The Seebeck effect
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  (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
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 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 concluded that there is heat adsorption or generation at
the junctions depending on the direction of current flow.
The Thomson effect
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
In 1851, Thomson (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.
do all of these effects come into play with thermoelectric devices?
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:
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,
assumed to be valid for all materials used in thermoelectrics.
was later in 1909 and 1911 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 of a thermoelectric material is defined as :
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.
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.
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  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)
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.
of thermoelectric cooling
(Peltier effect) Thermoelectric
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.
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).