5. Development of thermoelectric materials

where αpn is the Seebeck coefficient, R is the electrical resistivity, K is the thermal conductivity, V is electrical applied volt and ΔT = Th�T<sup>c</sup> is the temperature difference between the cold and

Vopt <sup>¼</sup> <sup>α</sup>pn <sup>Δ</sup><sup>T</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Th � Tc

Tm <sup>¼</sup> <sup>1</sup> 2

Th � Tc

<sup>Z</sup> <sup>¼</sup> <sup>α</sup><sup>p</sup> � <sup>α</sup><sup>n</sup> � �<sup>2</sup> ð Þ KR min

Similarly, the optimum coefficient of performance of heating COPh,opt can be expressed as:

1 � 2

<sup>¼</sup> <sup>α</sup><sup>2</sup> pn ð Þ KR min

pnT ð Þ KR min

A comprehensive parameter that described the thermoelectric characteristics is the figure of

This parameter can be made dimensionless by multiplying it by T (the average temperature of

The value of Z is related only to the physical properties of the thermocouple material. The higher the figure of merit Z for the material, the better the thermoelectric properties it has. The best commercial thermoelectric materials currently have ZT values around 1.0. The highest ZT

Maximizing Qc and COP can been obtained by optimizing some parameters like the number of thermoelement pairs for each stage and the applied electrical current [37]. For cascaded

ZT <sup>¼</sup> <sup>α</sup><sup>2</sup>

1 þ ZTm

<sup>R</sup> <sup>¼</sup> <sup>α</sup>pn <sup>Δ</sup>T=<sup>R</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZTm

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZTm <sup>p</sup> � Th

> > ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZTm

� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZTm <sup>p</sup> � <sup>1</sup> ZTm � �

Tc

<sup>p</sup> � <sup>1</sup> (4)

<sup>p</sup> � <sup>1</sup> (5)

<sup>p</sup> <sup>þ</sup> <sup>1</sup> � � (6)

ð Þ Th þ Tc (7)

(8)

(9)

(10)

the hot side of thermoelements at the ceramic plate locations.

252 Bringing Thermoelectricity into Reality

The corresponding maximum COPc,d, i.e., COPc,opt, will be;

For the optimum working voltage Vopt and optimum working current Iopt,

Iopt <sup>¼</sup> Vopt

COPc,opt <sup>¼</sup> Tc

where T<sup>m</sup> is the average temperature of the thermocouple defined as:

COPh,opt <sup>¼</sup> Th

value reported in research is about 3 at temperature of 550 K [36].

merit of the thermocouple Z which can be defined as:

the hot side and the cold side of the TE module):

As shown by the primary criterion of merit, a good thermoelectric material should possess high Seebeck coefficient, low thermal conductivity and high electrical conductivity. However, these three parameters are interrelated; hence they have to be optimized to get the maximized ZT [41, 42]. The changes in these parameters will unlikely lead to a net increase in ZT, since any favorable change in one parameter will be accompanied by an unfavorable change in the other parameters. For instance, if the electrical conductivity is too low, we might like to increase the carrier concentration. However, during increasing the carrier concentration which in turn will increase the electrical conductivity, the Seebeck coefficient will also decrease and the electronic contribution to the thermal conductivity will increase. This dilemma forced the maximum ZT of any thermoelectric material to be held at ZT = 1 for many years [43]. The devices made of these materials were operated at a power conversion efficiency of only 4–5%.

Conventional thermoelectric materials are bulk alloy materials such as Bi2Te3, PbTe, SiGe and CoSb3. Eventually it was determined that the most efficient bulk thermoelectric materials are high carrier concentration alloyed semiconductors. The high carrier concentration results in a good electrical conductivity while optimizing the electrical properties can be achieved by varying the carrier concentration. Transport of phonons (quantized lattice vibrations which carry heat) can be disrupted by alloying, which results in a reduced thermal conductivity. For this approach, it was discovered that good thermoelectric materials are phonon-glass electroncrystal material [44, 45], where high mobility electrons are free to transport charge and heat but the phonons are disrupted at the atomic scale from transporting heat. The recent trend to optimize the thermoelectric material's performance is achieved by reducing the material thermal conductivity, especially the lattice thermal conductivity [46]. Reducing the lattice thermal conductivity can be achieved by adding low sound velocity heavy elements, such as Bi, Te, and Pb. Examples of commercial thermoelectric alloys include BixSb2\_xTe3 at room temperature, PbTe–PbSe at moderate temperature, and Si80Ge20 at high temperature.

A new strategy for high efficiency "phonon-liquid electron-crystal" thermoelectric materials where a crystalline sublattice for electronic conduction is surrounded by liquid like ions was introduced. The results of an experiment performed on a liquid like behavior of copper ions around a crystalline sublattice of Se in Cu2xSe showed a very low lattice thermal conductivity which increased the value of ZT in this simple semiconductor [47].

applications including electronic devices cooling and air conditioning [90–94]. If the TE modules are employed with time-varying temperature distribution and cooling power output, either 1D or 3D transient modeling is needed to better capture the system performance. To capture the module performance, modeling temperature change in all thermoelements is very complicated. Therefore, energy equilibrium model can be applied to simplify the numerical analysis process, especially for those systems which include heat sinks in hot and cold sides. Positive Thomson coefficient improves TE cooling performance by 5–7% [95], while negative Thomson coefficient reduces cooling performance [96]. However, for commercially available TE coolers, Thomson effect is often small and negligible. Dimensionless analysis is a powerful tool to evaluate the performance of TE cooling system. New dimensionless parameters, such as dimensionless entropy generation number [78], dimensionless thermal conductance ratio and

Both COP and cooling capacity are dependent on the length of thermoelement, and this dependence becomes highly significant with the decrease in the length of thermoelement [97]. As a result, a long thermoelement is preferred to obtain a large COP, while a short thermoelement would be preferable to achieve maximum heat pumping capacity. Therefore, it is obvious that the design of the optimum module will be a tradeoff between the requirements for the COP and the heat pumping capacity. Most commercially available TE modules have thermoelement length range from 1.0 to 2.5 mm. Cooling power density also increases with

Typical TE modules have a size range from 4 � <sup>4</sup> � 3 mm<sup>3</sup> to about 50 � <sup>50</sup> � 50 mm<sup>3</sup>

development of micro-TE devices to further reduce the dimensions, that is compatible with standard microelectronic fabrication technology [98], has the potential to improve the microelectronic systems performance, achieve considerable reductions in size and improve the TE

Electrical and thermal contact resistances, especially thermal contact resistance at the thermoelement interface layer, are critical to achieve a further improvement in both TE cooling capacity and COP [84]. An enhanced formula for the COP of a Peltier module which takes into consideration both the electrical and the thermal contact resistances can be written as [34]:

> Tc Th � Tc

layer, k is the thermal conductivity of the thermoelements, kc is the thermal conductivity of the

In addition, an accurate fabrication technique is needed to provide high-quality and highperformance TE modules. The requirements include: precise measurements of the internal resistance for each module at ambient temperature; determination of the module supply leads

β � Th=Tc <sup>1</sup> <sup>þ</sup> <sup>β</sup> � rlc

l (12)

, l is the thermoelement length, lc is the thickness of the contact

. The

Thermoelectric Cooling

255

http://dx.doi.org/10.5772/intechopen.75791

dimensionless convection ratio [64] have been defined.

decreasing the ratio of thermoelement length to the cross-sectional area.

devices performance, which opens up new commercial applications.

COPopt <sup>¼</sup> <sup>l</sup>

where

<sup>β</sup> = 1 <sup>þ</sup> lZTM nþl <sup>1</sup>=<sup>2</sup>

, n = <sup>2</sup>Rc

contact layers and T<sup>M</sup> = ð Þ ThþTc

<sup>R</sup> , r <sup>¼</sup> <sup>k</sup> kc

<sup>2</sup> .

l þ 2rlc

The efficiency of TE devices can be further enhanced through nanostructural engineering [44] using two primary approaches: bulk materials containing nano-scale constitutes and nanoscale materials themselves. By the introduction of nanostructures, ZT was pushed to about 1.7 [48] with power conversion efficiency of 11–15%.

Many reviews have summed up progress on thermoelectric materials [49, 50], bulk thermoelectric materials [45] and low-dimensional thermoelectric materials [43, 51, 52]. Lowdimensional materials, including 2-D quantum wells, 1-D quantum wires and 0-D quantum dots, possess the quantum confinement effect of the electron charge carriers that would enhance the Seebeck coefficient and thus the power factor [53]. Furthermore, the introduced various interfaces will scatter phonons more effectively than electrons so that it reduces the thermal conductivity more than the electrical conductivity [18].

Two-dimensional Bi2Te3 quantum well improved ZT due to the enhancement of thermopower [54]. The ZT of Bi2Te3 quantum well structures are estimated to be much higher than its bulk material. The highest ZT observed was 2.4 using Bi2Te3–Sb2Te3 quantum well superlattices with a periodicity of 6 nm [55]. Similarly, the highest ZT value for its bulk material is only 1.1. Quantum-dot superlattices in the PbTe–PbSeTe system were developed under the quantum confinement may lead to an increased Seebeck coefficient and therefore higher ZT [56]. PbSe nanodots were embedded in a PbTe matrix and showed ZT of 1.6, which is much higher than their bulk materials of 0.34 [52]. Serial compound Ag1–<sup>x</sup>Pb18SbTe20 has a high ZT value of 2.2 at 800 K due to the special nanostructure that is still the most competitive TE material [57] and has ignited broad research interest [58–61]. These new technologies have pushed ZT to 2.4 [62] with predicted increase in the device conversion efficiency to a value between 15 and 20%.
