Thermoelectric Materials and Devices

By Lidong Chen, Ruiheng Liu and Xui Shi

Thermoelectric Materials and Devices summarizes the latest research achievements over the past 20 years of thermoelectric material and devices, most notably including new theory and strategies of thermoelectric materials design and the new technology of device integration. The book's author has provided a bridge between the knowledge of basic physical/chemical principles and the fabrication technology of thermoelectric materials and devices, providing readers with research and development strategies for high performance thermoelectric materials and devices. It will be a vital resource for graduate students, researchers and technologists working in the field of energy conversion and the development of thermoelectric devices.

• Discusses the new theory and methods of thermoelectric materials design
• Combines scientific principles, along with synthesis and fabrication technologies in thermoelectric materials
• Presents the design optimization and interface technology for thermoelectric devices
• Introduces thermoelectric polymers and organic-inorganic thermoelectric composites

• Language: English
• Publisher: Elsevier Science
• Release date: Sep 25, 2020
• ISBN: 9780128184141

Lidong Chen

Professor Lidong Chen received his Ph.D. from Tohoku University in Japan (1990). Since 1990, he has worked with Riken Corporation (Chief Engineer), the National Aerospace Laboratory, Tohoku University (Associate Professor) and University of Michigan (Visiting Scholar). He joined the Shanghai Institute of Ceramics, Chinese Academy of Sciences (SICCAS) as a professor in 2001. At present, he is the director of the State Key Lab of High Performance Ceramics and Superfine Microstructures and the Co-Editor-in-Chief of npj Computational Materials. Professor Chen’s research focuses on advanced thermoelectric (TE) materials and devices.. Prof. Chen’s research areas include wide-spectrum phonon scattering in cage-structured compounds, liquid-like phonon transport behaviour in ionic conductors, and high-throughput explorations of novel thermoelectric materials, all of which greatly promote TE performance in recent years. In addition, he has developed high efficiency thermoelectric devices using advanced TE materials, which has been a significant contribution to the field of thermoelectrics.

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Chapter 1

General principles of thermoelectric technology

Abstract

The three physical effects, that is, Seebeck effect, Peltier effect and Thomson effect, phenomenologically describe the process of direct conversion between thermal and electrical energies in solids. This chapter presents these three thermoelectric effects as well as the thermodynamic relevancy. The inherent mechanism is also discussed conceptually on the base of solid state physics. Then, the relationship between the thermoelectric conversion efficiency and the physical properties of materials for both power generation and refrigeration is also described.

Keywords

Seebeck effect; Peltier effect; Thomson effect; figure of merit; conversion efficiency

1.1 Introduction

The first thermoelectric effect, namely the Seebeck effect, was discovered in 1821, which describes the electromotive force generated by the temperature difference. In the following thirty years or more, Peltier effect and Thomson effect were successively discovered. These effects are the three main physical effects in thermoelectric technology that describe the direct conversion between thermal and electrical energies [1–3]. Although the discoveries of both Seebeck and Peltier effects were made using a circuit composed of two different conductors and the effects were only observed at the junctions between dissimilar conductors, they are actually the bulk properties of the materials involved, not the interfacial phenomena. Solid state physics developed in the following century reveals that all the three thermoelectric effects originate from the energy difference of carriers in different materials and/or in the different parts of materials under different temperatures.

Thomson built the relationship among the three effects, and developed the basic thermodynamic theories for thermoelectric effects [3]. Thomson’s work showed that a circuit composed of two conductors with positive and negative Seebeck coefficients (usually called the thermocouple) is a type of heat engine. Such heat engine can generate electrical power by virtue of the temperature difference, or pump heat to realize refrigeration. However, since the reversible thermoelectric effects are always accompanied by the irreversible Joule heat and heat conduction, its energy conversion efficiency is principally low. Thermoelectric effects have been widely used for temperature calibrations as thermocouples, but they had no practical application as heat engine, and there had been no useful theory to guide the design and fabrication of thermoelectric heat engines for a long time. Such situation did not change until 1911, when Altenkirch, for the first time, analyzed the relationship between the energy conversion efficiency and materials’ physical parameters (Seebeck coefficient, electrical conductivity, and thermal conductivity) in thermoelectric devices [4]. He pointed out that to enhance the energy conversion efficiency, large Seebeck coefficient and electrical conductivity, and low thermal conductivity are required. This outlines the embryo for the criterion that is nowadays used to judge the thermoelectric performance of materials—figure of merit (Z) or dimensionless figure of merit (ZT).

This chapter will briefly illustrate the thermoelectric effects and the relationship between the thermoelectric conversion efficiency and the physical properties of materials.

1.2 Thermoelectric effects

1.2.1 Seebeck effect

The direct conversion from heat to electricity in solid materials was discovered by a German scientist, Thomas Johann Seebeck, in 1821. It is thus named as the Seebeck effect. In the next 20–30 years, the researchers successively discovered the Peltier and Thomson effects. These three effects as well as the Joule effect are the physical foundations during the thermoelectric conversion processes.

Thomas Johann Seebeck connected two different metal wires end-to-end to form a loop, and then he observed a magnetic field around the circuit when heating one junction and holding the other at low temperature, as shown in Fig. 1.1A. He wrote in his paper that From the above described experiments, it follows that the main and important condition for the emergence of magnetism in these metal circuits is the presence of temperature difference in the circuit links [1]. Therefore, he named it as thermomagnetism. Soon after that, this phenomenon was reexplained by Hans Christian Oersted. Oersted’s experiment demonstrated that the magnetic field around the circuit was not directly contributed by the temperature difference. Instead, the temperature difference generated a voltage Vab and thus an electric current in the circuit to provide magnetism observed in experiment. Accordingly, he proposed the concept of thermoelectricity. Nonetheless, since the phenomenon was firstly discovered by Seebeck, it was named as the Seebeck effect until today.

Figure 1.1 (A) Experimental phenomenon and (B) equivalent diagram of Seebeck effect.

As shown in Fig. 1.1B, when two conductors (a) and (b) connect each other with cold-end temperature T and hot-end temperature T+ΔT, the electrical potential difference Vab in the circuit can be measured at the free ends (having the same temperature) of (b), which is expressed as

(1.1)

where Sab is the differential Seebeck coefficient of the two conductors with the unit of μV/K. Vab is directional, which depends on the intrinsic properties of two constituting materials and the direction of temperature gradient. Sab is defined as positive when the thermoelectric current flowing from hot end to cold end in conductor (a). Seebeck coefficient is also called thermopower or thermal EMF coefficient.

The generation of thermoelctric potential can be simply but principally explained by the fluctuation of charge distribution under a temperature gradient. As shown in Fig. 1.2, taking the p-type semiconductor (holes are majority carriers) as an example, when the temperature field is uniform, the distribution of carriers (concentration, energy, and velocity) is also uniform and the material as a whole is electrically neutral. When there is a temperature difference between the two ends of material, the hole carriers at the hot end (the temperature is T+ΔT) gain higher energy (E+ΔE) than the cold end (the temperature is T), and thus become more prone to diffuse toward the cold end. Driven by the temperature/energy difference, more holes diffuse to and accumulate at the cold end, and the distribution of charges becomes nonuniform anymore, forming an inner electric field. The inner electric field yields a reversed drift charge current. When a dynamic equilibrium is established between the thermal activated diffuse and inner field driven drift charge flows, a steady voltage V is formed.

Figure 1.2 Schematic depiction of Seebeck effect.

Based on the definition of thermoelectric potential described earlier, the absolute Seebeck coefficient of a material at temperature T is defined as

(1.2)

The relation between the differential Seebeck coefficient Sab and the absolute Seebeck coefficients Sa, Sb is

(1.3)

The absolute Seebeck coefficient is independent with the direction of temperature field and thus it is an intrinsic property of material. In p-type semiconductors, the majority charge carriers (holes) diffuse from hot end to cold end driven by the energy gradient, which has the same direction as thermoelectric potential inside the material. According to Eqs. (1.1)– (1.3), the absolute Seebeck coefficient is positive. Correspondingly, the direction of the thermoelectric potential in n-type semiconductors is from cold end to hot end, and the absolute Seebeck coefficient is negative. Normally, the Seebeck coefficient of metals is very small with the values about several microvolts per Kelvin (μV/K), while the Seebeck coefficient of semiconductors can reach several tens or hundreds of microvolts per Kelvin (μV/K).

1.2.2 Peltier effect

Peltier effect is the inverse process of Seebeck effect, which describes the phenomenon of directly pumping heat by carriers (holes and/or electrons). When applying a current in the circuit composed of two different conductors, in addition the generated Joule heat, extra heat will be released or absorbed at these two junctions (Fig. 1.3). This effect was firstly discovered by a French scientist, J.C.A. Peltier, in 1834 and thus was named as the Peltier effect. Peltier connected Bi and Sb wires and observed the freezing of the water droplets in one of the junctions of the two metals when applying an electric current on the circuit. After the current was reversed, the ice was melted (Fig. 1.3A).

Figure 1.3 (A) Experimental phenomenon and (B) schematic depiction of Peltier effect.

As shown in Fig. 1.3C, when two pieces of conductors with different Fermi levels are connected and if an electric current is applied on this link, the electrons will jump either from the high energy level to the low energy level or in the opposite direction across the interface potential barrier, and therefore either release heat or absorb heat at the junctions. For example, in the metal/n-type semiconductor link, when the electrons flow from latter to the former driven by the electric field, the electrons jump from high energy level to low energy level accompanied with heat release at the junction. Experimental results show that the heat absorbed or released per unit time is proportional to the electric current

(1.4)

when current flows from a to b. Here πab is the differential Peltier coefficient with the unit of V, t is the time, and I is the current. When current flows from metals to p-type materials (electron flows from low-energy-level conductor to the high one), heat is absorbed, and πab is negative. Apparently,

(1.5)

In analogy to Seebeck coefficient, the differential Peltier coefficient at the junctions is related to the absolute Peltier coefficients of the two constituting materials via

(1.6)

1.2.3 Thomson effect

The fact that both the Seebeck and Peltier effects occur only at junctions between different conductors might suggest that they are interfacial phenomena, but they are really dependent on the bulk properties of the materials involved. It is known nowadays that these two effects stem from the different properties of the materials connected together, that is, the difference in electron energies between the two conductors. The correlation between Seebeck and Peltier effects had not been realized until William Thomson (later became Lord Kelvin) recognized this issue in 1855. He analyzed the relationship between Seebeck effect and Peltier effect and then proposed that there must be the third effect, that is, when an electric current passes through a piece of uniform conductor with a temperature gradient, reversible heat absorption or release should occur through the whole piece beside the Joule heat. This effect was experimentally verified in 1867 and was termed as Thomson effect.

When an electric current I passes through a piece of conductor with temperature difference ΔT along the current direction, the heat released or absorbed per unit time is

(1.7)

where β is the Thomson coefficient with the unit of V/K. If the direction of current is consistent with that of the temperature gradient (from cold side to hot side) and the conductor absorbs heat, β is positive and vice versa. Considering the analogy of this expression with the definition of material’s specific heat, Thomson vividly called β as specific heat of the current. The origin of the Thomson effect is similar to the Peltier effect. The difference is that the potential difference in the Peltier effect comes from that of the carriers in different conductors, while it is caused by the temperature gradient in a single conductor for the Thomson effect. Compared to the aforementioned two effects, the Thomson effect contributes little to thermoelectric conversion and is therefore often neglected in the analysis of energy conversion processes and device design.

1.2.4 Relations between thermoelectric effects and coefficients

The Seebeck, Peltier, and Thomson effects are the intrinsic properties of bulk materials and these three coefficients are related to each other. Thomson derived the relations among these three coefficients according to equilibrium thermodynamics [3]

(1.8)

(1.9)

These are called the Kelvin relations. The exact derivation of the Kelvin relations should rely on irreversible thermodynamics [5]. These two equations are verified by the experimental investigations on numerous metals and semiconductors. For a single conductor, Eq. (1.9) can be rewritten as

(1.10)

It can be also rewritten as

(1.11)

The thermoelectric coefficients in Eqs. (1.8) and (1.9) are the differential values of two conductors. As demonstrated in Eqs. (1.3) and (1.6), the absolute Seebeck (or Peltier) coefficient becomes equal to the differential Seebeck (or Peltier) coefficient if the second material in the circuit is regarded as having zero Seebeck (or Peltier) coefficient. This can be realized in practice by using a superconductor as the second material, because both the Seebeck and Peltier coefficients are zero at the superconducting state. Generally, the absolute Seebeck coefficient of lead is calibrated by measuring the differential Seebeck coefficient in the circuit composed of lead and superconductor. If the absolute Seebeck coefficient of a material at low temperature is determined by connecting a circuit using a superconductor as the reference material, by using the Eq. (1.11), one can find the values at higher temperatures above the critical superconducting temperature after measuring the Thomson coefficient [6,7]. Absolute Seebeck coefficients of other materials can be calibrated by measuring the differential Seebeck coefficients in the circuit composed of lead and the target materials. The Peltier coefficient is difficult to measure in the experiment, and therefore it is often calculated via the Kelvin relation by using the measured Seebeck coefficient.

It is clear that, the Thomson effect is a spontaneous phenomenon as the Seebeck coefficient changes along a temperature gradient inside a conductor. Obviously, all the thermoelectric effects take place throughout the whole material caused by temperature gradients and/or electric current, though the Seebeck and Peltier effects are observed macroscopically at the junctions.

1.3 Theory of thermoelectric power generation and refrigeration

A practical thermoelectric device is usually constituted by n- and p-type materials (legs) connected electrically in series and thermally in parallel. A pair of n- and p-type legs, conveniently called as π-shape element, is the basic unit of a thermoelectric device. Usually, a number of π-shape elements make up a practical thermoelectric module via a parallel or series connection. The working principle of thermoelectric power generation and refrigeration can be schematically shown in Fig. 1.4.

Figure 1.4 Schematic depiction of thermoelectric (A) power generation and (B) refrigeration.

Thermoelectric devices can be designed into several configurations such as plate-like, cascaded, film, and ring-shaped devices for different applications and/or working environment. Among them, the plate-like device is the most typical one (Fig. 1.5), which has been widely used as power generation and refrigeration. Taking this type of device as an example, this chapter will describe the relationship between energy conversion efficiency and material performance (thermoelectric coefficients). To simplify the model and obtain a concise relation, the materials’ physical parameters are taken as temperature-independent constants. In addition, it is assumed that heat flows in the one way from the hot end to the cold end through thermoelectric legs, and there is no heat exchange (such as thermal radiation, conduction, and convection) between the legs and the surrounding medium. However, practically, the physical parameters (thermal conductivity, electrical conductivity, and the Seebeck coefficient) of thermoelectric materials are usually dependent on temperature, and it is not easy to keep unidirectional heat flow from heat source and sink because the heat exchange between thermoelectric legs and surrounding medium cannot be completely prevented. The performance prediction and design of practical devices are much more complex and will be discussed in detail in Chapter 7, Design and Fabrication of Thermoelectric Devices.

Figure 1.5 Structure and photo of plate-like thermoelectric devices.

1.3.1 Thermoelectric power generation

1.3.1.1 Efficiency η

Thermoelectric devices can generate electric power and drive the load when there is a temperature gradient between the two ends. The energy conversion efficiency is the most important performance indicator for thermoelectric devices. Giving the temperatures at the hot and cold ends of the π-shaped device as Th and Tl (shown in Fig. 1.6), respectively, the thermoelectric energy conversion efficiency (η) is defined as

(1.12)

where, P is the output power on the load, and Qh is the heat input at the hot end (supplied by heat source). Here we do not consider the thermal and electrical resistances at the interfaces as well as the Thomson heat within the legs. On the assumption of unidirectional heat flow without side heat dissipation, the net income heat at the hot junction will be transferred from hot end to cold end by thermal conduction [K(Th−Tl)] and Peltier pump. According to the Peltier effect, when taking a p-type conductor as example, heat will be absorbed at the current-in end (hot end in Fig. 1.6) and be released at the current-out end. The amount of Peltier pumped heat from hot end to cold end in Fig. 1.6 is πpnI, where I is the current and πpn is the total Peltier coefficient of the two legs. On the other hand, the net heat income at the hot junction is composed of two parts, the heat input (supplied from heat source) at the hot end (Qh) and the Joule heat (I²R/2, where R is the total electrical resistance of the two legs). Here, it is reasonable to assume that the Joule heat I²R transfers equally to the hot end and cold end, therefore only half of the Joule heat (I²R/2) reaches to the hot end. Then, we can obtain the following equation

(1.13)

Figure 1.6 Thermoelectric power generation.

Combining Eq. (1.8), the heat input is

(1.14)

where Spn is the total Seebeck coefficient of n and p legs. The Seebeck voltage in the circuit is

(1.15)

Giving the resistance of the load as Rl, the loop current and output power are

(1.16)

(1.17)

Eq. (1.12) can be refined as

(1.18)

Here it is convenient to define a parameter Z, called thermoelectric figure of merit, as

where Z in which ρ and κ are the electrical resistivity and thermal conductivity, respectively; A and l are the sectional area and length of the thermoelectric legs. Then the efficiency can be expressed as

(1.19)

is the Carnot cycle efficiency. One can define ε=Rl/R and obtain the maximum value of η . In ). Then the thermoelectric generator exhibits the maximum energy conversion efficiency

(1.20)

It is seen from Eq. (1.20) that the maximum efficiency is only related to the temperature difference and the ZT value. Like other heat engines, thermoelectric generator takes the Carnot cycle efficiency as the up limit of its energy conversion efficiency.

As discussed earlier, the parameter ZT of a device is a dimensionless value, which is determined by the properties of the thermoelectric material. It is conventionally to define the dimensionless figure of merit (ZT) of a material to evaluate its thermoelectric performance

(1.21)

Clearly, for a given operation temperature range, a larger ZT will produce higher efficiency. Fig. 1.7 demonstrates the relationship between the efficiency of thermoelectric power generation and the average ZT of the material for a given Tl=300K and different Th. For example, if we want to obtain a 25% efficiency using thermoelectric technology, a comparable level to the conventional heat engine, the average ZT of the constituent materials should be larger than 2.0 even under a hot side temperature of 1000K. Nowadays, for most of the state-of-the-art thermoelectric materials, the average ZT over wide temperature range is smaller than unity, and thus the conversion efficiency of practical device is much inferior to the conventional heat engines (Fig. 1.8). Therefore, enhancing materials’ ZT takes always priority in field of