Thermoelectric Power

The Seebeck Effect is the conversion of temperature differences directly into electricity. In other words, it is the generation of electricity in a circuit containing two different metals, or semiconductors, by keeping the junctions between them at different temperatures. This effect is due to two effects - Charge Carrier Diffusion and Phonon Drag. This principle is used in thermal diodes and thermoelectric generators.

The Seebeck Voltage is the voltage produced between the two junctions of a ferrite material, when they are maintained at two different temperatures. This voltage is produced due to the fact that when two junctions are two different temperatures, the majority charge carriers (holes/electrons) are diffused from the surface having high temperature to a surface having relatively low temperature.

This voltage can be mathematically expressed as V = (integral)(T1 to T2) [SB(T) - SA(T)]dT where SA and SB are Seebeck coefficients of two different metals A and B, T1 and T2 are temperatures of hot and cold junctions. Generally, V = (SB - SA)(T2 - T1).

The term Thermoelectric Power is a misnomer since it measures the voltage in response to temperature rather than power. It is also known as Seebeck coefficient. It is defined as the open circuit voltage produced between two points on a conductor, where a uniform temperature difference of 1K exists between those points. It is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material. It has units of V/K. It is also a measure of entropy per charge carrier in the material.

Mathematically it is represented as S = Thermoelectric Voltage / Temperature Difference. In terms of electric field, it is written as S = E / Temperature Gradient. If m is the Thompson coefficient of an material, then S = (integral) [m / T]dT.

Thermoelectric power determines the efficiency of a thermoelectric material. More the Seebeck coefficient better is the efficiency. Materials with high Seebeck coefficient are Bismuth Telluride and Uranium Dioxide.

One of the important applications of Seebeck coefficient is the determination of Fermi Energy Gap. For a n-type semiconductor, QT = Eg - Ef + 2KT and for a p-type semiconductor, QT = Ef - 2KT where,
Q - Seebeck coefficient
Eg - Energy gap of the ferrite semiconductor
Ef - Height of fermi energy level from the top of the filled valency band
2KT - the term, which accounts for the transfer of KE of the ferrite to a cold one

For certain materials, the conduction takes place in exceedingly narrow bands or in localized levels, so the KE term can be neglected, so for a n-type semiconductor, Ef = Eg - QT and for a p-type semiconductor, Ef = QT.

Another important application of the Seeback coefficient is the determination of Carrier Concentration. In the case of low mobility semiconductors such as ferrites, the activation energy is often associated with the mobility of charge carriers. They are considered as localized at the ions or vacant sites and the conduction occurs via a hopping type process, which implies a thermally activated electronic mobility. In such cases, it is appropriate to consider small polarons as charge carriers rather than electrons or holes. Further, it is known that the concentration (n) is given by Q = - (K/e) [ lnb(N-n)/n + St/K ] where,
St - Entropy transport term, which is negligible for ferrite materials
N - density of states or number of available sites
K - Boltzmann constant
e - electronic charge
b - degeneracy factor which includes both spin and orbital degeneracy and its value is taken as 1

Considering n << N, we can reduce the above formula to n = N exp (Q e/K). If V is the volume of the sample and the value of K/e is found to be 86.4, so we get n = N/V exp (Q / 86.4). In the case of ferrites having exceedingly narrow bands or localized levels, the value of N, the density of states can be taken as 10^(22) cm^(-3).

In the case of n-type semiconductor material, the hot junction becomes positively charged, as it loses some of its electrons. The cold surface of the semi conductor becomes negatively charged due to the diffusion of free electrons from the hot portion. Conversely in a p-type semiconductor, the hot surface becomes negative, and the cold one positive. Thus the type of conduction in a given semi conducting material can be determined from the sign of the thermo emf.