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The 3 TE effects are named for Seebeck, Peltier, and Thomson. The easiest way (I believe) to think about thermoelectricity is to realize that electrical and thermal currents are coupled. The particles that carry electric charge in a material also carry heat. The three TE effects are just three ways in which this coupling is realized, and all are closely related. In fact, knowing the Seebeck coefficient as a function of temperature allows one to calculate the Peltier and Thomson coefficients.
Below are some cartoons and descriptions that should be helpful in understanding the different effects and how they are related.
Imagine a conductor with an applied temperature gradient. Electrons (or holes) will thermally diffuse from the hot end to the cold end, and carry their charge with them. This charge builds up on the cold end and creates an electric field inside the sample. When the current generated by this electric field cancels the flow due to thermal diffusion, equilibrium is reached. The Seebeck coefficient (also called the thermopower) is the ratio between the elecric field and the temperature gradient (or equivalently, the ratio between the voltage difference and temperature difference between the ends of the sample). So, roughly speaking, the Seebeck coefficient can be thought of as a measure of the coupling between the thermal and elecrical currents in a material. Note that the sign of the Seebeck coefficient depends on the sign of the charge carriers (whether positive or negative charge builds up on the cold end). So measuring the Seebeck coefficient is a way to determine whether the charge carriers in a particular material are holes or electrons.
NOTE: What we have described here is known as the absolute Seebeck effect. If we wanted to measure this voltage, the wires that the attach to the ends of the sample to hook up to our voltmeter would also develop Seebeck voltages. What we would measure is the difference between our wires and our sample. This is called the differential Seebeck effect. See the discussion of thermocouples below.
Now consider passing a current through a junction between two
different materials held at a constant temperature. This elecrical
current will drag along a thermal current, the magnitude and direction
of which depends on the Seebeck coefficients. If they are different,
thermal energy will be leaving the junction at a different rate than it
is entering. Thus heat is generated or absorbed at the junction.
Imagine that the material on the left is p-type (positive charge
carriers moving to the right) and the one on the right is n-type
(negative charge carriers moving to the left). Both materials will be
carrying heat towards the junction, and power will be be evolved there.
The Peltier coefficient of the junction is a
property depending on both materials and is the ratio of the power
evolved at the junction to the current flowing through it.
For the Thomson effect, consider a material with a current flowing through it and a temperature gradient applied to it. In this situation, themal energy is generated (or absorbed) all along the sample. The reason for this is similar to the reasoning behind the Peltier effect, if one realizes that the Seebeck coefficient for this material depends on temperature. This means that the Seebeck coefficient is different at different places along the sample. So the sample can be thought of as a series of many small Peltier junctions, each of which is generating (or absorbing) heat. The Thomson coefficient is the ratio of the Power evolved per unit volume in the sample to the applied current and temperature gradient.
Thermocouples are the most common examples of TE devices. They take advantage of the differential Seebeck effect. A diagram of a thermocouple is shown below.
The two legs of the circuit are made of different materials, and the two junctions are held at different temperatures. T is the temperature to be measured, T0 is known. Two identical leads are connected to a break in the circuit in an isothermal region. The voltmeter measures the potential difference between the ends of the leads. Since the leads are identical and the temperature difference between the ends of the leads is the same, their contribution to the voltage cancels. What is measured is the difference between the thermoelectric voltage generated by the two legs of the thermocouple. If the Seebeck coefficients are know, this gives the difference between the temperatures T and T0.
Thermoelectric materials take advantage of the coupling between thermal and electrical currents, and are used for the direct conversion between thermal and electrical energy. With these materials, electricity can be used to pump heat (thermoelectic coolers) or waste heat can be used to generate electricity (thermoelectric generators).
Thermoelectric coolers are designed to utilize the Peltier effect described above. These types of coolers have no moving parts and as a result are quiet and require little maintenance. Because of these advantages, they are useful in a wide variety of niche applications: cooling laser diodes and computer electronics, providing air conditioning in submarines, powering space probes, and even to chill food and drinks in portable picnic coolers (powered by car batteries). Unfortunately, the best materials used in Peltier coolers today cannot compete with the efficiencies of traditional cooling devices, such as the compressor in a household refrigerator. Therefore, the primary objective of our research is to find new materials which could be used to make more efficient thermoelectric coolers. If more efficient devices could be made, there would be a number of new and exciting applications for Peltier coolers.
The Peltier junction mentioned above consists of two materials, one with a positive thermopower and one with a negative thermopower. Since the charge carriers in p-type materials and n-type materials have opposite sign, their thermopowers have opposite sign.
Schematic of a TE device. Since the charge carriers move in a different direction in each leg, each carries heat away from the cold end.
It is more than just the thermopower that determines the performance of a device. We need the electrical resistivity to be small so energy is not wasted in Joule heating. We also need the thermal conductivity to be small so heat we pump to the hot end stays there. For maximum device efficiency, we need to maximize each material's dimensionless Figure of Merit (ZT).
At present, the best materials are small band gap semiconductors; optimized Bi2Te3 has S = 220 µV/K and ZT = 1 at room temperature. However, a ZT greater than 3 is needed to compete with traditional cooling technologies. Our goal is to find new materials with ZT > 1 at or below room temperature.