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THERMOELECTRIC PROPERTIES OF METALS AND SEMICONDUCTORS

Lev I. Berger

There are three thermoelectric phenomena that result from correlation between propagation of heat through a conductor and displacement of the current carriers in the conductor. The Seebeck effect (Ref. 1) consists of formation of an electric current in an electrical circuit formed by two dissimilar conductors if the contacts between the conductors are held at different temperatures. A reverse phenomenon, the Peltier effect (Ref. 2), consists of formation of a temperature difference between the contacts in a circuit of this type if an electric current is created in the circuit by an external current source to which the circuit is connected. W. Thomson (Lord Kelvin), who explained both effects (Refs. 3,4), predicted and experimentally confirmed the existence of another thermoelectric phenomenon, named the Thomson effect, which consists of absorption or release of heat in a uniform conductor with a current passing through it when a temperature gradient (positive or negative) is present along the current direction.

The electromotive force, ΔU, which creates the Seebeck current in the circuit, is the algebraic sum of the emf’s created in each of the conductors, and is proportional to the temperature difference, ΔT, between the electrical contact points: ΔU = ΔU₁ + ΔU₂ = α₁ΔT + α₂ΔT. The coefficient of proportionality, α, called the Seebeck coefficient or thermoelectric power or thermal electromotive force (thermal emf), of each of the two materials depends on the electrical properties and temperature of the material. The Peltier effect is measured by the amount of heat, ΔQ, released or absorbed in a unit of time (in addition to the Joule heat) at a contact of two dissimilar conductors with electric current ΔI passing through the contact: ΔQ = Π·ΔI. Thomson showed that Π = αT. The Thomson effect’s heat, dQ, released or absorbed in a unit of time along a part of a conductor of length dx is proportional to the current magnitude I, the temperature gradient along the conductor ∂T/∂x, and the increment dx: dQ = τI(∂T/∂x)dx. Thomson showed that the magnitude of the coefficient of proportionality, τ, later named the Thomson coefficient, depends on only the properties of the conductor and the ambient temperature and correlates with the other thermoelectric parameters of a material through the equation τ = T(∂α/∂T).

Another thermoelectric phenomenon, called the Bridgman effect or the internal Peltier effect (Ref. 5), occurs when an electric current passes through an anisotropic crystal, resulting in absorption or liberation of heat because of non-uniformity in current distribution.

In view of the correlations between α, Π, and τ, we need only to present data for one of these parameters, namely, thermal emf α and its dependence on temperature. These values are presented below, first for metals (Table 1) and then for semiconductors (Table 2). In accordance with modern theory of solids, thermal emf in semiconductors is up to three or even four orders of magnitude higher than that in metals (Ref. 9).

The accuracy of the data presented in these tables is dependent on a number of factors. The thermal emf of a material is sensitive to negligibly small amounts of impurities in the material, which may be below the limits of sensitivity of the chemical analysis; to orientation of crystal grains in a sample of the material, and to thermal processing of the material.

References

Seebeck, T. J., Abhand. Deut. Akad. Wiss. Berlin, 265–373, 1822.
Peltier, J. C. A, Ann. Chem., LVI, 371–387, 1834.
Thomson, W., Proc. Roy. Soc. Edinburgh, 91–98, 1851.
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Bridgman, P. W., Proc. Natl. Acad. Sci. USA, 13(2), 46–50, 1927; Phys. Rev.30, 911–921 (1927). [https://doi.org/10.1103/PhysRev.30.911]
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TABLE 1. Thermal emf α (Seebeck Coefficient) of Elemental Metals

Metal	Name	α(100 K)/μV K^-1	α(300 K)/μV K^-1	α(500 K)/μV K^-1	α(1000 K)/μV K^-1	α(1500 K)/μV K^-¹
Continued on next page...
Ag	Silver	0.73	1.51	2.82	7.95
Al	Aluminum	-2.2	-1.66	1.96
Au	Gold	0.82	1.94	2.86	3.85
Ba	Barium	-4	12.1	28.5
Be	Beryllium	-2.5	1.7	2.7	7.9
Ca	Calcium	1.05	10.3	17.1
Cd	Cadmium	-0.05	2.55
Ce	Cerium	13.6	6.2	5.2	-4.8
Co	Cobalt	-8.43	-30.8	-44.8	-35.9	-7.8
Cr	Chromium	5	21.8	16.6	17.9	5.7
Cs	Cesium		-0.9
Cu	Copper	1.19	1.83	2.83	5.36
Dy	Dysprosium	-4.1	-1.8	0.9	2.3
Er	Erbium	-3.8	-0.1	1.9	4.2
Eu	Europium	5.3	24.5	46
Fe	Iron	11.6	15	3	0.4
Ga	Gallium	0.5
Gd	Gadolinium	-4.6	-1.6	-0.5	-0.8
Hf	Hafnium	0	5.5	5.7	-0.5

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THERMOELECTRIC PROPERTIES OF METALS AND SEMICONDUCTORS

References