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# Thermionic emission

Thermionic emission is the flow of charge carriers from a surface or over some other kind of electrical potential barrier, caused by thermal vibrational energy overcoming the electrostatic forces restraining the charge carriers. The charge carriers can be electrons or ions, and are sometimes referred to as "thermions". The total charge of the emitted carriers (either positive or negative) will be equal in magnitude and opposite in sign to the charge left in the emitting region. The most classical example of thermionic emission is the emission of electrons from a hot metal cathode into a vacuum (archaically known as the Edison effect), but the term is now used to refer to any thermally excited charge emission process, even when the charge is emitted from one solid-state region into another. This process is crucially important in the operation of a variety of electronic devices and can be used for power generation or cooling. The magnitude of the charge flow increases dramatically with increasing temperature and for vacuum emission from metals tends to only become significant for temperatures over 1000 K. The science dealing with this phenomenon is thermionics.

## History

The phenomenon was initially reported in 1873 by Daniel Lordan in Britain. While doing work on charged objects, Lordan discovered that a red-hot iron sphere with a negative charge would lose its charge (discharging electrons into vacuum). He also found that this did not happen if the sphere had a positive charge. He didn't understand what any of this meant.[citation needed] Other early contributors included Hittorf (1869–1883), Goldstein (1885), and Elster and Geitel (1882–1889).

The effect was rediscovered by Thomas Edison on February 13, 1880, while trying to discover the reason for breakage of lamp filaments and uneven blackening (darkest near one terminal of the filament) of the bulbs in his incandescent lamps.

Edison built several experiment bulbs, some with an extra wire, a metal plate, or foil inside the bulb which was electrically separate from the filament. He connected the extra metal electrode to the lamp filament through a galvanometer. When the foil was given a more negative charge than the filament, no current flowed between the foil and the filament because the cool foil emitted few electrons. However, when the foil was given a more positive charge than the filament, the many electrons emitted from the hot filament were attracted to the foil, causing current to flow. This one-way flow of current was called the Edison effect (although the term is occasionally used to refer to thermionic emission itself). He found that the current emitted by the hot filament increased rapidly with increasing voltage, and filed a patent application for a voltage regulating device using the effect on November 15, 1883 (U.S. patent 307,031, the first US patent for an electronic device). He found that sufficient current would pass through the device to operate a telegraph sounder. This was exhibited at the International Electrical Exposition in Philadelphia in September 1884. William Preece, a British scientist took back with him several of the Edison Effect bulbs, and presented a paper on them in 1885, where he referred to thermionic emission as the "Edison Effect." [1] The British physicist John Ambrose Fleming, working for the British "Wireless Telegraphy" Company, discovered that the Edison Effect could be used to detect radio waves. Fleming went on to develop the two-element vacuum tube known as the diode, which he patented on November 16, 1904.

The thermionic diode can also be configured as a device that converts a heat difference to electric power directly without moving parts (a thermionic converter, a type of heat engine).

Owen Willans Richardson worked with thermionic emission and received a Nobel prize in 1928 "for his work on the thermionic phenomenon and especially for the discovery of the law named after him".

## Richardson's Law

In any metal, there are one or two electrons per atom that are free to move from atom to atom. This is sometimes referred to as a "sea of electrons". Their velocities follow a statistical distribution, rather than being uniform, and occasionally an electron will have enough velocity to exit the metal without being pulled back in. The minimum amount of energy needed for an electron to leave the surface is called the work function. The work function is characteristic of the material and for most metals is on the order of several electronvolts. Thermionic currents can be increased by decreasing the work function. This often-desired goal can be achieved by applying various oxide coatings to the wire.

In 1901 Owen Willans Richardson published the results of his experiments: the current from a heated wire seemed to depend exponentially on the temperature of the wire with a mathematical form similar to the Arrhenius equation. The modern form of this law (demonstrated by Saul Dushman in 1923, and hence sometimes called the Richardson-Dushman equation) states that the emitted current density J (A/m2) is related to temperature T by the equation:

$J = A T^2 e^{-W \over k T}$

where T is the metal temperature in kelvin, W is the work function of the metal, k is the Boltzmann constant. The proportionality constant A, known as Richardson's constant, given by

$A = {4 \pi m k^2 e \over h^3} = 1.20173 \times 10^6 A m^{-2}K^{-2}$

where m and -e are the mass and charge of an electron, and h is Planck's constant.

Because of the exponential function, the current increases rapidly with temperature when kT is less than W. (For essentially every material, melting occurs well before kT=W.)

The thermionic emission equations are of fundamental importance in electronics, significantly affecting both older vacuum tube technology (e.g. CRT applications, like television picture tubes and computer monitors, as well as high end radio and microwave applications requiring the high power intrinsic to tube technology), and more modern semiconductor designs.

While A theoretically has a value of 1.20.106 A m-2 K-2, in practice it strongly depends on material used. See work function for some practical values for A and W for some commonly used materials.

## Enhancement of thermionic emission

In most electronic devices, especially electron guns, the thermionic emitter will be given an electrical potential bias (or voltage), which creates an electric field and increases the emission current if it has the same sign as the thermion charge or decreases it if the signs are opposite. The effect of the potential can usually be modeled by a simple modification of the Richardson-Dushman equation; the current emitted from the metal cathode into the vacuum depends on the metal's thermionic work function, and this function is lowered from its normal value by the presence of image forces and by the electric field at this cathode. This field enhancement is given by the field-enhanced thermionic emission (FEE) equation:

$J (E_s,T,W) = A T^2 e^{ - (W - \Delta W) \over k T}$
$\Delta W = \left[{e^3 E_c \over (4 \pi \epsilon_0)}\right]^{1/2}$,

where Ec is the electric field strength at the cathode spot, ε0 is the vacuum permittivity.

This equation is relatively accurate for electric field strengths lower than about 108 V m−1, in which range the enhancement is known as the Schottky effect. For electric field strengths higher than 108 V m−1, quantum tunneling begins to contribute some significant emission current, which is called field emission. In this regime, the combined effects of field-enhanced thermionic and field emission can be modeled by the Murphy-Good equation for thermo-field (T-F) emission.[2] At even higher fields, field emission can become dominant and thermionic emission will no longer be significant.

Thermionic emission can also be enhanced by interaction with other forms of excitation such as light.[3]

## References

1. ^ "Edison" by Matthew Josephson. McGraw Hill, New York, 1959, ISBN 07-033046-8
2. ^ E.L. Murphy and R.H. Good, "Thermionic Emission, Field Emission, and the Transition Region", Phys. Rev. 102(6), pp. 1464-1473 (1956).
3. ^ A.G. Mal'shukov1 and K.A. Chao, "Opto-Thermionic Refrigeration in Semiconductor Heterostructures," Phys. Rev. Lett. 86, pp. 5570-5573 (2001).