Thermionic emission

Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the forces restraining it. The charge carriers can be electrons or ions, and in older literature are sometimes referred to as "thermions". After emission, a charge will initially be left behind in the emitting region that is equal in magnitude and opposite in sign to the total charge emitted. But if the emitter is connected to a battery, then this charge left behind will be neutralized by charge supplied by the battery, as the emitted charge carriers move away from the emitter, and finally the emitter will be in the same state as it was before emission. The thermionic emission of electrons is also known as thermal electron emission.

The classical example of thermionic emission is the emission of electrons from a hot metal cathode into a vacuum (archaically known as the Edison effect) in a vacuum tube. However, the term "thermionic emission" 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. However, vacuum emission from metals tends to become significant only for temperatures over 1000 K. The science dealing with this phenomenon has been known as thermionics, but this name seems to be gradually falling into disuse.

In reading this history, it is necessary to remember that the electron was not identified as a separate physical particle until the 1897 work of J. J. Thomson. One therefore has to be careful in using the word "electron" when discussing experiments that took place before this date.

The phenomenon was initially reported in 1873 by Frederick Guthrie in Britain. While doing work on charged objects, Guthrie discovered that a red-hot iron sphere with a positive charge would lose its charge (by somehow discharging it into air). He also found that this did not happen if the sphere had a negative charge.^[1] 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 charge flowed between the foil and the filament. We now know that this was because the cool foil emitted few electrons. However, when the foil was given a more positive charge than the filament, negative charge apparently flowed from the filament through the vacuum to the foil. This one-way 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,^[2] 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." ^[3] 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).

Following J. J. Thomson's identification of the electron, the British physicist Owen Willans Richardson began work on the topic that he later called "thermionic emission". He received a Nobel Prize in Physics in 1928 "for his work on the thermionic phenomenon and especially for the discovery of the law named after him".

In any solid metal, there are one or two electrons per atom that are free to move from atom to atom. This is sometimes collectively 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 a 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 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. Later, he proposed that the emission law should have the mathematical form

${\displaystyle J=A_{\mathrm {G} }T^{2}\mathrm {e} ^{-W \over kT}}$

where J is the emission current density [SI unit: A/m²], T is the thermodynamic temperature of the metal [SI unit: kelvin (K)], W is the work function of the metal, k is the Boltzmann constant, and A_G is a parameter discussed next.

In the period 1911 to 1930, as physical understanding of the behaviour of electrons in metals increased, various different theoretical expressions (based on different physical assumptions) were put forwards for A_G, by Richardson, Dushman, Fowler, Sommerfeld and Nordheim. Over 60 years later, there is still no consensus amongst interested theoreticians as to what the precise form of the expression for A_G should be, but there is agreement that A_G must be written in the form

${\displaystyle A_{\mathrm {G} }=\;\lambda _{\mathrm {R} }A_{0}}$

where λ_R is a material-specific correction factor that is typically of order 0.5, and A₀ is a universal constant given by

${\displaystyle A_{0}={4\pi mk^{2}e \over h^{3}}=1.20173\times 10^{6}\,\mathrm {A\,m^{-2}\,K^{-2}} }$

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

In fact, by about 1930 there was agreement that, due to the wave-like nature of electrons, some proportion r_av of the outgoing electrons would be reflected as they reached the emitter surface, so the emission current density would be reduced, and λ_R would have the value (1-r_av). Thus, one sometimes sees the thermionic emission equation written in the form

${\displaystyle J=(1-r_{\mathrm {av} })A_{0}T^{2}\mathrm {e} ^{-W \over kT}}$.

However, a modern theoretical treatment by Modinos assumes that the band-structure of the emitting material must also be taken into account. This would introduce a second correction factor λ_B into λ_R, giving ${\displaystyle A_{\mathrm {G} }=\lambda _{\mathrm {B} }(1-r_{\mathrm {av} })A_{0}}$. Experimental values for the "generalized" coefficient A_G are generally of the order of magnitude of A₀, but do differ significantly as between different emitting materials, and can differ as between different crystallographic faces of the same material. At least qualitatively, these experimental differences can be explained as due to differences in the value of λ_R.

Considerable confusion exists in the literature of this area because: (1) many sources do not distinguish between A_G and A₀, but just use the symbol A (and sometimes the name "Richardson constant") indiscriminately; (2) equations with and without the correction factor here denoted by λ_R are both given the same name; and (3) a variety of names exist for these equations, including "Richardson equation", "Dushman's equation", "Richardson-Dushman equation" and "Richard-Laue-Dushman equation". The nomenclature preferred by the editor writing this paragraph is that the equation with only A₀ in should be called the "elementary Richardson-type equation", and the equation with the "generalized" coefficient A_G should be called the "generalized Richardson-type equation". In the literature, the elementary equation is sometimes given in circumstances where the generalized equation would be more appropriate, and this in itself can cause confusion. To avoid misunderstandings, the meaning of any "A-like" symbol should always be explicitly defined in terms of the more fundamental quantities involved.

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.)

In electron emission devices, especially electron guns, the thermionic electron emitter will be biased negative relative to its surroundings. This creates an electric field of magnitude F at the emitter surface. Without the field, the surface barrier seen by an escaping Fermi-level electron has height W equal to the local work-function. The electric field lowers the surface barrier by an amount ΔW, and increases the emission current. This is known as the "Schottky effect" or field enhanced thermionic emission. It can be modeled by a simple modification of the Richardson equation, by replacing W by (W − ΔW). This gives the equation^[4][5]

${\displaystyle J(F,T,W)=A_{\mathrm {G} }T^{2}e^{-(W-\Delta W) \over kT}}$

${\displaystyle \Delta W={\sqrt {e^{3}F \over 4\pi \epsilon _{0}}},}$

where ε₀ is the electric constant (also, formerly, called the vacuum permittivity).

Electron emission that takes place in the field-and-temperature-regime where this modified equation applies is often called Schottky emission. This equation is relatively accurate for electric field strengths lower than about 10⁸ V  m⁻¹. For electric field strengths higher than 10⁸ V m⁻¹, so-called Fowler-Nordheim (FN) tunneling begins to contribute significant emission current. 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.^[6] At even higher fields, FN tunneling becomes the dominant electron emission mechanism, and the emitter operates in the so-called "cold field electron emission (CFE)" regime.

Thermionic emission can also be enhanced by interaction with other forms of excitation such as light.^[7] For example, excited Cs-vapours in thermionic converters form clusters of Cs-Rydberg matter which yield a decrease of collector emitting work function from 1.5 eV to 1.0–0.7 eV. Due to long-lived nature of Rydberg matter this low work function remains low which essentially increases the low-temperature converter’s efficiency.^[8]

• Cathode
• Cold Cathode
• Space charge
• Thermionic converter
• Thermoelectric effect
• Vacuum tube
• Work function
• X-ray tube

• How vacuum tubes really work with a section on thermionic emission, with equations, john-a-harper.com.
• Owen Richardson's Nobel lecture on thermionics, nobel.se, December 12, 1929. (PDF)
• Derivations of thermionic emission equations from an undergraduate lab, csbsju.edu.