Thermoelectric effect

# Thermoelectric effect

Overview
The thermoelectric effect is the direct conversion of temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

differences to electric voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

and vice-versa. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, it creates a temperature difference. At the atomic scale, an applied temperature gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

causes charged carriers in the material to diffuse from the hot side to the cold side, similar to a classical gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...

that expands when heated; hence inducing a thermal current.
Discussion

Encyclopedia
The thermoelectric effect is the direct conversion of temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

differences to electric voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

and vice-versa. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, it creates a temperature difference. At the atomic scale, an applied temperature gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

causes charged carriers in the material to diffuse from the hot side to the cold side, similar to a classical gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...

that expands when heated; hence inducing a thermal current.

This effect can be used to generate electricity, measure temperature or change the temperature of objects. Because the direction of heating and cooling is determined by the polarity of the applied voltage, thermoelectric devices are efficient temperature controllers.

The term "thermoelectric effect" encompasses three separately identified effects: the Seebeck effect, Peltier effect and Thomson effect. Textbooks may refer to it as the Peltier–Seebeck effect. This separation derives from the independent discoveries of French physicist Jean Charles Athanase Peltier
Jean Charles Athanase Peltier
Jean Charles Athanase Peltier ]] – October 27, 1845, in Paris) was a French physicist.He discovered the calorific effect of electric current passing through the junction of two different metals...

and Estonian-German physicist Thomas Johann Seebeck
Thomas Johann Seebeck
Thomas Johann Seebeck was a physicist who in 1821 discovered the thermoelectric effect.Seebeck was born in Reval to a wealthy Baltic German merchant family. He received a medical degree in 1802 from the University of Göttingen, but preferred to study physics...

. Joule heating
Joule heating
Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor releases heat. It was first studied by James Prescott Joule in 1841. Joule immersed a length of wire in a fixed mass of water and measured the temperature...

, the heat that is generated whenever a voltage is applied across a resistive material, is related though it is not generally termed a thermoelectric effect. The Peltier–Seebeck and Thomson effects are thermodynamically reversible
Reversible process (thermodynamics)
In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...

, whereas Joule heating is not.

## Seebeck effect

The Seebeck effect is the conversion of temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

differences directly into electricity
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...

and is named for German physicist Thomas Johann Seebeck
Thomas Johann Seebeck
Thomas Johann Seebeck was a physicist who in 1821 discovered the thermoelectric effect.Seebeck was born in Reval to a wealthy Baltic German merchant family. He received a medical degree in 1802 from the University of Göttingen, but preferred to study physics...

, who, in 1821 discovered that a compass needle would be deflected by a closed loop formed by two metals joined in two places, with a temperature difference between the junctions. This was because the metals responded differently to the temperature difference, creating a current loop and a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

. Seebeck did not recognize there was an electric current involved, so he called the phenomenon the thermomagnetic effect. Danish physicist Hans Christian Ørsted
Hans Christian Ørsted
Hans Christian Ørsted was a Danish physicist and chemist who discovered that electric currents create magnetic fields, an important aspect of electromagnetism...

rectified the mistake and coined the term "thermoelectricity". The voltage created by this effect is on the order of several microvolts
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

per kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

difference. One such combination, copper-constantan
Constantan
Constantan is a copper-nickel alloy usually consisting of 55% copper and 45% nickel.Also known as Eureka.Its main feature is its resistivity which is constant over a wide range of temperatures...

, has a Seebeck coefficient of 41 microvolts per kelvin at room temperature.

The voltage V developed can be derived from:

where SA and SB are the thermopower
Thermopower
The thermopower, or thermoelectric power of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material...

s (Seebeck coefficient) of metals A and B as a function of temperature and T1 and T2 are the temperatures of the two junctions. The Seebeck coefficients are non-linear as a function of temperature, 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:

The Seebeck effect is used in the thermocouple
Thermocouple
A thermocouple is a device consisting of two different conductors that produce a voltage proportional to a temperature difference between either end of the pair of conductors. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert a...

to measure a temperature difference; absolute temperature may be found by setting one end to a known temperature. A metal of unknown composition can be classified by its thermoelectric effect if a metallic probe of known composition, kept at a constant temperature, is held in contact with it. Industrial quality control instruments use this as thermoelectric alloy sorting to identify metal alloys. Thermocouples in series form a thermopile
Thermopile
A thermopile is an electronic device that converts thermal energy into electrical energy. It is composed of several thermocouples connected usually in series or, less commonly, in parallel....

, sometimes constructed in order to increase the output voltage, since the voltage induced over each individual couple is small. Thermoelectric generators are used for creating power from heat differentials and exploit this effect.

### Thermopower

The thermopower or Seebeck coefficient, represented by S, of a material measures the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material, and the entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

per charge carrier in the material. S has units of V/K, though μV/K is more common. Values in the hundreds of μV/K, regardless of sign, are typical of good thermoelectric materials. The term "thermopower" is a misnomer since it does not measure power, but measures the voltage induced in response to a temperature difference. An applied temperature difference causes charged carriers in the material to diffuse from the hot side to the cold side. Mobile charged carriers migrating to the cold side leave behind their oppositely charged nuclei at the hot side thus giving rise to a thermoelectric voltage. Since a separation of charges creates an electric potential, the buildup of charged carriers onto the cold side eventually ceases at some maximum value since the electric field is at equilibrium. An increase in the temperature difference resumes a buildup of charge carriers on the cold side, leading to an increase in the thermoelectric voltage, and vice versa.
The material's temperature and crystal structure influence S; typically metals have small thermopowers because of half-filled bands caused by equal negative and positive charges cancelling each other contributing to the induced thermoelectric voltage. In contrast, semiconductors can be doped with excess electrons or holes, causing the magnitude of S to be large. The sign of the thermopower determines which charged carriers dominate the electric transport.

If the temperature difference between the two ends of a material is small, then the thermopower of a material is defined approximately as:

and a thermoelectric voltage of ΔV is seen at the terminals.

This can be written in relation to the electric field and the temperature gradient by the approximate equation:

The absolute thermopower of the material of interest is rarely practically measured because electrodes attached to a voltmeter must be placed onto the material in order to measure the thermoelectric voltage, inducing a thermoelectric voltage across one leg of the measurement electrodes. The measured thermopower then includes the thermopower of the material of interest and the material of the measurement electrodes and is written as:

Superconductors have S = 0 since the charged carriers produce no entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. This allows a direct measurement of the absolute thermopower of the material of interest, since it is the thermopower of the entire thermocouple. In addition, a measurement of the Thomson coefficient , of a material yields the thermopower through the relation

S is an important material parameter that determines the efficiency of a thermoelectric material; a larger induced thermoelectric voltage and a higher S mean a higher efficiency.

### Charge-carrier diffusion

The Seebeck effect is caused by two things: charge-carrier diffusion and phonon drag. Charge carrier
Charge carrier
In physics, a charge carrier is a free particle carrying an electric charge, especially the particles that carry electric currents in electrical conductors. Examples are electrons and ions...

s in the materials 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, and vice versa. If the conductor were left to reach thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

, this process would result in heat being distributed evenly throughout the conductor (see heat transfer
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...

). The movement of heat (in the form of hot charge carriers) from one end to the other is a heat current and an electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

as charge carriers are moving.

In a system where both ends are kept at a constant temperature difference, there is a constant diffusion of carriers. If the rate of diffusion of hot and cold carriers in opposite directions is equal, there is no net change in charge. The diffusing charges are scattered
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

by impurities, imperfections, and lattice vibrations or phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

s. If the scattering is energy dependent, the hot and cold carriers will diffuse at different rates, creating a higher density of carriers at one end of the material and an electrostatic voltage.

This electric field 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. This means the thermopower of a material depends greatly on impurities, imperfections, and structural changes that vary with temperature and electric field; the thermopower of a material is a collection of many different effects.

Early thermocouples were metallic, but many more recently developed thermoelectric devices are made from alternating p-type and n-type semiconductor elements connected by metallic connectors. Semiconductor junctions are common in power generation devices, while metallic junctions are more common in temperature measurement. Charge flows through the n-type element, crosses a metallic interconnect, and passes into the p-type element. If a power source is provided, the thermoelectric device may act as a cooler by the Peltier effect described below. Electrons in the n-type element move opposite the direction of current and holes in the p-type element will move in the direction of current, both removing heat from one side of the device. When a heat source is provided, the thermoelectric device functions as a power generator. The heat source drives electrons in the n-type element toward the cooler region, creating a current through the circuit. Holes in the p-type element then flow in the direction of the current. Therefore, thermal energy is converted into electrical energy.

### Phonon drag

Phonons are not always in local thermal equilibrium; they move against 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, hence losing momentum and contributing to the thermoelectric field. This contribution is most important in the temperature region where phonon-electron scattering is predominant. This happens for

where θD is the Debye temperature. At lower temperatures there are fewer 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.

## Peltier effect

The Peltier effect is the presence of heat at an electrified junction of two different metals and is named for French physicist Jean-Charles Peltier, who discovered it in 1834. When a current is made to flow through a junction made of materials A and B, heat is generated at the upper junction at T2, and absorbed at the lower junction at T1. The Peltier heat absorbed by the lower junction per unit time is equal to

where ΠAB is the Peltier coefficient for the thermocouple composed of materials A and B and ΠAB) is the Peltier coefficient of material A (B). Π varies with the material's temperature and its specific composition: p-type silicon typically has a positive Peltier coefficient below ~550 K, but n-type silicon is typically negative.

The Peltier coefficients represent how much heat current is carried per unit charge through a given material. Since charge current must be continuous across a junction, the associated heat flow will develop a discontinuity if ΠA and ΠB are different. Depending on the magnitude of the current, heat must accumulate or deplete at the junction due to a non-zero divergence there caused by the carriers attempting to return to the equilibrium that existed before the current was applied by transferring energy from one connector to another. Individual couples can be connected in series to enhance the effect. Thermoelectric heat pump
Heat pump
A heat pump is a machine or device that effectively "moves" thermal energy from one location called the "source," which is at a lower temperature, to another location called the "sink" or "heat sink", which is at a higher temperature. An air conditioner is a particular type of heat pump, but the...

s exploit this phenomenon, as do thermoelectric cooling
Thermoelectric cooling
Thermoelectric cooling uses the Peltier effect to create a heat flux between the junction of two different types of materials. A Peltier cooler, heater, or thermoelectric heat pump is a solid-state active heat pump which transfers heat from one side of the device to the other side against the...

devices found in refrigerators.

## Thomson effect

The Thomson effect was predicted and subsequently observed by Lord Kelvin
William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...

in 1851. It describes the heating or cooling of a current-carrying conductor with a temperature gradient.

Any current-carrying conductor (except for a superconductor) with a temperature difference between two points either absorbs or emits heat, depending on the material. If a current density J is passed through a homogeneous conductor, the heat production q per unit volume is:

where ρ is the resistivity
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...

of the material, dT/dx is the temperature gradient along the wire and μ is the Thomson coefficient. The first term is the Joule heating
Joule heating
Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor releases heat. It was first studied by James Prescott Joule in 1841. Joule immersed a length of wire in a fixed mass of water and measured the temperature...

, which does not change in sign; the second term is the Thomson heating, which follows J changing sign.

In metals such as zinc and copper, whose temperature is directly proportional to their potential, when current moves from the hotter end to the colder end, there is a generation of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

and the positive Thomson effect occurs. Conversely, in metals such as cobalt, nickel, and iron, whose temperature is inversely proportional to their potential, when current moves from the hotter end to the colder end, there is an absorption of heat and the negative Thomson effect occurs.

If the Thomson coefficient of a material is measured over a wide temperature range, it can be integrated using the Thomson relations to determine the absolute values for the Peltier and Seebeck coefficients. This needs to be done only for one material, since the other values can be determined by measuring pairwise Seebeck coefficients in thermocouples containing the reference material and then adding back the absolute thermopower
Thermopower
The thermopower, or thermoelectric power of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material...

of the reference material.

Lead is a main-group element in the carbon group with the symbol Pb and atomic number 82. Lead is a soft, malleable poor metal. It is also counted as one of the heavy metals. Metallic lead has a bluish-white color after being freshly cut, but it soon tarnishes to a dull grayish color when exposed...

is commonly stated to have a Thomson coefficient of zero; in fact, it is non-zero, albeit being very small. In contrast, the thermoelectric coefficients of all known superconductors are zero.

### Thomson relations

The Thomson coefficient is unique among the three main thermoelectric coefficients because it is the only one directly measurable for individual materials. The Peltier and Seebeck coefficients can only be determined for pairs of materials; hence, no direct methods exist for determining absolute Seebeck or Peltier coefficients for an individual material. In 1854, Lord Kelvin found relationships between the three coefficients, implying that only one could be considered unique.

The first Thomson relation is

where T is the absolute temperature, μ is the Thomson coefficient and S is the Seebeck coefficient. The second Thomson relation is

where Π is the Peltier coefficient. It predicted the Thomson effect before it was formalized.

## Figure of merit

The figure of merit
Figure of merit
A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. In engineering, figures of merit are often defined for particular materials or devices in order to determine their relative utility for an application...

Z for thermoelectric devices is defined as

where σ is the electrical conductivity, κ is the thermal conductivity, and S is the Seebeck coefficient. The dimensionless figure of merit ZT is formed by multiplying Z with the average temperature

A greater ZT indicates a greater thermodynamic efficiency, subject to certain provisions, particularly that the two materials in the couple have similar Z. ZT is therefore a method for comparing the potential efficiency of devices using different materials. Values of 1 are considered good; values in the 3–4 range are essential for thermoelectrics to compete with mechanical devices in efficiency. To date, the best reported ZT values are in the 2–3 range. Much of the research in thermoelectric materials has focused on increasing S and reducing κ by manipulating the nanostructure of the materials.

## Device efficiency

The efficiency of a thermoelectric device for electricity generation is given by η, defined as

The maximum efficiency ηmax is defined as

where TH is the temperature at the hot junction and TC is the temperature at the surface being cooled. is the modified dimensionless figure of merit, which takes into consideration the thermoelectric capacity of both thermoelectric materials being used in the device and is defined as

where ρ is the electrical resistivity, is the average temperature between the hot and cold surfaces and the subscripts n and p denote properties related to the n- and p-type semiconducting thermoelectric materials, respectively. Since thermoelectric devices are heat engines, their efficiency is limited by the Carnot efficiency, hence the TH and TC terms in . Regardless, the coefficient of performance of current commercial thermoelectric refrigerators ranges from 0.3 to 0.6, one-sixth the value of traditional vapor-compression refrigerators.

### Seebeck effect

The Seebeck effect is used in the thermoelectric generator, which functions like a heat engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...

, but is less bulky, has no moving parts, and is typically more expensive and less efficient. These have a use in power plants for converting waste heat
Waste heat
Waste heat sometimes called Secondary heat or Low-grade heat refers to heat produced by machines, electrical equipment and industrial processes for which no useful application is found. Energy is often produced by a heat engine, running on a source of high-temperature heat...

into additional power (a form of energy recycling
Energy recycling
Energy recycling is the energy recovery process of utilizing energy that would normally be wasted, usually by converting it into electricity or thermal energy. Undertaken at manufacturing facilities, power plants, and large institutions such as hospitals and universities, it significantly...

), and in automobiles as automotive thermoelectric generators (ATGs) for increasing fuel efficiency. Space probes often use radioisotope thermoelectric generator
A radioisotope thermoelectric generator is an electrical generator that obtains its power from radioactive decay. In such a device, the heat released by the decay of a suitable radioactive material is converted into electricity by the Seebeck effect using an array of thermocouples.RTGs can be...

s with the same mechanism but using radioisotopes to generate the required heat difference.

### Peltier effect

The Peltier effect can be used to create a refrigerator
Refrigerator
A refrigerator is a common household appliance that consists of a thermally insulated compartment and a heat pump that transfers heat from the inside of the fridge to its external environment so that the inside of the fridge is cooled to a temperature below the ambient temperature of the room...

which is compact and has no circulating fluid or moving parts; such refrigerators are useful in applications where their advantages out weigh the disadvantage of their very low efficiency

### Temperature measurement

Thermocouple
Thermocouple
A thermocouple is a device consisting of two different conductors that produce a voltage proportional to a temperature difference between either end of the pair of conductors. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert a...

s and thermopile
Thermopile
A thermopile is an electronic device that converts thermal energy into electrical energy. It is composed of several thermocouples connected usually in series or, less commonly, in parallel....

s are devices that use the Seebeck effect to measure the temperature difference between two objects, one connected to a voltmeter and the other to the probe. The temperature of the voltmeter, and hence that of the material being measured by the probe, can be measured separately using cold junction compensation
Thermocouple
A thermocouple is a device consisting of two different conductors that produce a voltage proportional to a temperature difference between either end of the pair of conductors. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert a...

techniques.