Thermionic Emission

Thermionic emission

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Close up of thefilamenton a low pressure mercurygas discharge lampshowing white thermionic emission mix coating on the central portion of the coil. Typically made of a mixture of barium,strontiumandcalciumoxides, the coating is sputtered away through normal use, often eventually resulting in lamp failure /

Thermionic emissionis the heat-induced flow ofcharge carriersfrom 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 beelectronsorions, 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 asthermal electron emission.

The classical example of thermionic emission is the emission of electrons from a hot metalcathodeinto a vacuum (archaicallyknown as theEdison effect) in avacuum 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 onesolid-stateregion into another. This process is crucially important in the operation of a variety of electronic devices and can be used forpower generationor 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 asthermionics, but this name seems to be gradually falling into disuse.

History

In reading this history, it is necessary to remember that theelectronwas not identified as a separate physical particle until the 1897 work ofJ. 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 in1873byFrederick Guthriein 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 includedHittorf(1869–1883),Goldstein(1885), andElsterandGeitel(1882–18

The Edison effect in a diode tube. A diode tube is connected in two configurations, one has a flow of electrons and the other does not. Note that the arrows represent electron current, not conventional current. The effect was rediscovered byThomas Edisonon 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 theEdison 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 physicistJohn 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-elementvacuum tubeknown as thediode, 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 (athermionic converter, a type ofheat engine).Following J. J. Thomson's identification of the electron, the British physicistOwen Willans Richardsonbegan work on the topic that he later called "thermionic emission". He received aNobel Prize in Physicsin 1928 "for his work on the thermionic phenomenon and especially for the discovery of the law named after him".

Richardson's Law

In any solid metal, there are one or two electrons peratomthat 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 thework function. The work function is characteristic of the material and for most metals is on the order of severalelectronvolts. 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 1901Richardsonpublished 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 theArrhenius equation. Later, he proposed that the emission law should have the mathematical form

whereJis the emissioncurrent density[SI unit: A/m2],Tis the thermodynamic temperature of the metal [SI unit:Kelvin(K)],Wis thework functionof the metal,kis theBoltzmann constant, andAGis a parameter discussed next.

In the period 1911 to 1930, as physical understanding of the behavior of electrons in metals increased, various different theoretical expressions (based on different physical assumptions) were put forwards forAG, 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 forAGshould be, but there is agreement thatAGmust be written in the form

whereλRis a material-specific correction factor that is typically of order 0.5, andA0is a universal constant given by

wheremand −eare the mass and charge of an electron, andhisPlanck's constant.

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

.

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 factorλBintoλR, givingAG= λB(1 −rav)A0. Experimental values for the "generalized" coefficientAGare generally of the order of magnitude ofA0, 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 ofλR.

Considerable confusion exists in the literature of this area because: (1) many sources do not distinguish betweenAGandA0, but just use the symbolA(and sometimes the name "Richardson constant") indiscriminately; (2) equations with and without the correction factor here denoted byλRare 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 onlyA0in should be called the "elementary Richardson-type equation", and the equation with the "generalized" coefficientAGshould 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 whenkTis less thanW. (For essentially every material, melting occurs well beforekT=W.)

Schottky emission

In electron emission devices, especiallyelectron guns, the thermionic electron emitter will be biased negative relative to its surroundings. This creates an electric field ofmagnitudeFat the emitter surface. Without the field, the surface barrier seen by an escaping Fermi-level electron has heightWequal 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 replacingWby (W−ΔW). This gives the equation[4][5]

whereε0is the electric constant (also, formerly, called thevacuum permittivity).

Electron emission that takes place in the field-and-temperature-regime where this modified equation applies is often calledSchottky emission. This equation is relatively accurate for electric field strengths lower than about 108V m−1. For electric field strengths higher than 108Vm−1, so-calledFowler-Nordheim (FN) tunnelingbegins 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 matterwhich yield a decrease of collector emitting work function from 1.5 eV to 1.0–0.7 eV. Due to long-lived nature ofRydberg matterthis low work function remains low which essentially increases the low-temperature converter’s efficiency.[8]

Photon-enhanced thermionic emission

Photon-enhanced thermionic emission (PETE), a process developed by engineers atStanford University, that harnesses both the light and heat of the sun to generate electricity and increases the efficiency of solar power production by more than twice the current levels. The device developed for the process reaches peak efficiency after it reaches 200°C; most siliconsolar cellsbecome inert after reaching 100°C. Such device will work best inparabolic troughcollectors, which reach temperatures around 800°C. Although the team used agallium nitridesemiconductor in its "proof of concept" device, it claims that the use ofgallium arsenidecan increase the device's efficiency to 55–60 percent, nearly triple that of existing systems.

Space charge

From Wikipedia, the free encyclopedia

Space chargeis a concept in which excesselectric chargeis treated as acontinuumof charge distributed over a region of space (either a volume or an area) rather than distinct point-like charges. This model typically applies whencharge carriershave been emitted from some region of a solid—the cloud of emitted carriers can form a space charge region if they are sufficiently spread out, or the charged atoms or molecules left behind in the solid can form a space charge region. Space charge usually only occurs indielectricmedia (includingvacuum) because in a conductive medium the charge tends to be rapidly neutralized orscreened. The sign of the space charge can be either negative or positive. This situation is perhaps most familiar in the area near ametalobject when it is heated toincandescencein avacuum. This effect was first observed byThomas Edisonin light bulbfilaments, where it is sometimes called theEdison effect, but space charge is a significant phenomenon in many vacuum andsolid-state electronicdevices.

Physical explanation

When a metal object is placed in a vacuum and is heated to incandescence, the energy is sufficient to causeelectronsto "boil" away from the surfaceatomsand surround the metal object in a cloud offree electrons. This is calledthermionic emission. The resulting cloud is negatively charged, and can be attracted to any nearby positively charged object, thus producing an electrical current which passes through the vacuum.

Space charge can result from a range of phenomena, but the most important are:

1. Combination of the current density and spatially inhomogeneous resistivity
2. Ionization of species within the dielectric to form heterocharge
3. Charge injection from electrodes and from a stress enhancement
4. Polarization in structures such aswater trees

It has been suggested that inACmost of carriers injected at electrodes during a half of cycle are ejected during the next half cycle, so the net balance of charge on a cycle is practically zero. However, a small fraction of the carriers can be trapped at levels deep enough to retain them when the field is inverted. The amount of charge in AC should increase slower than inDCand become observable after longer periods of time.

Hetero and Homo Charge

Hetero charge means that the polarity of the space charge is opposite to that of neighboring electrode, and homo charge is the reverse situation. Under high voltage application, a hetero charge near the electrode is expected to reduce the breakdown voltage, whereas a homo charge will increase it. After polarity reversal under ac conditions, the homo charge is converted to hetero space charge.

Mathematical explanation

If the "vacuum" has apressureof 10-6mmHg or less, the mainvehicleof conduction iselectrons. The emission current density(J) from thecathode, as afunctionof its thermodynamictemperatureT, in the absence of space-charge, is given by:

where

A0=1.2 × 106A m-2K-2

e= elementary positive charge (i.e., magnitude of electron charge),

m= electron mass,

k=Boltzmann's constant= 1.38 x 10-23J/K,

h=Planck's constant= 6.55 x 10-34J s,

φ=work functionof the cathode,

ř= mean electron reflection coefficient.

The reflection coefficient can be as low as 0.105 but is usually near 0.5. ForTungsten, (1 - ř)A0= 0.6 to 1.0 × 106A m-2K-2, andφ= 4.52 eV. At 2500 °C, the emission is 3000 A/m2.

The emission current as given above is many times greater than that normally collected by the electrodes, except in somepulsedvalvessuch as thecavity magnetron. Most of the electrons emitted by the cathode are driven back to it by therepulsionof thecloudof electrons in its neighborhood. This is called thespace charge effect. In the limit of large current densities,Jis given by the Child-Langmuir equation below, rather than by the thermionic emission equation above.

Occurrence

Space charge is an inherent property of allvacuum tubes. This has at times made life harder or easier forelectrical engineerswho used tubes in their designs. For example, space charge significantly limited the practical application oftriodeamplifierswhich lead to further innovations such as the vacuum tubetetrode.

On the other hand, space charge was useful in some tube applications because it generates a negativeEMFwithin the tube's envelope, which could be used to create a negative bias on the tube's grid. Grid bias could also be achieved by using an applied grid voltage in addition to the control voltage. This could improve the engineer's control and fidelity of amplification.

Space charges can also occur withindielectrics. For example, when gas near a high voltage electrode begins to undergodielectric breakdown, electrical charges are injected into the region near the electrode, forming space charge regions in the surrounding gas. Space charges can also occur within solid or liquid dielectrics that are stressed by highelectric fields. Trapped space charges within solid dielectrics are often a contributing factor leading to dielectric failure within high voltage power cables and capacitors.

Child's Law

Graph showing Child-Langmuir Law. S and d are constant and equal to 1.

Also known as the Child-Langmuir Law or the Three-Halves Power Law, Child's Law states that the space-charge limited current in a plane-parallel diode varies directly as the three-halves power of the anode voltageVaand inversely as the square of the distancedseparating the cathode and the anode. That is,

.

WhereIais the anode current,Jthe current density, andSthe area. This assumes the following:

The electrodes are planar, parallel, equipotential surfaces of infinite dimensions.

The electrons have zero velocity at the cathode surface.

In the interelectrode region, only electrons are present.

The current is space-charge limited.

The anode voltage remains constant for a sufficiently long time so that the anode current is steady.

Mott's steady-state space-charge-limited conduction model

The steady-state space-charge-limited conduction-current densityJin a plane-parallel dielectric sample with electrode separationLis proportional to the square of the applied voltageV. That is,