Flexible Thermoelectric Polymers and Systems. Группа авторовЧитать онлайн книгу.

Subscript normal c Baseline plus 1 right-parenthesis comma"/>

(1.5) upper S Subscript normal v Baseline equals StartFraction k Subscript upper B Baseline Over e EndFraction left-parenthesis StartFraction upper E Subscript normal upper F Baseline minus upper E Subscript normal v Baseline Over k Subscript upper B Baseline upper T EndFraction plus a Subscript normal v Baseline plus 1 right-parenthesis comma

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) upper S equals minus StartFraction pi squared k Subscript upper B Baseline upper T Over 3 e EndFraction left-bracket StartFraction d l n sigma left-parenthesis upper E right-parenthesis Over d upper E EndFraction right-bracket Subscript upper E equals upper E Sub Subscript normal upper F Subscript Baseline comma

(1.7) sigma left-parenthesis upper E right-parenthesis equals e n left-parenthesis upper E right-parenthesis mu left-parenthesis upper E right-parenthesis comma

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) n left-parenthesis upper E right-parenthesis equals g left-parenthesis upper E right-parenthesis f left-parenthesis upper E right-parenthesis period

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) upper S equals minus StartFraction upper E Subscript normal upper J Baseline minus upper E Subscript normal upper F Baseline Over q upper T EndFraction comma

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.

Schematic illustration of 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 1.4 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.

Schematic illustration of dependence of the Seebeck coefficient, electrical conductivity, and power factor on the charge carrier concentration.

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

The

Скачать книгу