Description of the phenomenon of thermionic emission. Emission of electrons from conductors. Dependence of thermionic current on temperature. Richardson-Deshman formula

Today the focus is on thermionic emission. Variants of the name of the effect, its manifestation in a medium and in a vacuum are considered. Temperature limits are explored. The dependent components of the saturation current density of thermionic emission are determined.

Names of thermionic emission effect

The term thermionic emission has other names. Based on the names of the scientists who discovered and first studied this phenomenon, it is defined as the Richardson effect or the Edison effect. Thus, if a person encounters these two phrases in the text of a book, he must remember that the same physical term is implied. Confusion was caused by disagreement between publications of domestic and foreign authors. Soviet physicists sought to give explanatory definitions to the laws.

The term “thermionic emission” contains the essence of the phenomenon. A person who sees this phrase on the page immediately understands that we are talking about the temperature emission of electrons, but it remains behind the scenes that this certainly happens in metals. But that’s why definitions exist, to reveal details. Foreign science is very sensitive to primacy and copyright. Therefore, a scientist who was able to record something receives a named phenomenon, and poor students must actually memorize the names of the discoverers, and not just the essence of the effect.

Determination of thermionic emission

The phenomenon of thermionic emission is when electrons are released from metals at high temperatures. Thus, heated iron, tin or mercury are the source of these elementary particles. The mechanism is based on the fact that there is a special connection in metals: the crystal lattice of positively charged nuclei is, as it were, a common base for all electrons that form a cloud inside the structure.

Thus, among the negatively charged particles that are located near the surface, there will always be those that have enough energy to leave the volume, that is, to overcome the potential barrier.

Thermionic emission effect temperature

Thanks to the metallic bond, there will be electrons near the surface of any metal that have enough strength to overcome the potential exit barrier. However, due to this same energy dispersion, one particle barely breaks away from the crystalline structure, while the other flies out and covers a certain distance, ionizing the environment around it. Obviously, the more kelvins in the medium, the more electrons acquire the ability to leave the volume of the metal. Thus, the question arises of what is the temperature of thermionic emission. The answer is not simple, and we will consider the lower and upper limits of the existence of this effect.

Temperature limits of thermionic emission

The connection between positive and negative particles in metals has a number of features, including a very dense energy distribution. Electrons, being fermions, each occupy their own energy niche (unlike bosons, which can all be in the same state). Despite this, the difference between them is so small that the spectrum can be considered continuous rather than discrete.

In turn, this leads to a high density of states of electrons in metals. However, even at very low temperatures close to absolute zero (remember, this is zero kelvin, or approximately minus two hundred seventy-three degrees Celsius) there will be electrons with higher and lower energies, since they cannot all be in the lowest state at the same time. This means that under certain conditions (thin foil) very rarely the release of an electron from the metal will be observed even at extremely low temperatures. Thus, the lower limit of thermionic emission temperature can be considered to be a value close to absolute zero.

On the other side of the temperature scale is metal melting. According to physicochemical data, this characteristic differs for all materials of this class. In other words, there are no metals with the same melting point. Mercury or liquid under normal conditions goes from crystalline form already at minus thirty-nine degrees Celsius, while tungsten - at three and a half thousand.

However, all these limits have one thing in common - metal ceases to be a solid body. This means that laws and effects change. And there is no need to say that thermionic emission exists in the melt. Thus, the upper limit of this effect becomes the melting temperature of the metal.

Thermionic emission in vacuum conditions

Everything discussed above relates to a phenomenon in a medium (for example, in air or in an inert gas). Now let us turn to the question of what is thermionic emission in a vacuum. To do this, we will describe the simplest device. A thin metal rod is placed in the flask from which the air has been pumped out, to which the negative pole of the current source is connected. Note that the material must melt at high enough temperatures so as not to lose its crystalline structure during the experiment. The cathode thus obtained is surrounded by a cylinder of another metal and the positive pole is connected to it. Naturally, the anode is also located in a vacuum-filled vessel. When the circuit is closed, we obtain a thermionic emission current.

It is noteworthy that under these conditions the dependence of current on voltage at a constant cathode temperature does not obey Ohm’s law, but the law of the second three. It is also named after Child (in other versions Child-Langmuir and even Child-Langmuir-Boguslavsky), and in German-language scientific literature - the Schottky equation. As the voltage in such a system increases, at a certain moment all the electrons emitted from the cathode reach the anode. This is called saturation current. On the current-voltage characteristic, this is expressed in the fact that the curve reaches a plateau, and further increase in voltage is not effective.

Thermionic emission formula

These are the features that thermionic emission has. The formula is quite complex, so we will not present it here. In addition, it is easy to find in any reference book. In general, there is no formula for thermionic emission as such; only the saturation current density is considered. This value depends on the material (which determines the work function) and the thermodynamic temperature. All other components of the formula are constants.

Many devices operate based on thermionic emission. For example, old large TVs and monitors have exactly this effect.

The phenomenon of thermionic emission was discovered in 1883 . famous American inventorEdison.

He observed this phenomenon in a vacuum lamp with two electrodes - an anode having a positive potential and
cathode with negative potential.

The cathode of the lamp can be a filament made of
refractory metal (tungsten, molybdenum
tantalum, etc.), heated by electric
electric shock

This lamp is calledvacuum diode .

Diodeconsists of made of glass or metal

housingfromfrom which the air has been pumped out. Soldered into the cylinder

two electrodes - cathode and anode. In a diode with a cathode

indirect heating there is a miniature “stove”,

which serves to heat the cathode. Usually the cathode is arranged

in the form of a cylinder inside which the heater is located, the anode is a cylinder that is located around the cathode. If you apply a positive potential to the anode of the lamp relative to the cathode
then the electric field between the anode and the cathode will promote the movement of electrons from the cathode to the anode.

If the cathode is cold, then the current in the cathode-anode circuit
practically absent.

As the temperature of the cathode in the circuit increases

cathode - anode an electric current appears, which
more, the higher the cathode temperature.

At a constant cathode temperature, the current in the circuit

cathode-anode increases with increasing difference

potentialsUbetween the cathode and anode and comes out

to some stationary value,

called saturation current / n .

In this case, all thermionic electrons emitted by the cathode
reach the anode. The anode current is not proportionalU, and therefore
For a vacuum diode, Ohm's law does not apply.

The phenomenon of electrons being emitted by heated bodies (emitters) into a vacuum is called thermionic emission.

Thermionic emission - electrons acquire kinetic energy when the metal is heated. A metal heated to 1000 - 1500°C will be surrounded by a “cloud” of electrons. A significant number of electrons will have kinetic energy greater than the work function, and these electrons can be ejected from the metal.

Vacuum diodes are used to rectify alternating electric current

The nature of current in liquids. Law of electrolysis. Electrolytes.

Not only metals and semiconductors are conductors of electric current. Electric current is carried out by solutions of many substances in water. As experience shows, pure water does not conduct electric current, that is, there are no free carriers of electric charges in it. Crystals of table salt and sodium chloride do not conduct electricity. However, sodium chloride solution is a good conductor of electric current. Solutions of salts, acids and bases that can conduct electric current are called electrolytes

The passage of an electric current through an electrolyte is necessarily accompanied by the release of a substance in a solid or gaseous state
on the surface of the electrodes. The release of a substance on the electrodes shows
that in electrolytes, electric charges are carried by charged atoms
substances are ions. This process is called electrolysis.

Law of Electrolysis

Michael Faraday, based on experiments with various electrolytes, established that during electrolysis the massmof the substance released on the electrode is proportional to the charge passed through the electrolyte∆ qor current strength I and time ∆tcurrent passage:

m = k ∆ q = kI ∆ t .

This equation is called the law of electrolysis. Coefficientk , depending on the released substance is called the electrochemical equivalent of the substance.

Conductivity of electrolytes

The conductivity of liquid electrolytes is explained by the fact that when dissolved
in water, neutral molecules of salts, acids and bases break down into
negative and positive ions. In an electric field, ions come into
movement and create an electric current.

Physical state of electrolytes

There are not only liquid, but also solid electrolytes. An example of a solid
glass can serve as electrolyte. Glass contains positive and negative ions. In its solid state, glass does not conduct electricity because ions cannot move in the solid.
When glass is heated, ions are able to move under the influence of an electric field, and the glass becomes a conductor.

Applications of Electrolysis

The phenomenon of electrolysis is used in practice to obtain many
metals from salt solution. Using electrolysis to protect against
oxidation or for decoration, coating of various
objects and machine parts with thin layers of metals such as chromium,
nickel, silver, gold.

An electric current in a vacuum is created by the directional movement of electrons emitted by the metal through thermionic emission (the emission of electrons from the surface of a metal heated to a high temperature). To escape from a metal, an electron must overcome a potential barrier near its surface. The work to overcome this barrier is called work function electron from metal. To do this work, the electron must have a certain energy. The electron receives this energy when the metal is heated.

the voltage at the cathode is measured with a voltmeter U K.Voltages U K And U A regulated by variable resistances R K And R A, currents in the cathode and anode circuits are recorded by ammeters I K And I A respectively. The cathode has a lower potential relative to the anode. The cathode and anode are contained inside a (usually) glass bottle, which creates a high vacuum.

Some of the thermionic electrons released from the cathode reach the anode even in the absence of voltage between the cathode and the anode. To stop the current through the diode, it is necessary to apply a counter field that prevents the movement of electrons. This field is created blocking voltage U z.

In the middle part of the current-voltage characteristic, the dependence of the anode current on the applied voltage is described by the equation:

This equation was theoretically obtained by Boguslavsky and Langmuir and is called the law of three second, bearing the name of these scientists. Coefficient WITH in this equation is equal to:

Here e/m specific electron charge, g is a constant value for a given diode that characterizes its geometry.

As the voltage between the cathode and anode increases, the current through the diode increases and reaches saturation current I n. The existence of a saturation current means that for a given field intensity (for a given voltage U A) and cathode temperature That's all electrons leaving the cathode reach the anode. The dependence of the saturation current on the cathode temperature is described by the formula:

Here And in the work function of an electron leaving the metal, k– Boltzmann constant, IN- constant value.

Studying the current-voltage characteristics of the diode at different cathode temperatures allows us to determine the specific charge of the electron e/m and work function And in electrons from metal.

THERMAL ELECTRON EMISSION-emission of electrons by heated bodies (emitters) into a vacuum or other medium. Only those electrons can leave the body whose energy is greater than the energy of the electron at rest outside the emitter (see. Work function).The number of such electrons (usually electrons with energies of 1 eV relative to the Fermi level in the emitter) under thermodynamic conditions. equilibrium in accordance with the Fermi-Dirac distribution is negligible at temp-pax T 300 K and grows exponentially with T. Therefore, the current T.e. noticeable only for heated bodies. The emission of electrons leads to cooling of the emitter. In the absence of a "suction" electric field (or at a low value), the emitted electrons form negative spaces near the emitter surface. , limiting current T.e.

Basic relationships. At low voltages V between the emitter and anode the current density is monoenergetic. electrons is described by a known law (the law of three second ones) j~ V 3/2 (see Langmuir formula); taking into account the spread of speeds of electrons crossing the created space. charge potential barrier, significantly complicates the process, but the nature of the dependence j(V)does not change; with increasing V spaces. the charge is dissolved and the current reaches saturation j 0, and with further growth V the current increases slightly in accordance with Schottky effect(fig.) - In strong ( E> 10 6 V/cm) electric. fields to T. e. is added auto-electronic emissions(thermofield emission).

Expression for saturation current density j 0, due to the principle of detailed equilibrium, can be obtained by calculating the flow of electrons from the vacuum to the emitter. Under thermodynamic conditions. equilibrium, this flow must coincide with the flow of electrons flying into the vacuum. Assuming that the emitter surface is homogeneous, ext. the field is small, and the coefficient. reflection of electrons from the emitter surface in a vacuum r in the energy field ~ kT near the vacuum level it weakly depends on energy and is not too close to unity, such a calculation leads to f-le (Richardson - Deshman formula)

Here A=A 0 (1-) (bar above r means averaging over electron energies), A 0 = 4p ek 2 m e /h= 120.4 A/cm 2. K 2, F - electron. Weak Dependency Assumption r from energy is violated only in exceptional (but still real) cases, when the vacuum level falls inside one of the forbidden zones in the electronic spectrum of a solid body or corresponds to k--l. other features in the spectra of bulk and surface states. The work function of metals weakly depends on temperature (due to thermal expansion); Usually this relationship is linear: F = F 0 + a T, a~10 -4 -10 -5 eV/deg; and the coefficient a can be either positive or negative. For this reason, however, determined by plotting the dependences j 0 /T 2 from 1 /T in semilogarithmic coordinates (Richardson straight line method), the values ​​differ from F and A from file (*). For most pure metals, the so-called values A vary from 15 to 350 A/cm 2. K 2.

Influence of impurities and defects. Surface impurities and defects, even at a low concentration (10 monolayers), can have a significant effect. influence on the thermionic properties of metals and and lead to a noticeable scatter in the work function values ​​(0.1 eV). Such emissively active impurities include, for example, atoms of alkali and alkaline earth elements and their oxides. Occurring during the adsorption of atoms and molecules of quantum chemistry. the bond induces a redistribution of charges between the adsorbed atoms (and atoms) and the emitter’s own surface atoms. At large distances from the adatom, the potential created by these charges can be described in terms of multipole expansion, i.e., as the sum of dipole, quadrupole, etc. potentials. The change in work function (dipole potential jump) is determined by the dipole moments DF = 4p eN s d, Where N s is the surface concentration of adatoms, d-dipole moment. With values d about several D (1 D = 10 -18 SGSE units) already small amounts of impurities ( N 5 10 12 -10 13 cm -2), constituting only 0.1-0.01 monolayer coating, lead to noticeable changes in the work function: DF~10 -2 - 10 -1 eV. Emission-active impurities are precisely characterized by high values d~ 1-10 D; record values d~ 10 D correspond to cesium adsorption. The change in work function describes the change in potential averaged along the surface. Microscopic The structure of the potential induced by adatoms near the surface is complex. In particular, on a certain part of the surface there is a potential. a barrier that makes it difficult for electrons with energies close to the threshold to escape into vacuum. However, in most cases d~ 1 D and at such d the barriers are tunnel-permeable - “transparent”. In these cases, the changes are associated with quantum mechanics. scattering and electrons. Impurities and defects can stimulate surface restructuring, which also affects the emissive properties. In addition to the adsorption of impurity atoms on the surface, segregation and surface processes, which are very effective at higher temperatures, can serve as sources of contamination. temp-pax. To eliminate the uncontrolled influence of contaminants and obtain reproducible results when studying the emission properties of surfaces, it is necessary to carry out measurements under ultra-high vacuum conditions of ~10 -9 - 10 -10 mm Hg. Art. (the flow of atoms from a gaseous medium to the surface, creating monolayer coatings in 1 s, corresponds to a pressure of ~ 10 -6 mm Hg at room temperature); At the same time, it is necessary to control the composition and structure of the surface using modern technology. surface spectroscopy methods. The best objects for studying emission mechanisms are dept. faces of single crystals of transition metals, allowing a high degree of purification and characterized by a high perfection of the surface structure.

Potential of image forces(PSI), which is not electrostatic. potential and not satisfying Poisson equation in a vacuum, describes the potential. energy of interaction of an electron with an emitter. PSI makes a significant contribution V work function (1 eV) and usually manifests itself at distances from the surface z100 A. Its special properties are associated with the “Coulomb” type of dependence on coordinates V~z -1 (up to distances from the surface of the order of interatomic ones). The motion of an electron in the field of such a potential turns out to be essentially quantum. Moreover, due to the formal analogy, the analysis of solutions to the corresponding Schrödinger equation and the properties of the solutions themselves are close to the case of the usual 3-dimensional Coulomb potential. In particular, if an electron cannot penetrate inside the emitter (due to the absence of bulk states with the corresponding energy there), then PSI induces surface states with a Coulomb-like spectrum (PSI states). If an electron can leave the level as a result of one process or another, but the probability of this event is small (as is often the case in reality), then the surface states become resonant, and the energy levels acquire a finite width. Electrons located in a continuous spectrum, moving above the potential. well, they “feel” the presence in it of a level of a bound state with a binding energy that is small compared to the depth of the well, if their energy is small (comparable to the depth of the level). In this case, due to the effects of multiple above-barrier reflection, the electron can be effectively captured in the region of action of the potential and the scattering acquires a resonant character. This phenomenon leads to resonant oscillations depending on the coefficient. reflections from external fields. The probability of an electron moving from inside a solid body to its surface entering a vacuum is associated with the coefficient. reflection by unitarity relations, which are a quantum analogue of the principle of detailed equilibrium and ensure the law of conservation of the number of particles. Therefore, in the field dependence of the current T.e. weak (but still noticeable) are also observed. In the limit of weak fields, the value r and addiction r from energy are significantly determined by the type of potential.

If the potential quickly enough (faster than z -2) tends to its asymptotic. meaning, then r tends to unity, and the probability of an electron leaving the vacuum becomes zero according to the law e | 1/2 near the emission threshold (e | - part of the electron energy relative to the vacuum level, corresponding to the motion of the electron normal to the surface, in other words, the normal component of the total electron energy). In the case of potentials that slowly change with z, which includes PSI, their presence does not add value. features in energy. addiction r near the vacuum level. Therefore, the value (1- r) from f-ly (*) in most cases turns out to be not too small. Only in cases where emission occurs in a medium with a small characteristic field screening length, not exceeding<= 100 (обычных для области действия ПСИ), r turns out to be close to unity.

Thermionic emission from semiconductors. F-la (*) is also applicable to describe T. e. from semiconductors. However, the influence of temperature, electrical fields, impurities in the emitter, etc. on the emission current and on the values ​​of F and A in this case is significantly different compared to metals. The differences are due to the low concentration of conduction electrons and the presence of localized surface electronic states that affect the location of the Fermi level on the surface of the semiconductor, up to its “fixation” at a certain point of the band gap (see Fig. Surface states, Surface). In this case, on the surface of the semiconductor and F are almost (with an accuracy of ~0.1 eV) independent of the volume (i.e., the type and concentration of the dopant). Such fixation is associated with surface states of sufficiently high (>=10 12 cm -2) concentrations, induced mainly by their own. crystal defects that arise when a semiconductor is exposed to decomposition. ext. factors such as adsorption, mechanical, thermal. processing, etc. In this case, the nature of T. e. similar to T. e. from metals.

On sufficiently clean and perfect semiconductor surfaces, the density of intrinsic (filled and empty) surface states in the band gap is small and the Fermi level on the surface can move inside the band gap, following its position in the bulk. Therefore, when the type and concentration of impurities in the volume of the semiconductor changes, F and current T change. In addition, electric the field in such semiconductors is not screened by charges of surface states and does not penetrate into the emitter. depth, which leads to a change in F due to the near-surface bending of zones and to heating by the field.

A similar situation arises when ext. the field exceeds a value sufficient to eliminate the shielding influence of surface states. For these reasons, the selection of emission current from semiconductors (as opposed to metals, where these effects are usually small) can lead to violation of thermodynamic balance. A special situation arises when emission from negative systems. electron affinity (see Photoelectron emission), in which the nonequilibrium nature of emission processes (including T. e.) is due to the initial features of the surface energy. emitter structures.

Influence of heterogeneities. The surface of most emitters is inhomogeneous; there are “spots” on it with different work functions. Df and electric appear between them. fields (spot fields) of ~Df/ R(Where R- characteristic size of heterogeneities). These fields create additional. potential barriers for emitted electrons, which leads to a stronger dependence of the current on the anode voltage (anomalous Schottky effect), and also increases the dependence of the current on T. Since the sizes of inhomogeneities are usually not small, >> 100, and the potential difference between neighboring spots is ~0.1 - 1 eV, the typical field values ​​of spots are not large (~10 4 V/cm or less) and require “opening” relatively small (compared to the case of the normal Schottky effect) ext. fields, which is responsible for the large magnitude (anomaly) of the effect in the case of inhomogeneous surfaces.

If the surface is highly inhomogeneous, so that the sizes of emission active spots r are much smaller than the distances between them, then the potential f is separate. spots at distances r from it can be represented as a sum of dipole, quadrupole, etc. terms. In particular, the dependence of the spot field on the distance to the surface z above the spot center in this case is close to a power law. The latter circumstance (in complete analogy with the normal Schottky effect) leads to a power-law or close to it dependence of the magnitude of the reduction in potential. barrier above the center of the spot Df from the outside. fields E(e.g. in the case of a pure dipole potential f~z -2 and Df~ E 2/3). In real conditions, the dependence of the potential on coordinates is more complex, but qualitatively the factors that determine the type of field dependence of the current under conditions of the anomalous Schottky effect remain the same. In addition, there is always a scatter in the values ​​of inhomogeneity parameters, and in some cases (for example, for emitters prepared from fine powders) the size hierarchy can be very rich (from 100 to 10-100 microns). In this case, as the field increases, the fields of the spots alternately open, which significantly expands the field range of manifestation of the anomalous Schottky effect.

Types of thermal emitters. To the number of most known eff. emitters include oxides of alkaline earth, rare earth and other elements, usually used in the form of mixtures with various (depending on the purpose of the cathode) additives (see. Thermionic cathode). The most popular is a cathode based on a mixture of Ba, Ca and Sr oxides - an oxide cathode. Being compounds with a pronounced ionic bond, oxides have a relatively small (<= 1 эВ) электронным сродством, широкой (порядка неск. эВ) запрещённой зоной и являются изоляторами при комнатных темп-pax. Для реализации высоких эмиссионных свойств используется процесс термообработки, во время к-рого происходят очистка поверхности, образование донорных центров, формирование структуры эмиттера и оптим. состава его поверхности. Доноры, к-рые в такого рода соединениях имеют, как правило, вакансионную природу, возникают в результате конкуренции между процессами и адсорбции атомов (происходящими при повыш. темп-pax в условиях относительно невысокого вакуума) с последующей диффузией вакансий в объём эмиттера, а также и в др. процессах. Возникающая нестехиометрия состава катода, особенно состава его приповерхностной области, значительна, но всё же не настолько, чтобы образовывались сплошные тонкослойные покрытия поверхности атомами металлов. Важную роль в формировании и работе катода играют процессы поверхностной диффузии атомов (в т. ч. и диффузия по границам зёрен). Они имеют обычно активац. характер; при этом энергия активации поверхностной диффузии (=< 1 эВ) заметно меньше, чем энергия активации объёмного процесса. Поэтому во мн. случаях поверхностная диффузия более эффективна. На контакте полупроводникового эмиссионного слоя с металлом подложки (керном) существует барьер контактной разности потенциалов - , к-рый "включён" в запирающем направлении и при отборе тока эмиссии препятствует транспорту электронов из металла в эмиссионный слой. Кроме того, из-за хим. реакций, протекающих в этой области при повыш. темп-pax (особенно при наличии в металле нежелат. примесей), возможно образование диэлектрич. прослойки между металлом и эмиссионным слоем, значительно ухудшающей свойства катода и приводящей к быстрой его деградации. Поэтому одна из задач, возникающая при создании эмиттера,- формирование хорошего контакта эмиссионного слоя с керном, сохраняющего свои свойства при работе катода. В отличие от технологий мн. др. приборов, в к-рых для создания омического контакта предпринимаются спец. меры, в оксидном катоде формирование контакта происходит в процессе термообработки заодно с др. процессами и не требует дополнит. операций. Иногда в материал контакта вводятся спец. активные присадки, способствующие образованию донорных центров в процессе термообработки. Эфф. термокатоды отличаются от др. эмиттеров прежде всего низкими значениями работы выхода. Достигнутые значения этой величины группируются ок. ~ 1 эВ, а дальнейшие усилия в направлении уменьшения работы выхода наталкиваются на серьёзные трудности. В связи с этим возникает вопрос о существовании факторов, препятствующих снижению работы выхода до величин, значительно меньших 1 эВ. К числу таких факторов могло бы относиться существование незаполненных поверхностных состояний (в частности, состояний ПСИ), накопление заряда на к-рых ограничивает возможность уменьшения Ф. Среди термокатодов др. типов можно назвать металлич. катоды (особенно вольфрамовые) и катоды из полуметаллов, напр. из гексаборида лантана, используемые для создания электронных пучков с повышенной плотностью тока.

Thermionic cathodes are used in many electric vacuum and gas-discharge devices, in scientific research. and technol. installations.

Lit.: Fomenko V.S., Emission properties of materials, 4th ed., K., 1981; Dobretsov L. N., Gomoyunova M. V., Emission Electronics, M., 1966; Thermionic cathodes, M.-L., 1966. S. G. Dmitriev.

Depending on the way in which energy is imparted to electrons, types of electron emission are distinguished. If electrons gain energy from the thermal energy of a body as its temperature increases, we can talk about thermionic emission. To observe thermionic emission, you can use a hollow lamp containing two electrodes: a cathode heated by current and a cold electrode that collects thermionic electrons - the anode. Such lamps are called vacuum diodes. Current in this circuit appears only if the positive pole of the battery is connected to the anode, and the negative pole to the cathode. This confirms that the cathode emits negative particles, electrons. The strength of the thermionic current in the diode depends on the magnitude of the anode potential relative to the cathode. The curve depicting the dependence of the current in the diode on the anode voltage is called the current-voltage characteristic. When the anode potential is zero, the current strength is small, determined only by the fastest thermionic electrons capable of reaching the anode. As the positive potential of the anode increases, the current increases and then reaches saturation, i.e. almost ceases to depend on the anode voltage. As the cathode temperature increases, the current value at which saturation is achieved also increases. At the same time, the anode voltage at which the saturation current is established also increases. Thus, the current-voltage characteristic of the diode turns out to be nonlinear, i.e. Ohm's law does not apply. This is explained by the fact that during thermionic emission a rather high electron density is created at the cathode surface. They create an overall negative charge, and electrons emitted at low speed cannot escape it. As the anode voltage increases, the electron concentration in the space charge cloud decreases. Therefore, the braking effect of the space charge becomes less, and the anode current grows faster than in direct dependence on the anode voltage. As the anode voltage increases, more electrons emitted from the cathode are sucked toward the anode. At a certain value, all electrons emitted from the cathode per unit time reach the anode. A further increase in the anode voltage cannot increase the strength of the anode current, since saturation is reached. The maximum thermionic current possible at a given cathode temperature is called the saturation current. As the temperature increases, the speed of the chaotic movement of electrons in the metal increases. In this case, the number of electrons capable of leaving the metal increases sharply. Saturation current density, i.e. The saturation current strength per unit of cathode surface S is calculated using the Richardson-Deshman formula: , where is the emission constant, k is the Boltzmann constant, =1.38 10-23 J/K. The saturation current density characterizes the emissivity of the cathode, which depends on the nature of the cathode and its temperature.