Recently Greenhouse effect is more serious and it speeds up the research for the alternative sources of energy in place of traditional fossil fuels. Power generation from the solar energy has attracted more attention, but it is still insufficient for the current huge energy consumption. Thermoelectric materials have the property for recovering the wasting heat to generate useful electric power and for reducing global warming effects. Since this energy conversion is done by electron moving in solid, we can make full use of solid. Firstly, the thermoelectric device has no moving part, and is operated almost without the maintenance. Besides, thermoelectric energy conversion has several advantages in comparison with the other energy sources. Secondly, it produces no waste matter through conversion process. Thirdly, it can be processed at a micro/nano size, and can be implemented into electronic devices1.
The efficiency of energy conversion for a thermoelectric material is measured by the dimensionless thermoelectric figure of merit, written as ZT, and it is defined by
where Se is Seebeck coefficient, σ is the electrical conductivity, kphonon and kelectron
are the thermal conductivity for the phonon and the electron respectively, and T is temperature. The ideal thermoelectric material would have a large Se, a large σ and a small k. For an insulator it usually has a large Se and a small k, but it has a small σ,
enhance ZT for thermoelectric materials is a very challenging problem, because material with a large σ is usually companied with a small Se and a large k. The trade off between the electrical conductivity and Seebeck coefficient can be seen in Fig. 12 for bulk silicon crystals2.
Fig. 1 Seebeck coefficient and ZT as a function of the electrical conductivity for bulk crystal Silicon at 373K2.
If ZT goes to zero, it means there is no energy conversion. But as ZT is increasing to infinity, it will reach the Carnot efficient limit, which applies to all heat engines3. The laws of thermodynamics tell us that a maximum efficiency, called the Carnot efficiency, cannot be exceeded. The Carnot efficiency can be written
Hot Cold
100%
Hot
T T
η = T − ×
(1.2)where THot and TCold are the temperatures of the hot and cold sides of the materials.
The comparison of ZT values with different materials can be seen in Fig. 24, where the most of materials are located below ZT=1. Non-oxide materials have
large ZT values and oxide materials have small ZT values, and the ZT values of SiGe crystals approach to 1, and the ZT values of β-FeSi2 is between 0.1 and 1.
β− FeSi
2The traditional thermocouple that is based on the two dissimilar metal wires is for the first time to apply for thermoelectrics. From the 1950s the semiconductors replaced the metals and especially in the 1990s the research of thermoelectric materials achieved the big progress3 and it can be demonstrated in Fig. 35. The research for thermoelectric silicide materials is grouped into two categories; one is alkaline-earth metal silicides and the other is transition metal disilicide. Magnesium silicide Mg2Si that is n-type semiconductor is widely used for the application to the thermoelectric devices, as it is abundant in the natural resources, besides it is non-toxic, inexpensive. Mg2Si is the well known promising thermoelectric material in temperature range from 500 to 800K6 and with narrow-band gap about 0.78 eV7. β-FeSi2 is another promising thermoelectric material according to its energy band
power in the temperature range from 500 too 900K6.
Fig. 3 Progress in thermoelectric materials figure of merit, ZT.
The Seebeck coefficient that is also called as thermopower is the important parameter to determine the thermoelectric conversion efficiency of thermoelectric materials and its magnitude depends on an induced thermoelectric voltage across the materials in response to a temperature difference. The Seebeck coefficient is usually calculated from the charge carrier motion of energy band gap, because an applied temperature difference will cause charge carriers (electrons or holes) in the materials to diffuse from the hot side to the cold side. As diffusions of charge carriers reach thermodynamic equilibrium, the net separation of carriers would create an electric potential. However, phonons are not always in local thermal equilibrium. They lose momentum by interacting with other carriers and tend to push electrons to one side of the materials. So the Seebeck coefficient is mainly affected by the following two reasons: charge carrier diffusion and phonon drag.
However, diffusing charge carriers would also be scattered by impurities, defects, phonons and other charge carriers, etc8. The above factors complicate the calculations of the Seebeck coefficient considerably in the conventional band structure theory.
We have found an alternative way to study the thermoelectric dynamics. It is based on the thermodynamic theory for the system in equilibrium with an electric field. As thermodynamics is considered as an exact theory in which all microscopic quantities can be averaged out systematically, it is possible to perform a more accurate calculation9.
In the present work, three semiconductor thermoelectric materials, Mg2Si, FeSi2 and SiGe, were investigated. In the first step, APT and Mulliken charges are computed with density function theory (DFT) method at various electric fields.
Four DFT functionals are chosen; B3LYP, BLYP, M05 and M05-2X. In the second step, APT and Mulliken charges are used to calculate dipole moments at a given electric field and then derivatives of dipole moments with respect to electric field lead to the electronic polarizability. In the final step, the dielectric constant is evaluated from the Clausis-Mossotti equation through the electronic polarizability.
The Seebeck coefficient is calculated from the thermodynamic method with chemical potential. This method is much simpler than energy band structure theory.
The Helmholtz free energies are computed as a function of the temperature, and then are fitted into an analytical function with respect temperatures as a variable.
Seebeck coefficient can be evaluated from partial derivative of Helmholtz free energy with respect to temperature, which is divided by dielectric constant evaluated previously and finally be considered as the Seebeck coefficient for a
example, the density of the material9.