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Thermoelectric materials are usually referred to electronic materials with high Seebeck coefficient. When there is a temperature gradient between the two ends of a thermoelectric material, a voltage will be generated between the two ends. This effect was first discovered by Alessandro Volta in 1794 and independently rediscovered by Thomas J. Seebeck in 1821. The Seebeck coefficient (S) is determined by the voltage (ΔV) and the temperature gradient (ΔT),

Figure 1.2 Chemical structures of some representative conducting polymers: (a) poly(3,4‐ethylenedioxythiophene):tosylate (PEDOT:Tos), (b) poly(3,4‐ethylenedioxythiophene): polystyrene sulfonate (PEDOT:PSS), (c) poly(3,4‐ethylenedioxythiophene): trifluoromethanesulfonate (PEDOT:OTf), (d) polyaniline (PANI), (e) polythiophene (PTh), (f) poly(3‐hexylthipohene) (P3HT), (g) polypyrrole (PPy), and (h) poly(nickel‐ethylenetetrathiolate) [poly(Ni‐ett)].

(1.1)

The Seebeck effect can be understood in terms of the temperature effect on the charge carrier distribution. For example, the electrons of a metal follow the Fermi–Dirac distribution,

(1.2)

where E is the electron energy and k _B the Boltzmann constant. The electron distribution near the Fermi level is affected by temperature. The f(E) value at E _F is 1 at 0 K and less than one at a temperature above 0 K. Consider two different temperatures, T _H and T _C, at the two ends of a metal, the Fermi–Dirac distributions at the two temperatures are shown in Figure 1.3. When the temperature (T _C) at the cold side is 0 K, the states above the Fermi level is completely empty, while all the states below the Fermi level is fully occupied. At the hot side, the temperature (T _H) is greater than 0 K. Thus, in terms of the Fermi–Dirac distribution, some states at the energy above E _F is occupied, while some states below the Fermi level are vacant. As a result, electrons with the energy higher than E _F will diffuse from the hot side to the cold side, while the electrons with the energy lower than E _F will migrate in the opposite direction. But the electron diffusions along the two directions are not equivalent. At equilibrium, some electrons accumulate at the hot or cold side, this leads to an internal electric field and a voltage between the two sides. If the electrons accumulate at the cold side, the potential of the cold side will be lower than the hot side. This will lead to a negative Seebeck coefficient, and the material is an n‐type thermoelectric material. Instead, if the electrons accumulate at the hot side, the cold side has a potential higher than the hot side. The Seebeck coefficient is positive, and it is a p‐type material.

Figure 1.3 (a) A metal with different temperatures at the two sides. (b) Voltage between the two sides induced by temperature gradient. (c) Fermi–Dirac distributions at two different temperatures of T _H and T _C and their difference.

By using the Fermi gas model, the Seebeck coefficient of metals is

(1.3)

where T _F is the Fermi temperature. This is the Mott formula in metals. In terms of this formula, metals usually have small Seebeck coefficient because of their large T _F value of 10⁴−10⁵ K. The absolute Seebeck coefficient values of metals are usually less than 10 μV K⁻¹ (Table 1.1).

The Seebeck coefficient of semiconductors depends on the doping level. For nondegenerated semiconductors, Eqs. (1.4) and (1.5) are the Mott formulae for the Seebeck coefficients in the conduction band and valence band, respectively,

(1.4)

(1.5)

where E _c is the minimum energy of the conduction band, E _v is the maximum energy of the valence band, and a _c and a _v are constants and they depend on materials. In terms of the Mott formulae in semiconductors, the Seebeck coefficient has the maximum value when a semiconductor is lightly doped.

Table 1.1 Seebeck coefficient of some metals, semiconductors, flexible materials at room temperature.

Metal	S (μV K−1)	Semiconductor	S (μV K−1)	Flexible materials	S (μV K−1)
Sb	+47	Se	+900	PEDOT:PSS	+14–20
Mo	+10	Te	+500	PEDOT:Tso	+30
Ag	+6.5	Si	+440	PA	+10
Cu	+6.5	Ge	+300	PPy	+10
Hg	+0.6	Sb2Te3	+185	PANi	+10–20
Pt	+0.0	Pb3Ge39Se58	+1670	Poly(Ni‐ett)	−125
Ni	−15	Pb15Ge37Se58	−1990	graphene	−10
Bi	−72	Bi2Te3	−230	Carbon nanotube	+20

For degenerated semiconductors, the Seebeck coefficient is given by

(1.6)

(1.7)

where n(e) and μ(E) are the charge carrier density and mobility at energy E. Hence, a semiconductor with a large variation in the carrier density near the Fermi level can have a high Seebeck coefficient. This can be achieved by changing the band structure. This way to increase the Seebeck coefficient is called “band structure engineering”. In addition, the charge carrier density n(E) is related to the density of states (DOS), g(E),

(1.8)

Thus, the Seebeck coefficient is related to the density of states near E _F. Controlling the density of states can vary the Seebeck coefficient, and this is called “DOS engineering”.

Another important formula is the dependence of the Seebeck coefficient on the difference between the average energy (E _J) of the transporting electrons and the E _F,

(1.9)

where q is the elementary charge. A simple picture of an n‐type semiconductor is shown in Figure 1.4. The charge carriers are the electrons in the conduction band. Their average energy is E _J. For n‐type semiconductors, E _J − E _F > 0, the Seebeck coefficient is negative. In contrast, E _J − E _F < 0 for p‐type semiconductors, the Seebeck coefficient is positive. When the |E _J − E _F| value is large, the material will have a high Seebeck coefficient. Increasing the doping level of an n‐type semiconductor can shift the Fermi level upward to the conduction band and thus lower the |E _J−E _F| value. Similar argument can be applied for p‐type semiconductors. Hence, the Seebeck coefficient decreases with the increase in the doping level.

Although increasing the doping level can decrease the Seebeck coefficient, it increases the electrical conductivity. The power factor (S ² σ) is dependent on the Seebeck coefficient and the electrical conductivity (σ). As shown in Figure 1.5, there is an optimal power factor in terms of the charge carrier density.

Figure 1.4 Band structure of an n‐type semiconductor. VB and CB are for the valence band and conduction band, respectively. The dots at the CB stand for electrons.

Figure 1.5 Dependence of the Seebeck coefficient, electrical conductivity, and power factor on the charge carrier concentration.

The dependence of the power factor on the charge carrier density is valid for conducting polymers as well. The Seebeck coefficient and electrical conductivity of conducting polymers strongly depend on the doping level. An undoped conducting polymer has a conductivity in the insulator range. The increase in the doping level can decrease the Seebeck coefficient while increase the electrical conductivity. Thus, doping engineering is an effective way to find the optimal power factor of conducting polymers as well. Chemical and electrochemical de‐dopings are popular methods to find the optimal doping level of conducting polymers in terms of the power factor. For example, Crispin et al. chemically de‐doped PEDOT:TsO with tetrakis(dimethylamino)ethylene (TDAE) and found the optimal doping level of ~0.22 (Figure 1.6) [5].

The Seebeck coefficient of conducting polymers is also related to the doping form. There are two types of doping forms for p‐type conducting polymers [6, 7]. Taking away electrons from the conjugated backbone is the oxidative doping. Oxidative doping is the main doping form for conjugated polymers such as polyacetylene and polythiophene. The oxidative doping can be de‐doped by reducing chemical agents. Another doping form is the protonic acid doping. It is the main doping form for polyaniline because polyaniline has ammine group [8]. Protonic acid doping was observed for polypyrrole and polythiophene as well [6, 7]. The protonic acid doping can be de‐doped by base. Yao et al. found that de‐doping the protonic acid doping by base is more effective in increasing the Seebeck coefficient than de‐doping the oxidative doping [3]. As shown in Figure 1.7, poly(3,4‐ethylenedioxythiophene):trifluoromethanesulfonate (PEDOT:OTf) can be de‐doped with reducing agents including glucose and ascorbic acid or NaOH. When PEDOT:PSS:OTf is de‐doped to the same doping level, the conductivity using glucose or ascorbic acid is similar with NaOH. But the latter can give rise to a higher Seebeck coefficient and thus the power factor than the former. This difference is ascribed to the different electronic structures by oxidative doping and protonic acid doping. The protonic acid doping takes place by attaching a proton to an α or β site of the thiophene ring of PEDOT. This distorts the conjugated structure and leads to more electrons near the Fermi level. Instead, the oxidative doping does not affect the conjugated structure. Thus, the removal of the protonic acid doping can more effectively increase the mean energy (E _J) of the charge carriers and thus increase the Seebeck coefficient more remarkably.

Figure 1.6 Dependences of the electrical conductivity, Seebeck coefficient, and power factor of PEDOT:Tso on the doping level. Oxidation level is used for the doping level, and α is used for the Seebeck coefficient.

Source: Bubnova et al. [5]. © Springer Nature.

The dependence of the Seebeck coefficient on the |E _J − E _F| values is often used to understand the energy filtering. Energy filtering is often observed when an electronic material like nano‐fillers is mixed into a conducting polymer with different Fermi levels [9–11]. The different Fermi levels of the matrix and nano‐fillers can induce the charge transfer and an internal electric field at the interface between them. This internal electric field at the interface can block the accumulation of the charge carriers with low energy and thus increase the mean energy (E _J) of the accumulated charge carriers under temperature gradient. Apart from composites of conducting polymers, energy filtering was reported when a certain material is coated on a conducting polymer film [12–14].

Figure 1.7 (a) Conductivity, (b) Seebeck coefficient, and (c) power factor of PEDOT:OTf films as a function of doping levels. NaOH, glucose, and ascorbic acid were used to de‐dope PEDOT:OTf.

Source: Yao et al. [7]. © Royal Society of Chemistry.