advantageous candidate. TE devices have shown excellent potential for those applications where heat is generated during the process. TE devices are also useful as a power source for several standalone electronic devices such as smart watches, flexible body sensors, etc.; herein, the body temperature can be the source of energy [2]. The conversion of heat energy into electricity basically depends on the Seebeck effect in which a temperature difference across conducting or semiconducting materials leads to an electrical voltage difference across the terminal [3]. The voltage generated is based on the conversion efficiency of heat to electricity from the TE device. The efficiency of TE devices mainly depends upon the operating temperature and properties of the TE materials [4]. The operating temperature is the external factor and relies on the type of system or environment, while TE properties of the material are crucial factors to design an efficient TE device. The performance of TE material is estimated by the figure of merit (zT), a dimensionless parameter. The TE properties of a material are also described by the Seebeck coefficient. These two parameters vary with the intrinsic electronic spectrum of the TE materials. The optimization of the Seebeck coefficient, electrical conductivity, and thermal conductivity of materials significantly enhances the TE performance [5]. However, the optimization of overall performance is challenging due to the interdependency of these properties. Nanoscale engineering is an effective solution to enhance TE performance [6]. The low-dimensional superlattice structures have been proposed to have a better TE performance by the engineering flow of the charge carriers [6]. At the Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00006-0 Copyright © 2021 Elsevier Ltd. All rights reserved.

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nanoscale dimension, materials exhibit an enhancement in the Seebeck coefficient. The confinement of charge carriers renders more electron occupancy in the higher energy states and improves the value of generated voltage. In addition, nanoscale materials yield a high surface area/interface area, which increases the phonon scattering that reduces thermal conductivity [7]. Hence, nanoscale engineering has several benefits and, therefore, a variety of nanomaterials are investigated for TE device applications. A large variety of two-dimensional (2D) materials have gained tremendous attention from the scientific community over the years; they have shown high-performance TE. 2D materials are sought as a very attractive class of materials for their layered composition and unique electronic behavior. These layered materials are potentially found suitable as efficient TE materials due to their exceptional advantages on the electronic, mechanical, and thermal properties. After the discovery of graphene, the first-ever 2D material came into existence; its remarkable properties at the nanoscale for a myriad of applications have become significant [8]. The unique and fascinating electronic properties of graphene led to several theoretical and experimental investigations on its TE effects. Various other 2D materials such as transition metal dichalcogenides (TMDCs), black phosphorus, MXene, and boron nitride have become potentially significant for TE application. The low-dimensional and thicknessdependent properties of 2D materials are promising for further enhancement in TE performance. Consequently, there has been a great deal of interest in 2D materials for TE applications due to their dimensional confinement, which facilitates tailorable performance.

10.2

Effect of dimensional confinement on thermoelectric materials

The TE figure of merit decides the overall heat to the electricity conversion efficiency of any material, and it is a dimensionless quantity expressed as [9]: zT ¼

S2 :σ T κ

where σ denotes electrical conductivity, S denotes the Seebeck coefficient, T denotes absolute temperature, and κ denotes thermal conductivity, respectively. To achieve maximum value of zT, a large Seebeck coefficient (S), high electrical conductivity (σ), and low thermal conductivity (к) are essential for a material. The efficient materials can be designed by tuning the Seebeck coefficient, electrical conductivity, and thermal conductivity. However, the optimization of these properties is a challenging task due to the interdependency of the properties, as given in Fig. 10.1. The electrical conductivity increases with an increase in charge carrier concentration, while the Seebeck coefficient is inversely proportional to the concentration of charge carriers. Therefore, both values cannot be the largest, and we are bound to select the optimum value of the parameters like the Seebeck coefficient and the electrical conductivity

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s = nem S sS2

1018

1019 1020 Carrier concentration n (cm–3)

1021

Fig. 10.1 The plots demonstrate the general profile (without unit) interdependency of the Seebeck coefficient and electrical conductivity for change in charge carrier concentration Reprinted from K.H. Lee, S. Kim, H.-S. Kim, S.W. Kim, Band convergence in thermoelectric materials: theoretical background and consideration on Bi–Sb–Te alloys, ACS Appl. Energy Mater. 3 (2020) 2214–2223. Copyright ACS Publications.

that defined as the power factor (Fig. 10.1). Adversely, a large charge carrier concentration increases the thermal conductivity (heat), which is not favorable to get the best and maximum value of zT. The confinement of the material dimension to nanosize offers several advantages and provides a better opportunity to overcome these limitations [10]. Nanomaterials have shown impressive performance with the figure of merit more than unity [11]. Hicks and Dresselhaus have proposed that nanoscale engineering of materials enhances the TE performance [12]. When materials reach nanoscale dimensions and the confinement of electrons occurs, it enhances the Seebeck coefficient. Furthermore, the value of generating voltage is also improved due to more electron occupancy in the higher energy states due to confinement of charge carriers. Therefore, the confinement of charge carriers in nanomaterials enhances the power factors and leads to improvement in the TE figure of merit [13]. If the size of the material is smaller than the phonon means free path, then thermal conductivity can also be controlled due to an increase in phonon scattering. The presence of surfaces/boundaries/interfaces increases the phonon scattering in the material and reduces the thermal conductivity without much compromise with electrical conductivity [7]. Hence, the scattering effect and quantum effect play very significant roles in nanosized materials and can be effectively used to design better materials for the TE application. The low-dimensional materials such as nanowires, nanotubes, superlattice, and ultrathin films have been studied and show quantum confinement effects on the charge carrier’s mobility and phonon’s scattering [14]. A process that includes low-dimensional superlattice to design and optimize their TE properties is called carrier pocket engineering. Investigations into the direction-controlled material’s growth and its TE properties have suggested that best TE properties in the thin film can be

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achieved by optimizing the growth direction of the material [11]. The thickness of the material plays a vital role to control the TE properties. In a study of Bi2Te3 and its alloys, such as GeTe/Be2Te3, the result of thickness on the thermal conductivity was presented in the form of a figure of merit. zT value of 1.32 was found in the case of 30 nm, whereas 1.56 was found in case of 50 nm for Bi2Te3, and it was reduced drastically to a value of 0.62–0.76 in the case of alloys of thickness 3 nm/3 nm [15]. In another study of BidTe thin film done by Haishan et al., they revealed that, on increasing a thin film’s thickness, it developed high pore density, and the TE properties were influenced by the film’s porosity [16]. Thus, the nanoscale engineering of materials has shown encouraging results and could be considered the best strategy to design efficient TE materials.

10.3

Thermoelectric properties of two- dimensional (2D) structures

The reduction of any one dimension of a material leads to the formation of a 2D structure with observable charge confinement effects. Ultrathin films, layered materials, and superlattices are usually considered 2D structures. Hence, this section is dedicated to understanding the effect on the TE properties of these 2D structures. TE properties of monolayer and few-layer 2D materials, for example, graphene, TMDCs (MoSe2, WS2, MoS2), boron nitride, phosphorene, and MXenes will be discussed in the next section of the chapter.

10.3.1 Thin films Thin film is a conventional example of 2D materials as charge carriers confined in the direction of thickness, thus allowing it to be an excellent material for the desired application. Epitaxially grown Bi2Te3 thin film shows around two times less thermal conductivity compared with the bulk at ambient temperature. Variation in thermal conductivity arises because of the scattering of phonons on surfaces [17]. The effect of substrates (SrTiO3 and Al2O3) on TE properties of alumina when doped with zinc oxide thin films were studied [18]. The formation of film on SrTiO3 has shown better performance compared with film grown on Al2O3. The role of film thickness on TE properties was investigated for lead sulfide films, and the TE power (TEP) factor increases with a decrease in film thickness [18]. Fig. 10.2 shows the effect of the thickness of PbS film on conductivity, carrier concentration, and Seebeck coefficient [19]. β-FeSi2 is one of the vastly studied semiconducting silicides in the field of TE applications. Suitable phase and doping in the thin film have been explored for achieving a high TE figure of merit (zT). In a polycrystalline thin film of β-FeSi2, doped and sintered film shows a higher power factor compared with presence of defects in the thin films [20]. Conducting polymer thin films such as poly(3,4ethylenedioxythiophene) tosylate (PEDOT-Tos) is a promising material for TE properties. However, the inability to control the surface morphology of organic thin films hinders its expected properties. The change in pH tunes the oxidation level and helps to tailor the

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Fig. 10.2 Effect of the thickness of PbS thin film (at room temperature) on the carrier density (A), Seebeck coefficient of PbS thin film (B), Electrical conductivity of PbS thin film (C), and charge carrier mobility of PbS thin film (D). Reprinted from E.I. Rogacheva, O.N. Nashchekina, Y.O. Vekhov, M.S. Dresselhaus, S.B. Cronin, Effect of thickness on the thermoelectric properties of PbS thin films, Thin Solid Films 423 (2003) 115–118. Copyright Elsevier.

thermoelectricity and enhance the power factor [21]. The thin-film structure has the ease of deposition, effective control on the thickness, and simplest integration into TE devices. Therefore, thin-film structure has enormous potential in the development of high-performing TE devices. However, control over defects, surface irregularities, material composition, and doping need to be carefully optimized.

10.3.2 Layered materials The most widely studied layered materials for TE applications are Bi2Te3, SnSe, and certain intercalated materials. In 1954, Goldsmid and co-workers [22] demonstrated the first practical use of Bi2Te3 in TE generation. Bi2Te3 is a layered structure having quintuple layers in which Bi atoms are octahedrally coordinated to hexagonally arranged Te atoms (two different equivalent sites). The weak Van der Waals interactions separate the Te layers, while the interactions between Te and Bi is polar-covalent, as given in Fig. 10.3A. As experimentally observed, Bi2Te3 has S, σ, and k-values of 220 μV/K, 4  102 S cm1, and 2.1  102 W/m K, respectively. The high TE behavior of the Bi2Te3 is because of low thermal conductivity, and its intricate electronic structure results in an increase in TE quality factor [23]. Furthermore, the TE performance of Bi2Te3 was optimized by doping with Sn and Sb [24, 25],

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Fig. 10.3 The crystal structures of thermoelectric materials (A) Bi2Te3, (B) SnSe, (C) BiCuSeO. Part figure (A) reprinted from A.I. Figueroa, G. van der Laan, S.E. Harrison, G. Cibin, T. Hesjedal, Oxidation effects in rare earth doped topological insulator thin films, Sci. Rep. 6 (2016) 22935. Copyright Springer Nature. Part figure (B) reprinted from S. Liu, N. Sun, M. Liu, S. Sucharitakul, X.P.A. Gao, Nanostructured SnSe: synthesis, doping, and thermoelectric properties, J. Appl. Phys. 123 (2018) 115109. Copyright AIP. Part figure (C) reprinted from D. Zou, Y. Liu, S. Xie, J. Lin, H. Zheng, J. Li, High pressure effect on the electronic structure and thermoelectric properties of BiCuSeO: first-principles calculations, RSC Adv. 4 (2014) 54819–54825. Copyright RSC.

making a composite with polymers (PEDOT:PSS) [26, 27]. The high zT values of 1.86 at 320 K and 1.23 at 480 K have been obtained for Sb- and Se-incorporated Bi2Te3 TE, respectively [28, 29]. It is the highest reported value for layered material Bi2Te3, but the high cost and complex fabrication processes are the limiting factors for commercialization. SnSe is another material that has been extensively investigated for TE applications. The structure of SnSe is orthorhombic, belonging to the Pnma space group at room temperature (Sn atoms bonded with 7 Se atoms), as shown in Fig. 10.3B. The small thermal conductivity (less than 0.4 W/m K (0.23–0.34)) of SnSe is helpful for better TE properties [30]. Single crystals of SnSe exhibit a high zT value of 2.6 at 923 K [31]. Polycrystalline SnSe has also been reported with enhancement in TE performance by doping with alkali atoms (Na, Li, K), and Na atoms doping showed better results with zT  0.8 at 800 K [32]. The doping/alloying of SnSe by Zn atoms [33], Ag [34], Ge [35], Br [36], Te [37], etc., were also reported, and highest zT of 1.1 was achieved in the Te alloy. The combination of Sn and Se atoms is an environment-friendly approach, and its low thermal conductivity is beneficial for TE applications. However, the issues of defects, vacancies, and effective doping in SnSe need to be investigated. BiCuSeO is also an important layer of material for TE applications. The BiCuSeO oxyselenide consists of alternating layers of (Cu2Se2)2 and (Bi2O2)2+ stacked along the c-axis perpendicularly on a tetragonal unit cell as displayed in Fig. 10.3C [38, 39]. BiCuSeO has S values of 350 μV/K at room temperature and increases to 425 μV/K at 923 K. The figure of merit (zT) was enhanced by doping with alkaline earth elements such as Mg (zT  0.67) [40], Ca (zT  0.9) [41], Ba (zT  1.1) [42], and Ag (zT value of 0.64) [43], at 923 K. The doping of BiCuSeO with silicon (Si) [44], cesium (Cs) [45], and rare earth elements such as Yb [46] and, indium [47] has also been explored to improve TE performance. Until now, the best zT (¼ 1.4) is obtained by

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239

incorporation of Ba in BiCuSeO by a hot-forging process; improvement in texture caused improvement in TE performance [48]. Still, the study of the layered material BiCuSeO is in the early stages of research, and more investigation is needed to understand the mechanisms to improve TE performance. Some other layered materials such as AgCrSe2 [49], Cu0.33TiSe2 [50], Sb2 xCuxTe3 [51], and ZrS2 xSex [52] have also been explored as candidates for TE performance enhancement. The doping of various atoms in the layered materials is helpful for significant improvement in the overall TE properties, but the requirement of the facile synthesis method and commercialization of the materials is a key challenge that requires more rigorous investigations.

10.3.3 Superlattice structures The initial studies by Hicks [53], Chung [54], and later by Broido [55] laid the foundation of the consideration of the TE performance of superlattice structures. The preliminary studies were done on Bi2Te3 superlattice structures, and they found that these structures have high zT values. A higher density of states per unit volume, the thickness of superlattice, conduction flow inside the superlattice (parallel or perpendicular conduction), and electron tunneling between the layers are key parameters that affect TE properties. A superlattice structure is formed by a combination of thin layers of two different materials. The properties of the superlattice structure depend strongly on the properties of the materials chosen to form the superlattice [56]. Several superlattice structures have been synthesized, and their TE performances were reported. Metal organic chemical vapor deposition (MOCVD)-grown Bi2Te3/Sb2Te3 superlattices were studied by Venkatasubramanian [57], which shows a high zT value of 2 at 300 K. They found that the superlattices have very low thermal conductivity, while the hole mobility is higher compared with the individual TE materials. Phonon scattering in the superlattice causes a decrease in thermal conductivity. It was observed that a reduction in the superlattice dimension below 30A0 caused further reduction in thermal conductivity (2 mW/cm K), which was four times less than the (BiSb) Te3 alloy film (10.7 mW/cm K). The first report of high TE performance was given by Dragmon in 2007 [58] in which a large Seeback coefficient of 30 mV/K was observed for the graphene superlattice by transfer matrix approach. Cheng et al. have theoretically predicted significant TE effects (approaching 260 mV/K at 300 K) in graphene superlattice by transfer matrix [59]. They found that defects are useful to achieve better TE performance in graphene superlattice. Dragmon and Cheng, and Valdovinos and co-workers [60] proposed a graphene superlattice device, which consists of graphene on top of SiO2 electrodes, then metal electrodes are attached to the top of the graphene layer [60] as presented in Fig. 10.4. By selection of appropriate angle of incidence of Dirac electrons, varying the number of superlattice periods, changing the width of the unit cell, and height of the barrier, improved TE performance can be achieved. These theoretical models can surely pave the way for further research in enhancing the TE performance of superlattice structures. Other 2D materials can also be explored as a superlattice to improve TE properties.

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ΔV

electrode SiO2 B

A

graphene layer SiO2 Si-back gate

heat

(A) e

Vo Eo

(B) (C)

Eo

e k

Vo

dB

dw

Fig. 10.4 (A) Graphene superlattice-based thermoelectric device. The arrow depicts the direction of heat flow. At the same time, V is the voltage applied between electrodes. (B) The arrangement of Dirac cones (conical band structure of graphene) in the graphene superlattice structure. (C) The band-edge profile of CB of the superlattice. E0, dB, dW, and V0 represent the energy of the incident electron, barrier, well height, and the strength of potential, respectively. Reprinted from S. Molina-Valdovinos, J. Martı´nez-Rivera, N.E. Moreno-Cabrera, I. Rodrı´guez-Vargas, Low-dimensional thermoelectricity in graphene: the case of gated graphene superlattices, Phys. E Low-Dimens. Syst. Nanostruct. 101 (2018) 188–196. Copyright Elsevier.

10.4

Thermoelectric properties of two-dimensional (2D) materials

10.4.1 Graphene and its derivatives Graphene is an atomically thin structure of the hexagonally organized carbon atoms. The carbon atoms in graphene are covalently bonded through sp2 hybridization, where the CdC atomic distance is 0.142 nm and thickness  0.335 nm [61–63]. The understanding of the intricately packed carbon atoms in honeycomb lattice structure reveals some unique and extraordinary physics out of this carbon nanomaterial [64–67]. In particular, the exceedingly high electrical mobility (μ, theoretically 200,000 cm2/V s) and fast carrier transport encouraged researchers to lead significant advancements in the field of nanoelectronics in the past few years [64, 68]. Besides, an incomparable thermal conductivity (k  5000 W/m K), ballistic transport, and negligible in-plane phonon scattering enable graphene to possess excellent thermal stability [69]. Fig. 10.5 displays the unique electronic band structure of graphene, in which both conduction and valence band meets at the Dirac point as a result of linear dispersion relation [62]. The unique and unmatched electronic as well as thermal properties of graphene make it a potential material for TE application.

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4

A δ3

δ1

a1

δ2

a2

(A)

B 2 Ek 0 4 2

–2 –4

(B)

–2

0 kx

0 –2 ky 2

4

–4

Fig. 10.5 Graphene lattice and lattice vectors (A) and electronic band structure of graphene and Dirac cone (B). Reprinted from A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81 (2009) 109–162. Copyright APS Physics.

Generally, materials with high electrical mobility and low thermal conductivity are considered for high-power factor and efficient TE generators [70, 71]. Importantly, the giant electrical mobility in graphene gives rise to a large electrical conductivity (σ  106 S cm1), much favorable to achieve a high power factor. However, because of the zero-energy band gap, a lower Seebeck coefficient was observed than the predicted value as a result of the cancellation effect arising from the ambipolar characteristic of carriers at the Dirac point. By introducing a significant band gap in graphene, large improvement can be expected in its TE properties [72]. Having a small band gap will eventually cause the conductivity to result from a single carrier flow in graphene, while it should maintain a high electrical conductivity to enhance the thermopower of graphene [73]. Interestingly, the inherent chemical structure of graphene allows wide variation in its physicochemical properties by modification of the electronic band structure [74]. The band gap problem in graphene can be resolved by suitable modification using functionalization, doping, size confinement, and electrical modulation. A variety of graphene derivatives has been developed to now, which mainly include doped graphene, graphene oxide (GO), reduced graphene oxide (rGO), graphene nanoribbons (GNRs), graphene quantum dots (GQDs), etc. [75–77]. The TE properties of graphene were first reported in 2009, where the dependency of the TEP or the Seebeck coefficient to the band structure relative to the charge density was presented [78]. Fig. 10.6 shows the TEP measurements on graphene, which confirmed a maximum TEP value of 80 μV K1 at room temperature. Several experimental and theoretical works have been reported so far to improve the TEP factor of graphene by tailoring the electronic band structure of graphene. It has been predicted that graphene could reach a TE figure of merit as high as 4 with Seebeck coefficient (S) higher than 500 μV K1 [79, 80]. On the contrary, it was reported that the maximum Seebeck coefficient exhibited by pristine graphene is only 80 μV K1 and zT values in the range 0.01–0.1, which is very low compared with the most efficient TE materials like bismuth telluride (Bi2Te3) alloys. The lower zT value is expected because of the high thermal conductivity (k) of graphene [71]. Thus, to achieve high TE efficiency, the thermal conductivity of graphene must be suppressed. Since

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Fig. 10.6 (A) Conductivity of graphene devices with respect to change in gate voltage and (B) thermoelectric power of graphene-based devices with respect to gate voltage at different temperatures. (C) Longitudinal Seebeck coefficient (Sxx) as a function of temperature (T). Part figure (B) reprinted from Y.M. Zuev, W. Chang, P. Kim, Thermoelectric and magnetothermoelectric transport measurements of graphene, Phys. Rev. Lett. 102 (2009) 96807. Copyright APS Physics. Part figure (C) reprinted from P. Wei, W. Bao, Y. Pu, C.N. Lau, J. Shi, Anomalous thermoelectric transport of Dirac particles in graphene, Phys. Rev. Lett. 102 (2009) 166808. Copyright APS Physics.

graphene offers the facility of tuning its electronic properties by the applied external gate voltage and band gap modulation, it provides good scope for improvement in the TE properties. The dependence of both conductivity and TE performance of graphene upon the variation in gate voltage and temperature was investigated [78]. The results showed a broad transition in the TEP value when the gate voltage crosses the Dirac point, depending upon its carrier type, indicating the electron-hole symmetry in the band structure of graphene (Fig. 10.6A and B). The Wei group also investigated the gate voltage dependence of the thermopower at different temperatures, as shown in Fig. 10.6C [81]. From the inset of Fig. 10.6C, the linear variation β in T indicates that Sxx (longitudinal Seebeck coefficient) varies linearly with the charge in density as n-1/2. The substantial deviation could be a result of the charged impurities in graphene devices with different degrees of disorder. However, this deviation was observed only for high-mobility graphene, while in agreement for the low-mobility graphene devices [82, 83]. The few-layer graphene (FLG) films showed an excellent enhancement in the TEP when treated in an oxygen plasma environment [84]. The opening of the disorderinduced band gap in plasma-treated graphene resulted in an enhanced TEP value of 700 μV K1, while maintaining good electrical conductivity. Fig. 10.7 shows the temperature-dependent thermopower at different band gap values, indicating an increase in TEP at increasing band gap. Besides, the power factor (S2σ) in the case of the treated FLGs was also enhanced by a factor of 15 times than those of the pristine FLG films, largely attributed to the originating structural defects. However, similar

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n=5x1011cm–2

7 6

Δ=0 eV

Δ=0.2 eV

Δ=0.4 eV

Δ=0.6 eV

Δ=0.8 eV

Δ=1.0 eV

S (KB/e)

5 4 3 2 1 0 200

300

400

500

600

700

Temperature (K) Fig. 10.7 Plots of simulated thermopower, S vs. temperature at different band gap values, where 1 KB/e ffi 86 μV K1. Reprinted from N. Xiao, X. Dong, L. Song, D. Liu, Y. Tay, S. Wu, L.-J. Li, Y. Zhao, T. Yu, H. Zhang, Enhanced thermopower of graphene films with oxygen plasma treatment, ACS Nano 5 (2011) 2749–2755. Copyright ACS Publications.

results could not be duplicated for the monolayer graphene and rGO films, as they suffer from low electrical conductivity. Similar works were also carried out by Choi et al. while investigating the TE effects on different oxidation levels of rGO [85]. They examined the correlation between the TEP parameters and the oxidation level of rGO by varying the hydrazine content for reduction. The GO surface contains numerous orders of structural defects as a consequence of the attained functionalities during the oxidation process and introduces a nonzero energy band gap. The existence of structural disorder due to oxidation results in a sharp fall in both electrical and thermal conductivity. The studies reported by Choi group [85] showed that, by lowering the oxidation level while conductivity is increased drastically, the Seebeck coefficient decreases sharply. The maximum Seebeck coefficient achieved for rGO was 60 μV K1 (at an oxidation level of 0.85), which is similar to that of a grown CVD or mechanically exfoliated graphene. However, the maximum zT value could be calculated as 1.1  104 at an oxidation level of 0.32, with the lowest k-value 0.30 W m1 K1 and power factor of 1.1  107 W m1 K7. Although the findings indicated successful alteration of the TEP values with the reduction level of rGO, further investigation must be done to improve the zT values for effective TE generators. The challenge remains for a higher reduction in the thermal conductivity of graphene for enhancing its thermoelectricity.

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1.5x10–4 0.1 mmol ACN

1.0x10–4

0.02 mmol ACN Pristine

5.0x10–5

Thermopower (V/K)

Thermopower (V/K)

In a quantitative investigation of the thermal stability of graphene, the hightemperature treated rGO (HT-rGO) could show great promise for improvement in the TE efficiency [86]. The thermal conductivity of the rGO films decreases with an increase in treating temperatures while electric conductivity remains high. The decrease in thermal conductivity is expected due to the rupture of sp2 clusters and structural defects that facilitate the phonon scattering. The HT-rGO films showed a maximum Seebeck coefficient of 150 μV K1 at a doping level of 1012 cm2 at 1200 K. The high-temperature treatment of the solution-processed GO exhibited a record high power factor of 54.5 μW cm1 K2 when the temperature increased from 500 K to 3000 K. This work showed a great promise for improving the TE efficiency of the rGO films by tuning the doping level at required temperatures. Few attempts were also devoted to the enhancement of the TE efficiency of the graphene derivative by functionalization and defect engineering [87, 88]. The classical and quantum mechanical approach realized that the power factor of functionalized graphene could be enhanced by two orders of magnitude than the pristine graphene. Sim et al. reported the TE properties of FLG films by chemical functionalization with 1,10-azobis (cyanocyclohexane) (ACN) and 1,3,6,8-pyrenetetrasulfonic acid (TPA) [89]. The functionalization with the aromatic molecules led to an improvement in the power factor of FLG films. By attaching the molecules, the maximum Seebeck coefficients were observed to be 180 μV K1 and 140 μV K1, respectively, for ACN and TPA functionalization, as given in Fig. 10.8. The power factor value was also enhanced by a factor of 4.5 for TPA and by 7 for ACN molecules attached to FLG films. The attached molecules led to the tuning of the electronic structure as well as the opening of the band gap. The zT values in defect-induced graphene films can reach three orders of magnitude higher with a controlled number of defects [88]. The power factor varies negligibly at a lower defect density (D/G  1) and remarkably increases at higher defect density. However, proper control over the defect density is required to reduce the

0.04 mmol TPA

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Fig. 10.8 Thermopower of FLG films functionalized with (A) ACN and (B) TPA molecules at different temperatures. Reprinted from D. Sim, D. Liu, X. Dong, N. Xiao, S. Li, Y. Zhao, L.-J. Li, Q. Yan, H.H. Hng, Power factor enhancement for few-layered graphene films by molecular attachments, J. Phys. Chem. C 115 (2011) 1780–1785. Copyright ACS Publications.

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thermal conductivity to dominate over the corresponding electrical conductivity and power factor. Although there is substantial improvement in the TE properties of graphene-based TE material, several optimizations are still needed to make it commercially competent to the highest efficient TE material available. GNRs, another derivative of graphene, also showed good promise for enhanced TE performance. The phonon thermal conductance could be suppressed by the significant contribution of edge disorder in zigzag GNRs, while maintaining the intact electrical conduction at the first conduction plateau [90]. Li group reported the enhanced TE performance of the as-grown suspended GNRs, where the quasiballistic phonon transport sharply reduced the thermal conductivity [91]. The increased TEP value of 127 μV K1 obtained at 220 K and zT value of 0.12 were observed for the suspended GNRs due to the band gap opening. The resulting zT is asserted to be the highest among the graphene nanostructures and very promising for graphene-based TE materials. Graphene composites have also attracted significant attention due to the possibility of tuning the TE properties. A study by Shaoba Han et al. demonstrated graphene and polypyrrole composite thin film using sodium dodecyl sulfate (SDS) as TE material [92]. A power factor of 0.0358 μW m1 K2 was seen when SDS and polypyrrole were taken together, but the power factor was enhanced 84 times in the case of rGO and polypyrrole-based composites, i.e., 3.01 μW m1 K2. The enhancement is caused due to two main factors: the high intrinsic conductivity of rGO and due to the morphology formed during the in-situ polymerization. This engagement enables the orderly alignment of the polypyrrole, resulting in an enhanced Seebeck coefficient [92]. Wang et al. explored polyaniline (PANI) and graphene (GP)-based thin film, using an in-situ polymerization as well as solution process. A remarkable increase of the Seebeck coefficient was observed, compared with bare materials conductivity of electrons, and Seebeck coefficient of 814 S cm1 and 26 μV/K, respectively, were seen, which highlights good power factor behavior [93]. TE properties of CuInTe2/graphene composite were investigated by Chen et al. where graphene sheets were synthesized using ball milling and CuInTe2 were synthesized by reacting to all the elements at 800 °C in fused silica ampoules. Mixing of the product was done in a ball mill to make a homogenous mixture, then the product was subjected to a well-known technique known as spark plasma sintering (SPS) process in which the product was processed at 500 °C for 10 min. Higher zT value at 700 K was obtained in the case of CuINTe2/graphene compared with bare CuInTe2 [94]. Hydrothermal approach for synthesizing composites of graphene and Bi2Te3 was studied by Liang et al., and they found that the effect of different graphene content plays a vital role in varying TE behavior of the material. Bi2Te3 particle sizes at a size range of 30–200 nm were decorated on graphene nanosheets and, eventually, 31% enhancement in zT value was obtained at 475 K with respect to Bi2Te3 [95]. A brief study of TE properties of graphene/Cu2SnSe3 was done by Degang Zhao et al., and they observed that a uniform distribution of the graphene over the Cu2SnSe3 matrix enables an increase of the conductivity while reducing the Seebeck coefficient. The obtained zT value in the composite at 700 °C was 0.44 [96]. Composites of graphene and MoS2 were also studied for TE properties by A K Gautam et al.

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where higher flow of electrons, termed as electrical conductivity, and Seebeck coefficient were obtained with lower thermal conductivity. The enhanced properties were due to the conducting path provided by the rGO, and the cause of thermal conductivity (heat) could be ascribed to the lattice phenomena of the rGO and MoS2 [97]. These studies indicate that graphene derivatives and composites have received tremendous interest in investigating TE properties. Since graphene serves as a costeffective and widely abundant material having excellent transport properties, it serves as a grand promise for future TE materials. However, the two significant challenges in graphene, viz., the high thermal conductivity and the negligible or zero band gap limit its TE performance for actualization in practical devices. There are reports on improvements in TE performance of graphene-based materials by inducing defects via oxidation and molecular functionalization, through structural modifications, composite formation, and other means. Nevertheless, further investigations need to be performed for future improvement and advancements in graphene-based TE materials.

10.4.2 Transition metal (TMDs) chalcogenides Chalcogenides are a novel class of materials referring to the chalcogen elements (S, Se, and Te) of the group VIA of the periodic table, combined with an electropositive counterpart. The chalcogenides are formed by covalent bonding and are found in a variety of structures, mostly arranged in octahedral or trigonal geometry [98, 99]. There are various types of chalcogenides, broadly including alkali metal chalcogenides and transition metal chalcogenides (TMCs), which again can be classified into mono-, di- and trichalcogenides. Notably, the layered (2D) TM dichalcogenides (TMDCs) gained tremendous attention in optoelectronic applications in recent years due to their excellent transport properties. The TMDCs consist of transition metals (Mo, W, etc.) and chalcogen atoms, briefly described by TX2 structure (shown in Fig. 10.9A), where T ¼ transition metals and X ¼ chalcogens [100]. The TMDCs emerged as a new exciting material with their inherent robustness and a wide range of electronic, physical, and mechanical properties. It is worthy to mention that TMDCs have sizable band gaps, which is not in the case of graphene [99]. Furthermore, the band gap can be modulated by introducing structural defects, dopants, and other means. The unique band structure and energy dispersion in the TMDCs makes them the ideal material for many thermal and electronic applications. The lower thermal conductivity (k) and a tunable band gap in TMDCs offer excellent potential for TE applications with superior performance compared with other 2D materials. The in-plane thermal conductivity of TMDCs is k  10 W m1 K1, and it further decreases along with the out-of-plane direction [101]. The lower thermal conductivity results due to the heavier elements and less covalent nature of the bonding in TMDCs [102]. These chalcogenides can be selectively tuned p-doped or n-doped by band gap engineering of the electronic properties. Besides, the transition from indirect to direct band gap in 2D TMDCs (for MoS2 shown in Fig. 10.9B), when shrunk to monolayers, allows useful tunability of the transport properties for improvement of TE efficiency. The TMDCs offer a relatively high TE effect with the Seebeck coefficient (S) in the range of 102 to 105 μV/K [103]. The possibility of tuning the

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Fig. 10.9 (A) Atomic arrangement of a typical TX2 structure in crystal. (B) Theoretically calculated electronic band structures of MoS2. Reprinted from A. Kuc, N. Zibouche, T. Heine, Influence of quantum confinement on the electronic structure of the transition metal sulfide T S 2, Phys. Rev. B 83 (2011) 245213. Copyright APS Physics.

underlying band structure makes them effectively suppress thermal conductivity by facilitating the scattering of phonons [104]. On the contrary, while most of the TMDCs offer high power factors due to their low thermal conductivity, they also suffer from nominal electronic conductivity that must be overcome. It is beneficial that these kinds of materials offer a considerable variation in the crystal structure that enables proper scope for further improvements in optimizing its TE properties. So far, TE properties of several TMDCs such as MoS2, WS2, MoSe2, and WSe2 have been investigated. MoS2, a semiconducting material having an indirect band gap about 1.2 eV [105], has received tremendous attention for its wide tunability of the TE properties. For example, the highest recorded power factor for semiconducting materials was achieved for the MoS2 bilayers, which is relatively large 8.5 mW m1 K2 [106]. This high power factor corresponded to the carrier density of n  1.06  1013 cm2 when the gate voltage approached 104 V (Fig. 10.10). Surprisingly, the power factor did not enter a peak and was expected to increase further at higher concentrations corresponding to an increase in gate voltage. This remarkable outcome corresponds to the large effective mass and valley degeneracy near the band edge of the conduction band. It is not surprising that, by adequately adjusting the gate voltage, a maximum Seebeck coefficient of 30 mV/K was attained in CVD-grown MoS2 monolayers [107]. MoS2 and its equivalent TMDCs possess a wide tunability in their thickness and temperature-dependent thermal conductivity, which is much beneficial to enhance their TE properties. The k-value for exfoliated MoS2 layers from independent measurement using Raman spectroscopy was found to be in the range 34.5–52 W m1 K1, whereas for MoSe2, WS2, and WSe2, much lower k-value is expected [101, 108–110]. Due to their low k-values, the peak zT value of these materials can reach >2 (as shown in Fig. 10.11), if applied to TE generators [111]. Although MoS2 and its equivalent TMDCs showed good promise for efficient TE materials, they still have a broad scope to achieve the expected efficiency for outstanding TE performance.

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(A) 1x10

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Fig. 10.10 Room temperature thermoelectric properties of monolayer, bilayer, and trilayer MoS2 for change in gate voltage, (A) conductivity, and (B) power factor. Reprinted from K. Hippalgaonkar, Y. Wang, Y. Ye, D.Y. Qiu, H. Zhu, Y. Wang, J. Moore, S.G. Louie, X. Zhang, High thermoelectric power factor in two-dimensional crystals of Mo S 2, Phys. Rev. B 95 (2017) 115407. Copyright APS Physics.

Fig. 10.11 zT for (A) MoSe2, (B) WS2, and (C) WSe2 as a function of reduced Fermi energy EF for different thickness at 300 K. Reprinted from D. Wickramaratne, F. Zahid, R.K. Lake, Electronic and thermoelectric properties of few-layer transition metal dichalcogenides, J. Chem. Phys. 140 (2014) 124710. Copyright AIP].

Apart from the TMDCs, other 2D chalcogenides from the group IVA-VIA compounds, mainly Sn- and Bi-based chalcogenides and their alloys, reported the highest performance as TE materials [23, 70, 112, 113]. Enhanced TE efficiency with a higher value of the Seebeck coefficient is noticed due to increased charged density at the charge neutrality point. The grain boundaries and interfaces cause phonon scattering and significantly reduce the thermal conductivity without changing the material

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electrical properties [114, 115]. Additionally, these chalcogenides can exhibit ultralow thermal conductivity due to presence of soft chemical bonding and lattice anharmonicity. Therefore, they possess the highest power factor (zT) operational for TE efficiency [23, 112, 116]. The k-value in SnSe can be obtained as low as 0.09 W m1 K1, and a zT value lying within a range of 0.7–2.0 can be expected [112, 113]. The substantial reduction in the k-value due to the higher amount of grain boundaries in the nanostructure must be the reason for the higher TE performance. The ultralow thermal conductivity of these materials triggers a growing interest in promoting further improvement in their TE performance. However, despite showing the highest TE performance, these materials are often limited by their poor electrical conductivity and high production cost for practical application. Regardless, they still hold proper scope for the comprehensive optimization of the TE properties to meet the demand of higher zT values for high-performance commercial TE materials. Hence, these 2D chalcogenides (TMDCs), SnSe and Bi2Te3, have seen a great interest in practical applications for TE materials. The significant advantage of these materials lies in their considerably lower thermal conductivity and tunable band gap, which results in a large power factor, and thus higher zT value is achieved.

10.4.3 Phosphorene The establishment of phosphorene in the class of 2D materials has prospered in many applications, as well as in TE properties. The phosphorene can be produced from black phosphorus. Black phosphorus is the most stable phosphorus allotrope under ambient condition, enabling it to be easily turned into two types, i.e., p-type and n-type configuration. TE properties in the case of phosphorene nanoribbons with zigzag and armchair edges were studied by J. Zhang et al. [117]. The zT value of nanoribbons and zigzag showed an impressive behavior related to TE applications, and phosphorene nanoribbons have shown a significantly high zT value of 6.4 at room temperature. The armchair and hydrogen-passivated nanoribbons of phosphorene have a significant effect on the Seebeck coefficient [117]. The effect of lattice strain on phosphorene has a distinct approach toward electronics and TE properties. H.Y. Lv et al. studied the strain effect using first-principle calculations. They reported that band modulation due to uniaxial strain and conduction band extrema relatively converged at critical strain [118]. As a result, the Seebeck coefficient is immensely affected due to band convergence. zT value of 1.65 is achieved in the case of zigzag directed strain, which is 50 times greater than the phosphorene without any strain [118]. The TE properties have also been investigated in blue phosphorene (another analog of black phosphorus). The schematic illustration of the two phosphorene is shown in Fig. 10.12. Sevik et al. [119] studied the properties of blue phosphorene, and they predicted that a high zT value of 2.5 could be achieved at a high temperature of 800 K. Liu et al. [120] observed that zT of 0.016 could be reached at 500 K. They also calculated the thermal conductivity of blue phosphorene, and the value was determined to be 130 mW/K at 300 K. A large amount of conductivity hinders the phonon scattering in blue phosphorene. Hence, the power generation values are very less compared with black phosphorene. However, blue phosphorene can be used in applications such as TE

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Fig. 10.12 Representation of top views and side views of layered structures of (A) black phosphorene and (B) blue phosphorene. The shaded region depicts the primitive cell. (C) Representation of how black phosphorene converts to blue phosphorene by dislocations. (D) Side view of AB-stacked blue phosphorene. Reprinted from Z. Zhu, D. Toma´nek, Semiconducting layered blue phosphorus: a computational study, Phys. Rev. Lett. 112 (2014) 176802. Copyright APS Physics.

cooling. Further studies are needed to have actual experimental verification of these theoretically predicted TE properties of blue phosphorene. The stability of phosphorene at ambient conditions [121, 122] is a big challenge for successful utilization. The lone pairs present in each phosphorus atom causes its degradation in air with the formation of an oxide layer. Therefore, researchers found that phosphorene oxide can be used for stabilizing the phosphorene structure. Lee et al. [123] explored TE properties and observed that phosphorene oxide could also be a potential candidate for TE applications. It shows low κ value of 2.42 W/mK along a zigzag direction, and 7.08 W/mK along armchair direction at 300 K was observed. The low thermal conductivity is always an ideal condition for successful use in TE devices. The puckered structure of phosphorene oxide causes higher phonon scattering leads to better TE properties. The oxygen atoms act as dangling atoms and help in further increasing the phonon scattering, causing a reduction in the lifetime of phonon. The various types of phosphorene have been explored to now, but still experimental knowledge is not very rich. Nonetheless, phosphorene materials have shown great

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promise as TE materials, and they can be explored further for successful commercialization.

10.4.4 MXenes MXenes were discovered only decades ago and belong to the 2D materials family, which are referred to as transition metal carbides and nitrides or carbon-nitrides [124]. These materials are widely described by the empirical formula, Mn+1XnTx (n ¼ 1, 2 or 3), in which M denotes a transition metal, and X denotes carbon or nitrogen. The surface functional groups (OH, O, F) are represented as T. MXenes are obtained from its MAX phase, where A represents the primary group SP elements (typically Al or Ga), through the selective etching of “A” element by using aqueous HF solutions. During the last decade, MXenes have triggered a growing interest and potential applications in many fields owing to its unique structural, electronic, and mechanical properties. Most of the MXenes bear metallic characters, while some of them (such as Sc2CTx, Ti2CTx, Zr2CTx, and Hf2CTx) are semiconductors. The ability of MXenes to possess high electrical conductivity (104 S cm1) and better thermal stability make them suitable for extensive studies on their TE applications [125]. Additionally, the surface-terminated functionalities enhance the TE properties of MXenes by significant tuning of their structural and electronic properties [126, 127]. Most of the semiconducting MXenes exhibit the Seebeck coefficient higher than 100 μV K1 (at 400 K), but only a few of them (e.g., Mo2C-MXenes) show high electrical conductivity [128]. Few earlier studies even predicted substantial Seebeck coefficients of more than 1000 μV K1 at low temperatures for semiconducting MXenes, such as Sc2C(OH)2 and Ti2CO2 [129]. However, the lower electrical conductivity of most of the MXenes makes them less suitable and requires further studies to improve their TE properties. According to theoretical studies, Mo2CF2 shows the most promising TE performance among the MXenes attributed to its narrow semiconducting band gap (0.25 eV) and peculiar band structure. Moreover, all the Mo2C-MXenes are predicted to exhibit the highest TEP factor compared with other functionalized MXenes [128]. For example, Kim et al. explored the TE performance of Mo2CTx, Mo2TiC2Tx, and Mo2Ti2C3Tx MXenes. [130]. It was reported that the Mo2TiC2Tx MXene exhibits 309 μW cm1 K2 as a power factor, among the MXene samples for its large Seebeck coefficient (47.3 μV K1) and electrical conductivity (1380 S cm1) obtained at 803 K (Fig. 10.13). Theoretical investigation reveals that TE properties (Seebeck coefficient and power factor (zT)) may vary up to 40% based on the structural model or properties of MXenes [127]. Another study says that the compositional tuning or alloying originate high TE behavior in five-layer BixSb2-xTe3 [131]. Even incorporation of p-type MXene in organic TE materials almost doubles the value of the Seebeck coefficient and power factor [132]. Photoinduced TE properties of Ti3C2Tx were reported by Alshareef et al., where they discussed the directed thermo-osmotic transport of hydrated cations due to lightinduced temperature gradient [133]. Experimental findings show high thermal sensitivity of Ti3C2Tx that can respond to a difference of 1 K temperature. These findings prove the enormous potential of the MXene materials toward excellent TE

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Fig. 10.13 Mo-based MXenes. (A) Temperature-dependent Seebeck coefficient and (B) TE power factor. The cooling cycle is represented by filled symbols, and the heating cycle is represented by open symbols. Reprinted from H. Kim, B. Anasori, Y. Gogotsi, H.N. Alshareef, Thermoelectric properties of two-dimensional molybdenum-based MXenes, Chem. Mater. 29 (2017) 6472–6479. Copyright ACS Publications.

performance, although further extensive investigations are needed to explore the real possibility of MXenes in TE devices.

10.4.5 Other 2D materials Many other 2D materials are being explored in the field of thermoelectricity and its related properties. Few layers h-BN studies demonstrate that thermal conductivity can approach the basal plane value of crystal at room temperature by varying the thickness of the material. Often, thermal conductivity decreases by decreasing the thickness of the h-BN. It can be explained that heat dissipation among layers can be concluded for thermal conductivity enhancement, which will turn out better for TE properties [134]. Silicene and germanene have also been reported to exhibit good TE properties. Yang and co-workers [135] theoretically calculated the zT values of silicene and germanene and found the value in the range of 1–2. A combination of silicene and germanene heterostructure was also reported to improve the TE properties on a silver substrate. Recently, Lin and group [136] observed TE behavior in selenene and tellurene, and respective zT values were 0.64 and 0.79. 2D metal oxide frameworks (MOFs) are also among the other materials have to low thermal conductivity, high electrical conductivity, and high Seebeck coefficient. MOFs performance was understood by estimating the zT value using the mean free path of carriers at ambient temperature using maximum value of the power factor. Thus, if the mean free path can be optimized, then a significant zT can be obtained in the case of 2D MOFs system. Developing high crystallinity and purity-based 2D MOF will help to establish novel TE materials [137]. Hexagonal boron nitride is another example of different 2D materials with its unique properties. Most of the other 2D materials are still in the early stages of

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development as efficient TE materials, and much more advanced experimental techniques for fabrication of these materials are yet required.

10.5

Summary and future prospective

Despite substantial progress that has been achieved in the field of TE materials, 2D materials have recently received massive attention owing to their suitable electronic and thermal properties. The TE studies of 2D materials are mostly based on theoretical calculations and simulations. The TE performance of 2D materials is yet not up to the range of desire. Hence, strategies such as efficient doping, band gap tuning, defect control, and composite fabrication need to be explored to improve TE performances. The large-scale and high-quality fabrication of 2D materials with consistent properties are other challenges. The controlled synthesis of 2D materials, facile tools for the transfer of the 2D layer, and device fabrication process are key issues that should be addressed. The TE devices based on 2D materials could provide a viable solution for the future energy scenario. Thus, a proper research strategy is essential for the effective implementation of these 2D materials. However, further deep understanding of 2D materials and experimental evidence are required for implementing realistic TE devices toward commercialization.

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Khalid Bin Masooda, Neha Jaina, Pushpendra Kumarb, Mushtaq Ahmad Malikd, and Jai Singha,c a Department of Physics, Dr. Hari Singh Gour University Sagar, Sagar, India, bCSIR-National Chemical Laboratory, Pune, India, cDepartment of Pure and Applied Physics, Guru Ghasidas University, Chhattisgarh, India, dDepartment of Chemistry, Govt. Degree College Pulwama, Jammu and Kashmir, India

11.1

Low-dimensionality in thermoelectric materials

The concept of low-dimensionality in thermoelectric materials was first introduced by Dresselhaus in 1993 after she was approached by the United States and French Navy to suggest new possibilities to optimize the zT of thermoelectric materials. Dresselhaus and Hicks calculated zT for the two-dimensional (2D) quantum well structure of Bi2Te3 and found an increment in zT by a factor of 2 in the case of 4-nm-thick quantum wells and by a factor of 3 in the quantum wells of 2-nm thickness [1]. They further carried out the calculations for one-dimensional (1D) Bi2Te3 nanowires and found that zT was enhanced concerning the 2D quantum well structure of Bi2Te3 [2]. The effects of low-dimensionality in 2D quantum well and 1D nanowire on zT was assumed based on the single and parabolic band in the materials [1, 2]. The effect of dimensionality of zT can be understood from the relation given by Eq. (11.1) [1–3]: 0 1 FN B C B C N=2BαN 2  ηCFN @ FN A 1 1 2 2 zN T ¼ (11.1)   F2N=2 1 N+4 + FN  β N BN 2 FN +1 1 2 2 Where N is the dimensional factor and has the value of 1, 2, and 3 for one dimension (1D), two dimensions (2D), and three dimensions (3D) respectively, η is the chemical potential, αN and βN are factors mainly dependent on N, Fi is the Fermi-Dirac function, and BN is the parameter depending on the material property. BN is the parameter that depicts the effect of dimensionality on zNT and is given by Eq. (11.2):  BN ¼ γ N

2kB T ћ2

N=2

kB2 Tμx eκl

Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00005-9 Copyright © 2021 Elsevier Ltd. All rights reserved.

(11.2)

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Where γ N depends on the dimensionality and is given by: γN ¼

ð3  N Þ! M1=2 Nπ ðN1Þ! a3N

(11.3)

Here, μx is the carrier mobility in the x-direction, κl is the lattice thermal conductivity, “a” is the width of nanowire or quantum well, M is the effective mass of carriers; for 1D, it is written as mx, for 2D, it is mxmy, and for 3D, it is mxmymz. It is interesting to note that the parameter “a” is absent in the case of 3D nanostructures; hence, zT in such cases cannot be optimized by varying the size. However, zT in 3D nanostructures can enhanced by optimal doping to optimize the chemical potential by increasing the carrier mobility and reducing the lattice thermal conductivity. All these factors increase BN thereby increasing zT following Eq. (11.1). In the case of 1D nanowires and 2D quantum well, in addition to the factors mentioned previously, the width also plays an important role in optimizing zT. The parameter γ N is inversely proportional to “a2” and “a” in the case of 1D and 2D structures implying that the dimensional effect is more pronounced in 1D structures. Low-dimensionality in thermoelectric materials is believed to enhance the Seebeck coefficient, S, to control the parameters S and electrical conductivity σ somewhat independently via quantum confinement, improving the density of states (DOS) near Fermi level, leading to the increment of power factor [1, 2, 4]. Also, the phonons contributing to the lattice thermal conductivity are scattered preferentially at various interfaces of the nanostructures, leading to the reduction in thermal conductivity [4]. 1D nanowires are proposed to have strong quantum confinement and phonon scattering compared with their 2D counterparts. Due to the additional phonon scattering on the outer and inner surfaces of nanotubes, the nanotubes are proposed to have lower lattice thermal conductivity in comparison to that of nanowires [5, 6]. Based on these predictions, various zero-dimensional (0D), onedimensional (1D), and two-dimensional (2D) structures of thermoelectric materials were fabricated to improve the thermoelectric properties. Record value of zT up to 2.4 was realized in 2D superlattice structure [7], which was a breakthrough because, for the past few decades, the maximum zT of bulk thermoelectric materials did not cross the maximum limit of unity. A high zT was also reported in 0D quantum dot superlattice with the maximum zT reaching a value greater than 3, and this value is almost 300% greater than that of bulk thermoelectric materials [8]. zT of Si nanowires was also reported to show an increment of up to 100-fold compared with that of bulk Si [9, 10]. The limitation of these high zT low-dimensional materials is that these materials cannot be practically used for large-scale commercial purposes because of the slow process and higher cost. Therefore, the fabrication of high-performance bulk nanostructured materials are highly desirable for use in industrial applications [11]. Also, in the case of 3D bulk nanomaterials, the DOS is a smooth function but acts as a step-like function in the case of low-dimensional systems, as shown in Fig. 11.1, allowing new trends to vary S, σ, and κ quasi-independently [4]. However, in the case of 3D bulk nanomaterials, it is very challenging to recognize the DOS with delta function-type features because of their smooth variation of DOS. So, in the case of these nanomaterials, the optimization of thermoelectric properties relies mainly on

(d)

Density of states

(c)

Density of states

(b)

263

Density of states

(a)

Density of states

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Energy

Energy

Energy

Energy

3-D

2-D

1-D

0-D

Fig. 11.1 Schematic of electronic density of states as a function of energy for (A) 3D, (B) 2D, (C) 1D, and (D) 0D nanomaterials. Reproduced from M. S. Dresselhaus, G. Chen, M. Y. Tang, R. Yang, H. Lee, D. Wang, Z. Ren, J. P. Fleurial,P. Gogna, New directions for low-dimensional thermoelectric materials, Adv. Mater. 19 (2007) 1043-1053, with permission from Wiley.

the preferential scattering of phonons at the interfaces of the nanomaterials to reduce the lattice thermal conductivity. To benefit from nanostructures, the lattice thermal conductivity must be degraded to a greater extent compared with the charge mobility. In other words, as the nanostructures also scatter charge carriers, any benefit from the nanostructuring can be obtained only if the mean free path (MFP) of phonons is considerably reduced to a greater extent in comparison to the MFP of charge carriers. To find the contribution of MFP of phonons and phonon scattering to the lattice thermal conductivity, a theoretical model for Si was developed. From the calculations, it was observed that the phonons, having MFP greater than 20 nm, are responsible for 90% of the lattice thermal conductivity accumulation [12]. Therefore, a reduction of almost 90% in the lattice thermal conductivity is possible by reducing the grain size to 20 nm without affecting the charge carrier mobility because they have the MFP of only a few nanometers for Si [13]. Nanostructuring helps improve TE properties of the materials, and such efficient features are not possible in the traditional bulk materials. The effect of nanostructuring on zT of some materials is presented in Fig. 11.2. Another feature of the low-dimensional materials is that Wiedemann-Franz law does not apply to the materials having delta-like DOS, hence, making the lowdimensional materials promising candidates in enhancing zT [14]. Moreover, in the case of multivalley cubic semiconductors with anisotropic Fermi surfaces, the quantum confinement due to low-dimensionality increases the charge mobility at a fixed carrier concentration. This opens a window for delta doping and modulation doping in these materials. One more critical aspect is the phonon drag, which has been ignored under normal temperature conditions, and in such circumstances, the carrier mobility is not dependent on the electron-phonon interactions [15, 16]. In the case of lowdimensional materials, the Seebeck coefficient can also be increased by energy filtering because the low energy charge carriers are filtered out by the formation of a small potential barrier at the interface of the matrix and nanoinclusions [17]. Various morphologies of nanostructured thermoelectric materials have also been developed, which show improved zT compared with their bulk counterparts. Some of the morphologies of nanostructured thermoelectric materials are discussed hereafter.

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Fig. 11.2 zT values as a function of temperature for recently developed nanostructured TE materials (solid lines) and the maximum zT values of the bulk TE materials (dashed lines). Adapted from A. Minnich, M. Dresselhaus, Z. Ren, G. Chen, Bulk nanostructured thermoelectric materials: current research and future prospects, Energy Environ. Sci. 2 (2009) 466-479, with permission from RSC.

Yang et al. developed hexagonal plate-like Bi2Te3 as shown in Fig. 11.3A with a maximum zT of 0.88, mainly because of the ultralow thermal conductivity [18]. Because of the stacking of plate-like structure of Bi2Te3 during the spark plasma sintering process, the high density of dislocations accommodated in the small-angle high-density grain boundaries are formed. Due to the existence of such high density of dislocations and the fine-grain nanostructures, the intermediate- and low-frequency

press direction –

e

quintuple layer –

e S

(A)

(B)

Intermediate wavelength phonons

S: small angle boundary

Short wavelength phonons

Fig. 11.3 (A) TEM image showing the hexagonal plate-like of Bi2Te3. (B) Representation of the phonon scattering mechanism for spark plasma sintered Bi2Te3 plates. Adapted with permission from L. Yang, Z.-G. Chen, M. Hong, G. Han,J. Zou, Enhanced thermoelectric performance of nanostructured Bi2Te3 through significant phonon scattering, ACS Appl. Mater. Interfaces 7 (2015) 23694-23699, from ACS.

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heat-carrying phonons can be strongly blocked to remarkably reduce lattice thermal conductivity as shown in Fig. 11.3B [18]. Song et al. reported one-dimensional nanorod bundles of Bi2Te3 with the maximum zT of about 0.43 [19]. The growth process of Bi2Te3 nanorod bundles, illustrated in Fig. 11.4, shows the deposition of Bi on Te nanorods. These nanorod bundles show the lattice thermal conduction of about 0.25 W m1 K1, and this value is much lower than that of the bulk and other Bi2Te3 nanostructures. Hence, these nanostructures act as scattering centers for phonons and thereby efficiently reduce the lattice thermal conductivity [19]. Zhou et al. synthesized PbTe nanocubes, as shown in Fig. 11.5, with a maximum zT of 0.78 [20]. The PbTe nanocubes show low electrical conductivity and a significant Seebeck coefficient, which can be attributed to the energy filtering effect. Moreover, the PbTe nanocubes show minimum thermal conductivity of 0.621 W/m K, and such low thermal conductivity can be attributed to the enhanced phonon scattering at the grain boundaries. This value of thermal conductivity is 50% less compared with annealed bulk PbTe ingot [20]. Dong et al. reported the synthesis of Sb2Te3 nanosheets, as shown in Fig. 11.6, with the maximum zT of 0.58 [21]. The Sb2Te3 nanosheets show low thermal conductivity of 0.76 W/m k with high electrical conductivity and a large Seebeck coefficient.

Fig. 11.4 Illustration of the growth mechanism of Bi2Te3 nanorod bundles by the deposition of Bi on Te nanorods. Adapted from Ref. S. Song, J. Fu, X. Li, W. Gao,H. Zhang, Facile synthesis and thermoelectric properties of self-assembled Bi2Te3 one-dimensional nanorod bundles, Chem. Eur. J. 19 (2013) 2889-2894, with permission from Wiley.

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Fig. 11.5 (A, B) TEM images of PbTe nanocubes. Adapted from J. Zhou, Z. Chen,Z. Sun, Hydrothermal synthesis and thermoelectric transport properties of PbTe nanocubes, Mater. Res. Bull. 61 (2015) 404-408, with permission from Elsevier.

Fig. 11.6 (A, B) High and low magnification TEM images of Sb2Te3 nanosheets. Reproduced from G.-H. Dong, Y.-J. Zhu, L.-D. Chen, Microwave-assisted rapid synthesis of Sb2Te3 nanosheets and thermoelectric properties of bulk samples prepared by spark plasma sintering, J. Mater. Chem. 20 (2010) 1976-1981, with permission from RSC.

The significant value of the Seebeck coefficient of Sb2Te3 nanosheets may be a result of quantum confinement size effects in these nanosheets. These effects help to adjust the transport of both electrons and phonons, and change the electronic DOS, the energy level, and the energy band structure, leading to an enhancement of the Seebeck coefficient. The low thermal conductivity is due to the efficient scattering of phonons by a large number of crystal interfaces in the sintered bulk sample of Sb2Te3 nanosheets [21]. Yang et al. reported the efficient thermoelectric performance in Cu2Se nanoplates, as shown in Fig. 11.7A, through nanostructure engineering with a maximum zT of 1.82 and minimum thermal conductivity of 0.2 W/m k [22]. This value of zT is 20% higher than that of the earlier reported zT of bulk Cu2Se. For such a low value of thermal conductivity, two factors are responsible. One is the liquid-like behavior of Cu+ ions, which contribute to the efficient scattering of phonons, and another factor is the nanostructure engineering. The structural characterizations reveal that Cu2Se nanoplates are arranged in a plate-stacking fashion in the sintered pellets, which leads to the

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Fig. 11.7 (A) SEM image of Cu2Se nanoplates. (B) Illustration of the mechanism of phonon scattering in the sintered pellets Cu2Se nanoplates. Adapted from L. Yang, Z.-G. Chen, G. Han, M. Hong, Y. Zou,J. Zou, High-performance thermoelectric Cu2Se nanoplates through nanostructure engineering, Nano Energy 16 (2015) 367-374, with permission from Elsevier.

formation of a high density of small-angle grain boundaries and the high density of dislocations. Due to the nanostructures with a high density of small-angle grain boundaries accommodated by the dislocations in the grain boundaries, the intermediate as well as low-frequency phonons are actively blocked to reduce the overall thermal conductivity. The scattering of intermediate- and long-wavelength phonons by the high-density small angle grain boundaries and the scattering of short-wavelength phonons by Cu+ ions is presented in Fig. 11.7B. Such a scattering of phonons of vast range of wavelengths does have only a minor influence on the transport of electrons. Due to such a massive scattering of phonons, the lattice thermal conductivity is reduced to a large extent, which has a significant contribution in securing high zT in Cu2Se nanoplates [22]. Shashlik-like Te-Bi2Te3 heteronanostructures were reported by Mei et al. showing the maximum zT of 0.54, and this enhanced zT is credited to the Te-Bi2Te3 heteronanostructure, which resulted in the introduction of interfaces and the second phase of Te in the bulk sample [23]. The minimum value of thermal conductivity for Te-Bi2Te3 heteronanostructures is 0.416 W/m k, and such a low value of thermal conductivity of bulk sample using Te-Bi2Te3 heteronanostructure powders is due to two aspects. One is that the phonons are scattered strongly at the interfaces and grain boundaries introduced by such heteronanostructures of Te-Bi2Te3. Another issue is that the phonons could also be scattered by the second phase of Te to reduce thermal conductivity. For the growth of Te-Bi2Te3 heteronanostructures, Te nanorods were first formed, and then Bi2Te3 nanoplates appear on the surface of Te nanorods creating shashlik-like structures. With the increasing reaction time, the relative content of Te decreased, and the content of Bi increased implying that the Te nanorods were first produced, which then reacted with Bi to produce Bi2Te3 nanoplates [23]. SEM images of the powder sample at different reaction times are reported in Fig. 11.8. Zhang et al. reported a high zT of 0.96 in Bi2Te3 nanowires, which is comparable to the best n-type commercial Bi2Te3 alloy [24]. The electrical conductivity of the Bi2Te3 nanowires is less compared with the other commercial Bi2Te3 alloys because

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Fig. 11.8 SEM images of the Te-Bi2Te3 sample at different reaction times. (A) After the reaction time of 12 h, some nanorods and very small amount nanoplates were found. (B) After the reaction time of 24 h, some Bi2Te3 nanoplates were observed on the surface of nanorods. (C) After the reaction time of 36 h, larger hexagonal nanoplates of Bi2Te3 were seen on the thin nanorods of Te. (D) After the reaction time 48 h, Te rods disappeared, and Bi2Te3 nanoplates became more pronounced. Adapted from Z.-Y. Mei, J. Guo, Y. Wu, J. Feng,Z.-H. Ge, Shashlik-like Te–Bi2Te3 hetero-nanostructures: one-pot synthesis, growth mechanism and their thermoelectric properties, CrystEngComm (2019) 21, with permission from RSC.

of the smaller grain size and diameter of Bi2Te3 nanowires. Due to the low electrical conductivity, the Bi2Te3 nanowires show a much higher Seebeck coefficient compared with the commercial Bi2Te3 alloy. The Bi2Te3 nanowires show the minimum thermal conductivity of 0.92 W/m k, which is due to the preferential scattering of phonons by the nanowires. Moreover, the SPS process involved in the sintering of pellets is also responsible for the enhanced thermoelectric properties of the Bi2Te3 nanowires because the grain and particle size is preserved by SPS process [24]. SEM image of Bi2Te3 nanowire film is shown in Fig. 11.9. Fig. 11.9 SEM image of Bi2Te3 nanowire film. Adapted from G. Zhang, B. Kirk, L. A. Jauregui, H. Yang, X. Xu, Y. P. Chen,Y. Wu, Rational synthesis of ultrathin n-type Bi2Te3 nanowires with enhanced thermoelectric properties, Nano Lett. 12 (2011) 56-60, with permission from the American Chemical Society.

Nanostructured thermoelectric materials

11.2

269

Nanocomposite thermoelectric materials

The use of nanocomposites as thermoelectric materials can be considered as a costeffective and potential replacement for expensive superlattices. The nanocomposites show reduced lattice thermal conductivity due to the preferential scattering of phonons at the interfaces. The interfaces are produced by the introduction of nanosized polycrystalline into bulk materials, which act as host materials, and the nanomaterials become a matrix. Due to the interfaces, the preferential scattering phonons are dominant compared with the scattering of charge carriers because the MFP of phonons ranges up to few hundred nanometers while the charge carriers exhibit the MFP of only few nanometers [25]. Therefore, the incorporation of different sizes of nanomaterials can help in the scattering of the phonons of broad range of MFP without much affecting the charge transport [25]. Even if the charge transport is affected by the mild scattering of charge carriers, the reduction of electrical conductivity is countered by the increment of S due to energy filtering or quantum confinement. This results in the increment of power factor, which in turn increases zT. Hence, the zT of material can be enhanced by the random assemblage of two different types of nanoparticles in the heterogeneous nanocomposites. However, the randomly oriented grains in these heterogeneous composites also pose a threat to the transport of electrons in addition to the transport of phonons, leading to the reduction of electrical conductivity as well. In such cases, the increment in zT is not as expected. To overcome these problems, the thermal conductivity must be reduced to a greater extent without risking the electrical conductivity, and this can be achieved by maintaining the electron transport properties to the required level by adequately choosing the electronic mismatch between the constituent species of the nanocomposites [26]. The advantage of nanocomposite thermoelectric materials is that these are easy to handle from the material’s characterization and transport properties measurement point of view and can be easily assembled into various shapes for the use in commercial market [14]. Recently developed thermoelectric nanocomposites show drastic change in lattice thermal conductivity compared with the previously developed materials, as shown in Fig. 11.10 [27]. Enhancement of zT has been observed in various nanocomposites of different families of thermoelectric materials like binary chalcogenide-based nanocomposites, lead telluride-based nanocomposites, SiGe-based nanocomposites, etc.

11.2.1 Binary chalcogenide-based nanocomposites Binary chalcogenides and their alloys are considered to be the best thermoelectric materials at room temperature and are widely used for thermoelectric refrigeration and power generation. Binary chalcogenides like Bi2Te3 have a layered structure composed of the Te-Bi-Te-Bi-Te unit, and each layer is connected by van der Waals bonds. Within the layer, the dominating bonds are both covalent and ionic hence, making the intralayer interaction much stronger than interlayer interaction. Such type of layered structure of binary chalcogenides makes the nanocomposite formation much easier compared with the other structures.

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FeNb0.88Hf0.12Sb

3.6

Mg1.96Al0.04Si0.97Bi0.03

3.2

InCo4Sb12 Ba8Ga16Ge30

Bi0.4Sb1.6Te3/Graphene

2.8

3

Ca2.95Tb0.5Co4O9 Cu2Se

SiGe

SnSe

2.4

KI (W m–1K–1)

KI (Wm–1k–1)

SiGe/YSi2

(PbTe)0.75(PbSe)0.20(PbS)0.05

2.0 1.6

CeFe3CoSb12 2 Hf0.75Zr0.25NISn Bi2Te3

1.2 1

PbTe

0.8 TAGS

0.4 0.0 200

(A)

400 600 Temperature (°C)

800

1000

0 0

(B)

Zn4Sb3 200

Ag2TITe5 La Te 3–x 4 Yb14MnSb11 400

Ba6Ga16Ge30 600 800

Temperature (°C)

Fig. 11.10 (A) Extremely low lattice thermal conductivity is reported in the recently developed nanocomposites. (B) Low lattice thermal conductivity is reported in complex material systems (Caltech unpublished data until 2008). From the comparison of these two figures, it is clear that there has been a significant reduction in the lattice thermal conductivity of other thermoelectric nanocomposites in addition to complex material systems. Adapted from K. B. Masood, P. Kumar, R. Singh, J. Singh, Odyssey of thermoelectric materials: foundation of the complex structure, J. Phys. Commun. 2 (2018) 062001, with permission from IOP publishing.

zT of 1.3 was observed in p-type Bi1.5Sb0.5Te3 by the nanoinclusion of ZnO particles by Jiang et al. [28]. As an intrinsic n-type semiconductor with low thermal conductivity, ZnO causes drastic reduction in the lattice and total thermal conductivity in p-type Bi1.5Sb0.5Te3 and thereby increases zT. The same enhancement in zT is not observed in n-type Bi2Te3 by the ZnO nanoinclusion because of the reduction of carrier concentration, thereby increasing resistivity and hence reducing the power factor [28]. It can also be concluded that the choice of guest and host in the nanocomposite formation is very essential to enhance the zT of a material. The highest power factor of 18.3 μW cm1 was achieved in MoS2/Bi2Te3 nanocomposite by Tang et al., and this value is about 30% higher in comparison to that of pristine Bi2Te3 [29]. The MoS2/Bi2Te3 nanocomposite shows a more compact microstructure compared with the pristine Bi2Te3. With the increase in the MoS2 concentration in the nanocomposite, the electrical conductivity increases up to a specified concentration of MoS2 (12 wt%) and then decreases when the concentration of MoS2 is further increased (17 wt%) at a particular temperature. At 17 wt% of MoS2, there is reduction in electrical conductivity because the MoS2 grains form a percolation network in the nanocomposite [29]. Hence it can be concluded that every doping concentration in a nanocomposite is not suitable for the optimization of thermoelectric properties, and to optimize the thermoelectric properties, proper doping concentration must be accomplished. Kim et al. reported the highest zT of 1.86 0.15 for Bi0.5Sb1.5Te3 composite thermoelectric material synthesized via the melt-spun process and then consolidated by spark plasma sintering process or liquid phase compaction process, which generates dense dislocation arrays as shown in Fig. 11.11 [30]. Such high zT was achievable

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Fig. 11.11 The representational image of the generation of dense dislocation arrays during the liquid-phase compaction process. The dislocation arrays embedded in the low-energy grain boundaries are formed by the expelling of liquid Te (red; dark gray in print versions) between the grains of Bi0.5Sb1.5Te3 during the compaction process. Adapted from S. I. Kim, K. H. Lee, H. A. Mun, H. S. Kim, S. W. Hwang, J. W. Roh, et al., Dense dislocation arrays embedded in grain boundaries for high-performance bulk thermoelectrics, Science 348 (2015) 109-114, with permission from AAAS.

because of the drastic reduction in lattice thermal conductivity due to the effective scattering of phonons at the dense dislocation arrays embedded in the grain boundaries. The electrical transport properties in the Bi0.5Sb1.5Te3 composite are conserved because these dislocation arrays embedded in the grain boundaries do not scatter the charge carriers [30]. Zheng et al. have managed to decouple the electrical and thermal transport properties by engineering a low-dimensional metal-semiconductor nanocomposite (Au-Sb2Te3) [31]. They have developed a unique architecture Au-Sb2Te3 (0D–2D) composite, as shown in Fig. 11.12A and B to synergistically optimize the electrical and thermal transport properties by strengthening the phonon scattering at the interface barrier. Au nanoparticles deliver a reduction in lattice thermal conductivity of Sb2Te3 by strengthening the scattering of the mid- to long-wavelength phonons, as

Fig. 11.12 (A–B) TEM images Au-Sb2Te3 composite showing that Au nanoparticles are evenly distributed on the surface of Sb2Te3 nanoplates. (C) Representational diagram of the morphology, phonon scattering, and band alignment in Au-Sb2Te3 nanocomposite. Reproduced from W. Zheng, Y. Luo, Y. Liu, J. Shi, R. Xiong,Z. Wang, Synergistical Tuning Interface Barrier and Phonon Propagation in Au–Sb2Te3 Nanoplate for Boosting Thermoelectric Performance, J. Phys. Chem. Lett. 10 (2019) 4903-4909, with permission from the ACS.

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shown in Fig. 11.12C. The band alignment in Au-Sb2Te3 nanocomposite is also shown in Fig. 11.12C. The zT of 0.8 was achieved in 1 mol% Au-Sb2Te3, which is much more significant compared with that of pristine Sb2Te3 having the zT value of 0.39. Such enhancement in zT is due to the active filtering of low-energy holes at the energy barrier between Au and Sb2Te3 and the hindrance in the propagation of mid- to longwavelength phonons because of the presence of Au nanoparticles [31].

11.2.2 Lead chalcogenide-based nanocomposites Lead telluride-based thermoelectric materials are promising thermoelectric materials [32, 33] because of their two-valence band (light hole L-band and substantial hole Σ-band) structure [34]. PbTe shows low lattice thermal conductivity due to its high anharmonicity, and also the Umklapp process is the dominating phonon scattering process [27]. Band engineering can be employed in lead chalcogenides to optimize the thermoelectric properties, and this band convergence can be achieved by the nanocomposite formation [35–37]. Hsu et al. gained spectacular success when they reported the zT value of 1.7 for p-type AgPb18SbTe20 composite, a LAST (lead, antimony, silver, and tellurium) family member created by alloying PbTe with AgSbTe3 [38]. These LAST structures show low lattice thermal conductivity because of the scattering of phonons due to the formation of endotaxial nanoinclusions form the replacement of Pb2+ with Ag1+ and Sb3+. These endotaxial nanoinclusions have no adverse effect on the mobility of charge carriers. The p-type variant of LAST, called LASTT, is formed by partially substituting Pb with Sn [39]. Various other variants of this family, such as p-type SALT [40] and n-type PLAT [41], are obtained by substituting Ag with Na and K, respectively. All these variants of the LAST family show excellent thermoelectric properties with the zT values higher than 1. Fu et al. reported zT of 2.2 in PbTe0.8Se0.2 with 8% MgTe and 2% Na by multifunctional alloying [35]. Because of the large zT of 1.8 in PbTe0.8Se0.2, it was taken as a base matrix [42]. Also, because of the larger band gap of MgTe compared with PbSe, alloying with MgTe is more helpful in maintaining the wider band gap, as shown in Fig. 11.13. The multialloying with Mg and Se benefits in the increment of the Fig. 11.13 Schematic diagram showing the widening of bands in PbTe alloyed with MgTe at different temperatures. Adapted from T. Fu, X. Yue, H. Wu, C. Fu, T. Zhu, X. Liu, et al., Enhanced thermoelectric performance of PbTe bulk materials with figure of merit zT > 2 by multi-functional alloying, J. Mater. 2 (2016) 141-149, with permission from Elsevier.

Energy (eV) C band 0.0

0

Mg Content

0.03

L band S band –0.4

–0.8

T

0.06 300K 500K 800K

Nanostructured thermoelectric materials

273 1.50

(PbTe)0.75–(PbSe)0.20–(PbSe)0.05

Average ZT = Zint Tavg

1.25

(PbTe)0.84–(PbSe)0.07–(PbSe)0.07 (PbTe)0.88–(PbS)0.12

1.00 (PbTe)0.75–(PbS)0.25

0.75

PbTe

0.50

0.25

0.00

(A)

(B)

Composition

Fig. 11.14 (A) HRTEM image of (PbTe)0.75(PbSe)0.20(PbS)0.05 showing nanoprecipitation in the matrix. (B) Average zT value depending on the composition. Reproduced from D. Ginting, C.-C. Lin, R. Lydia, H. S. So, H. Lee, J. Hwang, W. Kim, R. A. R. Al Orabi,J.-S. Rhyee, High thermoelectric performance in pseudo quaternary compounds of (PbTe)0.95  x(PbSe)x(PbS)0.05 by simultaneous band convergence and nano precipitation, Acta Mater. 131 (2017) 98-109, with permission from Elsevier.

Seebeck coefficient without showing any sign of bipolar diffusion as a result of the widening of band gap. Multialloying with Mg and Se also results in the reduction of the lattice thermal conductivity of PbTe by strengthening the effect of alloy scattering as the high-frequency phonons can be strongly scattered due to the atomic disorders induced from point defects [35]. Similarly, zT of 2.5 was observed in Na-doped PbTe-SrTe heavily alloyed system [36]. The heavy alloying of SrTe in PbTe enhances the valence band convergence and also increases the point defect phonon scattering, thereby simultaneously optimizing the electrical and thermal transport properties [36]. Large zT of 2.3 was reported in (PbTe)0.75(Pb)Se0.2(PbS)0.05 composite system by Ginting et al. [37]. The transmission electron microscopy (TEM) revealed that the PbS undergoes nanoprecipitation in the PbTe1 xSex matrix, as shown in Fig. 11.14A, and this matrix is itself formed by the solid solution of PbSe in PbTe. There was a reduction in the energy band gap between conduction and valence L-bands with the increase in Se concentration, and the increment in energy difference between L- and Σ-bands. This band convergence results in the enhancement of power factor, and the nanoscale precipitation of PbS in the matrix results in reduction of lattice thermal conductivity. Both these factors are responsible for such zT of (PbTe)0.95 x(PbSe)x(PbS)0.05 composite system. The variation of average zT with the composition is shown in Fig. 11.14B [37].

11.2.3 SiGe-based nanocomposites SiGe alloys are the promising thermoelectric materials possessing cubic crystal structure, therefore having excellent electrical properties [43, 44], and their thermoelectric properties can be optimized by reducing the lattice thermal conductivity. The formation of nanocomposites is a promising way to reduce the lattice thermal conductivity of SiGe alloys.

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Nozariasbmarz et al. reported that the thermal conductivity in SiGe alloys is reduced to a greater extent in comparison to the single-phase SiGe alloys by the nanoinclusions of silicide nanoparticles in SiGe alloys [45]. The thermal conductivities of SiGe-FeSi2 and SiGe-Mg2Si nanocomposites are lower than those of singlephased nanostructured SiGe. The lower thermal conductivity of the nanocomposites can be attributed to the scattering of phonons at the nanoinclusion interfaces. Due to the three-phonon scattering mechanism, the thermal conductivity reduces up to the temperature of 750°C, and after that, it starts to increase due to the polar thermal diffusion. However, the thermal conductivity of SiGe-Mg2Si is lower than that of SiGe-FeSi2 nanocomposite, implying that the nanoinclusions of Mg2Si are more effective in scattering the minority carriers compared with FeSi2 nanoinclusions. Due to these nanoinclusions apart from the reduction in thermal conductivity, the power factor is also increased resulting in the zT value of 1.3 for Si0.88Ge0.12-Mg2Si nanocomposite [45]. The comparison of various thermoelectric parameters of single-phased Si0.80Ge0.20 used in RTGs (Radioisotope Thermoelectric Generators), SiGe, FeSi2, Mg2Si, and nanocomposites SiGe-FeSi2 and SiGe-Mg2Si are represented in Fig. 11.15. Zebarjadi et al. introduced the concept of modulation doping in nanostructured SiGe bulk materials to increase the thermoelectric figure of merit [46]. They reported the maximum zT of 0.92 for (Si80Ge20)70(Si100B5)30, and this zT is higher than the single-phased Si80Ge20 and Si100B5. This increment in zT by the modulation doping is mainly achieved by the significant increase in the power factor because the twophase composite showed higher electrical conductivity compared with that of the individual components. The enhancement of the power factor can be credited to the increased mobility of charge carriers by sorting out these carriers spatially from their parent impurity atoms, which act as the scattering centers. This results in the reduction of charge carrier scattering rates, which in turn results in the elevated mobilities. The thermal conductivity is also lower in the case of modulation-doped (Si80Ge20)70(Si100B5)30 samples compared with the single-phased Si80Ge20 and Si100B5 because of the occurrence of various phonon scattering interfaces in the modulation-doped samples [46]. Ahmad et al. reported that the coherent boundaries of metallic YSi2 nanoinclusions at the nanoscale with SiGe matrix resulted in a significant reduction in thermal conductivity without affecting the power factor, leading to the zT of 1.81 for SiGeYSi2 nanocomposite [47]. The coherent boundaries between the p-type SiGe matrix and the YSi2 nanoinclusions are formed as a result of the similarities in the crystal structures of SiGe and YSi2. The coherent grain boundaries at the nanoscale in SiGe-YSi2 composite scatter the phonons without affecting the transport of charge carriers, as shown in Fig. 11.16. The scattering of phonons causes a drastic reduction in the lattice thermal conductivity. The electrical resistivity increases by the creation of nanoinclusions due to lowering of hole concentration, which is compensated by an increment of the Seebeck coefficient maintaining almost constant value of the power factor [47]. Various other nanocomposites belonging to other families of thermoelectric materials like Mg2X-based nanocomposites (Mg1.96Al0.04Si0.97Bi0.03 [48] Mg2Si0.53Sn0.4Ge0.05 Bi0.02 [49], Mg2Sn0.73Bi0.02Ge0.25 [50]), oxide nanocomposites (Ca2.95Tb0.5Co4O9 [51],

Nanostructured thermoelectric materials

275

1600

SiGe-5%Mg2Si SiGe Mg2Si

800

FeSi2

600 400 200

Power Factor x Temperature (W/mK)

(A)

(C)

0

0

250 500 750 Temperature (C)

Seebeck coefficient (mV/K)

–50 RTG SiGe-5%FeSi2-2.5%Ag

1000

–100 –150 –200 –250 –300 –350 0

(B)

5.0 4.0 3.0 2.0 1.0 0 0

250 500 750 Temperature (C)

1000

250 500 750 Temperature (C)

1000

5.0 Thermal conductivity (W/mK)

Electrical conductivity (S/cm)

1200

250 500 750 Temperature (C)

4.5 4.0 3.5 3.0 2.5 2.0 0

1000

(D)

1.50 RTG SiG-5%FeSi2-2.5%Ag

Figure-of-merrit, ZT

1.25 1.0

SiGe-5%Mg2Si SiGe Mg2Si FeSi2

0.75 0.50 0.25

(E)

0 0

250 500 750 Temperature (C)

1000

Fig. 11.15 (A) Electrical conductivity, (B) Seebeck coefficient, (C) power factor, (D) thermal conductivity, and (E) zT of single-phased Si0.80Ge0.20 (RTG), SiGe, FeSi2, Mg2Si, and nanocomposites of SiGe-FeSi2 and SiGe-Mg2Si. Adapted from A. Nozariasbmarz, P. Roy, Z. Zamanipour, J. H. Dycus, M. J. Cabral, J. M. LeBeau, J. S. Krasinski,D. Vashaee, Comparison of thermoelectric properties of nanostructured Mg2Si, FeSi2, SiGe, and nanocomposites of SiGe–Mg2Si, SiGe–FeSi2, APL Mater. 4 (2016) 104814, with permission from AIP.

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Coherent boundary

(111) SiGe

(101) YSi2

49.46°

(111) SiGe

h+

+

h+

h+

h +

h

hole +

h

h

+

+

h

b

D

a c

c a

Coherent boundary

phobon

Y Si Ge b a c

Fig. 11.16 Schematic illustration of the creation of coherent interfaces between SiGe (111) and YSi2 (101) plane, which scatters only the phonons, but the charge carriers are allowed to pass through the interfaces. Adapted from S. Ahmad, A. Singh, A. Bohra, R. Basu, S. Bhattacharya, R. Bhatt, et al., Boosting thermoelectric performance of p-type SiGe alloys through in-situ metallic YSi2 nanoinclusions, Nano Energy 27 (2016) 282-297, with permission from Elsevier.

Zn0.9Cd0.1Sc0.01O0.015 [52]), half-Heusler-based nanocomposites (Hf0.25Zr0.75NiSn0.985 Sb0.015 [53], Zr0.25Hf0.25Ti0.5NiSn0.994Sb0.006 [54], (Hf0.6Zr0.4)0.99V0.01NiSn0.995Sb0.005 [55], and skutterudite-based nanocomposites (La0.68Ce0.22Fe3.5Co0.5Sb12 [56], Li0.08 Ca0.18Co4Sb12 [57], Al0.3Yb0.25Co4Sb12 [58]) also show enhanced thermoelectric performance.

11.3

Graphene-based nanocomposite thermoelectric materials

Graphene consists of a single layer of carbon atoms arranged in a honeycomb lattice. The covalent bonds between nearest-neighbor atoms formed by sp2-hybridized states give graphene extraordinary mechanical strength. Moreover, these bonds provide enough stability to graphene to have had freely suspended monolayers [59]. The Dirac points at the corners of the hexagonal Brillouin zone are of great importance from the carrier transport point of view. In such an exceptional one-atom-thick carbon material, the transport of electrons ballistic in nature (no scattering due to small thickness) can be described by the Dirac equation rather than by the Schr€odinger equation, which is used to describe the behavior of charge carriers in conventional semiconductors. This is because, in the case of the traditional semiconductors, the behavior of charge carriers having finite effective mass can be well described by the Schr€odinger equation, while in the case of graphene, the new quasiparticles behaving like relativistic

Nanostructured thermoelectric materials

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massless particles formed due to the interaction with honeycomb lattice can be described by Dirac equation. There are also various other prominent differences between the physical effects in the conventional semiconductors and graphene, such as the Klein tunneling paradox [60], finite conductivity at zero density [61], and quantum Hall effect [62]. Apart from these effects, the outstanding transport properties of carriers in graphene is noticeable primarily because of the very high mobility, both in the suspended graphene sheets [63] and also in the layers of graphene deposited on a hexagonal boron nitride substrate having mobility values of 275,000 cm2/Vs and 125,000 cm2/Vs at 4.2 K and room temperature, respectively [64]. Although the transport mobility in graphene is very high, it still has some significant limitations in thermoelectric applications. Graphene, being a gapless semimetal, makes it difficult to decouple the effects of the opposite contributions of electrons and holes on the total Seebeck coefficient. However, according to Eq. (11.4), a finite value of Seebeck coefficient is achievable because of the intense energy dependence of the conductivity near the charge neutrality point [61].   π 2 kB dlnðσ ðEÞÞ S¼ kB T dE 3 e E¼EF

(11.4)

σ ðEÞÞ Hence, the enhancement in the energy-dependence of conductivity dlnðdE is required to enhance the Seebeck coefficient, S. That can be achieved by increasing the energydependence of the density n(E), which depends directly on the DOS g(E). A higher dg(E)/dE is provided by 2D, 1D, and 0D systems compared with 3D systems, which must be reflected on S. The maximum value of the Seebeck coefficient for pristine graphene is reported to be smaller than 100 μV/K because of the balance maintained between the gapless character of graphene and its conductivity behavior [65]. By taking advantage of the high mobility of graphene, the high Seebeck coefficient and power factor in graphene are achieved by introducing proper nanostructuring. One more limitation of graphene in its thermoelectric application is its high thermal conductivity. For single-layer graphene (n ¼ 1), the value of thermal conductivity is 4000 W m1 K1, which has a value of 1000 W m1 K1 for graphite (n> 4), implying that the thermal conductivity is strongly dependent on the number of graphene layers [66, 67]. Hence graphene can be considered as one of the best conductors of heat. At room temperature, the MFP of phonons is about 1 mm [68], while the MFP of electrons is about 100 nm [69]. The size of the sample strongly affects the thermal conductivity of graphene [68, 70]. Hence, such a high value of thermal conductivity of graphene can be reduced by making use of defect engineering and proper nanostructuring [71]. Although graphene has major drawbacks for the use of thermoelectric applications, it can be utilized to enhance the thermoelectric performance of other thermoelectric materials. By forming a nanocomposite of thermoelectric materials with graphene, the carrier concentration and mobility are increased, and lattice thermal conductivity can be reduced by the scattering of phonons from the interfaces introduced in the matrix. Various graphene-based nanocomposites have been reported with enhanced zT.

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Xie et al. reported the enhanced zT of 1.25 in Bi0.48Sb1.52Te3 (BST) by the incorporation of graphene [72]. The carrier concentration in the BST alloy increases by the addition of graphene, but the increment in carrier concentration is not that much, so that it can negatively affect the Seebeck coefficient. The thermal conductivity in BST/graphene composite is much lower compared with the pristine BST alloy. The lower lattice thermal conductivity in the BST/graphene composite is due to the effective phase boundary scattering of phonons. Due to the ultrahigh specific surface area of graphene, more interfaces are formed, which scatter a large number of phonons to reduce the lattice thermal conductivity. The lattice thermal conductivity is reduced from 1.1 W/m k in pristine BST alloy to 0.6 W/m k in BST/graphene composite [72]. The presence of graphene at the edge of grains in the composite is shown in Fig. 11.17. The variation of different parameters of BST/graphene composite with different content of graphene used is shown in Fig. 11.17E. Li et al. reported the increment of zT in Bi2Te3/graphene quantum dots (GQDs) hybrid nanosheets [73]. This hybrid composite has a unique structure in which GQDs are homogeneously embedded in the matrix of Bi2Te3 nanosheets. With the introduction of GQDs in the matrix, the carrier mobility is reduced because of scattering arising from the Bi2Te3/ GQDs interface, thereby decreasing electrical conductivity. GQDs play several roles like impurity and electron donor and nucleation center, thus having a complex effect on the electronic transport properties of Bi2Te3/GQDs hybrid composites. The Bi2Te3/GQDs hybrid nanostructure has a significant effect on thermal conductivity. The Bi2Te3/GQDs possess extremely low thermal conductivity value of 0.38 W/m K, which is much lesser compared with the total thermal conductivity of 1.06 W/m K for pristine Bi2Te3. In the hybrid composites, both overall and lattice thermal conductivity decrease, which could be due to the increased scattering of phonons at the Bi2Te3/GQDs interface and grain boundaries. Furthermore, the thermoelectric performance of Bi2Te3/GQDs hybrid nanocomposite can be enhanced by varying the size of GQDs, which could optimize the density and dispersion of GQDs in the matrix of Bi2Te3. The maximum zT of 0.55 was achieved in the Bi2Te3/GQDs hybrid nanocomposite, with the size of GQDs being 20 nm [73]. The illustration of the synthesis process and the formation of Bi2Te3/GQDs hybrid nanocomposite is shown in Fig. 11.18. Zong et al. reported the enhanced zT 1.5 in n-type YbyCo4Sb12 and 1.06 in p-type CeyFe3CoSb12, respectively, by the addition of graphene [74]. The enhancement in zT values in these skutterudites is mainly due to the reduction in lattice thermal conductivity. Skutterudite structures have a reputation of scattering the low-wavelength phonons to reduce the thermal conductivity. To further reduce the thermal conductivity, in addition to merely reducing the grain size, grain boundary engineering is also employed. By the addition of graphene sheets, the grain boundary thermal resistivity is increased up to a factor of 5 compared with the grain boundaries with the absence of graphene. The addition of graphene has a minimal effect on the electronic transport properties of the skutterudites. The presence of graphene in the matrix of CeyFe3CoSb12 and the schematic of the encapsulation of skutterudite by graphene sheets are presented in Fig. 11.19. This figure shows that the matrix particles surrounded and separated by graphene layers. Also, the graphene sheets are interconnected and construct a continuous network along the grain boundaries [74].

Nanostructured thermoelectric materials

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Fig. 11.17 FESEM images of (A) pristine BST alloy, (B, C) BST/graphene composite, (D) and graphene sheets. EDX of areas A and B are presented in (C), showing the variation of carbon content in these areas. (E) Various parameters of BST/graphene composites with different content of graphene used. x is the wt% of graphene used. Adapted from D. Xie, J. Xu, G. Liu, Z. Liu, H. Shao, X. Tan, J. Jiang,H. Jiang, Synergistic optimization of thermoelectric performance in p-type Bi0.48Sb1.52Te3/graphene composite, Energies 9 (2016) 236, with permission from MDPI.

Dong et al. reported the enhanced zT value of 0.7 in PbTe/graphene nanocomposite, and this zT value is six times more than that of pure PbTe [75]. The PbTe/graphene nanocomposites show improved electrical conductivity compared with pure PbTe due to the ultrahigh electron mobility of graphene. Moreover, the addition of graphene and the intercalative structure hinders the growth of PbTe nanoparticles, which increases the concentration of interfaces resulting in the reduced thermal conductivity of the

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Thermoelectricity and Advanced Thermoelectric Materials

Fig. 11.18 Schematic of the synthesis and formation of Bi2Te3/GQDs hybrid nanosheet composite. Adapted from S. Li, T. Fan, X. Liu, F. Liu, H. Meng, Y. Liu,F. Pan, Graphene quantum dots embedded in Bi2Te3 nanosheets to enhance thermoelectric performance, ACS Appl. Mater. Interfaces 9 (2017) 3677-3685, with permission from the ACS.

Fig. 11.19 (A) Low-magnification TEM image of CeyFe3CoSb12/graphene composite. (B, C) High-magnification TEM image of CeyFe3CoSb12/graphene composite. (D) Highmagnification TEM image of the yellow circled area (light gray in print versions) in (A). (E) The wrapping of skutterudite grain by graphene sheets. Adapted from P.-A. Zong, R. Hanus, M. Dylla, Y. Tang, J. Liao, Q. Zhang, G. J. Snyder, L. Chen, Skutterudite with graphene-modified grain-boundary complexion enhances zT enabling high-efficiency thermoelectric device, Energy Environ. Sci. 10 (2017) 183-191, with permission from RSC.

PbTe/graphene nanocomposite. The addition of graphene reduces the thermal conductivity, which increases with the increase in graphene content. However, the thermal conductivity of all the PbTe/graphene nanocomposites with different amounts of graphene used remains well below that of the pristine PbTe. The extraordinary low value of the lattice thermal conductivity is because of the enhanced grain boundary scattering of

Nanostructured thermoelectric materials

No.

Nominal composition

281

Electrical

Hall coefficient

Carrier

Carrier

conductivity

cm3 C–1

concentration

mobility

N (cm–3)

(cm2/Vs)

5.61

1.11’1018

129

18

–(104 Sm–1)

1

PbTe/G-0

0.229

2

PbTe/G-1

0.228

–5.93

1.05’10

135

3

PbTe/G-3

2.34

–2.16

2.89’1018

506

18

4

PbTe/G-5

3.11

–1.06

5.87’10

332

5

PbTe/G-7

4.16

–5.75

1.09’1019

240

6.14

–6.79

18

417

6

PbTe/G-10

9.20’10

Fig. 11.20 FESEM images of (A) fractured bulk sample and (B) powder of PbTe/graphene nanocomposite. The red arrows (light gray in print versions) in (B) show the wrinkles of graphene present. (C) Table showing the different parameters of PbTe/graphene composite at room temperature. PbTe/G-0 is PbTe with 0 wt% graphene, and the rest of the composites are named accordingly. Adapted from J. Dong, W. Liu, H. Li, X. Su, X. Tang, C. Uher, In situ synthesis and thermoelectric properties of PbTe–graphene nanocomposites by utilizing a facile and novel wet chemical method, J. Mater. Chem. A 1 (2013) 12503-12511, with permission from RSC.

phonons on the countless interfaces in PbTe/graphene unique structure as shown in Fig. 11.20A and B [75]. Some room temperature parameters of PbTe/graphene nanocomposites with different content of graphene are depicted in Fig. 11.20C. Li et al. reported ultrahigh thermoelectric performance in Cu2Se with zT of 2.44 by the incorporation of graphene [76]. A frequency disparity is observed between the phonon DOS of cubic Cu2Se and the carbon honeycomb phases. The scattering mechanism of phonons at the interfaces of composite material is provided by such a disparity in the frequency of phonons; moreover, the scattering of phonons significantly reduces the thermal conductivity of the lattice and therefore enhances the thermoelectric performance. Incorporation of graphene in Cu2Se showed almost 50% reduction in the thermal conductivity from 0.8 W/m K in pure Cu2Se to 0.4 W/ m K in Cu2Se/graphene composite [76]. The inclusion of carbon in the matrix and grain boundaries and the different types of scattering processes of phonons at the interface are shown in Fig. 11.21. Kaleem et al. reported the enhanced zT of 0.55 in Bi2Te3/graphene [77] composite and 1.2 in BiSbTe/graphene composite [78]. The addition of graphene to Bi2Te3 increases its electrical conductivity; thus, an increase in electrical conductivity does not have any adverse effect on the Seebeck coefficient, which may be partly credited

282

Thermoelectricity and Advanced Thermoelectric Materials

Fig. 11.21 (A) TEM image showing the presence of graphene at the grain boundary. (B) TEM image showing the inclusion of graphene in the matrix. (C) Schematic diagram showing the two different types scattering processes of phonons: specular reflection and diffuse scattering, at the Cu2Se/graphene interface. Adapted from M. Li, D. L. Cortie, J. Liu, D. Yu, S. M. K. N. Islam, L. Zhao, et al., Ultra-high thermoelectric performance in graphene incorporated Cu2Se: role of mismatching phonon modes, Nano Energy 53 (2018) 993-1002, with permission from Elsevier.

to the potential barrier scattering in combination with the percolation effect [79]. The increase in the effective mass of the charge carriers in Bi2Te3/graphene composites could also increase the Seebeck coefficient [80]. On the other hand, the electrical conductivity in BiSbTe/graphene composite is in contrast to that of Bi2Te3/graphene composite, and it reduces by the addition of graphene [78]. The reduction in electrical conductivity is due to a decrease in carrier mobility because of the increased scattering of carriers from the high specific area of graphene and grain boundaries [81]. This reduction in the electrical conductivity increases the Seebeck coefficient in BiSbTe/graphene composite. The increment and reduction in the electrical conductivity of Bi2Te3 and BiSbTe, respectively, by the addition of graphene might also be attributed to the n-type and p-type behavior of pure Bi2Te3 and BiSbTe alloys. The thermal conductivity in both the composites Bi2Te3/graphene and BiSbTe/graphene is reduced, and this reduction is attributed to the enhanced scattering of phonons at the interfaces and the grain boundaries [77, 78] Wang et al. reported the improved electrical conductivity and Seebeck coefficient in polyaniline (PANI) by the incorporation of graphene [82]. This enhanced electrical conductivity and Seebeck coefficient resulted in the enhancement of power factor, and the power factor of 55 μW/m K2 was obtained in PANI/graphene composite, which is one of the best values for polymer/graphene composites. A slight percolation phenomenon of carriers was observed in the PANI/graphene composites, which may be attributed to the graphene bridge effect on the charge carrier transport. The PANI/graphene composites showed enhanced Seebeck coefficient, and the value increased with the increase in graphene content. The reason for the increased Seebeck coefficient of PANI/graphene composites may be attributed to the amplified ordering degree of PANI molecular chain arrangement. The TEM image of PANI/graphene composite is shown in Fig. 11.22, which indicates that the graphene surface is tightly bound to PANI in the composites [82].

Nanostructured thermoelectric materials

283

Fig. 11.22 The TEM image of PANI/graphene composite. Adapted with permission from L. Wang, Q. Yao, H. Bi, F. Huang, Q. Wang,L. Chen, PANI/graphene nanocomposite films with high thermoelectric properties by enhanced molecular ordering, J. Mater. Chem. A 3 (2015) 7086-7092, with permission from RSC.

11.4

Carbon nanotube (CNT)-based nanocomposite thermoelectric materials

Carbon nanotubes (CNTs) have unique properties, are relatively simple, and can be used for various practical applications. CNTs are of multiple types like single-walled CNTs (SWCNTs), multiwalled CNTs (MWCNTs), and double-walled CNTs (DWCNTs), as shown in Fig. 11.23. Out of all these CNTs, SWCNTs are relatively simpler and can be thought of as the single atomic layer of 2D graphite rolled up into a flawless cylinder [83]. SWCNTs are considered to be metallic or semiconducting [84, 85] having diameter-dependent electrical and optical band gaps [85–87] and extremely high charge carrier mobilities [88]. The metallic and semiconducting behavior of SWCNTs depends on the roll-up vector, and the electronic structure of SWCNTs is denoted by a set of (n,m) indices, which is defined by the chiral angle (α) and magnitude of this roll-up vector, as shown in Fig. 11.24 [89]. Of all the SWCNTs, two-thirds are considered to have a semiconducting electronic structure, and the rest are considered to have a metallic electronic structure. SWCNTs follow the Seebeck coefficient relation presented in Eq. (11.4), which shows that the Seebeck coefficient is directly associated with the DOS near the Fermi level. This equation implies that, for a significant intrinsic Seebeck coefficient, a high curvature within the DOS near the Fermi level is a significant contributing factor. Various early studies showed the Seebeck coefficient of the mixed sample of both metallic

284

Thermoelectricity and Advanced Thermoelectric Materials

Fig. 11.23 Representation of (A) SWCNTs, (B) MWCNTs, and (C) DWCNTs. Adapted from M. Dresselhaus, Y. Lin, O. Rabin, A. Jorio, A. Souza Filho, M. Pimenta, R. Saito, G. Samsonidze,G. Dresselhaus, Nanowires and nanotubes, Mater. Sci. Eng. C 23 (2003) 129-140, with permission from Elsevier.

Fig. 11.24 The chiral indices (n,m) shown by the segment of a graphene sheet related to the SWCNT formed by the rolling of graphene sheet from (0,0) to (n,m) alongside the highlighted roll-up vector to form a cylinder. The chiral indices corresponding to semiconducting SWCNTs (white hexagons), the chiral indices corresponding to metallic SWCNTs (gray hexagons), and the chiral indices corresponding to the semiconducting SWCNTs (green hexagons) represent a distinguished group of commercial SWCNTs produced by the HiPCO process. Adapted from J. L. Blackburn, A. J. Ferguson, C. Cho,J. C. Grunlan, Carbon-nanotube-based thermoelectric materials and devices, Adv. Mater. 30 (2018) 1704386, with permission from Wiley.

Nanostructured thermoelectric materials

285

and semiconducting SWCNTs in the range of 11–65 μV/K [90–95].The later studies show the Seebeck coefficient of the sample containing only metallic SWCNTs in the range 10–20 μV/K, and such a low value of Seebeck coefficient is because the metallic SWCNTs have a relatively low DOS [96, 97]. On the other hand, the sample containing only semiconducting SWCNTs showed the value of Seebeck coefficient in the range 80–160 μV/K [96, 97]. Hence the Seebeck coefficient of the mixed sample of SWCNTs can be increased by increasing the concentration of semiconducting SWCNTs in the network. Semiconducting SWCNTs have relatively lower electrical conductivity compared with the metallic SWCNTs because of the fewer charge carriers present. However, the electrical conductivity in semiconducting SWCNTs can be increased by heavy doping [98, 99], and it also depends on the diameter of SWCNTs. By increasing the width of SWCNTs, the carrier mobility increased, thereby increasing the electrical conductivity [100]. Therefore, to optimize the thermoelectric power factor of SWCNTs, heavily doped semiconducting SWCNTs with appropriate diameter are required. The Seebeck coefficient of SWCNTs is reported to increase with the increase in temperature for metallic, semiconducting, and mixed network of SWCNTs [96, 100, 101]. The thermal conductivity of SWCNTs is considered to be very large, and metallic SWCNTs are predicted to have thermal conductivity value of 6600–9500 W/m K at 300 K, which is comparable to the value of graphene, and such a substantial value results from the more significant MFP of phonons [102, 103]. There are some contradictory studies about the thermal conductivity of graphene and SWCNTs. Some studies predict that the thermal conductivity of SWCNTs is larger than graphene, and as the diameter of SWCNTs increases, its thermal conductivity approaches asymptotically to that of graphene [104, 105]. Other studies predict that the thermal conductivity of SWCNTs is lower than graphene and increases asymptotically as the diameter of SWCNTs is increased [106, 107]. For a single SWCNT, the thermal conductivity increases with the increasing temperature below room temperature, and above room temperature, it starts to decrease with the increase in temperature [108, 109]. For the network of semiconducting SWCNTs, it is observed that the thermal conductivity decreases or remains constant with increasing temperature [100, 110]. Hence for a network of semiconducting SWCNTs, both the electrical conductivity and Seebeck coefficient tend to increase with the rising temperature while the thermal conductivity tends to decrease, which implies that zT should continue the increasing behavior with increasing temperature above room temperature. The addition of CNTs in the matrix of thermoelectric materials forming a nanocomposite can enhance the thermoelectric properties of the materials. The incorporation of CNTs into the ceramic matrix noticeably improved its electrical conductivity and also resulted in a significant reduction in thermal conductivity, thereby improving its thermoelectric performance [111, 112]. Kim et al. reported the maximum zT of 0.85 in Bi2Te3/CNTs nanocomposite, mainly due to the reduction in thermal conductivity [113]. The CNTs were homogeneously dispersed in the Bi2Te3 matrix, as shown in Fig. 11.25, due to the presence of interfacial bonding agents of oxygen atoms on the surface of CNTs. The Bi2Te3/CNTs composite showed increased electrical resistivity due to the newly formed interfaces,

286

Thermoelectricity and Advanced Thermoelectric Materials

Fig. 11.25 (A) Low-magnification TEM image of the Bi2Te3/CNTs composites. (B) HRTEM image showing the CNT embedded in the matrix of Bi2Te3. (C) HRTEM image showing the tip of MWCNT present at the triple point of Bi2Te3 grains in the matrix. (D) HRTEM image showing the roughness of Bi2Te3/CNTs interface. Adapted from K. T. Kim, S. Y. Choi, E. H. Shin, K. S. Moon, H. Y. Koo, G.-G. Lee,G. H. Ha, The influence of CNTs on the thermoelectric properties of a CNT/Bi2Te3 composite, Carbon 52 (2013) 541-549, with permission from Elsevier.

but the mobility of carriers was significantly increased. The increased resistivity increased the Seebeck coefficient. The CNTs in the composite alter the range of energy band gap in n-type Bi2Te3 matrix toward the reduction of carrier concentration in the Bi2Te3/CNTs matrix, thereby increasing the electrical resistivity and Seebeck coefficient [114, 115]. The thermal conductivity is significantly reduced in CNT/Bi2Te3 composite compared with that of the bare Bi2Te3. The thermal conductivity is primarily reduced by the simultaneous lattice phonon dissipation and hot carrier scattering at the newly formed Bi2Te3/CNTs interface. The atoms-ordering change of Bi2Te3 phase at the Bi2Te3/CNT interface further accelerates such behavior, which causes a reduction in thermal conductivity [113]. Nunna et al. reported ultrahigh thermoelectric performance in Cu2Se/CNTs nanocomposite with the maximum zT value of 2.4 [116]. The dispersed CNTs show a high degree of homogeneity in the Bi2Te3 matrix, as shown in Fig. 11.26. With the increase in CNTs content, the grain size of Cu2Se is significantly reduced. The Cu2Se nanoparticles grow on the surface of CNTs, which ensures that the grains are densely surrounding the CNT’s surface and preventing the reagglomeration of CNTs. The Seebeck coefficient is increased in Cu2Se by expanding the content of CNTs with the reduction in electrical conductivity. The thermal conductivity is hampered upon

Nanostructured thermoelectric materials

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Fig. 11.26 (A) Low-magnification TEM image of Cu2Se/CNTs composite in which CNTs are reported by light contrast marked by yellow arrows (light gray in print versions). (B) Low-magnification HAADF image of Cu2Se/CNTs composite displaying the CNTs with a dark contrast marked by red arrows (dark gray in print versions). (C) HRTEM image of CNTs at Cu2Se grain boundaries. These figures show the dense distribution of CNTs in the Cu2Se matrix. Adapted from R. Nunna, P. Qiu, M. Yin, H. Chen, R. Hanus, Q. Song, et al., Ultrahigh thermoelectric performance in Cu2Se-based hybrid materials with highly dispersed molecular CNTs, Energy Environ. Sci. 10 (2017) 1928-1935, with permission from RSC.

the addition of CNTs, and the minimum thermal conductivity value in Cu2Se/CNTs composite is 0.4 W/m K. Such an amount of thermal conductivity is because of the strong scattering of phonons at the Cu2Se/CNTs hybrid interface [116]. Chu et al. reported enhanced zT in Na-doped polycrystalline SnSe by the dispersion of CNTs in the matrix and obtained the maximum zT of 0.96 [117]. Polycrystalline Na0.015Sn0.985Se showed a slight reduction in electrical conductivity on the addition of CNTs due to the decrease in carrier mobility and carrier concentration. During the fabrication process of Na0.015Sn0.985Se, some Na atoms may be left inside the CNTs, and these CNTs can then also absorb holes from Na0.015Sn0.985Se by acting as a Na donor to Na0.015Sn0.985Se and therefore reduce the carrier concentrations. The Seebeck coefficient of Na0.015Sn0.985Se is slightly increased by the addition of CNTs. By the introduction of CNTs, the thermal conductivity is reduced, and the Na0.015Sn0.985Se/CNTs composite showed the minimum thermal conductivity of 0.40 W/m K. The thermal conductivity is reduced because of the scattering of phonons at the new interfaces formed between Na0.015Sn0.985Se and CNTs. The Na0.015Sn0.985Se/CNTs composite also showed the enhanced mechanical properties compared with bare Na0.015Sn0.985Se. The presence of CNTs in the freshly fractured surfaces of Na0.015Sn0.985Se/CNTs composite is presented in Fig. 11.27 [117]. Kim et al. reported the enhanced zT of 0.9 in Bi2(SeTe)3/CNTs composite by the homogeneous dispersion of CNTs in the Bi2(SeTe)3 matrix [118]. Fig. 11.28 shows the uniform distribution of CNTs in the matrix and the implanted CNTs on the Bi2(SeTe)3 matrix grains. By the addition of CNTs, the electrical resistivity increased, thereby increasing the Seebeck coefficient. The resistivity is enhanced by the reduction in carrier concentration and carrier mobility. The new interfaces generated in Bi2(SeTe)3 matrix by the presence of CNTs reduced the carrier mobility due to the scattering of carriers. The thermal conductivity is significantly reduced by the addition of CNTs regardless of the acquisition of Se, and the composite showed the minimum

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Fig. 11.27 FESEM image of Na0.015Sn0.985Se/CNTs composite at different magnifications. Adapted from F. Chu, Q. Zhang, Z. Zhou, D. Hou, L. Wang,W. Jiang, Enhanced thermoelectric and mechanical properties of Na-doped polycrystalline SnSe thermoelectric materials via CNTs dispersion, J. Alloys Compd.741 (2018) 756-764, with permission from Elsevier.

total thermal conductivity value of 0.6 W/m K. The phonon and carrier scattering at the freshly formed Bi2(SeTe)3/CNTs interface and the grain boundaries may be the origin of the low thermal conductivity [118]. Yao et al. reported the enhanced thermoelectric performance in PANI/SWCNTs hybrid nanocomposite [119]. Fig. 11.29 shows the nanocable structures of the PANI/SWCNTs composites showing the bundle of SWNTs coated and enclosed by PANI. The electrical conductivity and Seebeck coefficient in PANI/SWCNTs nanocomposites is much more than that of pure PANI. The nanocomposites show the maximum electrical conductivity and Seebeck coefficient of 1.24 104 S/m and 40 μV/K, respectively. This value of electrical conductivity is more than one order of magnitude, and this value of Seebeck coefficient is more than two orders of magnitude higher compared with the pure PANI. This increment is attributed to the increased charge carrier mobility in the ordered chain structures of the pure PANI [119]. Li et al. reported the improved thermoelectric properties in poly(3,4-ethylene dioxythiophene)/graphene/CNTs (PEDOT/graphene/CNTs) ternary composite [120]. The morphology of the ternary composites and the dispersion of CNTs in these composites are shown in Fig. 11.30. The electrical conductivity in PEDOT increases with the addition of graphene and CNTs, and the electrical conductivity follows the sequence PEDOT/graphene/CNTs ternary composite greater than PEDOT/graphene binary composite greater than pure PEDOT. In ternary composite, the electrical conductivity increased with the increase in SWCNTs content. The electrical conductivity in the ternary composite is up to 40 S/m, which is almost 5.4 times higher than that of pure PEDOT. This improved electrical conductivity may be a result of the construction of an effective electrical network and the formation of ordered alignment structures for the molecules of PEDOT. The electrical conductivity of the composites can thus be enhanced by acid treatment. Furthermore, the acid-treated ternary composite showed electrical conductivity of up to 210 S/m. The binary and ternary composites show enhanced Seebeck coefficient compared with the pure PEDOT because of the molecular conformation transition and the ordered alignment of PEDOT chains. The ternary composite showed the pre- and post-acid treatment power factor of 1.96 and 9.10 μW/m K2, respectively [120].

Fig. 11.28 The dispersion of CNTs in Bi2(SeTe)3 as observed from (A) SEM image and (B) TEM image. (C) Implanted CNTs on the Bi2(SeTe)3 matrix grains. Adapted from K. T. Kim, Y. S. Eom,I. Son, Fabrication process and thermoelectric properties of CNT/Bi2(Se,Te)3 composites, J. Nanomater. 16 (2015) 83, with permission from Hindawi Publishing Corporation.

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Fig. 11.29 TEM images of PANI/SWCNT at different magnifications. Inset of (A) represents the SEM top view of the nanocable. Adapted from Q. Yao, L. Chen, W. Zhang, S. Liufu, X. Chen, Enhanced thermoelectric performance of single-walled carbon nanotubes/polyaniline hybrid nanocomposites, ACS Nano 4 (2010) 2445-2451, with permission from ACS.

Fig. 11.30 FESEM images of (A) pure PEDOT, (B) PEDOT/graphene binary composite, (C, D) PEDOT/graphene/CNTs with 5 and 10 wt% of CNTs. Adapted from X. Li, L. Liang, M. Yang, G. Chen,C.-Y. Guo, Poly (3, 4-ethylenedioxythiophene)/graphene/carbon nanotube ternary composites with improved thermoelectric performance, Org. Electron. 38 (2016) 200-204, with permission from Elsevier.

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11.5

291

Nanocaged thermoelectric materials (Skutterudites and Clathrates)

The thermoelectric materials with nanocage structures are believed to show better Phonon-Glass Electron-Crystal behavior, and the typical examples of these nanocage structures include skutterudites and clathrates. Both types of nanocage thermoelectric structures possess excellent electronic transport properties because of their cubic structure. The nanocages or voids in these thermoelectric materials are filled with foreign (guest) atoms, which then act as independent oscillators. For the large nanocages, the amplitude of these oscillators is more than that of the atomic displacement of structural atoms, and this effect is called the rattling effect. This rattling effect causes the formation of low-frequency resonant modes, which act as traps for low-frequency or heat-carrying phonons thereby decreasing the lattice thermal conductivity. Due to the electropositivity of these rattlers present in the nanocages, the electrical conductivity is also enhanced [27].

11.5.1 Skutterudites This group of nanocage thermoelectric materials possesses the general formula of TX3, where T is the transition metal, primarily Co, Rh, or Ir, and X is a pnictogen, generally P, As, or Sb. The binary skutterudite thermoelectric materials can be filled by an electropositive element A, which may be rare-earth elements [121, 122], alkaline-earth elements [123, 124], or alkali metals [122, 125] to form the ternary skutterudite A2T8X24. The crystal structure of filled skutterudites showing the nanocages to be filled by guest atoms is shown in Fig. 11.31. CoSb3 skutterudites are considered promising thermoelectric materials because of their low electrical resistivity, high carrier mobility, good Seebeck coefficients, and high atomic mass [126, 127]. The only limitation of CoSb3 skutterudites in the thermoelectric applications is their high lattice thermal conductivity [128, 129], Fig. 11.31 Structural representation of a filled skutterudite. Adapted from J. Prado-Gonjal, P. Vaqueiro, C. Nuttall, R. Potter, A. V. Powell, Enhancing the thermoelectric properties of single and double filled p-type skutterudites synthesized by an up-scaled ball-milling process, J. Alloys Compd.695 (2017) 3598-3604, with permission from Elsevier.

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which can be significantly reduced by filling the nanocages with proper guest atoms. Filled CoSb3-based skutterudites possess the lowest lattice thermal conductivity because of the large cages present in these skutterudites; the amplitude of vibration of the guest atoms is amplified, which can then strongly interfere with the low-frequency phonons, thereby causing the reduction in lattice thermal conductivity. The electronegativity difference between the host Sb atom and the guest atom also defines whether the guest atom can serve as appropriate filler in the nanocage or not [130, 131]. The Einstein-like vibrational modes are responsible for the reduction in lattice thermal conductivity in filled skutterudites. These vibrational modes arise from the weak bonding between the host Sb atoms and the guest atoms causing the normal phonon modes with same energies to scatter [132]. A defect-free unfilled CoSb3 skutterudite behaves like a good intrinsic semiconductor having low carrier density on the order of 1016–1017 cm3 [128]. The guest atoms inside the nanocages of CoSb3 are believed to donate their valence electrons into the skutterudite framework, thereby making the system behave as a heavily doped semiconductor with high carrier density on the order of 1020 cm3 [130]. By changing the filling fraction of guest atoms, the electron density in a partially filled CoSb3 skutterudite can easily be adjusted. Shi et al. reported that the partially filled CoSb3 skutterudite realized the enhanced zT of 1.2 compared with the unfilled CoSb3 skutterudite having the zT of 0.5 [133]. The types of guest atoms determine the nature of vibrational frequencies, and the strongest vibrational frequencies are maintained by the alkali atoms [134]. By introducing two or more guest atoms in the nanocages, different vibrational frequencies are produced, which can interfere with the phonons of a vast range of frequencies and thereby cause a significant reduction in lattice thermal conductivity. Such an effect on the lattice thermal conductivity by the multifilling of nanocages was observed by Shi et al., who reported the enhanced zT of 1.7 in Ba0.08La0.05Yb0.04Co4Sb12 skutterudite [135]. The multifilling also helps to optimize the electronic transport properties by increasing the electronic concentration in the skutterudites. The distribution of fillers in CoSb3 matrix, as shown in Fig. 11.32, are the HRTEM images of Ba0.08La0.05Yb0.04Co4Sb12 skutterudite [135]. Meng et al. demonstrated that the simultaneous improvement in the DOS near the Fermi level and the rate of phonon scattering could be obtained due to the coherency strain fields arising from spinodal decomposition in p-type multiple-filled skutterudite La0.8Ti0.1Ga0.1Fe3CoSb12 resulting in the enhanced zT of 1.2 [136]. The coherency strain fields cause a reduction in lattice thermal conductivity due to phonon scattering without having any negative effect on the electrical conductivity. The coherency strain fields always remain in the state of tension due to which the DOS near the Fermi level is increased thereby increasing the Seebeck coefficient. High- and low-magnification SEM images of the multiple-filled skutterudite are shown in Fig. 11.33, and the TEM image shows a lot of rough strain fields in the skutterudite [136]. Garleighi et al. reported the enhanced zT of 1.0 in InxCo4Sb12 single-filled skutterudite by the nanoinclusion of the InSb phase [137]. The In0.04Co4Sb12(InSb)0.05 nanocomposite skutterudite shows high electrical conductivity and significant reduction in the lattice thermal conductivity compared with pure Co4Sb12. The electrical conductivity is improved because of the high mobility of charge carriers

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Filler Co Sb

(B) intensity prosite

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25000 20000 15000 10000 5000 0

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Fig. 11.32 (A) HAADF-STEM image along [001] direction of Ba0.08La0.05Yb0.04Co4Sb12 multiple-filled skutterudite. (B) Illustration of the detailed atomic arrangement of a selected area from (A). (C) A random distribution of guest atoms in the nanocages of the multiple-filled skutterudite indicated by the significant intensity fluctuation among the columns of the guest atoms. Adapted from X. Shi, J. Yang, J. R. Salvador, M. Chi, J. Y. Cho, H. Wang, et al., Multiple-filled skutterudites: high thermoelectric figure of merit through separately optimizing electrical and thermal transports, J. Am. Chem. Soc. 133 (2011) 7837-7846, with permission from ACS.

Fig. 11.33 (A,B) Low- and high-magnification image of La0.8Ti0.1Ga0.1Fe3CoSb12 multiple-filled skutterudite. (C) Bright-field TEM image of the skutterudite. Adapted from X. Meng, W. Cai, Z. Liu, J. Li, H. Geng, J. Sui, Enhanced thermoelectric performance of p-type filled skutterudites via the coherency strain fields from spinodal decomposition, Acta Mater. 98 (2015) 405-415, with permission from Elsevier.

provided by InSb nanoinclusions, and the thermal conductivity is reduced because of the additional scattering of phonons at the InSb nanoinclusions apart from the scattering of phonons by the fillers in nanocages. The partial filling of In and the InSb nanoinclusions also compromise with the bipolar transition [137]. The presence of InSb nanoinclusions in the InxCo4Sb12 skutterudite is shown in Fig. 11.34.

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Fig. 11.34 Low- and high-magnification SEM images of In0.06Co4Sb12-(InSb)0.36 nanocomposite skutterudite. The smaller particles on the surface of larger particles are confirmed as the InSb nanoinclusions by EDX. Reproduced from A. Gharleghi, P.-C. Hung, F.-H. Lin, C.-J. Liu, Enhanced ZT of InxCo4Sb12–InSb nanocomposites fabricated by hydrothermal synthesis combined with solid–vapor reaction: a signature of phonon-glass and electron-crystal materials, ACS Appl. Mater. Interfaces 8 (2016) 35123-35131, with permission from ACS.

Khan et al. reported the highest zT of 1.6 in an unfilled skutterudite without employing the rattling effect by a porous architecture containing different sizes and shapes of randomly oriented pores to scatter the phonons of the wide range of frequencies [138]. The Si- and Te-doped CoSb2.75Si0.075Te0.175 unfilled skutterudite showed a significant reduction in thermal conductivity compared with the pristine sample without any degradation of electrical conductivity. This implies that the decrease in thermal conductivity is mainly by the scattering of phonons causing the drastic reduction in lattice thermal conductivity [138]. The porosity in the unfilled skutterudite is shown in Fig. 11.35. The enhanced thermoelectric properties has been reported in various other singlefilled skutterudites like La0.29Co4Sb12, zT¼ 1.06 [139]; Ca0.31Co4Sb12, zT ¼ 1.15 [140]; Yb0.35Co4Sb12, zT¼ 1.5 [141]; and In1Co4Sb12, zT ¼ 1.5 [142]; and multifilled skutterudites like La0.68Ce0.22Fe3.5Co0.5Sb12, zT¼ 1.15 [56]; Li0.08Ca0.18Co4Sb12, zT ¼ 1.18 [57]; Al0.3Yb0.25Co4Sb12, zT ¼ 1.36 [58]; Ce0.5Yb0.5Fe3.25Co0.75Sb12, zT ¼ 0.93 [143]; Nd0.6Yb0.4Fe3CoSb12, zT ¼ 1.02 [144]; and Co-free skutterudite Ce0.9Fe3.75Ni0.25Sb11.9Te0.1, zT ¼ 1 [145].

11.5.2 Clathrates Similar to skutterudites, the clathrate structure also consists of an open framework with nanocages or voids, which are filled by guest atoms. These guest atoms induce the rattling effect and thereby help in the reduction of lattice thermal conductivity [146]. In clathrates, Al, Si, Ga, Ge, Sn, etc. atoms are tetrahedrally coordinated with the nanocages of different sizes. These nanocages are large polyhedrons with the atoms situated at the vertices of these polyhedrons. Clathrates are classified into various types like type-I clathrates, type-II clathrates, type-III clathrates, type-VII clathrates, type-VIII clathrates, type-XI clathrates, and twisted clathrates. The classification of clathrates are based on shape and number of cages. Two main types of clathrates to be discussed are type-I and type-II clathrates. The crystal structure of

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Fig. 11.35 SEM images of the sample (A) before annealing. (B) After annealing, pores appear on the surface marked by white circles. (C) Nanosized and microsized pores observed along the grain boundaries (D) shows the lack of free Te and/or pores in CoSb2.875Si0.125 skutterudite after annealing. Adapted from A. U. Khan, K. Kobayashi, D.-M. Tang, Y. Yamauchi, K. Hasegawa, M. Mitome, et al., Nano-micro-porous skutterudites with 100% enhancement in ZT for high performance thermoelectricity, Nano Energy 31 (2017) 152-159, with permission from Elsevier.

type-I clathrate is shown in Fig. 11.36. Type-I clathrates consist of two polyhedrons and are represented by the formula U2V6E46 where U and V are the guest atoms trapped in two different polyhedrons E20 and E24, while E represents the elements Al, Si, Ga, Ge, Sn, etc. of the framework. The rattling of the guest atoms in the clathrate nanocages occurs similar to that of skutterudites causing the strong scattering of phonons, thereby resulting in the low lattice thermal conductivity. The most substantial vibration amplitudes are shown by the guest atoms in the cage E24 [147]. In the case of type-II clathrates, the crystal structure consists of the largest (having 28 vertices and 16 faces) and smallest clathrate forming polyhedrons. Type-II clathrates have the general formula MXE136 and contain 8 large and 16 small polyhedrons These polyhedrons can be filled by the same or different types of guest atoms. M represents the guest atoms of more than one kind, and these include Na, K, Rb, Cs, Ba, Sr, Ca, Cl, Br, I, Eu, P, Te, Li, and Mg; X can range from 0 to 24; and E represents the atoms of Si, Ge, Sn, Al, Ga, etc. X ¼ 0 denotes the unfilled nanocage, which is the unique property of the type-II clathrates to allow the partial filling of polyhedrons, contrasting to type-I clathrates, which allows only complete filling. The partial filling of type-II clathrates helps in adjusting the electrical properties [148].

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Fig. 11.36 Representational image of type-I clathrate viewing the two types of cages, the 20-vertex cages shown in red (dark gray in print versions) and the 24-vertex cages are shown in blue (light gray in print versions). Adapted from F. Sui, S. M. Kauzlarich, Tuning thermoelectric properties of type I clathrate K8–x BaxAl8+xSi38–x through Barium substitution, Chem. Mater. 28 (2016) 3099-3107, with permission from ACS.

Sun et al. have reported an excellent zT value of 1.14 in type-I clathrate Ba8Ga16Ge30, and this enhanced zT is attributed to both the improved power factor and reduced lattice thermal conductivity [149]. The enhanced boundary phonon scattering and the alloying effect are the reasons for the lower lattice thermal conductivity of Ba8Ga16Ge30 clathrate. The lower lattice thermal conductivity is the reason for overall thermal conductivity in Ba8Ga16Ge30 clathrate, and the total thermal conductivity of 0.7 W/m K was observed. Other factors that may be responsible for the lower thermal conductivity are the abundant grain boundaries, nanosized domains, lattice defects, and the large number of dislocations. These defects are formed by the high pressure employed for the synthesis process [149]. Various other type-I clathrates have been reported with enhanced zT such as K6.5Ba1.5Al9Si37, zT¼ 0.4 [150]; Ba8Cu5(Si,Ge, Sn)41, zT¼ 0.43 [151]; Sr7.92Ga15.04Sn0.35Ge30.69, zT¼ 1.0 [152]; Ba8Cu6Si16Ge24, zT ¼ 0.55 [153]; and Ba7.7Yb0.3Ni0.1Zn0.54Ga13.8 Ge31.56, zT ¼ 0.91 [154]. Utsunomiya et al. reported a high zT of 0.82 for K9Ba15Al31Ga8Sn97 and 0.57 in K9Ba15Al38Sn98 type-II clathrates due to low lattice thermal conductivity [155]. The K9Ba15Al31Ga8Sn97 clathrate showed lower carrier mobilities compared with K9Ba15Al38Sn98 clathrate because of the presence of large defect densities. The lattice thermal conductivity is much smaller in K9Ba15Al31Ga8Sn97 compared with K9Ba15Al38Sn98, maybe because of the strong rattling effect of the guest atoms in the nanocages. In addition to the strong rattling effect, the alloy-disorder phonon scattering in K9Ba15Al31Ga8Sn97 might also be the reason for decreased lattice thermal

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conductivity [155]. Kishimoto et al. have also reported zT of 0.43 in type-II clathrate (K, Sr)24(Ga, Ge)136 [156]. This type-II clathrate showed higher carrier mobility because of small inertial mass, but the reduction in lattice thermal conductivity was not significant, perhaps because the rattling effect was not as strong [156].

11.6

Nanowire thermoelectric materials

The impact of low-dimensionality on thermoelectric materials has already been discussed in Section 11.1. It has also been considered why the 1D nanowires and nanotubes can show better thermoelectric performance compared with their 2D nanosheet counterparts because of the stronger quantum confinement effect. In this section, the thermoelectric behavior of 1D nanowires is discussed in detail. Considering the size of nanowires, the more pronounced quantum confinement effect is observed in long thin nanowires [157, 158]. It has been reported that the metals such as Ni [159, 160] and Co [160, 161], IV–VI compounds such as PbTe [162, 163], the isotropic materials such as Si [164], oxides such as SiO2 or In2O3, and III-V and II-VI semiconducting compounds [165, 166] all tend to form nanowire. Multiple 1D nanostructures, including nanowires [157, 158], nanotubes [167], and nanolines [168], can quickly be produced by materials like Bi. In the case of Bi, it is possible to make various thorough predictions about the electronic properties of Bi nanowires based on the features of bulk Bi because the Bi nanowires up to the diameter of 7 nm preserve the same rhombohedral structure with corresponding values of lattice constants as bulk Bi [83]. The diameter of Bi nanowires has a strong correlation with its electronic properties because bismuth is a semimetal possessing small band overlap energy. Sufficiently reducing the diameter of Bi nanowires increases the band gap and decreases the carrier density. By further reducing the width of nanowires, the semimetallic behavior of Bi nanowires vanishes and is transformed into a semiconductor, as illustrated in Fig. 11.37.

a

b

c Semiconductor

Semimetal

Fig. 11.37 Schematic diagram of the electronic transition from semimetal to semiconductor in Bi nanowires. As the diameter decreases, the highest valence sub-band at the T-point moves down, and the lowest conduction sub-band at the L-point moves up in energy. (A) Nanowire diameter greater than 50 nm, (B) nanowire diameter equivalent to 50 nm, and (C) nanowire diameter less than 50 nm. Adapted from M. Dresselhaus, Y. Lin, O. Rabin, A. Jorio, A. Souza Filho, M. Pimenta, R. Saito, G. Samsonidze,G. Dresselhaus, Nanowires and nanotubes, Mater. Sci. Eng. C 23 (2003) 129-140, with permission from Elsevier.

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This transition from semimetal to semiconductor behavior allows us to take advantage of the strong anisotropic electronic properties of Bi for use in a new class of applications. One more advantage of Bi for thermoelectric applications is the heavy mass of ions, which are highly adequate for the scattering of phonons and long MFPs of carriers, which help maintain electronic properties. Also by alloying Bi isoelectronically with Sb, high mobility of carriers is obtained thereby providing more significant opportunity in manipulating the properties of bismuth-related nanowires for thermoelectric and other applications [157, 158]. It has been predicted that, for same nanowire diameter, the Bi1 xSbx alloy nanowires show better thermoelectric performance than bare Bi nanowires [169]. Also, as the mobilities of p-type Bi nanowires are much lower compared with their n-type counterparts, their capabilities can be improved by alloying with Sb [157, 158]. The variation of Seebeck coefficient for nanowires of different diameters and Sb content concerning temperature is shown in Fig. 11.38. From the figure, it is clear that the Seebeck coefficient increases by increasing Sb content and decreasing the diameter of nanowires [170]. Boukai et al. reported the enhanced zT of 1.0 for Si nanowires of 20-nm width, which is 100-fold greater than the bulk Si with zT of 0.01 [9]. In the case of nanowires, the diameter is smaller than the MFP of phonons and much larger than that of electrons and holes. This causes a strong scattering of phonons thereby causing a potential reduction in the lattice thermal conductivity without affecting the electronic transport and Seebeck coefficient. Phonon drag and strong quantum confinement in Si nanowires are also assumed to improve the Seebeck coefficient [9]. Some studies have been reported in which the diameter of nanowires is not small enough to show strong quantum confinement, but the thermal conductivity is still compact by the nanostructure. For example, SiGe nanowires showed reduced thermal conductivity of 1.2 W/m K resulting in the enhanced zT of 0.46 compared with bulk Si for the nanowires of 100-nm width [171], and the Bi2Te3 nanowires were reported to show the minimum thermal conductivity of 1.37 W/m K for the nanowire diameter of 200–400 nm [172].

0

65-nm Bi 40-nm Bi 65-nm Bi0.06Sb0.06 45-nm Bi0.05Sb0.05

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bulk Bi S (µV/K)

Fig. 11.38 The plot of the Seebeck coefficient as a function of temperature for Bi and Bi0.95Sb0.05 nanowire with different diameters. Adapted from Y.-M. Lin, O. Rabin, S. Cronin, J. Y. Ying,M. Dresselhaus, Semimetal–semiconductor transition in Bi1xSbx alloy nanowires and their thermoelectric properties, Appl. Phys. Lett. 81 (2002) 2403-2405, with permission from AIP.

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Moon et al. presented the thermoelectric power factor measurement on single Ge/Si core-shell nanowires with Ge core diameters varying from 11 to 25 nm and found that the Seebeck coefficient of the nanowires with Ge core diameters of 11 nm still shows the behavior of bulk Ge [173]. It was also revealed that the suppression of ionic impurities and the surface charge scattering could improve the carrier mobility in individual nanowires. The similarity between the behavior of Seebeck coefficient of nanowires and bulk Ge indicates that the electronic structure of nanowires is still bulk-like, and the nanowire does not show significant quantum confinement effect at room temperature [173]. The quantum confinement effect has been experimentally reported in some nanowires like InAs nanowire with a diameter of around 20 nm by Tian et al. [174]. The quantum confinement effect in InAs nanowires significantly enhanced the power factor making the InAs nanowires eligible for thermoelectric applications. Wu et al. reported sizeable thermoelectric power factor enhancement in InAs nanowires that is greater than the value predicted by the single-band bulk model [175]. This enhancement is attributed to quantum-dot-like states that form in non-uniform nanowires because of the interference between 0D resonances and propagating states [175]. Fardy et al. synthesized the lead chalcogenide (PbS, PbSe, PbTe) nanowire thermoelectric materials with a nanowire diameter of up to 40–200 nm [176]. PbSe nanowires showed a significant increment in the scattering of phonons compared with bulk PbSe at low temperatures. A smaller diameter of nanowire is expected to effectively scatter the phonons at higher temperatures because of the deterioration of bulk scattering processes when the MFP of phonons becomes less than the diameter of nanowire. Due to the phonon scattering, the thermal conductivity of PbSe nanowires is significantly reduced compared with the bulk PbSe by up to three orders of magnitude [176]. Liang et al. reported zT of 0.12 at room temperature for PbSe nanowires [177]. The PbSe nanowires showed similar Seebeck coefficient as that of the bulk PbSe but a significant reduction in thermal conductivity. The significant decrease in thermal conductivity is attributed to the strong scattering of phonons [177]. Taggart et al. reported the enhanced Seebeck coefficient and electrical conductivity in PEDOT nanowires of 40–90 nm diameter [178]. The PEDOT nanowires showed higher Seebeck coefficient and electrical conductivity compared with PEDOT thin films because of greater electron mobility in PEDOT nanowires by a factor of 3 [178].

11.7

Quasi-one-dimensional (Q1D) organic thermoelectric materials

In recent years, organic compounds have attracted more attention from researchers as they are less expensive, largely availability, and mainly environment-friendly. These organic compounds show more diverse and unusual properties compared with their organic counterparts [179]. The organic compounds have the potential for use in thermoelectric applications. The organic compound thin film of p-type poly(3,4-ethylene dioxythiophene) (PEDOT) by doped by poly(styrene sulphonate) (PSS) has shown a zT of 0.42 [180]. High zT up to 1.0 has also reported in PP-PEDOT/Tos films

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[181]. But unfortunately the organic compounds have been weakly investigated for their use in thermoelectric applications. Among organic compounds, the quasi-onedimensional (Q1D) organic compounds have fascinating properties. The Q1D organic compounds do not show strong anisotropy but form a new class of crystals. Q1D organic crystals are formed from the linear chains or stacks of molecules packed into a 3D lattice. The mechanical properties of the Q1D organic crystals show anisotropic behavior because the interaction in the longitudinal direction of the chains is much weaker compared with the interaction along the chains. The Q1D crystals have needle-like shape with the length of 6–20 nm and thickness of 20–60 μm [182]. As a result of this anisotropy, the mechanism of conduction between the chains of these Q1D crystals is hopping-like, making it difficult because of the minimal overlap of electronic wave functions; along the chains, it is band-like, made easier by the significant overlap of wave functions [183]. The carriers are primarily moving along the strings where they were formed and seldom jump from one chain to another. The transversal hopping motion can be neglected in the first approximation, and the charge carriers are considered to be moving in a 1D conduction band analogous to the movement of charge carriers along the chains. Only the lowest band is sufficient to be found in the weak field. The zT in some Q1D organic crystals, including those of TTT2I3 [179] and of TTT(TCNQ)2 [184], has been predicted. The physical model has been applied to Q1D organic crystal by Casian et al. [185], investigating only carrier mobility and electrical conductivity. They have considered the two mechanisms of electron-phonon interaction and also the carrier scattering from impurities. The first mechanism is similar to the deformation potential, which is determined by the disparity of the transfer energy W of an electron between the nearest neighbor molecules along the chain caused by acoustic vibrations. The coupling constant of this first interaction mechanism is proportional to the derivative W0 of the transfer energy W of the electron concerning the intermolecular distance. The second mechanism is similar to the polaron similar, which is determined by the disparity of the polarization energy of molecules neighboring the conduction electron caused by the same acoustic vibrations. The coupling constant of this second interaction mechanism is proportional to the mean polarizability α0 of the molecule. The interference between these electron-phonon interactions under certain conditions is possible. As a result, for some states in the conduction band, the two interactions appreciably compensate each other, and for such states, the relaxation time as a function of carrier energy will have a maximum value. Moreover, the mobilities of carriers in these states will also have increased values, which are favorable for thermoelectric applications. This model also predicts the increased Seebeck coefficient at room temperature for Q1D organic crystals [183]. Casian et al. have also predicted the violation of Wiedemann-Franz law in Q1D organic crystals [186]. By considering the two interaction mechanisms and the scattering on impurity discussed before, a substantial violation has been found in the Wiedemann-Franz law. For a considerable interval of Fermi energy, the Lorentz number is diminished because of the two main reasons. One is by decreasing the conduction band width, thermal conductivity decreases faster compared with the electrical conductivity, and the other reason is due to the strong correlation between the

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relaxation time and carrier energy. As the Lorentz number becomes strongly dependent on purity of crystal, in comparison to the ordinary materials, it may be reduced by up to 10 times and even more. This reduction in the Lorentz number can significantly reduce thermal conductivity, which is favorable for the increment of thermoelectric figure of merit zT. The Lorentz number in tetrathiotetracene-iodide (TTT-I) is predicted to be reduced by 1.6 times compared with its usual value, and after the optimization of carrier concentration, zT of 1.4 is expected [186].

11.8

Conclusion

Low-dimensional thermoelectric materials like quantum dots, nanowires, and nanosheets are considered as the efficient thermoelectric materials compared with their bulk counterparts. So, the nanostructuring of thermoelectric materials is regarded as a promising solution to enhance the efficiency of these materials and to convert waste heat into electricity. The electrical transport properties are optimized by nanostructuring, and the thermal conductivity is significantly reduced by the scattering of phonons at the grain surface. The scattering of phonons is greatly enhanced in nanocomposites due to the presence of various phases, which cause a drastic reduction in thermal conductivity. All the families of thermoelectric materials show improved thermoelectric efficiency via the nanocomposite formation. The introduction of graphene and CNTs in the matrix of thermoelectric materials is also an efficient way to promote the scattering of phonons from the newly formed interfaces, thereby reducing the thermal conductivity without affecting the transport of charge carriers. The nanocaged thermoelectric materials (skutterudites and clathrates) show efficient thermoelectric properties upon the filling of the nanocages by suitable guest fillers. Q1D organic thermoelectric materials are that class of rarely investigated thermoelectric materials that have been predicted to show fascinating thermoelectric properties, and more studies need to be focused on that class of thermoelectric materials.

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Ranber Singh Department of Physics, Sri Guru Gobind Singh College, Chandigarh, India

12.1

Introduction

The use of fossil fuels such as oil, natural gas, coal, etc. for energy production in automobiles, airplanes, thermal power plants, and manufacturing industries causes global warming and environmental degradation [1, 2]. Moreover, resources of fossil fuels are limited in nature. Reducing the use of fossil fuels and finding their replacements is one of the major concerns of today’s energy challenge. One of the important parts of the solution to today’s energy challenge is the use of renewable energy resources that are present in abundance in nature, for example, wind energy, solar energy, geothermal energy, and hydro energy. The use of these energy resources has increased over the last couple of decades [3–7]. In fossil fuel-based thermal power plants, automobiles, manufacturing industrial plants, and nuclear power plants, a large amount of heat is wasted. This waste heat dissipated to the environment leads directly or indirectly to global warming as well as polluting the atmosphere. Developing and deploying sustainable energy technologies can reduce this waste heat dissipation [8]. Converting this waste heat into electricity through the use of thermoelectric (TE) materials is another important part of the solution to today’s energy challenge [9]. In the last couple of decades, TE power generation from waste heat has received considerable attention [10, 11]. Thermoelectricity is an intrinsic property of all solid materials. The electrical and heat currents in a solid material are intercoupled, which give rise to TE phenomena. There are three types of TE phenomena known as TE effects, which describe TE properties of a solid, namely (1) Seebeck effect: a phenomenon that a temperature difference across a thermocouple creates an electric potential; (2) Peltier effect: a phenomenon that an electric potential across a thermocouple creates a temperature difference; and (3) Thomson effect: a phenomenon that reversible heating or cooling within a conductor takes place when there is both an electric current and a temperature gradient. In most materials, these TE effects are too small to be useful. However, there are some narrow band gap semiconductors that have sufficiently strong TE effects [10, 11]. The efficiency of a TE device depends upon the dimensionless figure of merit (zT) of the TE materials used to make that device. In the last couple of decades, huge research efforts have been devoted to enhance the zT of materials [8, 10–21]. Reducing electrical resistivity and thermal conductivity will enhance the zT of a material. Thermoelectricity and Advanced Thermoelectric Materials. https://doi.org/10.1016/B978-0-12-819984-8.00011-4 Copyright © 2021 Elsevier Ltd. All rights reserved.

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However, electrical resistivity and thermal conductivity are intercoupled. It is a great challenge to increase zT of TE materials by tuning the electrical conductivity and thermal conductivity independently [13–15]. The narrow band gap semiconducting materials have been demonstrated with relatively larger values of zT as compared to metals and large band gap insulating materials [10, 11, 22]. To achieve higher zT of TE materials is one the motivations for the research in TE materials. Based upon the understanding of TE effects and properties of solids, several approaches including the design of TE modules, searching for new materials with high values of zT, nanostructuring, tuning electronic band structure, and thermal conductivity have been developed to enhance the performance of TE devices [16, 17, 23, 24]. Applications of TE materials cover a wide range of spectrum including simple coolers and power generators to highly sophisticated temperature control systems used in missiles and space vehicles. In this chapter, we discuss advances in the designing, assembly, and applications of TE materials.

12.2

Thermocouple and TE modules

A typical simplest TE device is a junction formed from two different metals or semiconductors, one containing positive charge carriers (p-type semiconductor) and the other negative charge carriers (n-type semiconductor). This system of two different conducting materials is known as a thermocouple. Each conducting material within a thermocouple is known as thermoelement. When an electric current is passed in an appropriate direction through a thermocouple, the charge carriers move away from one junction to the other, thus cooling one junction and heating the other. This phenomenon is known as a Peltier effect. Similarly, a temperature difference across two junctions of a thermocouple causes charge carriers to flow away from one junction to the other junction. This phenomenon is known as a Seebeck effect. The thermocouples in power generation mode (Seebeck effect) and in refrigeration mode (Peltier effect) are schematically illustrated in Fig. 12.1. A thermocouple in power generation mode produces a temperature-dependent voltage as a result of the Seebeck effect. This voltage can be interpreted as a measure of temperature. Thus, the simplest typical applications of a thermocouple are temperature measurement, heat sensing, and the detection of radiations. Thermocouple sensors are widely used in thermostats and as flame sensors in safety devices. There are several types of metallic thermocouples that have been characterized as different types depending upon their composition materials and their applications. A tiny thermovoltage in microvolts per unit Kelvin of temperature difference between two conductors (or semiconductors) of a thermocouple is generated. A number of TE elements are connected electrically in parallel and/or in series to make a practical TE device. Connecting thermocouples in series increases the voltage capability, while connecting them in parallel increases the current capacity. Such an array of thermocouples is called a thermopile or a TE module. These TE modules can also be cascaded in the form of a multistage design. A typical multistage thermocouple consists of two ceramic substrates that are used to provide insulation to the

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Fig. 12.1 Schematic illustration of a thermocouple for power generation (Seebeck effect) and a thermocouple for heating or cooling (Peltier effect). The heat absorption or dissipation at a junction of a thermocouple depends upon the direction of current in the Peltier effect. A TE module consisting of a number of thermocouples for power generation has also been illustrated.

thermoelements. A TE module for power generation constructed by connecting a number of thermocouples in series has been shown schematically in Fig. 12.1. Using the Peltier effect, a TE module can also be designed as a heat pump that pumps heat from one side to the other side. It is known as a TE cooler or Peltier cooler. Its components are the same as that of a TE generator, but the design of the components may differ. TE modules have many applications in refrigeration, temperature

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control, thermal management, etc. We will discuss these TE power generators (TEG) and TE coolers (TEC) in detail in latter sections of this chapter.

12.3

Power and efficiency calculation of a TE device

The potential of a TE material for its applications in TE modules is determined by its thermopower (P) and zT defined as P ¼ σS2 zT ¼

σS2 T S2 T ¼ κ e + κ l ρðκ e + κ l Þ

(12.1) (12.2)

Here, σ is electrical conductivity, ρ is electrical resistivity, S is the Seebeck coefficient, κe is electrical thermal conductivity, and κl is lattice thermal conductivity of a material at temperature T. The larger the values of P and zT, the better the material for TE applications. Thus, the materials with low electrical resistivity and thermal conductivity are required for making the TE modules. In other words, TE materials need to be good electric conductors and good thermal insulators at the same time. The efficiency (η) of a TE device for power generation is determined as the ratio of output energy produced to the total amount of heat induced. It depends upon the values of P and zT of TE materials used to make a TE device. There are many approximate models to estimate the values of P and zT of TE materials. The value of P depends on S and σ of a TE material. The S is defined as the generated thermovoltage per unit temperature gradient to which a material is exposed. Conventionally it is positive for p-type semiconductors and negative for the n-type semiconductors. Quantitatively, the S is related to the energy derivative of energy-dependent electrical conductivity (σ(E)) taken at Fermi energy EF given as [22, 25]
 ðπkB Þ2 T d½ ln ½σðEÞ S¼ 3e dE E¼EF

(12.3)

where kB is the Boltzmann constant, e is the electron charge, h is the Planck’s constant, n is the charge carrier concentration, m* is the effective mass of the charge carrier, and T is the temperature in Kelvin. The (σ) is given as 1 σðEÞ ¼ ¼ enðEÞμðEÞ ρ

(12.4)

where μ is the mobility of charge carriers. Using this mobility and concentration dependent expression of σ, the expression for S can be written as S¼


 ðπkB Þ2 T 1 dnðEÞ 1 dμðEÞ + 3e n dE μ dE E¼EF

(12.5)

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Thus, S can be enhanced by increasing μ(E) and/or n(E). For degenerate semiconductors [25], the expression for S is given as S¼

∗ 8π 2 kB 2 m T  π 2=3 3eh2 3n

(12.6)

From the previous expressions, we notice that the S and σ depend on charge carrier concentration. Increasing carrier concentration increases σ but decreases S. Thus, it is not possible to have high S and σ at the same time. The charge carrier concentration has to be optimized to get the maximum value of thermopower. This is typically optimized through doping of narrow band semiconducting materials to adjust the carrier concentration. The high power factor is always desired to achieve high values of zT. In addition to high values of power factor, the low thermal conductivity is required for high TE performance of TE materials. Both electrons and phonons contribute to the thermal conductivity of materials. Increasing the carrier concentration also increases the thermal conductivity. It is hard to tune one property without changing the other. The peak values of zT exist for carrier concentrations in the narrow band gap semiconductors. Theoretically, the Seebeck coefficient and transport properties of charge carriers (electrons and holes) are generally computed using the semiclassical Boltzmann transport theory. The σ and κe are computed as στ and κτe within the constant τ approximation in the BoltzTrap code [26]. The τ for charge carriers can be computed from the electronic band structures using the deformation potential theory [27, 28] given as τ¼

pffiffiffiffiffi 2 2π ħ4 Ci 3ðEbi Þ2 ðm∗ kB TÞ3=2

(12.7)

where m*, T, Ci, Ebi , respectively, are the effective mass, temperature in Kelvin, elastic constant, and deformation potential for the deformation direction along ith axis of a crystalline solid. The uniaxial deformation potentials of electrons and holes are calculated by calculating the changes in the conduction band minimum (CBM) and valence band maximum (VBM) under the deformation along the ith axis. The deformation potential of a cubic crystal is defined as b Ebi ¼ Eba ¼ ∂E ∂a a0 for the deformation direction along a axis. Here, a0 is the lattice constant at equilibrium. The superscript b stands for CBM or VBM of a material. The elastic properties can be computed using the thermo_pw package [29] interfaced with the Quantum-Espresso Package. Using the τ computed by Eq. (12.7), the σ and κe can be computed from σ/τ and κe/τ computed using the BoltzTrap code as mentioned earlier. The lattice thermal conductivity (κ l) can be calculated using Slack’s equation given as [30] kl ¼

Aγ Mδ1=3 θ3D γ 2 N 2=3 T

(12.8)

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    0:228 where Aγ ¼ 2:43  108 = 1  0:514 + is a constant dependent on the 2 γ γ Gruneisen parameter (γ) [31, 32]. The M, δ, θD, and N, respectively, are average ˚ 3, Debye temperature in Kelvin, and the atomic mass in amu, volume per atom in A number of atoms in the primitive unit cell. More accurately, the lattice thermal conductivity is computed by solving the phonon Boltzmann transport equation (BTE) as implemented in the ShengBTE code [33]. It is based on the second-order harmonic and third-order (anharmonic) interatomic force constants combined with an iterative self-consistent algorithm to solve the BTE. Thus, P and zT of a material are computed as a function of charge carrier concentration and temperature. The efficient TE materials are doped narrow band gap semiconductors with high power factors and low thermal conductivity. Carrier concentration of these semiconductors can be easily controlled by doping. Optimization of charge carrier concentration is important for optimizing the TE performance of a material. The efficiency of TE devices is determined by Carnot efficiency [(TH  TC)/TH] and the zT of TE materials used to make TE modules. The theoretical maximum value of efficiency [10] of a TE generator is given as 2 3

pffiffiffiffiffiffiffiffiffiffiffiffi 7 TH  TC 6 6 1 + zT  1 7 η¼ (12.9) 4 p ffiffiffiffiffiffiffiffiffiffiffi ffi T TH C5 1 + zT + TH where TC and TH are the temperatures in Kelvin of cold and hot sides of a TE device, respectively. Thus, efficiency of a TE generator is determined by the temperature difference between cold side and hot side, and zT of the TE materials used to make a TE device. The energy conversion efficiency of TE devices has significantly improved in recent times. Similarly, the theoretical maximum value of efficiency of a TE refrigerator is given as η¼

TH TH  TC



2pffiffiffiffiffiffiffiffiffiffiffiffi T 3 C 1 + zT  TH 7 6 4 pffiffiffiffiffiffiffiffiffiffiffiffi 5 1 + zT + 1

(12.10)

TE devices are heat pumps that pump heat from one side to the other. Their efficiency is limited by the Carnot efficiency. The efficiency of commercially available TE refrigerators is quite low compared with traditional vapor-compression refrigerators. The average value (zT ) of figure of merit of a TE device is computed as zT ¼

ðSp  Sn Þ2 T ½ðρp κp Þ1=2 + ðρn κ n Þ1=2 2

(12.11)

where T is the average temperature between the hot and cold surfaces. The subscripts “n” and “p” denote properties related to the n- and p-type semiconducting TE materials, respectively. Using this average value of zT , the average efficiencies of TE are computed.

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319

Advances in the assembly and scalable manufacturing of TE materials

The TE materials are able to convert the waste heat into electricity and vice versa. However, their zT, manufacturing cost, and scalability are still important issues for their practical applications. The practical realization of TE materials in devices is limited by their low zT, toxicity, and cost of manufacturing. To produce commercially viable TE devices, the balance between TE performance and the cost of TE devices must be carefully examined. If the cost of synthesizing a certain TE material is high, its zT value needs to be enhanced to make a useful TE material. The zT of some TE materials may be low, but their manufacturing cost can be crucial to make commercially viable TE devices. Recently, cost-effective synthesis methods such as solution process have been developed to synthesize novel TE nanomaterials [48]. Scalable manufacturing of TE materials is important for enhancing their TE performance and applications. There are different strategies of scalable manufacturing of TE materials such as alloying, doping, nanostructuring, additive manufacturing, etc. [12, 49–51]. The materials that have emerged as excellent TE materials in different temperature ranges and have drawn significant interest from the researchers are Bi-, Pb-, and Sn-based chalcogenides, skutterudites, oxides, half-Heusler alloys, electrically conducting polymers, nanomaterials, superlattice structures, etc. One of the primary challenges in developing advanced TE materials is to decouple the electrical conductivity, thermal conductivity, and Seebeck coefficient of materials. Nanostructuring is one of the approaches that is able to decouple electrical and thermal conductivities of a material [14]. Heat-carrying phonons are scattered by the grain boundaries of the nanostructures in the material, while the electrical conductivity is maintained almost the same. This method has significantly improved the zT of conventional TE materials. Another approach is the synthesis of TE materials with tailored electronic structures. This includes the synthesis of high purity materials that are then intentionally doped to tailor their electronic band structures. Other approaches to synthesize TE materials include chemical routes that can directly induce nanostructuring in the materials thereby reducing their thermal conductivity through phonon scattering. In the last two decades, there has been tremendous progress in the theoretical understanding, computations, designing new assemblies, discovery of new materials, and development of new synthesis methods of TE materials. Several outstanding materials with zT of around 2 or greater than 2 have been reported [34–40, 43, 45– 47]. The maximum values of zT of several experimental materials are given in Table 12.1. In addition to high values of zT and low cost of manufacturing, the mechanical strength and thermal stability are also crucial for real applications of these materials. The conventional processes such as hot press, cold press, spark plasma sintering, plasma-activated sintering, and others require TE-alloyed powders as raw materials to form TE bulk materials. These synthetic methods of alloyed materials require very long time of combination reactions. A rapid and scalable synthetic method using selective laser melting (SLM) of powder bed has been developed to synthesize TE

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Table 12.1 In last couple of decades, a large number of TE materials with zT around 2 or greater than 2 have been successfully synthesized. Material

zT (at T K)

p-type or n-type

Reference

Bi2Te2.79Se0.21 Pb0.975Na0.025S3%CdS βZn4Sb3 Pb0.98Na0.02Se2%HgSe PbS4.4%Ag PbSe0.998Br0.0022%Cu2Se Bi0.5Sb1.5Te3 AgPbmSbTe2+m Bi2Te3/Sb2Te3 Cu2Sex%CNT SrTiO3/SrTi0.8Nb0.2O3 Pb0.98Na0.02Te8%SrTe SnSe SnSe1xBrx

1.2 (357) 1.3 (923) 1.4 (750) 1.7 (973) 1.7 (850) 1.8 (723) 1.86 (320) 2.2 (800) 2.4 (300) 2.4 (1000) 2.4 (300) 2.5 (923) 2.6 (923) 2.8 (773)

n p p p n n p n n p n p p n

[34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47]

CNT, carbon nanotube. Note: We have listed some of these materials in this table.

materials [52, 53]. The zT values of these SLM-synthesized materials are comparable with that of bulk materials obtained using conventional melting technology [52, 53]. SLM-synthesized method therefore opens up a novel way for rapid, scalable, and lowcost manufacturing of TE materials. Kim et al. [40] have developed a method for growing relatively inexpensive TE materials with improved efficiency. They showed a significant improvement in zT in bismuth telluride samples by quickly squeezing out excess liquid during compaction. This method introduces grain boundary dislocations in the material in a way that leads to a substantially lower lattice thermal conductivity but avoids degrading its electrical conductivity. The multiscale microstructures of Bi2Te3-based materials by hot deformation method lead to significantly enhanced zT of 1.2 at 357 K [34]. The nonequilibrium processing of hole-doped PbTe and SrTe leads to high level of Sr alloyed into the PbTe matrix [45]. It results into widening of the band gap and convergence of the two valence bands of PbTe, which boosts its power factor with maximal value more than 30 μW cm1 K2. The best composition is found to be PbTe8%SrTe. The maximum value of zT of 2.5 at 923 K has been achieved for this material. PbSe is much less expensive than PbTe, but it has inferior TE performance due to a smaller value of zT. Recently, a p-type Pb0.98Na0.02Se2%HgSe has been successfully synthesized, which has relatively high values of P  20μW cm1 K2 at 963 K. This enhancement has been attributed to a combination of high carrier mobility and the early onset of band convergence in the Hg-alloyed samples. These large values of P combined with a decrease in thermal conductivity gives a value of zT of 1.7 at 970 K [37]. The n-type PbSe0.998Br0.002 2%Cu2Se exhibits maximum zT of 1.8 at

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723 K [39]. The enhanced value of zT is due to the fact that Cu2Se enhances the electrical conductivity of n-type PbSe but decreases its thermal conductivity. Due to the ultralow thermal conductivity of layered SnSe crystals, the record high values of zT of 2.6 at 923 K has been recently reported [46]. The bromine doping of SnSe maintains its low thermal conductivity in layered structure of SnSe material but increases the charge carrier concentration [47]. This results in further enhancing its zT to 2.8 at 773 K in n-type SnSe crystals along the out-of-plane direction. Recently, carbon-based organic TE materials have also received considerable attention due to their various merits, such as low cost, low thermal conductivity, easy processing, and good flexibility [11]. However, their TE efficiency is limited to approximately 5%10%. Their TE efficiency need to be enhanced for their commercial applications.

12.5

Nanostructuring of TE materials

Nanostructuring is one of strategies to decouple thermal and electrical transport by introducing energy filtering and new scattering mechanisms [54–56]. The materials that consist of nanoscale constituents are known as nanostructured materials. This strategy has attracted increased research attention as it has great potential to improve performance and applicability of TE materials [56]. Through a rational designing of nanostructure of a TE material, its electrical conductivity and thermal conductivity can be tuned independently to enhance its TE performance. There exist bottom-up and top-down approaches for nanostructuring of a material. It can be divided into one-dimensional (1D), two-dimensional (2D), and threedimensional (3D) by synthesizing a material in the form of nanowires (1D), thin films or monolayers (2D), and assembly of various nanostructures or nanoscale lithography (3D). This has been schematically illustrated in Fig. 12.2. Nanostructures in TE materials allow effective phonon scattering of a significant portion of the phonon spectrum, but phonons with long mean free paths remain largely unaffected. These heat-carrying phonons with long mean free paths can be scattered by controlling and fine-tuning the mesoscale architecture of nanostructured TE materials. The size effect on the transport properties of TE materials has been reviewed and discussed in detail by Mao et al. [57]. It has been observed that the size effect on thermal transport of good bulk TE materials is relatively weak. However, in some other materials, the size effect on the transport properties is relatively quite large [58, 59].

12.5.1 Advances in bulk nanomaterials In the last couple of decades, TE nanostructured materials have been extensively investigated [54–57, 60]. The zT values of TE materials have been enhanced in nanostructured materials compared with their conventional bulk counterparts. The TE nanocomposite materials include the formation of a material from nanomaterials or inclusion of nanograins into the main material [60]. This results in enhancing the power factor and/or the reduction of thermal conductivity. The typical methods are

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Fig. 12.2 Schematic illustration of nanostructuring of a material. Nanostructuring of a bulk leads to bulk nanomaterials, thin films, monolayers, or nanowires. In bulk nanomaterials, the conduction of charge carriers is in three dimensions (3D). However, in thin films or monolayers, it is in 2D, and in nanowire-based materials, it is in 1D.

the powder metallurgy and melt metallurgy method. The powder metallurgy method is to prepare nanocomposite materials from presynthesized nanoparticles by physical or chemical routes with fast powder compaction to avoid grain growth. The melt metallurgy method usually applies melting and quick cooling to obtain small grain size or even amorphous materials. The embedding of metallic nanocrystalline grains into the matrix of a main material increases the carrier concentration as well as decreases the thermal conductivity. For example, in the PbSAg nanostructured system, the Ag nanodomains are embedded into the PbS crystal structure [38]. These Ag nanodomains contribute to block phonon propagation as well as provide electrons to the PbS host semiconductor. The PbSAg nanocomposites exhibit reduced thermal conductivities, higher charge carrier concentrations, and mobilities than pure PbS material. A significantly improved value of zT of 1.7 at 850 K in PbSAg nanostructured material has been achieved [38].

12.5.2 Advances in thin films and monolayer stacked structures Among low-dimensional materials, the 2D TE materials have also been a subject of intense studies. In the early 1990s, Hicks and Dresselhaus suggested a new approach to enhance zT of TE materials by introducing the size effects in the form of thin film

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superlattice structures [61]. This has led to the discovery of new materials with zT greater than 1 [42, 62, 63]. There are a large number of 2D materials theoretically predicted and/or experimentally synthesized as promising TE materials [64–68]. Some 2D materials show negative correlation between σ and κ [64]. For example, it has been observed that, as the thickness of SnS2 nanosheets decreases, the σ increases, whereas κ decreases. This leads to an enhanced zT about 1000 times the zT of single-crystal SnS2 [64]. Two-dimensional materials in the form of monolayers are a new class of promising low-dimensional TE materials for TE applications [64–68]. The van der Waals heterostructures can be formed by stacking monolayers of same and/or different materials. The in-plane heterostructure can also be grown by combining two materials of nearly same lattice parameters. These materials have extreme anisotropic transport properties both along stacking direction as well as in the stacking plane. Recently, carbon-based materials such as graphene, graphene nanomesh, carbon nanotube (CNT), graphene, and nanocomposites of CNT, graphene and polymers have also received considerable interest for TE applications [11, 69, 70]. Main advantages of these materials are large electrical conductivity, flexibility, and large mechanical strength. Their main drawback is their large thermal conductivity that prevents the application of these materials as TE materials in their original forms. However, by introducing isotopes, vacancies, nanoholes, dislocations, or grain boundaries, the thermal conductivity of these can be significantly reduced [71– 75]. The interaction between metal Cu and multiwalled CNTs leads to the growth of Cu2Se/CNT hybrid materials [43]. A record-high zT of 2.4 at 1000 K has been achieved in these hybrid materials. The 2D TE materials including monolayers and carbon-based nanocomposites have been discussed in detail in the previous chapters.

12.5.3 Advances in nanowires The nanowire-based materials have good electrical conductivity but reduced lattice thermal conductivity due to phonon scattering at the surface and interfaces [58, 59]. Thus, nanowires are promising TE materials at the nanoscale. Recent reviews on the TE properties of nanowires have presented recent advances in the experimental synthesis and TE performance of nanowires [58, 59]. Recently, several new techniques have been developed to synthesize nanowires of various semiconducting materials along different crystal directions with varying sizes, cross-sections (circle, hexagon, square), surface roughness, as well as core-shell structures [76]. The enhancement in the zT values of nanowire-based materials compared with bulk counterparts have been reported in the literature [77–79]. By varying the size and doping levels of Si nanowires, an approximately 100-fold enhancement in the zT value has been achieved compared with that of bulk Si over a broad temperature range [77]. The TE nanowires are the potential candidates to make micro/nanosized TE generators [80–83]. Recently, it was shown that SiGe nanowire-based TEGs can harvest 7.1 μW cm2 at a temperature of 200°C [82].

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12.5.4 Advances in quantum-confined TE materials In early 1990s, Hicks and Dresselhaus suggested a new approach to enhance zT of TE materials by introducing the size effects in the form of QWire or QW superlattice structures [61, 84]. If the effective de Broglie wavelength of charge carriers in a material is comparable to its characteristic thickness in a certain direction, the quantum size effects drastically modifies the energy dispersion relations of charge carriers. These quantum-confined materials along with their electronic density of states have been schematically shown in Fig. 12.3. The sharp spikes in the density of states of charge carrier in quantum-confined systems lead to the enhancement in the power factor [85]. Additionally the interfaces in these nanostructured materials lead to the scattering of heat carrying phonons and consequently the decrease in the lattice thermal conductivity. There is also phonon confinement effects in these materials that lead to further decrease in the lattice thermal conductivity. The p-type Bi2Te3/Sb2Te3 QW superlattices have been observed with an enhanced zT  2.4 [42]. The TE properties of n-PbTe/p-SnTe/n-PbTe QW superlattice decreases monotonically with decrease in thickness of p-SnTe QW [86]. The TE devices made of PbSeTe-based QD superlattice materials have been demonstrated to produce larger cooling effects relative to the bulk counterparts [62]. The Ge0.5Si0.5/Si QD superlattices have significantly reduced thermal conductivity with a peak value shifted toward the high temperatures compared with bulk counterparts [87]. This reduction in the thermal conductivity in Si/Ge QD superlattices has been attributed to the increased physical roughness at the interfaces, which creates additional phonon-resistive processes beyond the interfacial vibrational mismatch [88, 89].

Fig. 12.3 Schematic illustration of superlattice structures of quantum confined TE materials. In the lower panels, the electronic density of states for a 2D quantum well (QW), a 1D quantum wire (QWire), and a 0D quantum dot (QD) are also schematically illustrated.

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12.6

325

TE power generators

A TE generator (TEG) refers to a solid-state TE device that directly converts heat into electricity. The source of heat can be solar energy, geothermal energy, or the waste heat produced in automobiles, thermal power plants, industrial manufacturing plants, human body heat, etc. The working principle of a TEG is based upon the Seebeck effect. That is why a TEG is also sometimes called a Seebeck device or Seebeck generator. Maintaining a temperature difference across the two sides of a TEG generates thermovoltage. A schematic design of a TEG is shown in Fig. 12.4. A practical TEG consists of a heat source, heat exchangers, TE modules, a heat sink, and assembly components. The ceramic plates are normally used as heat exchangers. It is one of the crucial parts of a TEG. The efficiency of heat exchangers is detrimental in the coefficient of performance of a TEG. Another important part of a TEG is the TE module consisting of a number of alternating p- and n-type semiconducting pillars that are thermally parallel to each other and electrically connected in series. This TE module is sandwiched between two ceramic plates (heat exchangers). A TEG acts as a heat pump, which pumps heat from the hot side to the cold side. The heat exchanger connected to a heat source absorbs heat from the heat source and then transfers it to the hot side of a TE module. The temperature difference between the hot side and cold side of the TE module give rise to the thermovoltage, which makes charge carriers move from the hot side to the cold side. In this process, the heat is transferred by the TE modules to the cold side. The heat exchanger connected to the

Fig. 12.4 Schematic illustration of a TE power generator. It consists of a heat source, heat exchangers, TE modules, a heat sink, and assembly components. Maintaining a temperature difference across the two sides of a TEG generates thermovoltage.

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cold side transfers heat to a heat sink so that the cold side remains at some nearly constant temperature. The efficiency of a TEG is given as [90] ηTEG ¼ ηHE  ηTE  E

(12.12)

where ηHE is the efficiency of heat exchangers, ηTE is the efficiency of TE modules, and E is the ratio of heat passed through TE modules and heat passed from the hot side to the cold side. In recent years, the efficiency of TEG devices has improved considerably because of the advances in the TE materials and high-performance optimum designs. The zT value of TE materials is now approaching a relatively high value of 3 [46, 47], which is sufficient to make relatively efficient TE devices. Other approaches to enhance the efficiency of TE devices include the improvements in the efficiency of heat exchangers and innovative designs for reducing the thermal resistance and enhancing the heat transfer. Recently, a new design consisting of segmented TE materials and asymmetrical semiconductor pillars with varying crosssectional area along the length has been demonstrated with 19%–21% enhanced output power [91]. Depending upon the type of heat source, the TEGs are divided into the following categories.

12.6.1 Wearable TEG Recently, wearable flexible TEGs have gained increasing attention due to their potential to power wearable and biointegrated devices [48, 92]. A wearable TEG is a specially designed TEG that is capable of converting human body heat to electricity. It can be designed to generate power of microwatts to several milliwatts. It is desirable in the upcoming technology of so-called Internet of Things to power wearable electronic devices and other healthcare monitoring devices [93, 94]. However, it is still a great challenge to design wearable TEGs that can produce large enough power. Several designs of wearable TEGs have been presented in the literature by researchers. One of the promising designs consists of TE modules sandwiched between two polydimethylsiloxane plates and aluminum oxide ceramic heads as heat spreaders [95]. Recently, a design consisting of a substrate of flexible printed circuit board and TE modules made of p-type and n-type Bi2Te3-based powder material have been demonstrated to generate an open-circuit voltage of 37.2 mV at ΔT ¼ 50 K [96]. The use of copper foam as a heat sink enhances the output power of wearable TEGs [97]. One of the main drawbacks of a wearable TEG is the small temperature difference created by body heat, which limits its practical applications. Introducing a local solar absorber in the design of a wearable TEG can increase the temperature difference and consequently the output power of the TEG [98].

12.6.2 Solar TEG It is a solid-state TE device that generates electricity from concentrated sunlight. It is also called STEG. To construct an STEG, a heat exchanger that is able to absorb heat from the concentrated solar energy and transfer it to the hot side of TE modules is

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required. Model simulations of STEGs show that STEGs have potential to convert solar energy at greater than 15% efficiency [99]. Future developments will depend on the TE materials that can provide higher operating temperatures or higher material efficiency. For example, an STEG with zT ¼ 2 at 1500°C would have an efficiency of 30.6% [100]. Recently, a new design of an STEG consisting of segmented TE materials and asymmetrical semiconductor pillars with the varying cross-sectional areas along the length shows 19%–21% enhanced output power [91]. The hybrid solar TE photovoltaic generators consisting of a PV cell placed directly on top of a TEG leads to an efficiency gain of 4%–5% with respect to the sole PV case [101].

12.6.3 Automotive waste heat harvesting TEG It is a specially designed solid-state TE device that generates electricity from the waste heat dissipated to the atmosphere through an exhaust pipe and engine coolant radiator. It is also called ATEG. About two-thirds of the heat produced in automotives is dissipated to the atmosphere as waste heat in exhaust and engine coolant. Installing ATEGs with the exhaust pipe and engine heat radiators, some of the waste heat can be harvested [102, 103]. This will enhance the fuel efficiency and reduce the emission of greenhouse gases. The electricity generated by the ATEGs can be stored and/or utilized for various electrical inputs of an automobile. Recently, ATEGs have received great attention from the automotive industry because they can be used for waste heat recovery to meet new standards of automotive emissions. The efficiency of an ATEG is limited by the zT value of the TE material in the TE modules as well as the efficiency of heat exchangers on the cold and hot sides of TE modules. The heat exchanger connected to the hot side of TE modules must be able to efficiently capture heat from the exhaust gases and transfer it to the hot side of the TE modules. The heat sink connected to the cold side of TE modules must be able to efficiently remove the heat. The efficiency of these ATEGs is yet to be enhanced greater than 5%. With the recent advances in the values of zT and synthesis processes of TE materials, the efficiency of ATEGs is expected to be enhanced above 5%. A concentric cylindrical ATEG consisting of an annular TE module and a heat pipe to enhance the heat transfer has been proposed [103]. The simulations with this model of an ATEG system shows a higher power output. The water inside this concentric cylindrical ATEG produces a higher power output of 29.8 W compared with the gas-inside system, which could only produce a power output of 4.8 W.

12.6.4 Radioisotope TEG It is designed to convert the heat released by the decay of a suitable radioactive material into electricity. It is also known as RTEG. The first RTEG was invented in 1954 by scientists Ken Jordan and John Birden at Mound Laboratories. The main component of an RTEG is a container of a radioactive material that produces heat through radioactive decay. TE modules are placed in the walls of the container, with the outer ends of the TE modules connected to a heat sink. The temperature difference between the container and the heat sink generates electricity.

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A radioactive material used in an RTEG must have long enough half-life so that it will produce heat at a relatively constant rate for a reasonable amount of time. Depending on the half-life of the radioactive material, the typical RTEGs are active for several decades. Radiations produced by the radioactive decay must be of the type that are easily absorbable and transferable into thermal energy. These RTEGs are mostly useful in the situations where fuel cells, batteries, or other conventional generators are not suitable to provide power for a long time economically. They have been used to power spacecrafts, the Mars science laboratory, the scientific experiments left on the Moon by the crews of Apollo missions, and other uncrewed remotely controlled facilities. Since the lifespan of an RTEG depends mainly on the half-life of a radioactive material, therefore using a suitable radioactive material an RTEG can be designed to power interstellar precursor missions and interstellar probes for over 1000 years or so [104].

12.6.5 Geothermal TEG The conventional geothermal power generators are based on the conversion of geothermal energy to mechanical work and then to electricity. The geothermal TEGs can also be designed to directly convert geothermal heat to electricity [105, 106]. A geothermal TEG system has been built and tested with different TE materials to generate power of over 160 W with a temperature difference of 80°C [107]. The cost of this GTEG system is close to that of a photovoltaics system for same output power generations.

12.7

Peltier cooler

It is a solid-state semiconductor TE device that directly converts electricity to thermal energy. Similar to a TEG, a Peltier cooler consists of heat exchangers, TE modules, and a heat sink. However, the shape and design of these components may be significantly different than those of a TEG. It is also called as Peltier device, solid-state refrigerator, Peltier heat pump, and TE cooler (TEC). It functions as a heat pump that pumps heat from the cold side to the hot side with the consumption of electrical energy. While a TEG requires a heat source for its operation, a TEC requires a DC power supply. The direction of DC current through TE modules determines the direction of heat flow. It means it can also be used as a heater or a temperature controller. A schematic design of a TEC is shown in Fig. 12.5. The heat exchanger on the cold side absorbs heat from the system to be cooled. This absorbed heat is then transferred by the TE modules to the hot side. A heat sink is connected to the hot side so that it remains at an ambient temperature. The crosssectional areas and lengths of p- and n-type semiconductor pillars in TE modules are carefully designed to maximize the performance of a TEC. The heat transferred from the cold side to hot side is given as Q ¼ ΠIt

(12.13)

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where Π is the Peltier coefficient of the material used in TE modules at a given temperature, I is the current through the TE modules, and t is the time. The TEC devices are desirable for applications such as portable coolers, precise temperature controllers, cooling charge-coupled devices, and other electronic components whose operation are highly dependent upon the temperature. TEC devices are also used in spacecraft and satellites to absorb the heat of direct sunlight and then dissipate it from the shaded side. In recent years, the efficiency of TEC devices has improved considerably because of the advances in the TE materials and high performance optimum designs. The construction of solar energy-based TECs is also becoming popular. In these devices, the solar energy is used to generate the electrical energy either using photovoltaic-based solar panels or solar TEGs. The generated power is then used to operate a TEC. This kind of device is desirable in remote areas where there is no electrical supply from the grid and in the zero-energy buildings. The TECs can also be directly integrated into the building structure. The solar energy and/or waste heat of domestic applications can be used to generate electricity, which will then operate TEC air conditioners integrated into the building structure. A model of such building-integrated TECs have been recently proposed [108]. The solar TECs driven by the power generated using photovoltaic-based solar panels are soon expected to be an integral part of zero-energy buildings [109].

Fig. 12.5 Schematic illustration of a Peltier cooler. Similar to a TEG, it consists of heat exchangers, TE modules, a heat sink, and assembly components. It functions as a heat pump that pumps heat from the cold side to the hot side with the consumption of electrical energy. While a TEG requires a heat source for its operation, a Peltier cooler requires a DC power supply. The direction of DC current through TE modules determine the direction of heat flow.

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Advantages and disadvantages of TE devices over the conventional mechanical devices

12.8.1 Advantages of TE devices 12.8.1.1 Direct heat to electricity conversion TE devices convert heat directly into electricity and vice versa. They are comparatively less complex in design compared with some other mechanical devices. Many conventional energy conversion technologies require intermediate steps to convert heat into electricity. For example, in thermal and nuclear power plants, the heat is first converted to the mechanical energy of turbines, which then generates electricity in a generator. The intermediate steps add to losses in the form of waste heat.

12.8.1.2 No moving parts The TE devices have no moving parts, therefore they have quiet operation unlike mechanical systems. They can be used for several years without any maintenance requirements. For example, the Voyager 1 spacecraft RTEG is still operational after more than 40 years without any maintenance or repairs. They exhibit very high reliability due to their solid-state construction. They can be operated in any orientation as well as situation such as zero gravity. Thus, they are used in space missions and aerospace probe applications.

12.8.1.3 Compact size and light weight The TE modules for cooling, heating, or electrical power generation are relatively smaller in size and lighter in weight compared with the similar mechanical systems. It is much easier to design TE devices according to specific requirements. These modules can also be made in a variety of sizes and configurations based upon the requirements.

12.8.1.4 Wide range of heat sources The TEGs do not have any kind of restrictions on the heat sources. They can be designed for all kinds of heat sources. They are also highly scalable to output power levels from microwatts to larger than kilowatts.

12.8.1.5 Same TE module can be used for heating or cooling A TE module can be used to either heat or cool a specific region depending upon the polarity of the applied DC power. This feature eliminates the necessity of providing separate heating and cooling functions within a given system. In a TEC, the flow of heat from one side to the other is controlled by the applied DC current. It means a TEC can also be used for precise control of temperature.

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12.8.1.6 Spot cooling or heating In some local cooling or heating problems, they are only solutions. With a TE cooler (heater), it is possible to cool (heat) only a specific component or area, thereby eliminating the need to cool (heat) an entire package or enclosure.

12.8.1.7 Environmental friendly Conventional refrigeration systems use chlorofluorocarbons or other chemicals for their operation. These chemicals are extremely harmful to the atmosphere. They are responsible for the depletion of the ozone layer of the atmosphere of Earth. The TECs do not use gases of any kind. On the other hand, TEGs generate electricity from the waste heats from the sun, geothermal, automotives, thermal power plants, and industrial manufacturing units, etc. This waste heat otherwise leads to global warming and pollution of the atmosphere. Thus, TE devices are environmental friendly.

12.8.2 Disadvantages of TE modules Although there are several advantages of TE devices over mechanical systems, they also have many disadvantages. Due to these disadvantages, TE devices are yet not so popular in the market where other alternate mechanical devices are available. The TE devices are expensive compared with other available mechanical systems. The TEGs have higher values of cost per watt of power production. They require a relatively constant heat source for their operation. The efficiency of a TE device is very poor compared with other easily available mechanical systems. The design and engineering expertise required to effectively use TE devices in applications is not adequate. It has also been shown that the TEGs display a reduction in power generation performance after several cycles of operation [110]. This reduction in the power generation performance is primarily due to the increase of the internal resistance of the TEGs.

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Index Note: Page numbers followed by t indicate tables. A Absolute methodology, 57–58 ALD. See Atomic layer deposition (ALD) Alloying, 124–128 Amorphous molecular films, 199–200 Anharmonicity, 31–32 Arc melting, 76 Assembly of thermoelectric (TE) materials, advantages of, 319–321 Atmosphere pressure, 85 Atomic layer deposition (ALD), 216 Automotive waste heat harvesting thermoelectric generator (TEG), 327 B Ball milling mechanical alloying, 84 mechanical grinding, 84 Band gap, 49–50 Bilayer heterojunction devices, 213–214 Binary chalcogenide-based nanocomposites, 269–272 Bismuth telluride nanoparticles, 170–171 Boltzmann transport equation (BTE), 108–109 Bulk heterojunction devices, 214 C Carbon nanotubes (CNTs), 171, 283–290 Carrier concentration, 12 Carrier density, 143–146, 220–225 CBM. See Conduction band minimum (CBM) Chain-polymers, 206 Characterization, 58–59 Chemical doping, 124–128 Chemical potential, 50 Chemical vapor deposition (CVD), 93–95, 205 Clathrates, 294–297 CNTs. See Carbon nanotubes (CNTs)

Comparative method, 58–59 Computational materials design decreasing thermal conductivity, 111–113 enhancing seebeck coefficient, 109–111 Conduction band minimum (CBM), 110 Conjugated polymers, 206–207 Controlling the nanostructures, 74 Conventional solvothermal synthesis, 86 Copolymers, 206 CVD. See Chemical vapor deposition (CVD) D Decreasing thermal conductivity, 111–113 Defect creation, 130–131 Density functional perturbation theory (DFPT), 33–34 Density functional theory (DFT), 38–41, 108 Density functional theory (DFT) + U method, 41–43 Density of states (DOS), 110 Design. See Computational materials design DFPT. See Density functional perturbation theory (DFPT) DFT. See Density functional theory (DFT) Diamagnetism, 200 Dip coating, 204 Direct method, 31–33 Doping/alloying, 95–97 Doping concentration, 50 Doping organic semiconductors, 212 DOS. See Density of states (DOS) Double-Heusler compounds, 181 Drop casting, 203 Dynamic cation off-centering, 113 E Effective mass, 46–48 Electrical conductivity, 13, 55–56, 169–170 methods for, 67–68 Electrodeposition, 90–92

340

Electronic transport free electron theory, 22–25 semiclassical theory, 25–29 Energy harvesting, 233 Energy saving, 73 Enhancing Seebeck coefficient, 109–111 F Ferromagnetism, 201 Field-effect transistor (FET), 222–224 Figure of merit (FOM), 3–4, 11–14, 21, 106, 117–118, 163–164 challenges, 146–149 Four probe methods, 67 Free electron theory, 22–25 Functional hybrid materials, 211 G Geometric phase analysis (GPA), 75–76 Geothermal thermoelectric generator (TEG), 328 GQDs. See Graphene quantum dots (GQDs) Grain boundaries, 112 Graphene, 240–246 nanocomposite thermoelectric materials, 276–282 Graphene quantum dots (GQDs), 278 H Half-Heusler compounds, 177–181 Heat transport, 29–31 High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), 77–79 High mobility oxides, 164 High-pressure synthesis techniques, 90 High resolution transmission electron microscopy (HRTEM), 75–76 Homopolymers, 206 HRTEM. See High resolution transmission electron microscopy (HRTEM) Hybrid materials, 211–212 Hybrid thermoelectric materials bismuth telluride nanoparticles, 170–171 carbon nanotubes, 171 inorganic and organic molecules, 171 metal nanoparticles, 169–170

Index

I Indium-tin-oxide (ITO), 164 Induction melting, 76–79 Inkjet printing, 205–206 Inorganic molecules, 171 Inorganic semiconductors, 196, 198 Ionic intercalation, 87–88 L Laser flash method, 61–62 Lattice thermal conductivity, 113 Layered cobalt oxides, 165 Layered materials, 237–239 Layered thermoelectric materials, 86–89 LB. See Longmuir-Blodgett (LB) Lead chalcogenide-based nanocomposites, 272–273 Levitation melting, 79–80 Liquid exfoliation, 86–89 Longmuir-Blodgett (LB), 204–205 Low-dimensionality, 261–268 M Magnesium silicide (Mg2Si), 182–183 Magnesium sulfide (Mg2S), 90 Magnetic properties, 200–201 Manganese silicide, 181–184 Material quality factor, 4 Materials efficiency, 11–14 history, 7–11 Mechanical alloying, 84 Mechanical grinding, 84 Mechanical properties, 201–202 Melting method arc melting, 76 induction melting, 76–79 levitation melting, 79–80 melt-spinning, 80–83 self-propagation high-temperature synthesis (SHS), 80 solid-state reaction, 74–76 zone melting, 74 Melt-spinning, 80–83 Mercaptohexanoic acid (MHA), 169–170 Mercaptopropionic acid (MPA), 169–170 Metal chalcogenides, 171–173 Metal nanoparticles, 169–170

Index

341

Metal oxide frameworks (MOFs), 252–253 Mg2S. See Magnesium sulfide (Mg2S) Mg2Si. See Magnesium silicide (Mg2Si) MHA. See Mercaptohexanoic acid (MHA) Microwave-assisted solvothermal method, 86 MLD. See Molecular layer deposition (MLD) Mobility test, 220–225 MOFs. See Metal oxide frameworks (MOFs) Molecular crystals, 199 Molecular layer deposition (MLD), 216 Molecule structure, 218–220 Monolayer stacked structures, 322–323 MPA. See Mercaptopropionic acid (MPA) Multiwalled carbon nanotubes (MWCNTs), 202 MXenes, 251–252

classes, 198–200 doping, 212 vs. inorganic semiconductors, 198 properties, 200–202 structures, 213–214 Organic thermoelectric materials (OTEs), 208 quasi-one-dimensional (Q1D), 299–301 Oxidative polymerization, 205 Oxide materials high mobility oxides, 164 layered cobalt oxides, 165 perovskite-based oxides, 165 ZnO-based oxides, 166

N

Parallel technique, 60 Paramagnetism, 201 PDI. See Poly dispersity index (PDI) PEDOT. See P-type polymer (PEDOT) PEDOT-PSS. See Poly (3,4-ethylenedioxythiphene)-poly styrene sulfonate (PEDOT-PSS) Peltier cooler, 328–329 Peltier effect, 6 Perovskite-based oxides, 165 PGEC. See Phonon glass electron crystal (PGEC) Phase engineering, 128–130 Phonon band structure, 29–31 Phonon glass electron crystal (PGEC), 4–5, 56–57, 118–119 Phonon lifetime, 34–35 Phonon liquid electron crystal (PLEC), 56–57 Phonon mass fluctuation scattering, 112 Phonons density functional perturbation theory (DFPT), 33–34 direct method, 31–33 heat transport, 29–31 thermal expansion coefficient, 36 thermodynamical properties, 35–36 Phosphorene, 249–251 Physical vapor deposition (PVD), 205 PLEC. See Phonon liquid electron crystal (PLEC) Poly dispersity index (PDI), 207–208

Nanocage, 291–297 Nanocomposites binary chalcogenide-based nanocomposites, 269–272 carbon nanotubes (CNTs), 283–290 graphene, 276–282 lead chalcogenide-based nanocomposites, 272–273 SiGe-based nanocomposites, 273–276 Nanostructured materials, 151–156 Nanostructures, 120–124, 245, 262–263 bulk nanomaterials, 321–322 monolayer stacked structures, 322–323 nanowires, 323 quantum-confined TE materials, 324 thin films, 322–323 Nanowires, 297–299, 323 Nowotny Chimney Ladder (NCL), 182–183 N-type organic thermoelectric polymers, 216–218 O Optical properties, 200 Organic-inorganic hybrid materials, 210–212 Organic-inorganic superlattice structures, 215–216 organic semiconductor structures, 213–214 Organic molecules, 171 Organic semiconductors, 195–206 challenge, 225–226

P

342

Poly (3,4-ethylenedioxythiphene)-poly styrene sulfonate (PEDOT-PSS), 169–170 Power factor, 165 Power generators, 325–328 PRTRM. See Pulse radiolysis time-resolved microwave conductivity (PRTRM) P-type polymer (PEDOT), 216–217 Pulsed technique, 61 Pulse radiolysis time-resolved microwave conductivity (PRTRM), 224–225 PVD. See Physical vapor deposition (PVD)

Q Q1D. See Quasi-one-dimensional (Q1D) QHA. See Quasiharmonic approximation (QHA) Quantum-confined thermoelectric (TE) materials, 324 Quantum confinement, 153, 215 Quasiharmonic approximation (QHA), 36 Quasi-one-dimensional (Q1D), 299–301 R Radial heat flow method, 59–60 Radioisotope thermoelectric generators (RTG), 4, 327–328 Resistance temperature transducers (RTD), 57 Rigid band approximation (RBA), 49 RTG. See Radioisotope thermoelectric generators (RTG) S SAED. See Selected area electro diffraction (SAED) Seebeck coefficient, 12–13, 69, 233–234 Seebeck effect, 2–3, 5–6 Selected area electro diffraction (SAED), 75–76 Self-propagation high-temperature synthesis (SHS), 80 Semiclassical theory, 25–29 SHS. See Self-propagation high-temperature synthesis (SHS) SiGe-based nanocomposites, 273–276 Single-layer device, 213

Index

Single phonon mode relaxation time (SMRT), 30 Single-walled carbon nanotubes (SWCNTs), 283 Skutterudite antimonides, 174–177 Skutterudites, 291–294 SMRT. See Single phonon mode relaxation time (SMRT) Solar thermoelectric generator (TEG), 326–327 Solid-state reaction, 74–76 Solution synthesis atmosphere pressure, 85 conventional solvothermal synthesis, 86 microwave-assisted solvothermal method, 86 Solvent vapor annealing (SVA), 204 Spin coating, 203 Steady state methodology, 63–64 Steady-state trap-free space charge limited current (TF-SCLC) method, 222 Superlattices, 112–113, 215–216, 239 SVA. See Solvent vapor annealing (SVA) SWCNTs. See Single-walled carbon nanotubes (SWCNTs) Synthesis methods dip coating, 204 drop casting, 203 inkjet printing, 205–206 Longmuir-Blodgett (LB), 204–205 oxidative polymerization, 205 solvent vapor annealing (SVA), 204 spin coating, 203 vapor deposition, 205 Synthesis of thermoelectric materials. See Solution synthesis T TEG. See Thermoelectric generator (TEG) Ternary half-Heusler compounds, 179–181 TF-SCLC. See Steady-state trap-free space charge limited current (TF-SCLC) method Thermal conductivity, 13–14 in bulk materials, 56–62 in thin films, 63–66 Thermal expansion coefficient, 36 Thermal properties, 201–202

Index

Thermocouple, 314–316 Thermodynamical properties, 35–36 Thermoelectric efficiency chemical doping/alloying, 124–128 defect creation, 130–131 nanostructuring, 120–124 phase engineering, 128–130 Thermoelectric generator (TEG), 105–106, 325 automotive waste heat harvesting, 327 efficiency, 106–108 geothermal, 328 radioisotope, 327–328 solar, 326–327 wearable, 326 Thermoelectricity, 117–118 effects, 5–7 energy scenario, 14–15 figure of merit, 11–14 materials, 7–11 principle, 5 Thermoelectric (TE) materials advantages, 330–331 assembly and scalable manufacturing, 319–321 band gap, band features and prediction, 44 calculation of efficiency, 44–45 disadvantages, 331 formation energy, 43 nanostructuring, 321–324 power and efficiency, 316–318 power generators, 325–328 structural stability, 43 Thermoelectric (TE) modules, 314–316 Thermoelectric plastics, 208–210 Thermoelectric properties band gap, 49–50 chemical potential and doping concentration, 50 effective mass, 46–48 two-current model, 48–49 Thermoelectric test and errors, 69–70 Thermoelectric transport, 37–38 Thermomagnetism, 2 Thermopower, 55–56 challenges, 146–149 measurement, 69 Thin films, 236–237, 322–323

343

Thomson effect, 6–7 3ω method, 65–66 Time of flight (TOF), 221 TMDs chalcogenides. See Transition metal (TMDs) chalcogenides Traditional thermoelectric materials doping of, 149–150 effect, 150–151 intermetallic compounds, 142 nanostructured, 151–156 oxide-based compounds, 141 transport coefficients, 140t Zintl-phase compounds, 141–142 Transition metal (TMDs) chalcogenides, 246–249 Transport coefficients, 3–4 Two-current model, 48–49 Two-dimensional (2D) thermoelectric materials effect, 234–236 graphene, 240–246 layered materials, 237–239 metal oxide frameworks (MOFs), 252–253 MXenes, 251–252 phosphorene, 249–251 superlattice structures, 239 thin films, 236–237 transition metal (TMDs) chalcogenides, 246–249 Two-dimensional thermoelectrics, 113–114 Two probe methods, 67 V Valence band maximum (VBM), 110 Van der Pauw method, 68 Vapor deposition, 205 W Wearable thermoelectric generator (TEG), 326 Wettability, 202 Z Zintl phase-based thermoelectric materials, 166–169 ZnO-based oxides, 166 Zone melting, 74