Thermoelectrics - electricity from heat

Author: Prof. Dr. Jens Pflaum and Prof. Dr. Jochen Fricke, Institute of Physics, University of Würzburg (as of May 2016) Energy efficiency is cited as a crucial prerequisite for a successful energy transition. Energy efficiency means the realization of a certain task with the lowest possible energy input. Thus, power plants, electric drives and combustion engines, heating systems, but also procedural processes in the chemical industry should operate and be carried out with the highest possible efficiency. However, all these plants and the processes taking place produce large amounts of unused "waste heat"; in Germany, this amounts to several thousand TWh annually, and it is estimated that at least 20% of the annual energy consumption of more than 50,000 TWh worldwide is lost in the form of low-temperature heat (< 200 °C). If this amount could be harnessed, the electrical energy needs of the entire European Community could be met [1]. However, the waste heat accumulates at very different temperatures. The higher the temperatures, i.e. the higher the differences (see below) compared to the ambient temperature, the better the chances of utilizing waste heat instead of releasing it into the environment. Many processes and devices for waste heat utilization are already technically applied today. We encounter names such as Steam Rankine Cycle, Organic Rankine Cycle, Kalina, combined heat and power, recuperator, turbocharger, and condensing boiler.

Thermoelectrics - an overview

Increasingly, however, research is also being conducted into thermoelectric converters (TEWs) for the direct conversion of waste heat into electrical power.  The underlying Seebeck effect was discovered by Thomas Johann Seebeck in 1821: If the contacts of two metals (metals a and b in Fig.1) are brought to different temperatures Th and Tk, a (thermo) voltage US can be measured between them. This is proportional to the temperature difference ΔT = Th -Tk and is  for ΔT =100K for a metal combination copper-constantan-copper about 4 mV. Such a thermocouple is - miniaturized -  ideal for temperature measurement. 

Much higher thermoelectric voltages of typically 20 mV/100 K can be generated with n- and p-doped semiconductors (HL) (Fig.2). The electrons in the n-doped HL as well as the holes in the p-doped HL are driven from the hot to the cold side of the TEW, i.e. from top to bottom in the schematic diagram, due to their thermally induced velocity distribution, so that a current I flows through the load R (the technical current direction is shown). 

In order to increase the voltage and thus the electrical power of thermoelectric converters, it is  necessary to connect the individual HL thermocouples  electrically in series and thermally in parallel. A corresponding arrangement is shown in Fig. 3.

Generally, different material concepts are available for the realization of efficient thermoelectric conversion, ranging from granular to lithographically fabricated layers. As a result of the optimization of materials, their manufacturing processes as well as the device architecture, the efficiency of thermoelectric converters has been steadily increased. A quantitative measure of the efficiency of a TEW is the so-called ZT value. This quality factor depends linearly on the electrical conductivity σ and the square of the Seebeck coefficient α, and inversely proportional to the thermal conductivity λ:                           ZT=(α^2 σ)/λ T . 

The latter consists of a phonic contribution λph due to the thermally excited lattice vibrations and an electronic contribution λe due to the flux of free charge carriers. In the case of metallic solids, if only the electrical contribution to the thermal conductivity is considered, it follows from the Wiedemann-Franz law λe = LT ZT = α^2/L with Lorenz number L = 2.4-10-8 V2 K-2, so that a ZT value of 1 requires a Seebeck coefficient of at least 155 µV/K.    

Optimizing the individual material-specific parameters is a major challenge, since they cannot be varied independently. Increasing the dopant concentration, for example, can increase the charge carrier density in semiconductors and thus their electrical conductivity σ. However, increasing doping also reduces the Seebeck coefficient α, due to the decreasing potential energy of the free charge carriers. In addition, the electronic contribution λe to the thermal conductivity increases with the charge carrier density and counteracts an increase in the ZT value as a result of the reciprocal relationship. The complex dependencies of the thermoelectric quantities on the charge carrier concentration are illustrated in Figure 4 for the transition from dielectric to metallic solids, where for "conventional" TEWs an optimum of ZT ≈ 1 in the semiconductor region is obtained for densities of about n ≈ 1019 cm-3. 

Figure 5 shows that the realized ZT maxima of intermetallic alloys occur at very different temperatures and allow applications in a wide temperature range. It should be noted here that the charge transport of electrons and holes, and thus the ZT values of a p-doped and n-doped alloy, can differ greatly. Therefore, solid solution systems are often used for applications, such as (Sb0.8Bi0.2)2Te3 for the n-type and Bi2(Te0.8Se0.2)3 for the p-type TEW component. If TEWs are considered as heat engines, their thermodynamic efficiency can be expressed as follows: η=⏟((T_h-T_k)/T_h )┬(η_Carnot )  (√(1+ZT ̅ )-1)/(√(1+ZT ̅ )+T_k/T_h ) where T ̅=(T_h-T_k)/2 corresponds to the averaged temperature of the hot and cold heat reservoirs. The ZT values can thus be converted to thermodynamic efficiencies, and a ZT ≈ 1 roughly corresponds to an efficiency of η ≈ 0.2∙ηCarnot, i.e., the TEWs operate well below Carnot efficiency. Accordingly, they convert waste heat into electrical energy only to a very small extent. 

To improve this, non-conventional, nanostructured TEWs are being developed nowadays. The aim is to reduce the thermal conductivity without significantly reducing the electrical conductivity. This is achieved by building the thermoelectric materials from very thin layer stacks (see inset in Fig. 6) or quantum dots. The spatial restriction of the active transport regions leads to a strong scattering of the phonons, as the carriers of the solid-state thermal conduction. The electrons, on the other hand, can "tunnel" through the built-in structural barriers, i.e., the electrical conductivity remains generally high. With this approach, ZT values of up to 3 could be realized (Fig.6), but at a correspondingly high preparative cost.

An alternative approach is represented by TEWs based on polymeric or molecular semiconductors. Research on organic thermoelectric converters is motivated not only by the prospect of low-cost fabrication, e.g., using offset printing techniques, but there are a variety of other reasons, ranging from the enormous range of nontoxic organic compounds to the use of flexible substrates to a very good power-to-weight ratio. In addition, organic solids have some inherent material advantages over inorganic semiconductors with respect to thermoelectric applications. The constituents of polymeric and molecular solids interact with each other predominantly by weak van der Waals forces, which already results in a very low thermal conductivity of about 1 W m-1 K-1 or smaller. If the semiconductors are additionally doped with suitable organic or inorganic dopants, electrical conductivity values of up to 2000 S cm-1 can be achieved in crystalline molecular arrangements; these are then also referred to as organic metals. In addition, organic semiconductors offer a wide range of doping possibilities due to their large band gaps of 1 - 3 eV. E.g., for tetracene compounds, which essentially consist of four linearly conjugated benzene rings, a p- or n-semiconducting organic material can be realized and used for TEWs, depending on the electronic structure of the dopant. Probably the best-known application of TEWs for power generation  was the  power supply of the Cassini spacecraft on its 7-year journey to Saturn,  its moons and beyond. The heat source in this case was not "waste heat" but the heat (730°C) generated by 22 kg of radioactive plutonium238.

Outlook

Today, development activities are focused not only on improving the ZT value but also on thermally optimized coupling of TEWs to waste heat sources. The use of waste heat in the exhaust tract of motor vehicles is expected to yield up to 1 kW of electrical power and save several percent of fuel. There is also great potential for "waste heat to electricity" in cogeneration plants, where the use of waste heat is expected to generate up to 5% more electricity. There is also significant potential for waste heat utilization with TEWs in many industrial operations. Figures 1 to 6: J. Fricke u. W. Borst, "Essentials of Energy Technology," Wiley-VCH, Weinheim 2013, and "Energy," Oldenbourg Verlag, Munich 1984. [1] These estimates are based on a 2006 U.S. study, "The Energy Information Administration, Existing Capacity by Energy Source, 2006. http://www.eia.doe.gv/cneaf/electricity/epa/epat2p2.html. Significantly higher figures, ranging from 29 to 50%, are cited in reports by the Commission's Euroheat and Power Initiative (www.managenergy.net/actors/2287).