The high electrical conductivity of metals is due to the presence in them of a large number of free electrons detached from the atoms. These electrons - conduction electrons - form the so-called electron gas in the metal. Free electrons undergo thermal motion and have kinetic energy, but are retained inside the metal due to their Coulomb interaction with the positively charged crystal lattice. For an electron to leave the metal, work must be done against these forces, which is called work function electrons.

There are two reasons leading to the emergence of work function. The first is as follows. When an electron tries to leave the metal, an induced positive charge appears on its surface (the so-called electrostatic mirror). As a result, an attractive force arises between the electron and the metal, directed towards the metal, preventing the electron from leaving and manifesting itself outside the body (Fig. 1). Work against the force of attraction towards a positively charged body is the main part of the work function. This part of the work function is similar to the ionization energy of atoms or molecules.

In addition, there is a contribution to the work function associated with the presence of a double electric layer in the near-surface region of any body (Fig. 2). It occurs even on a perfectly regular and clean crystal surface. Individual electrons constantly leave the surface of the metal, move away from it at several interatomic distances, and then stop under the influence of the uncompensated charge of positively charged ions and turn back. As a result, the metal finds itself surrounded by a thin cloud of electrons (Fig. 2).

The thickness of the double layer is on the order of several interatomic distances (10 -10 h10 -9 m). Due to the electric field of the double layer, a force acts on the electrons directed into the crystal. The work to overcome the force acting due to the electric field of the double layer at the boundary of the body is the second component of the work function. Beyond the double layer region outside the crystal, only the Coulomb force, which was discussed above, acts on the electrons.

When passing through the surface into a vacuum, the electron potential increases compared to the potential inside the metal by a certain amount ts, which is called the surface potential difference. It is related to the work function as follows:

Where e - electron charge modulus. The work function is usually expressed in electronvolts (eV):

1 eV = 1.6·10-19 Joule.

To remove an electron from a metal volume beyond its boundaries, the kinetic energy of the electron must exceed the work function.

Where m- electron mass, v- its speed. When condition (2) is met, the phenomenon of electron emission is observed, i.e. emission of electrons from a metal surface. To observe electron emission, it is necessary to impart energy to the electrons.

Depending on the method of energy transmission, four types of emissions are distinguished:

• 1. Thermionic emission- emission of electrons by heated metals. With increasing temperature, the number of electrons sharply increases, the kinetic energy of thermal motion of which is greater than the work function, and the phenomenon of thermionic emission becomes more noticeable.
• 2. Photoelectron emission. Emission of electrons from a metal under the influence of radiation. In this case, the electron receives additional energy due to the energy of the photon:

Where h, - Planck's constant, n- frequency of incident radiation.

• 3, Secondary electron emission - the emission of electrons when a surface is bombarded from the outside with a beam of electrons or other particles.
• 4. Field emission - emission of electrons from the surface of a metal under the influence of a strong external electric field.

All types of emission are used in various electronic devices, but the most controlled thermionic emission is used most often.

The work function is a characteristic of the surface of a body. The faces of the same crystal, formed by different crystallographic planes or coated with different substances, have different work functions. For example, to reduce the work function, the tungsten surface is coated with a thin layer of thorium, cesium, barium or oxides of certain metals (activated cathodes). The layer thickness is several tens of thousands of interatomic distances.

Emission of electrons from metal

At normal temperatures, the energy of electrons is not enough to leave the body. To obtain electron emission, it is necessary to impart additional energy to the electrons.

The lack of emission at normal temperatures is explained by two reasons .

First is that electrons having the highest energy ( W 0 or more), with their random movement, approach the surface of the metal, but they are attracted back by the positive ions of the spatial lattice. An “electronic film” is formed on the surface (Fig. 5.3, A). Of course, it is not “frozen”, but is in dynamic equilibrium. New electrons come into this “film”, and those that previously got into it go back into the depths of the metal.

There is an electric field between the electron film and the positive ions, which slows down the electrons trying to leave the body (Fig. 5.3, b). They say that an electrical double layer (a layer of electrons above a layer of ions) is formed on the surface of the metal. To pass through this layer, the electron must have more energy W 0 .

Fig.5.3. Electronic film (a) and electric field of the electric double layer (b)

Second cause, preventing electrons from escaping, lies in the fact that a metal deprived of some electrons becomes positively charged. An electric field arises between it and the emitted electrons, under the influence of which the electrons are attracted back to the metal. The strength of this attraction quickly decreases as the electron moves away from the metal surface. It can be considered equal to zero when the electron moves away from the metal surface to several interatomic distances.

Thus, In order to fly into a vacuum and not be bound to the metal, the electron must have, in addition to the energy W 0, the energy necessary to overcome the force of reverse attraction to the metal.

The energy that must be imparted to an electron to exit the metal in addition to the maximum energy W 0 available at absolute zero temperature is called the effective work function or simply the work function(W out).

The total work done by an electron when leaving the metal is equal to W 0 + W exit She is sometimes called total work function, and the quantities W 0 and W output accordingly internal and external work function.

The work done to move an electric charge, divided by the magnitude of the charge, is equal to the potential difference that the charge passes through. If work W 0 + W out divided by the charge of the electron e, then you get some potential difference.

Since an electron expends energy when leaving a metal, the potential in a vacuum is negative relative to the metal. Taking the metal potential as zero, we can write that the potential φ in a vacuum near the metal surface is equal to:

where φ 0 is the potential at the boundary of the electron film and vacuum;

φout - potential corresponding to the work function.

In Fig. 5.4, A shows a graph of the change in potential during the transition from metal to vacuum. The vertical is the negative potential φ, the horizontal is the distance X. At the boundary between metal and vacuum, a potential “jump” or “potential barrier” for electrons is obtained. In the electron film, the potential increases in the negative direction by φ 0 and then in vacuum it increases further by φ out. The total “height” of the barrier is φ 0 + φ out. D la To overcome the barrier, the electron must have an energy of at least W 0 + W out electron-volts or “speed” is not less than φ 0 + φ out volts.

Fig.5.4. Potential barrier at the interface between metal and vacuum (a)

and its mechanical analogy (b)

A visual mechanical model of electron yield is shown in Fig. 5.4, b. The potential barrier is replaced by a hill turning into a plateau, and the electrons are replaced by balls located at the foot. In order for the balls to roll up the slide, they must have a certain kinetic energy, depending on the height h. If there is not enough energy, the balls roll back. By analogy with the movement of electrons in a vacuum, it is believed that balls roll without friction. For a convenient transition to such a mechanical analogy, the negative potential in Fig. 5.4 is put upward.

The work function varies for different metals and amounts to several electron volts. The larger it is, the more difficult it is to obtain electronic emission. Metals with large interatomic distances have a lower work function. These include alkali and alkaline earth metals, such as cesium, barium, and calcium.

A study of the electron emission phenomenon showed that impurities of other substances on the metal surface have a significant effect on the work function.

If on the surface of the base metal there are atoms of substances that donate electrons to this metal, then an increase in emission is observed. Such substances are called activating. Their influence is explained by the fact that atoms that have donated some electrons to the base metal turn into positive ions and form a double electric layer on the surface of the metal (Fig. 5.5).

Fig.5.5. Electric field between metal and positive

ions of the activating substance

The electric field of this layer is accelerating for electrons trying to escape from the metal, and the work function decreases. The smallest work function is obtained when positive impurity ions are arranged in a single-atomic layer.

The field between the film of the activating substance and the base metal is similar to the field in a capacitor with plates in the form of metal meshes (gratings). In a capacitor, the field exists only between the plates, and if an electron enters this field through the hole in the negatively charged plate, it will fly out with increased speed through the hole in the positively charged plate.

Atoms of some substances, when in contact with a metal, take away electrons from it and turn into negative ions. A layer of such atoms on the metal surface prevents electron emission. A field appears between these atoms and the base metal, inhibiting the emitted electrons, and the work function increases.

For example, oxygen atoms on the surface of tungsten increase the yield to 9.2 EV. They say that the metal reduces its emissivity due to “poisoning” with oxygen. When constructing cathodes, activating layers are usually created on the surface of the base metal, reducing the work function, and measures are taken to ensure that the cathode surface is not “poisoned” by oxygen atoms.

It is also possible to reduce the work function by coating metal surfaces with layers of alkali and alkaline earth metal oxides called oxides. Then, the work function is even less than in the case of monatomic films.

Purpose of the work: construction and study of the current-voltage characteristics of the diode; study of the dependence of the saturation current density during thermal emission on the cathode temperature; determination of the work function of an electron from tungsten.

INTRODUCTION

Current carriers in metals are free electrons, i.e. electrons weakly bound to the ions of the metal crystal lattice. Free electrons at room temperature practically do not leave the metal. This is explained by the fact that in the surface layer of the metal there is a retarding electric field that prevents the electron from leaving the metal. The work required to remove an electron from a metal is called work A.

Electrons, leaving the metal, move away from it at distances of the order of atomic sizes and create an “electron cloud” above the metal surface. This cloud, together with the outer layer of positive ions of the lattice and the induced positive charges induced as a result of the emission of electrons, forms a double electric layer, the field of which is similar to the field of a flat-plate capacitor. This field prevents the further escape of free electrons from the metal. The thickness of this electric layer is (10 -10 – 10 -9) m. Thus, when an electron leaves the metal, it must overcome the electric field of the double layer that holds it back.

Potential difference Dj in this layer, called the surface potential jump, is determined by the work function A electron from metal:

Where e – electron charge. The work function is usually measured in electron volts ( eV ): 1 eV equal to the work done by field forces when an electron passes through a potential difference 1 V. Hence: 1 eV = 1.6 ×10 -19 J. The work function depends on the chemical nature of the metals, on the cleanliness of their surface and has values ​​of several electron volts.

If the electrons in the metal are given the energy necessary to overcome the electric field of the double layer that retards it, i.e. energy equal in value to the work function, then some of the electrons will leave the metal, i.e. The phenomenon of electron emission from a metal is observed - electron emission.

Thermionic emission is the emission of electrons from heated metals. As the temperature increases, the number of electrons leaving the metal increases. The study of the laws of thermionic emission can be carried out using the simplest two-electrode electron tube - a vacuum diode, which is an evacuated cylinder containing two electrodes: a cathode TO and anode A . The cathode is usually a tungsten filament. If the diode is connected to the circuit (see Fig. 1), then when the cathode is heated and a positive voltage is applied to the anode, a current arises in the anode circuit of the diode.

The cathode is heated by the current generated by the incandescent battery B N, The cathode temperature can be changed by adjusting using a rheostat R H filament current strength. The electrodes are supplied with voltage from the anode battery B A. this voltage can be changed using a potentiometer P and measure with a voltmeter V. The strength of the anode current is measured with a milliammeter mA.

At a constant cathode filament current, the curve of the dependence of the anode current strength on the anode voltage has the form shown in Fig. 2.

This curve is called the current-voltage characteristic of the diode. Different curves correspond to different cathode temperatures. Let's consider the characteristic features of curves. At = 0 a weak current flows in the circuit, determined by the number of electrons reaching the anode. To make a current equal to 0 , it is necessary to apply some negative voltage between the cathode and anode.

From Fig. 2 it can be seen that Ohm’s law for a vacuum diode is not satisfied. The initial section of the curve follows quite well the theoretically obtained Langmuir and Boguslavsky law three second, according to which the strength of the anode current changes proportionally. With an increase, more and more electrons reach the anode; at a certain value, all electrons emitted from the cathode reach the anode - the current stops growing, i.e., saturation occurs. The maximum thermionic current possible at a given cathode temperature is called saturation current - I A us.

As the temperature increases, the speed of the chaotic movement of electrons in the metal increases, so the number of electrons capable of leaving the metal increases sharply. The saturation current density, that is, the saturation current per unit of anode cathode surface, is calculated using the Richardson-Deshman formula:

, (2)

Where IN – constant emission; k =1.38 ×10 -23 J/K – Boltzmann constant.

DESCRIPTION OF THE LABORATORY INSTALLATION AND MEASUREMENT METHOD

The electrical circuit for conducting the experiment is shown in Fig. 3.

Here IP - power supply; FPE-06/05 – a cassette with an assembled electrical circuit (see Fig. 1); PV - voltmeter for measuring filament voltage ; V And A - voltmeter and ammeter on the power supply panel, the voltmeter measures the anode voltage , ammeter - filament current I nak; RA - milliammeter for measuring anode current I A .

By experimentally measuring the dependence of the saturation current on temperature, it is possible to determine the work function for a given cathode. In this work, to determine the work function, the Richardson straight line method is used, which is as follows. Let's take the logarithm of formula (2):

(3)

The graph of function (3) is a straight line, the slope of which is equal to : tga = A out / k. From here you can find the work function:

. (4)

To plot the graph, you need to know the density of the anode saturation current j us and cathode temperature T. The temperature is calculated as follows. The power supplied to the cathode is spent mainly on thermal radiation. For tungsten, the dependence of the cathode temperature was experimentally determined T from the power spent on heating it per unit area of ​​the cathode surface R/S k.

T, K

0 50 100 150 200 250 300 350 400 450 R/S k,

W/cm2

This dependence is shown in Fig. 4. From this graph, knowing the power supplied to the cathode, you can determine its temperature.

PROCEDURE FOR PERFORMANCE OF THE WORK

1. Connect the cassette FPE-06 connecting cable to the power supply IP (see Fig. 3). Maximum filament current value I nak, measured by the ammeter on the power supply panel should not exceed 2.2 A. Filament voltage measured by voltmeter PV, which connects to the terminals where the voltage is indicated 2.5 – 4.5 V . The anode voltage is adjusted using a knob on the power supply panel located under the voltmeter V . To measure anode current I A ammeter used RA, which connects to the cassette FPE-06. It should operate in milliammeter mode, measuring current up to 20 mA.

Set filament voltage = 3.7 V, record the filament current value I nak, and, increasing the anode voltage from 10 to 100 V through 10 V, measure anode current values I A .

2. Carry out similar measurements for the filament voltage in the range 3.7 – 4.2 V, changing it through 0.1 V, while fixing the filament current values. Enter the measurement data into table 1.

3. For each value of the filament current, construct a current-voltage characteristic; the inflection point on the resulting curves is considered the saturation point. Knowing the scale of the graph, determine the saturation current I H .

4. For all filament voltage values, calculate using the formula P = I H U H the power released at the cathode, as well as the power per unit surface area of ​​the cathode. Take the cathode surface area to be equal to S K =3.52 ×10 -2 cm 2.

5. According to the schedule (see Fig. 4), knowing the values R/S to, determine the cathode temperature for each value of power released at the cathode.

Table 1

6. Calculate the density of the anode saturation current using the formula: , accept S=11×10 -6 m2.

7. Enter all received data into table 2.

Table 2

8. Build a dependence graph .

9. Determine the tangent of the angle of inclination of the straight line to the abscissa axis and calculate the work function using formula (4). Convert the resulting value to eV.

CHECK QUESTIONS FOR PERMISSION TO WORK

1. Draw a schematic diagram of the laboratory setup and explain the use of the instruments.

2. Explain the procedure for performing the work and the methodology for taking readings from measuring instruments.

3. What is a vacuum diode?

4. What dependence is called the current-voltage characteristic of a diode?

5. What is the nature of the forces that prevent electrons from leaving the metal?

6. How to convert the unit of energy expressed in joules to electron volts?

7. How is the density of the anodic saturation current determined in the work?

8. How is the filament temperature of the cathode determined in operation?

9. Explain how the work calculates the absolute and relative measurement error.

TEST QUESTIONS FOR PASSING THE WORK

1. What is the work function of an electron leaving a metal?

2. What is called thermionic emission?

3. Explain how an electric double layer occurs around the surface of a metal. What is its thickness?

4. Draw an electrical circuit to obtain the current-voltage characteristic of the diode.

5. How to prove that negatively charged particles - electrons - fly out of the cathode during thermionic emission?

6. Draw the current-voltage characteristics of the diode at various temperatures.

7. What is saturation current? How is saturation current achieved?

8. Why does the saturation current depend on temperature?

As experience shows, free electrons at ordinary temperatures practically do not leave the metal. Consequently, there must be a retarding electric field in the surface layer of the metal, preventing electrons from escaping from the metal into the surrounding vacuum. The work required to remove an electron from a metal into a vacuum is called work function. Let us indicate two probable reasons for the appearance of the work function:

1. If an electron is removed from a metal for some reason, then an excess positive charge arises in the place where the electron left and the electron is attracted to the positive charge induced by itself.

2. Individual electrons, leaving the metal, move away from it at distances on the order of atomic and thereby create an “electron cloud” above the surface of the metal, the density of which quickly decreases with distance. This cloud, together with the outer layer of positive ions of the lattice, forms electrical double layer, the field of which is similar to the field of a parallel-plate capacitor. The thickness of this layer is equal to several interatomic distances (10 -10 - 10 -9 m). It does not create an electric field in external space, but prevents free electrons from escaping from the metal.

Thus, when an electron leaves the metal, it must overcome the electric field of the double layer that retards it. The potential difference  in this layer, called surface potential jump, determined by work function (A) electron from metal:

Where e- electron charge. Since there is no electric field outside the double layer, the potential of the medium is zero, and inside the metal the potential is positive and equal to . The potential energy of a free electron inside a metal is equal to - e and is negative relative to vacuum. Based on this you can

The work function is expressed in electron volts(eV): 1 eV is equal to the work done by field forces when moving an elementary electric charge (a charge equal to the charge of an electron) when it passes through a potential difference of 1 V. Since the charge of an electron is 1.6 l0 -19 C, then 1 eV = 1.6 10 -1 9 J.

The work function depends on the chemical nature of the metals and the cleanliness of their surface and varies within a few electron volts (for example, for potassium A = 2.2 eV, for platinum A = 6.3 eV). By choosing the surface coating in a certain way, you can significantly reduce the work output. For example, if you apply tungsten to the surface (A=4.5 eV) layer of alkaline earth metal oxide (Ca, Sr, Ba), then the work function is reduced to 2 eV.

§ 105. Emission phenomena and their application

If we provide the electrons in metals with the energy necessary to overcome the work function, then some of the electrons can leave the metal, resulting in the phenomenon of electron emission, or electronic emission. Depending on the method of imparting energy to electrons, thermionic, photoelectronic, secondary electron and field emission are distinguished.

1. Thermionic emission - This is the emission of electrons by heated metals. 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 - vacuum diode, which is an evacuated cylinder containing two electrodes: a cathode TO 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 the diode is connected to the circuit, as shown in Fig. 152, then when the cathode is heated and a positive voltage is applied to the anode (relative to the cathode), a current arises in the anode circuit of the diode. If you change the polarity of battery B a, the current stops, no matter how hot the cathode is heated. Consequently, the cathode emits negative particles - electrons.

If we maintain the temperature of the heated cathode constant and remove the dependence of the anode current I and from the anode voltage U a- current-voltage characteristic(Fig. 153), it turns out that it is not linear, that is, for a vacuum diode Ohm’s law is not satisfied. Dependence of thermionic current I from the anode voltage in the region of small

positive values U described law of three second(established by Russian physicist S. A. Boguslavsky (1883-1923) and American physicist I. Langmuir (1881 - 1957)):

I=B.U. 3/2 ,

Where IN - coefficient depending on the shape and size of the electrodes, as well as their relative position.

As the anode voltage increases, the current increases to a certain maximum value Ius, called 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 Richardson - Deshman formula, derived theoretically on the basis of quantum statistics:

j us =CT 2 e -A/(kT) .

Where A - work function of electrons leaving the cathode, T - thermodynamic temperature, WITH- constant, theoretically the same for all metals (this is not confirmed by experiment, which is 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.

In Fig. 153 shows the current-voltage characteristics for two cathode temperatures: T 1 And T 2 , and T 2 >T 1 . As the cathode temperature increases, the emission of electrons from the cathode becomes more intense, and the saturation current also increases. At U a =0, ​​an anode current is observed, i.e., some electrons emitted by the cathode have sufficient energy to overcome the work function and reach the anode without applying an electric field.

The phenomenon of thermionic emission is used in devices in which it is necessary to obtain a flow of electrons in a vacuum, for example in vacuum tubes, X-ray tubes, electron microscopes, etc. Electron tubes are widely used in electrical and radio engineering, automation and telemechanics for rectifying alternating currents, amplification electrical signals and alternating currents, generating electromagnetic oscillations, etc. Depending on the purpose, additional control electrodes are used in the lamps.

2. Photoelectron emission - This is the emission of electrons from a metal under the influence of light, as well as short-wave electromagnetic radiation (for example, X-rays). The main principles of this phenomenon will be discussed when considering the photoelectric effect.

3. Secondary electron emission - This is the emission of electrons from the surface of metals, semiconductors or dielectrics when bombarded with a beam of electrons. The secondary electron flow consists of electrons reflected by the surface (elastically and inelastically reflected electrons), and “true” secondary electrons - electrons knocked out of the metal, semiconductor or dielectric by primary electrons.

Secondary electron number ratio n 2 to the number of primary n 1 , causing the emission is called secondary electron emission coefficient:

=n 2 / n 1 .

Coefficient b depends on the nature of the surface material, the energy of the bombarding particles and their angle of incidence on the surface. Semiconductors and dielectrics have more b than metals. This is explained by the fact that in metals where the concentration of conduction electrons is high, secondary electrons, often colliding with them, lose their energy and cannot leave the metal. In semiconductors and dielectrics, due to the low concentration of conduction electrons, collisions of secondary electrons with them occur much less frequently and the probability of secondary electrons leaving the emitter increases several times.

For example in Fig. 154 shows the qualitative dependence of the secondary electron emission coefficient b on energy E incident electrons for KCl. With increasing electron energy, b increases, since primary electrons penetrate deeper into the crystal lattice and, therefore, knock out more secondary electrons. However, at a certain energy of the primary electrons 6 begins to decrease. This is due to the fact that as the depth of penetration of primary electrons increases, it becomes increasingly difficult for secondary electrons to escape to the surface. The value of max for KCl reaches 12 (for pure metals it does not exceed 2).

The phenomenon of secondary electron emission is used in photomultiplier tubes(PMT), used to amplify weak electrical currents. The photomultiplier is a vacuum tube with a photocathode K and anode A, between which there are several electrodes - emitters(Fig. 155). Electrons ejected from the photocathode under the influence of light enter the emitter E 1, passing through the accelerating potential difference between K and E 1.  electrons are knocked out from the emitter E 1. Strengthened this way

the electron flow is directed to emitter E2, and the multiplication process is repeated on all subsequent emitters. If the PMT contains n emitters, then at anode A, called collector, The result is a photoelectron current amplified by 6 times.

4. Autoelectronic emissions - This is the emission of electrons from the surface of metals under the influence of a strong external electric field. These phenomena can be observed in an evacuated tube, the configuration of the electrodes of which (cathode - tip, anode - inner surface of the tube) allows, at voltages of approximately 10 3 V, to obtain electric fields with a strength of approximately 10 7 V / m. With a gradual increase in voltage, already at a field strength at the cathode surface of approximately 10 5 -10 6 V/m, a weak current arises due to the electrons emitted by the cathode. The strength of this current increases with increasing voltage across the tube. Currents arise when the cathode is cold, so the described phenomenon is also called cold emission. An explanation of the mechanism of this phenomenon is possible only on the basis of quantum theory.

Conduction electrons in a metal are in random motion. The fastest moving electrons, which have a sufficiently large kinetic energy, can escape from the metal into the surrounding space. At the same time, they perform work both against the attractive forces from the excess positive charge arising in the metal as a result of their emission, and against the repulsive forces from the previously emitted electrons, forming an electron “cloud” near the surface of the conductor. A dynamic equilibrium is established between the electron gas in the metal and the electron “cloud”. The work that must be done to remove an electron from a metal into a vacuum is called the work function. It is equal to , where e is the electron charge and is the output potential. The work function is produced by electrons - due to a decrease in their kinetic energy. Therefore, it is clear that slowly moving electrons cannot escape from the metal. The work function depends on the chemical nature of the metal and the state of its surface; contamination; traces of moisture, etc. change its value. For pure metals, the work function varies within a few electron volts. A conduction electron can fly out of any metal if its energy exceeds the work function A of the electron from the metal. The phenomenon of electrons being emitted by heated metals is called thermionic emission.

The concentration of conduction electrons in the metal is very high; their thermal velocities at a given temperature are different and distributed, according to classical concepts, in accordance with Maxwell's law. This means that even at average temperatures there is a sufficiently large number of conduction electrons in the metal that can perform the work function and fly out of the metal. In this case, the work function is equal to the decrease in kinetic energy

where m, e are the mass and charge of the electron, respectively, and are the speeds of the electron before and after leaving the metal. At ordinary temperatures, the number of electrons with sufficient speed to escape is very small. There are several ways of imparting additional energy to electrons necessary to remove them from the metal: heating the conductor (thermionic emission); irradiation of metals with visible and ultraviolet light (photoelectron emission); exposure to an accelerating external electric field (field emission, or cold emission); bombardment of a metal with electrons or ions.

In order to obtain a significant flow of electrons, the so-called emitter is heated to temperatures of the order of 2000÷2500 K.

To study thermionic emission, you can use a setup consisting of two electrodes - anode A and cathode K, which are placed in a vacuum (Fig. 18.1). The cathode is made in the form of a thread, the anode - in the form of a coaxial cylinder. The cathode, which is a source of electrons, is heated using a special incandescent battery Bn.

The anode battery Ba serves to create an electric field Evn between the cathode and the anode. When the filament is heated, an electron cloud appears, carrying a negative charge. As a result of turning on the battery Ba anode, the flow of electrons begins to move between the cathode and the anode, i.e. Electric current begins to flow in the circuit. The current strength depends on the temperature of the filament,

the voltage Ua that the anode battery creates, the cathode material and the geometry of the electrodes. The dependence of the anode current recorded by the galvanometer G on the anode voltage I=f(Ua) is called the current-voltage characteristic of the installation.

This characteristic can be removed experimentally by maintaining the filament voltage constant and changing the voltage Ua (Fig. 18.2). Three areas can be distinguished in this current-voltage characteristic. Region I corresponds to the case when a retarding potential difference is applied to the electrodes (the negative pole of the battery is connected to the anode), i.e. field E slows down electrons. However, current still flows in the circuit because some of the electrons escaping from the hot filament have energy sufficient to overcome the retarding potential difference. This part of the current-voltage characteristic is called the “delay curve”. In addition to the electric field Evn created by the anode battery, the existing field between the cathode and the anode is due to its appearance by flying electrons. Electrons moving from the cathode to the anode create a certain space charge, which causes an electric field Eob to decelerate the electrons as they leave the cathode and accelerate them as they approach the anode. As the potential difference Ua increases, the field E0b will decrease. Therefore, an increasing number of electrons will reach the anode and the current strength will increase (region II).

At a certain value of the potential difference U a =U 0, the total field E in + E about at the cathode becomes equal to zero. In this case, all electrons escaping from the cathode at a given temperature will reach the anode. Therefore, a further increase in voltage Ua will not lead to an increase in the anode current I. The current strength will become constant (region III). This current is called saturation current. The strength of the saturation current, other things being equal, depends on the emitter temperature. The dependence of the saturation current density jH on the absolute temperature T is satisfactorily described by the Richardson-Dashman formula.

(18.7)

where is the average reflection coefficient of electrons from the emitter-vacuum boundary, B is a constant depending on the cathode material, A is the electron work function, k is Boltzmann’s constant.