The Seebeck effect

The voltage difference, dV, produced across the terminals of an open circuit made up of a pair of dissimilar metals, A and B, whose two junctions are held at different temperatures, is directly proportional to the difference of the hot and cold junction temperatures, Kh - Kc, and does not depend in any way on the distribution of temperature along the metals between the junctions. The factor of proportionality, SAB, is called the relative Seebeck coefficient, thermoelectric power, or just thermopower, of the bi-metalic couple, and in general this coefficient also varies with the level of the temperature at which the temperature difference occurs. If the circuit is closed, a current will flow in the metals, which can be detected by the magnetic field produced around the wires, or by the joule heating produced by the resistance in the wires, or closing the circuit with a capacitor or condensor of sufficient capacity to accumulate a measurable charge for the transient current which will flow in this case, or by a galvanometer or ammeter placed in the circuit to measure the current, or by measuing the amount of chemical substance deposited at the positive and/or negative electrodes in an electrochemical cell.

The discovery of thermoelectricity dates back to Seebeck [1] (1770-1831). Thomas Johann Seebeck was born in Revel (now Tallinn), the capital of Estonia which at that time was part of East Prussia. Seebeck was a member of a prominent merchant family with ancestral roots in Sweden. He studied medicine in Germany and qualified as a doctor in 1802. Seebeck spent most of his life involved in scientific research. In 1821 he discovered that a compass needle deflected when placed in the vicinity of a closed loop formed from two dissimilar metal conductors if the junctions were maintained at different temperatures. He also observed that the magnitude of the deflection was proportional to the temperature difference and depended on the type of conducting material, and does not depend on the temperature distribution along the conductors. Seebeck tested a wide range of materials, including the naturally found semiconductors ZnSb and PbS. It is interesting to note that if these materials had been used at that time to construct a thermoelectric generator, it could have had an efficiency of around 3% - similar to that of contemporary steam engines.

The Seebeck coefficient 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.

The Peltier effect

While the Seebeck effect occurs in a single piece of conducting material, the Peltier effect is observed when two different conductors are brought together at a junction. Because the Fermi levels of the two materials are usually different, some electrons will cross the junction until an electric field is generated which is sufficiently large to impede further electron flow across the junction. The size of the potential difference established across this Peltier junction depends on the kind of metals used as well as the temperature of the junction. Additionally, there is a temperature drop at the junction due to the fact that the electrons must use some of the metal's energy to make the jump across the junction.
It was later in 1834 that Peltier[2] described thermal effects at the junctions of dissimilar conductors when an electrical current flows between the materials. Peltier failed however to understand the full implications of his findings and it wasn't until four years later that Lenz[3] concluded that there is heat adsorption or generation at the junctions depending on the direction of current flow.

The Thomson effect

Having the smallest magnitude of the three effects, the Thompson effect accounts for the heat absorbed (or emitted) in a single piece of conducting material when an electric current flows through it and when it has a temperature gradient across it. Its existence was first noted by Thompson (in the mid-19th century), when he tried to resolve discrepancies between the Seebeck voltages he measured in a thermoelectric circuit and the voltages he expected to detect in a (reversible) system that obeys the laws of thermodynamics.

In 1851, Thomson[4] (later Lord Kelvin) predicted and subsequently observed experimentally the cooling or heating of a homogeneous conductor resulting from the flow of an electrical current in the presence of a temperature gradient. This is know as the Thomson effect and is defined as the rate of heat generated or absorbed in a single current carrying conductor subjected to a temperature gradient.

How do all of these effects come into play with thermoelectric devices?

Take two conductors, one n-type (excess of electrons) and one p-type (deficiency of electrons, or excess of "holes") and create a junction between them. When a current is applied across the junction, some heat is absorbed in order to compensate for the heat generated by thermal conductance at equilibrium as well as by Joule (resistive) heating. It is this balancing condition which is characterized by each material's figure of merit, Z:

Z= S2/(rk)
Here, S is the Seebeck coefficient (thermopower), r is the electrical resistivity, and k is the thermal conductivity. The magnitude of the difference between the thermopowers of the two materials is directly proportional to the Peltier coefficient of the junction. In a physical sense, the Peltier coefficient can be thought of as the amount of energy each electron carries across the junction relative to the Fermi energy.

To find the most efficient thermoelectric cooling device, it is necessary to optimize each material's figure of merit, making Z as large as possible. This is a difficult task since the thermopower, electrical conductivity, and thermal conductivity are each determined by the specific electronic structure of the material; it is not possible to change one parameter without changing the others.

The three thermoelectric effects above are related by the Kelvin relationships[5], assumed to be valid for all materials used in thermoelectrics.

Thermoelectric Materials

It was later in 1909[6] and 1911[7] that Altenkirch showed that good thermoelectric materials should possess large Seebeck coefficients, high electrical conductivity and low thermal conductivity. A high electrical conductivity is necessary to minimise Joule heating, whilst a low thermal conductivity helps to retain heat at the junctions and maintain a large temperature gradient. These three properties were later embodied in the so-called figure-of-merit, Z. Since Z varies with temperature, a useful dimensionless figure-of-merit can be defined as ZT.

Figure-of-merit, Z

The figure-of-merit of a thermoelectric material is defined as :

where is the Seebeck coefficient of the material (measured in microvolts/K), is the electrical conductivity of the material and is the total thermal conductivity of the material.

Metals

Although the properties favoured for good thermoelectric materials were known, the advantages of semiconductors as thermoelectric materials were neglected and research continued to focus on metals and metal alloys. These materials however have a constant ratio of electrical to thermal conductivity (Widemann-Franz-Lorenz law) so it is not possible to increase one without increasing the other. Metals best suited to thermoelectric applications should therefore possess a high Seebeck coefficient. Unfortunately most possess Seebeck coefficients in the order of 10 microvolts/K, resulting in generating efficiencies of only fractions of a percent.

Semiconductors

It was during the 1920's that the development of synthetic semiconductors with Seebeck coefficients in excess of 100 microvolts/K increased interest in thermoelectricity. At this time it was not apparent that semiconductors were superior thermoelectric materials due to their higher ratio of electricall conductivity to thermal conductivity, when compared to metals.

Abram F. Ioffe
As early as 1929 when very little was known about semiconductors, Abram Fedorovich Ioffe (1880-1960) showed that a thermoelectric generator utilising semiconductors could achieve a conversion efficiency of 4%, with further possible improvement in its performance. By the 1950's, Ioffe and his colleagues [8] had developed the theory of thermoelectric conversion, which forms the basis of all modern thermoelectric theory.
A large number of semiconductor materials were being investigated by the late 1950's and early 1960's , several of which emerged with Z values significantly higher than in metals or metal alloys. No single compound semiconductor evolved that exhibited a uniform high figure-of-merit over a wide temperature range, so research focused on developing materials with high figure-of-merit values over relatively narrow temperature ranges. Of the great number of materials investigated, those based on bismuth telluride, lead telluride and silicon-germanium alloys emerged as the best for operating to temperatures of about 450K, 900K and 1400K respectively.

Illustration of thermoelectric generation (Seebeck effect)
Thermoelectric
Generation
The simplest thermoelectric generator consists of a thermocouple, comprising a p-type and n-type thermoelement connected electrically in series and thermally in parallel. Heat is pumped into one side of the couple and rejected from the opposite side. An electrical current is produced, proportional to the temperature gradient between the hot and cold junctions.

Illustration of thermoelectric cooling
(Peltier effect) Thermoelectric
Cooling
If an electric current is applied to the thermocouple as shown, heat is pumped from the cold junction to the hot junction. The cold junction will rapidly drop below ambient temperature provided heat is removed from the hot side. The temperature gradient will vary according to the magnitude of current applied.

The Thermoelectric Module

A typical thermoelectric module is shown left. The module consists of pairs of p-type and n-type semiconductor thermoelements forming thermocouples which are connected electrically in series and thermally in parallel.

In cooling mode, an electrical current is supplied to the module. Heat is pumped from one side to the other (Peltier effect), the result is that one side of the module becomes cold.
In generating mode, a temperature gradient is maintained across the module. The heat flux passing through the module is converted into electrical power (Seebeck effect).