Peltier–Seebeck effect: Encyclopedia II - Peltier–Seebeck effect - Seebeck effect

Peltier–Seebeck effect - Seebeck effect

The Seebeck effect is the conversion of heat differences directly into electricity.

This effect was first discovered, accidentally, by the Estonian physicist Thomas Johann Seebeck in 1821, who found that a voltage existed between two ends of a metal bar when a temperature gradient existed in the bar.

He also discovered that a compass needle would be deflected when a closed loop was formed of two metals with a temperature difference between the junctions. This is because the metals respond differently to the heat difference, which creates a current loop, which produces a magnetic field.

A voltage, the thermoelectric EMF, is created in the presence of a temperature difference between two different metals or semiconductors. This usually causes a continuous current to flow in the conductors. The voltage created is on the order of several microvolts per degree of difference.

In the circuit:

(which can be in several different configurations and be governed by the same equations), the voltage developed can be derived from:

S_A and S_B are the Seebeck coefficients (also called thermoelectric power or thermopower) of the metals A and B, and T₁ and T₂ are the temperatures of the two junctions. The Seebeck coefficients are non-linear, and depend on the conductors' absolute temperature, material, and molecular structure. If the Seebeck coefficients are effectively constant for the measured temperature range, the above formula can be approximated as:

Thus, a thermocouple works by measuring the difference in potential caused by the dissimilar wires. It can be used to measure a temperature difference directly, or to measure an absolute temperature, by setting one end to a known temperature. Several thermocouples in series are called a thermopile.

This is also the principle at work behind thermal diodes and thermoelectric generators (such as radioisotope thermoelectric generators or RTGs) which are used for creating power from heat differentials.

The Seebeck effect is due to two effects: charge carrier diffusion and phonon drag.

Peltier–Seebeck effect - Thermopower

If the temperature difference between the two nodes is small,

and a voltage ΔV is seen at the terminals, then the thermopower of the entire thermocouple is defined as:

This can also be written in relation to the electric field E and the temperature gradient , by the equation

Superconductors have zero thermopower, and can be used to make thermocouples. This allows a direct measurement of the thermopower of the other material, since it is the thermopower of the entire thermocouple as well.

In semiconductors the sign of the thermopower is used to decide whether the charge carriers are electrons or holes.

Peltier–Seebeck effect - Charge carrier diffusion

Charge carriers in the materials (electrons in metals, electrons and holes in semiconductors, ions in ionic conductors) will diffuse when one end of a conductor is at a different temperature than the other. Hot carriers diffuse from the hot end to the cold end, since there is a lower density of hot carriers at the cold end of the conductor. Cold carriers diffuse from the cold end to the hot end for the same reason.

If the conductor were left to reach equilibrium, this process would result in heat being distributed evenly throughout the conductor (see heat transfer). The movement of heat (in the form of hot charge carriers) from one end to the other is called a heat current. As charge carriers are moving, it is also an electrical current.

In a system where both ends are kept at a constant temperature relative to each other (a constant heat current flows from one end to the other), there is a constant diffusion of carriers. If the rate of diffusion of hot and cold carriers in opposite directions were equal, there would be no net change in charge. However, the diffusing charges are scattered by impurities, imperfections, and lattice vibrations (phonons). If the scattering is energy dependent, the hot and cold carriers will diffuse at different rates. This creates a higher density of carriers at one end of the material, and the distance between the positive and negative charges produces a potential difference; an electrostatic voltage.

This electric field, however, opposes the uneven scattering of carriers, and an equilibrium is reached where the net number of carriers diffusing in one direction is canceled by the net number of carriers moving in the opposite direction from the electrostatic field. This means the thermopower of a material depends greatly on impurities, imperfections, and structural changes (which often vary themselves with temperature and electric field), and the thermopower of a material is a collection of many different effects.

Peltier–Seebeck effect - Phonon drag

Phonons are not always in local thermal equilibrium; they move along the thermal gradient. They lose momentum by interacting with electrons (or other carriers) and imperfections in the crystal. If the phonon-electron interaction is predominant, the phonons will tend to push the electrons to one end of the material, losing momentum in the process. This contributes to the already present thermoelectric field. This contribution is most important in the temperature region where phonon-electron scattering is predominant. This happens for

where θ_D is the Debye temperature. At lower temperatures there are less phonons available for drag, and at higher temperatures they tend to lose momentum in phonon-phonon scattering instead of phonon-electron scattering.

This region of the thermopower-versus-temperature function is highly variable under a magnetic field.

Adapted from the Wikipedia article "Seebeck effect", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki