Emission of electrons and ions is the release of charged particles that occurs at the interface of a solid with a vacuum or gas when the emitter is exposed to thermal heating, light radiation, electron or ion bombardment, constant or high-frequency electric field, etc.

The phenomenon of emission of electrons into a vacuum by a heated body is called thermionic emission.

It has been established that when T = 0 there cannot be emission of electrons from the crystal, since the energies of even the fastest electrons are insufficient to overcome the potential barrier at its boundary.

When a solid is heated, the vibration amplitudes of the atoms of the crystal lattice increase. With increasing temperature, an increasing number of electrons (Fig. 2.10) acquire energy sufficient to overcome the potential barrier at the boundary of a solid body with a vacuum.

If every cubic meter of metal contains dn u, u,u free electrons with velocity components from u x before u x + du x, from u y before u y + +du y and from u z before u z + du z, (Where u x– velocity component in the direction perpendicular to the surface of the body), then the flux of such electrons arriving at the surface is equal to

Only electrons whose velocity component is in the direction of X sufficient to overcome the potential barrier, i.e.

To determine the number of electrons leaving 1 m2 of a metal surface per unit time at a given temperature, it is necessary to substitute the electron velocity distribution function in the metal into the formula and integrate the resulting expression.

According to quantum mechanical theory, not all electrons escape into the vacuum; there is a possibility of their reflection from the potential barrier. Therefore, the concept of transparency of barrier D is introduced.

The Richardson-Deshman equation determines the thermal emission current density:

where is a universal constant and does not depend on the type of emitter.

The Fermi energy is determined by the relation It can be seen that it does not depend on temperature to a first approximation and therefore can be replaced by the effective work function , then

where is the work function, expressed in joules.

The Richardson-Deshman equation shows that the current density of thermionic emission from a metal surface depends on the temperature and the effective work function of the material.

The equation for determining thermionic emission current density is applicable not only to metal, but also to semiconductor cathodes of any type. The specificity, however, is that if in metals the position of the Fermi level could, to a first approximation, be considered independent of temperature and consider j eff. as a constant of a given material, then in impurity semiconductors the position of the Fermi level depends on temperature. Temperature coefficient of work function ( a) was determined for metals to be êa½ ~ 10 –5. and semiconductors a ~ 10 –4. Considering that the coefficient is affected a large number of factors and there is no precise definition of it, which contributes an insignificant part in determining the thermal emission current density, we will use the Richardson-Deshman formula for all types of thermionic cathodes.

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 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 medium 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.

It has already been noted that when crossing the interface between a conductor and a vacuum, the intensity and induction of the electric field change abruptly. Specific phenomena are associated with this. The electron is free only within the boundaries of the metal. As soon as it tries to cross the “metal-vacuum” boundary, a Coulomb force of attraction arises between the electron and the excess positive charge formed on the surface (Fig. 6.1).

An electron cloud forms near the surface, and an electric double layer with a potential difference () is formed at the interface. Potential jumps at the metal boundary are shown in Figure 6.2.

A potential energy well is formed in the volume occupied by the metal, since within the metal the electrons are free and their interaction energy with lattice sites is zero. Outside the metal, the electron gains energy W 0 . This is the energy of attraction. In order to leave the metal, the electron must overcome the potential barrier and do work

(6.1.1)

This work is called work function of an electron leaving a metal . To accomplish this, the electron must be provided with sufficient energy.

Thermionic emission

The value of the work function depends on the chemical nature of the substance, on its thermodynamic state and on the state of the interface. If energy sufficient to perform the work function is imparted to the electrons by heating, then The process of electrons leaving a metal is called thermionic emission .

In classical thermodynamics, a metal is represented as an ionic lattice containing an electron gas. It is believed that the community of free electrons obeys the laws of an ideal gas. Consequently, in accordance with the Maxwell distribution, at temperatures other than 0 K, the metal contains a certain number of electrons whose thermal energy is greater than the work function. These electrons leave the metal. If the temperature is increased, the number of such electrons also increases.

The phenomenon of emission of electrons by heated bodies (emitters) into a vacuum or other medium is called thermionic emission . Heating is necessary so that the energy of thermal motion of the electron is sufficient to overcome the forces of Coulomb attraction between a negatively charged electron and the positive charge induced by it on the metal surface when removed from the surface (Fig. 6.1). In addition, at a sufficiently high temperature, a negatively charged electron cloud is created above the metal surface, preventing the electron from leaving the metal surface into the vacuum. These two and, possibly, other reasons determine the work function of an electron from a metal.

The phenomenon of thermionic emission was discovered in 1883 by Edison, the famous American inventor. He observed this phenomenon in a vacuum tube with two electrodes - an anode with a positive potential and a cathode with a negative potential. The cathode of the lamp can be a filament made of a refractory metal (tungsten, molybdenum, tantalum, etc.), heated by an electric current (Fig. 6.3). Such a lamp is called a vacuum diode. If the cathode is cold, then there is practically no current in the cathode-anode circuit. As the cathode temperature increases, an electric current appears in the cathode-anode circuit, which is greater the higher the cathode temperature. At a constant cathode temperature, the current in the cathode-anode circuit increases with increasing potential difference U between the cathode and anode and comes to some stationary value called saturation current I n. Wherein all thermionics emitted by the cathode reach the anode. The anode current is not proportional U, and therefore For a vacuum diode, Ohm's law does not apply.

Figure 6.3 shows the vacuum diode circuit and current-voltage characteristics (volt-ampere characteristics) Ia(Ua). Here U h – delay voltage at which I = 0.

Cold and explosive emission

Electron emission caused by the action of electric field forces on free electrons in a metal is called cold emission or field electronic . For this, the field strength must be sufficient and the condition must be met

(6.1.2)

Here d– thickness of the double electrical layer at the interface. Usually in pure metals and we obtain In practice, cold emission is observed at a strength value of the order of magnitude. This discrepancy is attributed to the inconsistency of classical concepts for describing processes at the microlevel.

Field emission can be observed in a well-evacuated vacuum tube, the cathode of which is a tip, and the anode is a regular electrode with a flat or slightly curved surface. Electric field strength on the surface of the tip with radius of curvature r and potential U relative to the anode is equal

At and , which will lead to the appearance of a weak current due to field emission from the cathode surface. The strength of the emission current increases rapidly with increasing potential difference U. In this case, the cathode is not specially heated, which is why the emission is called cold.

Using field emission, it is in principle possible to obtain current density but this requires emitters in the form of a collection of a large number of tips, identical in shape (Fig. 6.4), which is practically impossible, and, in addition, increasing the current to 10 8 A/cm 2 leads to explosive destruction of the tips and the entire emitter.

The AEE current density under the influence of space charge is equal to (Child-Langmuir law)

Where – proportionality coefficient determined by the geometry and material of the cathode.

Simply put, Childe-Langmuir's law shows that current density is proportional (law of three second).

The field emission current, when the energy concentration in microvolumes of the cathode is up to 10 4 J×m –1 or more (with a total energy of 10 -8 J), can initiate a qualitatively different type of emission, due to explosion of microtips on the cathode (Fig. 6.4).

In this case, an electron current appears, which is orders of magnitude greater than the initial current - observed explosive electron emission (VEE). VEE was discovered and studied at the Tomsk Polytechnic Institute in 1966 by a team of employees led by G.A. Months.

VEE is the only type of electron emission that allows one to obtain electron flows with a power of up to 10 13 W with a current density of up to 10 9 A/cm 2 .

	Rice. 6.4	Rice. 6.5

The VEE current is unusual in structure. It consists of individual portions of electrons 10 11 ¸ 10 12 pieces, having the character of electron avalanches, called ectons(initial letters " explosive center") (Fig. 6.5). Avalanche formation time is 10 -9 ¸ 10 -8 s.

The appearance of electrons in the ecton is caused by rapid overheating of micro-sections of the cathode and is, in essence, a type of thermionic emission. The existence of an ecton is manifested in the formation of a crater on the cathode surface. The cessation of electron emission in the ecton is due to cooling of the emission zone due to thermal conductivity, a decrease in current density, and evaporation of atoms.

Explosive emission of electrons and ectons play a fundamental role in vacuum sparks and arcs, in low-pressure discharges, in compressed and high-strength gases, in micro-gaps, i.e. where there is a high intensity electric field at the cathode surface.

The phenomenon of explosive electron emission served as the basis for the creation of pulsed electrophysical installations, such as high-current electron accelerators, powerful pulsed and X-ray devices, and powerful relativistic microwave generators. For example, pulsed electron accelerators have a power of 10 13 W or more with a pulse duration of 10 -10 ¸ 10 -6 s, an electron current of 10 6 A and an electron energy of 10 4 ¸ 10 7 eV. Such beams are widely used for research in plasma physics, radiation physics and chemistry, for pumping gas lasers, etc.

Photoelectron emission

Photoelectron emission (photoeffect) consists of “knocking out” electrons from a metal when exposed to electromagnetic radiation.

The setup diagram for studying the photoelectric effect and current-voltage characteristics are similar to those shown in the figure. 6.3. Here, instead of heating the cathode, a stream of photons or γ-quanta is directed at it (Fig. 6.6).

The laws of the photoelectric effect are even more inconsistent with the classical theory than in the case of cold emission. For this reason, we will consider the theory of the photoelectric effect when discussing quantum concepts in optics.

In physical instruments that record γ - radiation, they use photomultiplier tubes (PMT). The device diagram is shown in Figure 6.7.

It uses two emission effects: photoeffect And secondary electron emission, which consists of knocking electrons out of a metal when it is bombarded with other electrons. Electrons are knocked out by light from the photocathode ( FC). Speeding between FC and the first emitter ( KS 1), they acquire energy sufficient to knock out a larger number of electrons from the next emitter. Thus, the multiplication of electrons occurs due to an increase in their number during the successive passage of a potential difference between neighboring emitters. The last electrode is called the collector. The current between the last emitter and the collector is recorded. Thus, PMT serves as a current amplifier, and the latter is proportional to the radiation incident on the photocathode, which is used to assess radioactivity.

Thermionic emission

Thermionic emission (Richardson effect, Edison effect) - the phenomenon of emission of electrons by heated bodies. The concentration of free electrons in metals is quite high, therefore, even at average temperatures, due to the distribution of electron speeds (energy), some electrons have sufficient energy to overcome the potential barrier at the metal boundary. With increasing temperature, the number of electrons, the kinetic energy of thermal motion of which is greater than the work function, increases, and the phenomenon of thermionic emission becomes noticeable.

The study of the laws of thermionic emission can be carried out using the simplest two-electrode lamp - a vacuum diode, which is an evacuated cylinder containing two electrodes: cathode K and anode A. In the simplest case, the cathode is a filament made of a refractory metal (for example, tungsten), heated by an electric current. The anode most often takes the form of a metal cylinder surrounding the cathode. If a diode is connected to a circuit, then when the cathode is heated and a positive voltage (relative to the cathode) is applied to the anode, a current arises in the anode circuit of the diode. If you change the polarity of the battery, the current stops, no matter how hot the cathode is. Consequently, the cathode emits negative particles - electrons.

If you keep the temperature of the heated cathode constant and remove the dependence of the anode current on the anode voltage - the current-voltage characteristic - it turns out that it is not linear, that is, Ohm’s law does not hold for a vacuum diode. The dependence of the thermionic current on the anode voltage in the region of small positive values ​​is described by the law of the second three (established by the Russian physicist S. A. Boguslavsky (1883-1923) and the American physicist I. Langmuir (1881-1957)): , where B is a coefficient depending on shapes and sizes of electrodes, as well as their relative position.

As the anode voltage increases, the current increases to a certain maximum value, called the saturation current. This means that almost all the electrons leaving the cathode reach the anode, so a further increase in field strength cannot lead to an increase in thermionic current. Consequently, the saturation current density characterizes the emissivity of the cathode material. The saturation current density is determined by the Richardson-Deshman formula, derived theoretically on the basis of quantum statistics: , where A is the work function of electrons from the cathode, T is the thermodynamic temperature, C is a constant, theoretically the same for all metals (this is not confirmed by experiment, which, according to apparently explained by surface effects). A decrease in the work function leads to a sharp increase in the saturation current density. Therefore, oxide cathodes are used (for example, nickel coated with an alkaline earth metal oxide), the work function of which is 1–1.5 eV.

The operation of many vacuum electronic devices is based on the phenomenon of thermionic emission.

Literature

• Physics course Trofimova T.I.

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• Curia-Muria
• tidal power station

See what “Thermionic emission” is in other dictionaries:

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... Physical encyclopedia

THERMAL ELECTRON EMISSION- emission of electrons by heated bodies (emitters) into a vacuum or other medium. Only those electrons whose energy is greater than the energy of an electron at rest outside the body can leave the body (see WORK WORK OF EXIT). The number of such electrons under thermodynamic conditions. balance, in... ... Physical encyclopedia

THERMAL ELECTRON EMISSION- emission of electrons by heated solids or liquids (emitters). Thermionic emission can be considered as the evaporation of electrons from the emitter. In most cases, thermionic emission is observed at temperatures... ... Big Encyclopedic Dictionary

thermionic emission- thermionic emission; industry thermionic emission Electron emission caused solely by the thermal state (temperature) of a solid or liquid body emitting electrons ... Polytechnic terminological explanatory dictionary

thermionic emission- Electron emission due only to the temperature of the electrode. [GOST 13820 77] Topics: electrovacuum devices... Technical Translator's Guide

THERMAL ELECTRON EMISSION- THERMAL ELECTRON EMISSION, “evaporation” of ELECTRONS from the surface of a substance when it is heated... Scientific and technical encyclopedic dictionary

THERMAL ELECTRON EMISSION- emission of electrons by heated bodies (emitters) into a vacuum or other medium. The phenomenon is observed at temperatures significantly above room temperature; in this case, part of the electrons of the body acquires energy exceeding (million equal) work function... ... Big Polytechnic Encyclopedia

thermionic emission- emission of electrons from heated solids or liquids (emitters). Thermionic emission can be considered as the evaporation of electrons upon their thermal excitation. In most cases, thermionic emission is observed when... ... encyclopedic Dictionary

Thermionic emission- Richardson effect, the emission of electrons by heated bodies (solids, less often liquids) into a vacuum or into various environments. First explored by O. W. Richardson in 1900 1901. T. e. can be considered as the process of evaporation of electrons in... ... Great Soviet Encyclopedia

THERMAL ELECTRON EMISSION- emission of electrons from a heated surface. Even before 1750 it was known that near heated solids, air loses its usual property of being a poor conductor of electricity. However, the cause of this phenomenon remained unclear until the 1880s. In a number... ... Collier's Encyclopedia

thermionic emission- termoelektroninė emisija statusas T sritis chemija apibrėžtis Elektronų spinduliavimas iš įkaitusių kietųjų kūnų arba skysčių. atitikmenys: engl. thermoelectronic emission rus. thermionic emission... Chemijos terminų aiškinamasis žodynas

Control questions .. 18

9. Laboratory work No. 2. Study of thermionic emission at low emission current densities . 18

Work order .. 19

Report requirements . 19

Control questions .. 19

Introduction

Emission electronics studies phenomena associated with the emission (emission) of electrons from a condensed medium. Electron emission occurs in cases when part of the electrons of a body acquires, as a result of external influence, energy sufficient to overcome the potential barrier at its boundary, or if an external electric field makes it “transparent” to part of the electrons. Depending on the nature of the external influence, there are:

• thermionic emission (heating of bodies);
• secondary electron emission (bombardment of the surface with electrons);
• ion-electron emission (bombardment of the surface with ions);
• photoelectron emission (electromagnetic irradiation);
• exoelectronic emission (mechanical, thermal and other types of surface treatment);
• field emission (external electric field), etc.

In all phenomena where it is necessary to take into account either the exit of an electron from a crystal into the surrounding space, or the transition from one crystal to another, the characteristic called “Work function” acquires decisive significance. The work function is defined as the minimum energy required to remove an electron from a solid and place it at a point where its potential energy is assumed to be zero. In addition to describing various emission phenomena, the concept of work function plays an important role in explaining the occurrence of a contact potential difference in the contact of two metals, a metal with a semiconductor, two semiconductors, as well as galvanic phenomena.

The guidelines consist of two parts. The first part contains basic theoretical information on emission phenomena in solids. The main attention is paid to the phenomenon of thermionic emission. The second part provides a description of laboratory work devoted to the experimental study of thermionic emission, the study of contact potential difference and the distribution of work function over the surface of the sample.

Part 1. Basic theoretical information

1. Electron work function. Influence on the work function of the surface state

The fact that electrons are retained inside a solid indicates that a retarding field arises in the surface layer of the body, preventing electrons from leaving it into the surrounding vacuum. A schematic representation of a potential barrier at the boundary of a solid is shown in Fig. 1. To leave the crystal, an electron must do work equal to the work function. Distinguish thermodynamic And external work function.

The thermodynamic work function is the difference between the zero-level energy of vacuum and the Fermi energy of a solid.

External work function (or electron affinity) is the difference between the energy of the zero vacuum level and the energy of the bottom of the conduction band (Fig. 1).

Rice. 1. Form of crystal potential U along the line of location of ions in the crystal and in the near-surface region of the crystal: the positions of the ions are marked by dots on the horizontal line; φ=- U /е – work function potential; E F – Fermi energy (negative); E C– energy of the bottom of the conduction band; W O – thermodynamic work function; W a – external work function; the shaded area conventionally represents filled electronic states

There are two main reasons for the emergence of a potential barrier at the boundary of a solid and vacuum. One of them is due to the fact that an electron emitted from a crystal induces a positive electric charge on its surface. An attractive force arises between the electron and the surface of the crystal (electric image force, see Section 5, Fig. 12), tending to return the electron back to the crystal. Another reason is due to the fact that electrons, due to thermal motion, can cross the surface of the metal and move away from it to short distances (on the order of atomic). They form a negatively charged layer above the surface. In this case, after the electrons escape, a positively charged layer of ions is formed on the surface of the crystal. As a result, an electrical double layer is formed. It does not create a field in external space, but it also requires work to overcome the electric field inside the double layer itself.

The work function value for most metals and semiconductors is several electron volts. For example, for lithium the work function is 2.38 eV, iron – 4.31 eV, germanium – 4.76 eV, silicon – 4.8 eV. To a large extent, the work function value is determined by the crystallographic orientation of the single crystal face from which electron emission occurs. For the (110) plane of tungsten, the work function is 5.3 eV; for the (111) and (100) planes these values ​​are 4.4 eV and 4.6 eV, respectively.

Thin layers deposited on the surface of the crystal have a great influence on the work function. Atoms or molecules deposited on the surface of a crystal often donate an electron to it or accept an electron from it and become ions. In Fig. Figure 2 shows the energy diagram of a metal and an isolated atom for the case when the thermodynamic work function of an electron from the metal W 0 greater than ionization energy E ion of an atom deposited on its surface. In this situation, the electron of the atom is energetically favorable tunnel into the metal and descend in it to the Fermi level. The metal surface covered with such atoms becomes negatively charged and forms a double electric layer with positive ions, the field of which will reduce the work function of the metal. In Fig. 3, a shows a tungsten crystal coated with a monolayer of cesium. Here the situation discussed above is realized, since the energy E ion cesium (3.9 eV) is less than the work function of tungsten (4.5 eV). In experiments, the work function decreases by more than three times. The opposite situation is observed if tungsten is covered with oxygen atoms (Fig. 3 b). Since the bond of valence electrons in oxygen is stronger than in tungsten, when oxygen is adsorbed on the surface of tungsten, an electric double layer is formed, which increases the work function of the metal. The most common case is when an atom deposited on the surface does not completely give up its electron to the metal or takes in an extra electron, but deforms its electron shell so that the atoms adsorbed on the surface are polarized and become electric dipoles (Fig. 3c). Depending on the orientation of the dipoles, the work function of the metal decreases (the orientation of the dipoles corresponds to Fig. 3c) or increases.

2. Thermionic emission phenomenon

Thermionic emission is one of the types of electron emission from the surface of a solid. In the case of thermionic emission, the external influence is associated with heating of the solid.

The phenomenon of thermionic emission is the emission of electrons by heated bodies (emitters) into a vacuum or other medium.

Under thermodynamic equilibrium conditions, the number of electrons n(E), having energy in the range from E before E+d E, is determined by the Fermi-Dirac statistics:

,(1)

Where g(E)– number of quantum states corresponding to energy E; E F – Fermi energy; k– Boltzmann constant; T– absolute temperature.

In Fig. Figure 4 shows the energy diagram of the metal and the electron energy distribution curves at T=0 K, at low temperature T 1 and at high temperatures T 2. At 0 K, the energy of all electrons is less than the Fermi energy. None of the electrons can leave the crystal and no thermionic emission is observed. With increasing temperature, the number of thermally excited electrons capable of leaving the metal increases, which causes the phenomenon of thermionic emission. In Fig. 4 this is illustrated by the fact that when T=T 2 the "tail" of the distribution curve goes beyond the zero level of the potential well. This indicates the appearance of electrons with energy exceeding the height of the potential barrier.

For metals, the work function is several electron volts. Energy k T even at temperatures of thousands of Kelvin is a fraction of an electron volt. For pure metals, significant electron emission can be obtained at a temperature of about 2000 K. For example, in pure tungsten, noticeable emission can be obtained at a temperature of 2500 K.

To study thermionic emission, it is necessary to create an electric field at the surface of a heated body (cathode), accelerating electrons to remove them (suction) from the emitter surface. Under the influence of an electric field, the emitted electrons begin to move and an electric current is formed, which is called thermionic. To observe thermionic current, a vacuum diode is usually used - an electron tube with two electrodes. The cathode of the lamp is a filament made of a refractory metal (tungsten, molybdenum, etc.), heated by an electric current. The anode usually has the shape of a metal cylinder surrounding a heated cathode. To observe thermionic current, the diode is connected to the circuit shown in Fig. 5. Obviously, the strength of the thermionic current should increase with increasing potential difference V between the anode and cathode. However, this increase is not proportional V(Fig. 6). Upon reaching a certain voltage, the increase in thermionic current practically stops. The limiting value of the thermionic current at a given cathode temperature is called the saturation current. The magnitude of the saturation current is determined by the number of thermionic electrons that are able to exit the cathode surface per unit time. In this case, all the electrons supplied by thermionic emission from the cathode are used to produce an electric current.

3. Dependence of thermionic current on temperature. Formula Richardson-Deshman

When calculating the thermionic current density we will use the electron gas model and apply Fermi-Dirac statistics to it. It is obvious that the thermionic current density is determined by the density of the electron cloud near the crystal surface, which is described by formula (1). In this formula, let us move from the energy distribution of electrons to the electron momentum distribution. In this case, we take into account that the allowed values ​​of the electron wave vector k V k -space are distributed evenly so that for each value k accounted for volume 8 p 3 (for a crystal volume equal to one). Considering that the electron momentum p =ћ k we obtain that the number of quantum states in the volume element of momentum space dp xdp ydp z will be equal

(2)

The two in the numerator of formula (2) takes into account two possible values ​​of the electron spin.

Let's direct the axis z rectangular coordinate system normal to the cathode surface (Fig. 7). Let us select an area of ​​unit area on the surface of the crystal and build on it, as on a base, a rectangular parallelepiped with a side edge v z =p z /m n(m n– effective electron mass). Electrons contribute to the saturation current density of the component v z axis speed z. The contribution to the current density from one electron is equal to

(3)

Where e– electron charge.

The number of electrons in the parallelepiped, the velocities of which are contained in the considered interval:

In order for the crystal lattice not to be destroyed during the emission of electrons, an insignificant part of the electrons must leave the crystal. For this, as formula (4) shows, the condition must be satisfied HERF>> k T. For such electrons, unity in the denominator of formula (4) can be neglected. Then this formula is transformed to the form

(5)

Let us now find the number of electrons dN in the scope under consideration, z-the impulse component of which is contained between R z And R z +dp z. To do this, the previous expression must be integrated over R x And R y ranging from –∞ to +∞. When integrating, it should be taken into account that

,

and use the table integral

,.

As a result we get

.(6)

Now, taking into account (3), let us find the density of the thermionic current created by all the electrons of the parallelepiped. To do this, expression (6) must be integrated for all electrons whose kinetic energy is at the Fermi level E ≥E F +W 0 Only such electrons can leave the crystal and only they play a role in calculating the thermocurrent. The component of the momentum of such electrons along the axis Z must satisfy the condition

.

Therefore, the saturation current density

Integration is performed for all values. Let us introduce a new integration variable

Then p z dp z =m n du And

.(8)

As a result we get

,(9)

,(10)

where is the constant

.

Equality (10) is called the formula Richardson-Deshman. By measuring the density of the thermionic saturation current, one can use this formula to calculate the constant A and the work function W 0 . For experimental calculations, the formula Richardson-Deshman it is convenient to represent it in the form

In this case, the graph shows the dependence ln(js/T 2) from 1 /T expressed by a straight line. From the intersection of the straight line with the ordinate axis, ln is calculated A , and by the angle of inclination of the straight line the work function is determined (Fig. 8).

4. Contact potential difference

Let us consider the processes that occur when two electronic conductors, for example two metals, with different work functions approach and come into contact. The energy diagrams of these metals are shown in Fig. 9. Let EF 1 And EF 2 is the Fermi energy for the first and second metal, respectively, and W 01 And W 02– their work functions. In an isolated state, metals have the same vacuum level and, therefore, different Fermi levels. Let us assume for definiteness that W 01< W 02, then the Fermi level of the first metal will be higher than that of the second (Fig. 9 a). When these metals come into contact opposite the occupied electronic states in metal 1, there are free energy levels metal 2. Therefore, when these conductors come into contact, a resulting flow of electrons arises from conductor 1 to conductor 2. This leads to the fact that the first conductor, losing electrons, becomes positively charged, and the second conductor, gaining additional negative charge is charged negatively. Due to charging, all energy levels of metal 1 shift down, and metal 2 shifts up. The process of level displacement and the process of electron transition from conductor 1 to conductor 2 will continue until the Fermi levels of both conductors are aligned (Fig. 9 b). As can be seen from this figure, the equilibrium state corresponds to the potential difference between the zero levels of conductors 0 1 and 0 2:

.(11)

Potential difference V K.R.P called contact potential difference. Consequently, the contact potential difference is determined by the difference in the work function of electrons from the contacting conductors. The obtained result is valid for any methods of exchanging electrons between two materials, including by thermionic emission in a vacuum, through an external circuit, etc. Similar results are obtained when metal contacts a semiconductor. A contact potential difference arises between the metals and the semiconductor, which is approximately the same order of magnitude as in the case of contact between two metals (approximately 1 V). The only difference is that if in conductors the entire contact potential difference falls almost on the gap between the metals, then when a metal comes into contact with a semiconductor, the entire contact potential difference falls on the semiconductor, in which a sufficiently large layer is formed, enriched or depleted of electrons. If this layer is depleted of electrons (in the case when the work function of an n-type semiconductor is less than the work function of the metal), then such a layer called blocking and such a transition will have straightening properties. The potential barrier that arises in the rectifying contact of a metal with a semiconductor is called Schottky barrier, and diodes operating on its basis - Schottky diodes.

Volt-ampereCharacteristics of a thermionic cathode at low emission current densities. Schottky effect

If a potential difference is created between the thermionic cathode and the anode of the diode (Fig. 5) V, preventing the movement of electrons to the anode, then only those that fly out from the cathode with a reserve of kinetic energy not less than the energy of the electrostatic field between the anode and the cathode will be able to reach the anode, i.e. -e V(V< 0). To do this, their energy in the thermionic cathode must be no less W 0 –еV. Then, replacing in the formula Richardson-Deshman (10) W 0 on W 0 –еV, we obtain the following expression for the thermal emission current density:

,(12)

Here j S– saturation current density. Let's take logarithm of this expression

.(13)

At a positive potential at the anode, all electrons leaving the thermionic cathode land on the anode. Therefore, the current in the circuit should not change, remaining equal to the saturation current. Thus, volt-ampere The characteristic (current-voltage characteristic) of the thermal cathode will have the form shown in Fig. 10 (curve a).

A similar current-voltage characteristic is observed only at relatively low emission current densities and high positive potentials at the anode, when a significant electron space charge does not arise near the emitting surface. Current-voltage characteristics of the thermionic cathode taking into account the space charge, discussed in Section. 6.

Let us note another important feature of the current-voltage characteristic at low emission current densities. The conclusion is that the thermocurrent reaches saturation at V=0, is valid only for the case when the cathode and anode materials have the same thermodynamic work function. If the work functions of the cathode and anode are not equal, then a contact potential difference appears between the anode and cathode. In this case, even in the absence of an external electric field ( V=0) there is an electric field between the anode and cathode due to the contact potential difference. For example, if W 0k< W 0a then the anode will be charged negatively relative to the cathode. To destroy the contact potential difference, a positive bias should be applied to the anode. That's why volt-ampere the characteristic of the hot cathode shifts by the amount of the contact potential difference towards the positive potential (Fig. 10, curve b). With an inverse relationship between W 0k And W 0a the direction of the shift of the current-voltage characteristic is opposite (curve c in Fig. 10).

Conclusion about the independence of the saturation current density at V>0 is highly idealized. In real current-voltage characteristics of thermionic emission, a slight increase in thermionic emission current is observed with increasing V in saturation mode, which is associated with Schottky effect(Fig. 11).

The Schottky effect is a decrease in the work function of electrons from solids under the influence of an external accelerating electric field.

To explain the Schottky effect, consider the forces acting on an electron near the surface of a crystal. In accordance with the law of electrostatic induction, surface charges of the opposite sign are induced on the surface of the crystal, which determine the interaction of the electron with the surface of the crystal. In accordance with the method of electrical images, the action of real surface charges on an electron is replaced by the action of a fictitious point positive charge +e, located at the same distance from the crystal surface as the electron, but on the opposite side of the surface (Fig. 12). Then, in accordance with Coulomb's law, the force of interaction between two point charges

,(14)

Here ε o– electrical constant: X is the distance between the electron and the surface of the crystal.

The potential energy of an electron in the electric image force field, if counted from the zero vacuum level, is equal to

.(15)

Potential energy of an electron in an external accelerating electric field E

Total potential energy of an electron

.(17)

A graphical determination of the total energy of an electron located near the surface of the crystal is shown in Fig. 13, which clearly shows a decrease in the work function of an electron from the crystal. The total electron potential energy curve (solid curve in Fig. 13) reaches a maximum at the point x m:

.(18)

This point is 10 Å from the surface at an external field strength » 3× 10 6 V/cm.

At the point X m total potential energy equal to the decrease in the potential barrier (and, therefore, the decrease in the work function),

.(19)

As a result of the Schottky effect, the thermal diode current at a positive voltage at the anode increases with increasing anode voltage. This effect manifests itself not only when electrons are emitted into a vacuum, but also when they move through metal-semiconductor or metal-insulator contacts.

6. Currents in vacuum limited by space charge. The law of "three second"

At high thermionic emission current densities, the current-voltage characteristic is significantly influenced by the volumetric negative charge that arises between the cathode and anode. This negative bulk charge prevents electrons escaping from the cathode from reaching the anode. Thus, the anode current turns out to be less than the electron emission current from the cathode. When a positive potential is applied to the anode, the additional potential barrier at the cathode created by the space charge decreases and the anode current increases. This is a qualitative picture of the influence of space charge on the current-voltage characteristic of a thermal diode. This issue was theoretically explored by Langmuir in 1913.

Let us calculate, under a number of simplifying assumptions, the dependence of the thermal diode current on the external potential difference applied between the anode and cathode and find the distribution of the field, potential and electron concentration between the anode and cathode, taking into account the space charge.

Rice. 14. To the conclusion of the law of "three second"

Let's assume that the diode electrodes are flat. With a small distance between the anode and cathode d they can be considered infinitely large. We place the origin of coordinates on the surface of the cathode, and the axis X Let's direct it perpendicular to this surface towards the anode (Fig. 14). We will maintain the cathode temperature constant and equal T. Electrostatic field potential j , existing in the space between the anode and cathode, will be a function of only one coordinate X. He must satisfy Poisson's equation

,(20)

Here r – volumetric charge density; n– electron concentration; j , r And n are functions of the coordinate X.

Considering that the current density between the cathode and anode

and the electron speed v can be determined from the equation

Where m– electron mass, equation (20) can be transformed to the form

, .(21)

This equation must be supplemented with boundary conditions

These boundary conditions follow from the fact that the potential and electric field strength at the cathode surface must vanish. Multiplying both sides of equation (21) by dj /dx, we get

.(23)

Considering that

(24a)

And ,(24b)

we write (23) in the form

.(25)

Now we can integrate both sides of equation (25) over X ranging from 0 to that value x, at which the potential is equal j . Then, taking into account boundary conditions (22), we obtain

Integrating both parts (27) ranging from X=0, j =0 to X=1, j= V a, we get

.(28)

By squaring both sides of equality (28) and expressing the current density j from A according to (21), we get

.(30)

Formula (29) is called Langmuir's "three-second law".

This law is valid for electrodes of arbitrary shape. The expression for the numerical coefficient depends on the shape of the electrodes. The formulas obtained above make it possible to calculate the distributions of potential, electric field strength and electron density in the space between the cathode and anode. Integration of expression (26) ranging from X=0 to the value when the potential is equal j , leads to the relation

those. the potential varies proportionally to the distance from the cathode X to the power of 4/3. Derivative dj/ dx characterizes the electric field strength between the electrodes. According to (26), the magnitude of the electric field strength E ~X 19 . Finally, the electron concentration

(32)

and, according to (31) n(x)~ (1/x) 2/9 .

Dependencies j (X ), E(X) And n(X) are shown in Fig. 15. If X→0, then the concentration tends to infinity. This is a consequence of neglecting the thermal velocities of electrons at the cathode. In a real situation, during thermionic emission, electrons leave the cathode not with zero speed, but with a certain finite emission speed. In this case, the anode current will exist even if there is a small reverse electric field near the cathode. Consequently, the volume charge density can change to such values ​​that the potential near the cathode decreases to negative values ​​(Fig. 16). As the anode voltage increases, the minimum potential decreases and approaches the cathode (curves 1 and 2 in Fig. 16). At a sufficiently high voltage at the anode, the minimum potential merges with the cathode, the field strength at the cathode becomes zero and the dependence j (X) approaches (29), calculated without taking into account the initial electron velocities (curve 3 in Fig. 16). At high anodic voltages, the space charge is almost completely dissolved and the potential between the cathode and anode changes according to a linear law (curve 4, Fig. 16).

Thus, the potential distribution in the interelectrode space, taking into account the initial electron velocities, differs significantly from that which is the basis of the idealized model when deriving the “three second” law. This leads to a change and dependence of the anode current density. Calculation taking into account the initial electron velocities for the case of the potential distribution shown in Fig. 17, and for cylindrical electrodes gives the following dependence for the total thermionic emission current I (I=jS, Where S– cross-sectional area of ​​the thermocurrent):

.(33)

Options x m And Vm determined by the type of dependence j (X), their meaning is clear from Fig. 17. Parameter X m equal to the distance from the cathode at which the potential reaches its minimum value = Vm. Factor C(x m), except x m, depends on the radii of the cathode and anode. Equation (33) is valid for small changes in the anode voltage, because And X m And Vm, as discussed above, depend on the anode voltage.

Thus, the law of the “three second” is not universal; it is valid only in a relatively narrow range of voltages and currents. However, it is a clear example of the nonlinear relationship between current and voltage in an electronic device. The nonlinearity of the current-voltage characteristic is the most important feature of many elements of radio and electrical circuits, including elements of solid-state electronics.

Part 2. Laboratory work

7. Experimental setup for studying thermionic emission

Laboratory work No. 1 and 2 is performed on one laboratory installation, implemented on the basis of a universal laboratory stand. The installation diagram is shown in Fig. 18. The measuring section contains an EL vacuum diode with a directly or indirectly heated cathode. The front panel of the measuring section displays the contacts of the filament “Incandescent”, the anode “Anode” and the cathode “Cathode”. The filament source is a stabilized direct current source of type B5-44A. The I icon in the diagram indicates that the source operates in current stabilization mode. The procedure for working with a direct current source can be found in the technical description and operating instructions for this device. Similar descriptions are available for all electrical measuring instruments used in laboratory work. The anode circuit includes a stabilized direct current source B5-45A and a universal digital voltmeter B7-21A, used in the direct current measurement mode to measure the anode current of the thermal diode. To measure the anode voltage and cathode heating current, you can use devices built into the power source or connect an additional voltmeter RV7-32 for a more accurate measurement of the voltage at the cathode.

The measuring section may contain vacuum diodes with different working cathode filament currents. At the rated filament current, the diode operates in the mode of limiting the anode current by space charge. This mode is necessary to perform laboratory work No. 1. Laboratory work No. 2 is performed at reduced filament currents, when the influence of space charge is insignificant. When setting the filament current, you should be especially careful, because Excess of the filament current above its nominal value for a given vacuum tube leads to burnout of the cathode filament and failure of the diode. Therefore, when preparing for work, be sure to check with your teacher or engineer the value of the operating filament current of the diode used in the work; be sure to write down the data in your workbook and use it when drawing up a report on laboratory work.

8. Laboratory work No. 1. Studying the influence of space charge on volt-amperethermal current characteristics

Purpose of the work: experimental study of the dependence of thermionic emission current on the anode voltage, determination of the exponent in the “three-second” law.

Volt-ampere The characteristic of thermionic emission current is described by the law of “three second” (see Section 6). This mode of diode operation occurs at sufficiently high cathode filament currents. Typically, at rated filament current, the vacuum diode current is limited by space charge.

The experimental setup for performing this laboratory work is described in Sect. 7. During work, it is necessary to measure the current-voltage characteristic of the diode at the rated filament current. The value of the operating current scale of the vacuum tube used should be taken from a teacher or engineer and written down in a workbook.

Work order

1. Familiarize yourself with the description and procedure for operating the instruments necessary for the operation of the experimental setup. Assemble the circuit according to Fig. 18. The installation can be connected to the network only after checking the correctness of the assembled circuit by an engineer or teacher.

2. Turn on the cathode filament current power supply and set the required filament current. Since when the filament current changes, the temperature and resistance of the filament changes, which, in turn, leads to a change in the filament current, adjustment must be carried out using the method of successive approximations. After completing the adjustment, you must wait approximately 5 minutes for the filament current and cathode temperature to stabilize.

3. Connect a constant voltage source to the anode circuit and, by changing the voltage at the anode, measure the current-voltage characteristic point by point. Take the current-voltage characteristic in the range 0...25 V, every 0.5...1 V.

Ia(V a), Where Ia– anode current, V a– anode voltage.

5. If the range of changes in the anode voltage is taken to be small, then the values x m, C(x,n) And Vm, included in formula (33), can be taken constant. At large V a size Vm can be neglected. As a result, formula (33) is transformed to the form (after transition from the thermocurrent density j to his full meaning I)

6. From formula (34) determine the value WITH for three maximum values ​​of the anode voltage on the current-voltage characteristic. Calculate the arithmetic mean of the obtained values. Substituting this value into formula (33), determine the value Vm for three minimum voltage values ​​at the anode and calculate the arithmetic mean value Vm.

7. Using the obtained value Vm, plot the dependence of ln Ia from ln( V a+|Vm|). Determine the degree of dependence from the tangent of the angle of this graph Ia(V a + Vm). It should be close to 1.5.

8. Prepare a report on the work.

Report requirements

5. Conclusions on the work.

Control questions

1. What is the phenomenon of thermionic emission called? Define the work function of an electron. What is the difference between thermodynamic and external work function?

2. Explain the reasons for the emergence of a potential barrier at the solid-vacuum boundary.

3. Explain, based on the energy diagram of the metal and the electron energy distribution curve, the thermal emission of electrons from the metal.

4. Under what conditions is thermionic current observed? How can you observe thermionic current? How does the thermal diode current depend on the applied electric field?

5. State the law Richardson-Deshman

6. Explain the qualitative picture of the influence of a negative volume charge on the current-voltage characteristic of a thermal diode. Formulate Langmuir's "three second" law.

7. What are the distributions of potential, electric field strength and electron density in the space between the cathode and anode at currents limited by space charge?

8. What is the dependence of the thermal emission current on the voltage between the anode and cathode, taking into account the space charge and initial electron velocities? Explain the meaning of the parameters that determine this dependence;

9. Explain the design of the experimental setup for studying thermionic emission. Explain the purpose of individual elements of the circuit.

10. Explain the method for experimentally determining the exponent in the law of “three-seconds”.

9. Laboratory work No. 2. Study of thermionic emission at low emission current densities

Purpose of the work: to study the current-voltage characteristics of a thermal diode at a low cathode heating current. Determination from experimental results of the contact potential difference between the cathode and anode, the cathode temperature.

At low thermal current densities volt-ampere the characteristic has a characteristic appearance with an inflection point corresponding to the modulus of the contact potential difference between the cathode and anode (Fig. 10). The cathode temperature can be determined as follows. Let us proceed to equation (12), which describes the current-voltage characteristic of thermionic emission at low current densities, from the thermocurrent density j to its full value I(j=I/S, Where S– cross-sectional area of ​​the thermocurrent). Then we get

Where I S– saturation current.

Taking logarithms of (35), we have

.(36)

To the extent that equation (36) describes the current-voltage characteristic in the area to the left of the inflection point, then to determine the cathode temperature it is necessary to take any two points in this area with anode currents I a 1, I a 2 and anode voltages U a 1, U a 2 respectively. Then, according to equation (36),

From here we obtain the working formula for the cathode temperature

.(37)

Work order

To perform laboratory work you must:

1. Familiarize yourself with the description and procedure for operating the instruments necessary for the operation of the experimental setup. Assemble the circuit according to Fig. 18. The installation can be connected to the network only after checking the correctness of the assembled circuit by an engineer or teacher.

2. Turn on the cathode filament current power supply and set the required filament current. After setting the current, you must wait approximately 5 minutes for the filament current and cathode temperature to stabilize.

3. Connect a constant voltage source to the anode circuit and, by changing the voltage at the anode, measure the current-voltage characteristic point by point. Volt-ampere take the characteristic in the range of 0...5 V every 0.05...0.2 V.

4. Present the measurement results on a graph in ln coordinates Ia(V a), Where Ia– anode current, V a– anode voltage. Since in this work the contact potential difference is determined graphically, the scale along the horizontal axis should be chosen so that the accuracy of determination V K.R.P was not less than 0.1 V.

5. Using the inflection point of the current-voltage characteristic, determine the contact potential difference between the anode and cathode.

6. Determine the cathode temperature for three pairs of points on the inclined linear section of the current-voltage characteristic to the left of the inflection point. The cathode temperature should be calculated using formula (37). Calculate the average temperature from these data.

7. Prepare a report on the work.

Report requirements

The report is drawn up on a standard sheet of A4 paper and must contain:

1. Basic information on the theory.

2. Diagram of the experimental setup and its brief description.

3. Results of measurements and calculations.

4. Analysis of the obtained experimental results.

5. Conclusions on the work.

Control questions

1. List the types of electron emission. What causes the release of electrons in each type of electron emission?

2. Explain the phenomenon of thermionic emission. Define the work function of an electron from a solid. How can we explain the existence of a potential barrier at the solid-vacuum boundary?

3. Explain, based on the energy diagram of the metal and the electron energy distribution curve, the thermal emission of electrons from the metal.

4. State the law Richardson-Deshman. Explain the physical meaning of the quantities included in this law.

5. What are the features of the current-voltage characteristics of the thermionic cathode at low emission current densities? How does the contact potential difference between the cathode and anode affect it?

6. What is the Schottky effect? How is this effect explained?

7. Explain the decrease in the potential barrier for electrons under the influence of an electric field.

8. How will the cathode temperature be determined in this lab?

9. Explain the method for determining the contact potential difference in this work.

10. Explain the diagram and purpose of individual elements of the laboratory setup.