ABSTRACT
Thermoelectricity is a well-known phenomenon, investigated since the beginning of the 19th century, when Thomas Johann Seebeck (Tallinn 1770; Berlin 1831) discovered that an electrical current flows if different metals, maintained at different temperatures, are connected together (Pennelli 2014). In simple words, if a difference of temperature ΔT = TH − TC (TH stands for THot and TC stands for TCold ; see Figure 26.1a) is maintained between the ends of a conductor, or of a semiconductor, a potential difference ΔV is generated. ΔV is proportional to ΔT: ΔV = SΔT, where S is the Seebeck coefficient. The sign of the potential difference depends on the sign of the charge carriers in the conductor. Charge carriers tend to move from the hot end to the cold end of the material. In static conditions, when the electrical current I (current density J) is 0, the charges accumulate at the ends, so an electrical potential is generated and any further carrier movement is prevented. Therefore, in metals and in n-doped semiconductors, where charge carriers are electrons, the TH end is positive with respect to the TC end where electrons are accumulated, and S is negative as V C − VH = S(TH − TC ). Conversely, in p-doped semiconductors, holes are accumulated at the cold end, meanwhile an excess of negative charge is left at the hot end, so S is positive. In practical cases, the equipment (voltmeter) used for the measurement of the potential difference has a uniform temperature, which can be THot or TCold . Figure 26.1b shows that if only one kind of material is used, it is not possible to measure any potential difference in a closed loop. Even in the presence of a temperature gradient, the total temperature difference in the loop is 0, therefore ΔV = SΔT = 0, because the two ends, where the voltmeter is applied, are both at the cold temperature TC . Using instead metals with different Seebeck coefficients, the measured voltage drop is proportional both to the temperature difference and to the difference of the Seebeck coefficients, as shown Figure 26.1c. The winning strategy for the achievement of a potential difference as high as possible is to combine semiconductors with complementary n and p doping, so that the difference of the Seebeck coefficients results in the sum of the absolute values of S for the p (positive S) and n (negative S) materials. The sketch shown in Figure 26.1d is a basic design of a thermoelectric module, made of n- and a p-doped pieces of a semiconductor, interconnected in a suitable configuration for the generation of electrical power. As shown in Figure 26.1d, the two pieces of the semiconductor, which are named the “legs” of the thermoelectric module, are connected electrically in series and thermally in parallel.
