Emission physicist. Electron emission

Electron emission resulting from heating is called thermionic emission (TE). The TE phenomenon is widely used in vacuum and gas-filled devices.

Electrostatic or Field emission

Electrostatic (field emission) is the emission of electrons caused by the presence of a strong electric field at the surface of a body. In this case, additional energy is not imparted to the electrons of the solid body, but due to a change in the shape of the potential barrier, they acquire the ability to escape into the vacuum.

Photoelectron emission (PE) or external photoelectric effect is the emission of electrons from a substance under the influence of radiation incident on its surface. FE is explained on the basis of quantum theory of solids and band theory of solids.

The emission of electrons by the surface of a solid body when it is bombarded with electrons.

The emission of electrons by a metal when it is bombarded with ions.

The emission of electrons as a result of local explosions of microscopic regions of the emitter.

Cryogenic electron emission

Emission of electrons from ultracold surfaces cooled to cryogenic temperatures. A little studied phenomenon.

Emission of electrons in the volume. Depending on the method of excitation, a trace is distinguished. basic types of electron emission: thermionic emission, photoelectron emission (see External photoelectric effect), secondary electron emission, field emission... Big Encyclopedic Polytechnic Dictionary

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Explosive electron emission, G. A. Mesyats, ... Category: Electricity and magnetism
Secondary electron emission, I.M. Bronstein, B.S. Fraiman, The book is devoted to one of the issues of modern physical electronics - secondary electron emission. Measurement methods are considered: secondary emission coefficient (SE), inelastic and elastic... Category: Solid state physics. Crystallography Series: Engineer's Physics and Mathematics Library Publisher:

Electronic emission

emission of electrons from the surface of a solid or liquid. E. e. occurs in cases when, under the influence of external influences, part of the electrons of the body acquires energy sufficient to overcome the potential barrier (See Potential barrier) at the boundary of the body, or if, under the influence of an electric field, the surface potential barrier becomes transparent to part of the electrons that have the highest energies inside the body . E. e. may occur when bodies are heated (Thermionic emission) , when bombarded by electrons (Secondary electron emission), ions (Ion-electron emission) or photons (Photoelectron emission) . Under certain conditions (for example, when current is passed through a semiconductor with high electron mobility or when a strong electric field pulse is applied to it), conduction electrons can “heat up” much more than the crystal lattice, and some of them can leave the body (hot electron emission) .

To observe E. e. it is necessary to create an externally electron-accelerating electric field at the surface of the body (emitter), which “sucks” electrons from the surface of the emitter. If this field is large enough (≥ 10 2 h/cm), then it reduces the height of the potential barrier at the boundary of the body and, accordingly, the work function (Schottky effect) , as a result of which E. e. increases. In strong electric fields (Electron emission 10 7 h/cm) the surface potential barrier becomes very thin and a tunnel “leakage” of electrons through it occurs (Tunnel emission) , sometimes also called field emission. As a result of the simultaneous influence of 2 or more factors, thermoautoelectronic or photoautoelectronic emission may occur. In very strong pulsed electric fields (Electron emission 5․10 7 h/cm) tunnel emission leads to rapid destruction (explosion) of microtips on the emitter surface and to the formation of dense plasma near the surface (See Plasma). The interaction of this plasma with the surface of the emitter causes a sharp increase in the electrical current. up to 10 6 A with a current pulse duration of several tens nsec(explosive emission). With each current pulse, microquantities are transferred (Electron emission 10 -11 G) emitter substances to the anode.

Lit.: Dobretsov L.N., Gomoyunova M.V., Emission Electronics, M., 1966; Bugaev S. P., Vorontsov-Velyaminov P. N., Iskoldsky A. M., Mesyats S. A., Proskurovsky D. I., Fursey G. N., The phenomenon of explosive electron emission, in the collection: Discoveries in the USSR 1976 of the year, M., 1977.

T. M. Lifshits.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what “Electronic emission” is in other dictionaries:

Electron emission is the phenomenon of the emission of electrons from the surface of a solid or liquid. Types of Emission Thermionic Emission Electron emission resulting from heating is called thermionic emission (TE). The phenomenon of TE... ... Wikipedia

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electronic emission- The emission of electrons from the surface of a material into the surrounding space. [GOST 13820 77] Topics: electrovacuum devices... Technical Translator's Guide

Books

Explosive electron emission, G. A. Mesyats, ... Category: Electricity and magnetism
Secondary electron emission, I.M. Bronstein, B.S. Fraiman, The book is devoted to one of the issues of modern physical electronics - secondary electron emission. Measurement methods are considered: secondary emission coefficient (SE), inelastic and elastic... Category: Solid state physics. Crystallography Series: Engineer's Physics and Mathematics Library Publisher:

Lecture 2

Formation of negative ions

It has been established that halogens, when ionized, are capable of adding electrons to form negative ions (halogens: F, Cl, Br, J). F has the greatest electron affinity, which is often introduced into the arc in the form of salts (CaF2) to suppress porosity in the weld metal. The addition of negative ions by F atoms leads to the fact that the concentration of free electrons in the arc plasma decreases, although the total number of charged particles remains constant. Electrons carry the bulk of the current. Negative F ions are heavy, sedentary particles that carry current much worse. Therefore, when substances containing F are introduced into the welding zone, the stability of the arc sharply deteriorates, especially when welding with alternating current. Therefore, electrodes of the UONI 13/45 type, which contain a significant amount of CaF2, are used on direct current. If welding must be carried out using alternating current, then ionizing substances are introduced into the composition of such coatings, or arc stabilization is used using oscillators or pulse generators.

Emission of electrons from the cathode surface

To pull an electron out of the cathode, it is necessary to overcome the forces of attraction of the electron by the positive charges of the cathode. To do this, it is necessary to expend a certain amount of work, which is called the work function. The work function value depends on the cathode material and the state of its surface (presence of oxide and other films). For the process in a welding arc, two types of electron emission are of primary importance: thermionic and field emission.

Thermionic emission occurs when the cathode surface is heated. In this case, individual electrons can receive energy sufficient to perform the work function and leave the cathode surface. In the absence of an electric field, an electron cloud forms above the cathode surface, and further process of electron emission stops.

Over time, individual electrons from the space charge return to the body of the charge and are drawn into the metal. Electrons are simultaneously emitted and drawn back into the metal. When a metal is heated for a long time at a constant temperature, an equilibrium emission density is established (the number of electrons emitted is equal to the number of electrons drawn in).

The electron current density can be calculated using the formula:

j = AT 2 exp(-j/kt)

where j is the work function.

With increasing temperature, the current density of thermionic emission increases. At the temperature of the welding arc, a density of thermionic emission is established that is sufficient to maintain a stable arc discharge.

Vehicle emission. In order to facilitate the emission of electrons from the metal, the heated metal cathode is placed in an alternating electric field. The field poles are located as follows: ²-² on the metal, ²+² on the opposite electrode - the anode.

The electric field completely or partially destroys the spatial electric charge. This facilitates the emission of electrons from the cathode and increases the equilibrium emission density, which is calculated using the same dependence.

The equation for the thermal and field emission current takes the form:

In an electric field, the electron work function decreases by the amount

Δj= 0 3/2 E 1/2,

where E is the field strength.

Emission under the influence of an electric field is called field emission. Welding is characterized by both types of emissions.

Reducing the work function from the electrode surface can serve as one of the ways to stabilize the arc discharge.

Table - Work function from the cathode surface for various materials

If there are oxide films on the electrode surface, the work function decreases significantly; films of oxides of alkali and alkaline earth metals reduce j especially strongly. In order to improve the stability of the arc during welding W electrodes introduce oxides into the composition of the electrodes La, such electrodes are called lanthanum electrodes. Previously used electrodes contained 1.5-2.5% thorium dioxide. VT-15 and VT-25 (1.5-2.5% thorium dioxide). In this case, the arc does not wander along the surface of the metal.

Abroad and in our country, attempts have been made to increase stability by reducing the j electron from the surface of the consumable electrode. For this purpose, an activated wire was used, i.e. covered with a thin layer of salts. The best effect is provided by cesium salts (provides low ionization potential). In this case, drops of molten metal are crushed.

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) I a(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.

Let us consider the physical foundations of emission electronics, i.e. the phenomenon of emission (emission) of electrons and ions occurring at the boundary of a solid with a vacuum or gas when the emitter surface is exposed to a constant or high-frequency electric field, light radiation, electron or ion bombardment, thermal heating, mechanical treatment, etc.

Spontaneous (spontaneous) emission of electrons from a solid is prevented by the presence of a potential threshold U0 at the boundary, caused by the interaction forces between electrons escaping from the substance at distances exceeding atomic dimensions and the remaining uncompensated positive charge of the lattice ions (Fig. 1).

The maximum possible kinetic energy of conduction electrons in a metal at absolute zero temperature is equal to E F (Fermi energy). To pull out one electron from the E F level outside the emitter, additional energy eφ=U 0 –E F is required, equal to the work function of the electron from the given metal.

Spontaneous, or auto-electronic emissions, is possible only if the potential threshold is transformed into a potential barrier through which electrons can “leak” and “tunnel” due to a purely quantum mechanical effect, similar to the tunnel effect during the spontaneous emission of alpha particles from radioactive nuclei. The term “field electron emission” means that the release of electrons outside the solid body occurs spontaneously, i.e. is not associated with the expenditure of additional energy. Electrons that “leaked” beyond the barrier acquire energy from the electric field E only in the emitter–anode vacuum gap.

The greater the external electric field strength E, the steeper the potential energy of the electron changes with a change in distance x from the surface U(x)=–е E x in this field, the narrower the potential barrier, and, consequently, the higher the field emission current density j A, depending on the quantum mechanical transparency coefficient of the barrier (see §3.7). An external electric field not only leads to the transformation of the potential threshold into a barrier, but also reduces the height of the barrier ( Schottky effect), which also contributes to an increase in field emission current (see §9.7). Dependence j A ( E) is exponential in nature: j A ~exp[–С/ E], where C is a constant determined by the work function of the electron leaving the emitter.

According to calculations, for the appearance of significant field emission currents, field strengths are required E~10 8 ¸10 9 V/m.

An electric field at the surface of a solid can be formed not only due to an external potential difference accelerating electrons between the cathode and anode, but also due to the field of positive ions located at the cathode surface. Such a layer of ions can appear at the cathode, for example, due to the evaporation of part of the substance of the field emission cathode when it is heated by the field emission current itself. Subsequent ionization of the evaporated atoms leads to the creation of a layer of dense nonequilibrium gas-discharge plasma at the cathode surface. The strong electric field in the emitter-plasma boundary region is localized within the so-called Debye radius, which depends on the plasma concentration. The appearance of this field causes an additional increase in field electron emission. This process of transition from ordinary field emission to abnormally high emission current densities is abrupt, explosive in nature and, as a rule, ends in a vacuum breakdown (arc). The stage of emission of field electrons from a metal or semiconductor in the interval between the end of normal field emission and the beginning of a vacuum arc is called explosive emissions.

In the case of semiconductors, the electric field can penetrate deep into the emitter. This causes, firstly, a change in the nature of the band structure in the near-surface region (band bending) and, secondly, heating of the electron gas in the conduction band of the semiconductor due to the fact that electrons, taking energy from the field at the mean free path, then experience quasi-elastic scattering by vibrations of lattice atoms (phonons). With such scattering, the direction of the electron momentum changes sharply (scattering is, as a rule, spherically symmetrical in nature), and the electron energy changes little. Obviously, in this case the average electron energy will increase, i.e. the temperature of the electron gas will “detach” from the lattice temperature. As a result, one can observe the emission of “hot” electrons from the cold semiconductor cathode. The current of this emission will be greater, the lower the affinity of the emitter for the electron χ, since only those electrons whose energy E x =p x 2 /2m e, associated with the momentum component normal to the surface, will be greater than χ, will be able to escape into the vacuum.

A special class of emitters are semiconductor cathodes, in which the bottom of the conduction band in the emitter volume is located above the vacuum level. These are emitters with negative electron affinity, obtained, for example, by sputtering onto the surface of a p-type semiconductor (with downward band bending) monomolecular layers of Cs atoms or Cs 2 O molecules. From such emitters it is possible to emit not only “hot” ones, but also thermolyzed (“cold”) electrons.

The electric field penetrates metals to a depth not exceeding one or two atomic layers (~10 -10 m). Under normal conditions in metals, due to the high concentration of electrons, it is impossible to increase the temperature of the electron gas using the energy of the electric field. However, it is possible to create a special emitter by covering the dielectric substrate with a thin metal film with an “island” structure. The dimensions of the metal “islands” should not exceed ~10 nm, i.e. must be less than the mean free path of electrons in the metal. In such films, called dispersed metal films, an electric field is created by applying a voltage between solid metal contacts specially applied to the film.

In the frequency range of the electromagnetic field corresponding to the light range (ν~10 15 –10 16 Hz), the energy of one quantum hν may be greater than the work function of an electron from the metal eφ. The phenomenon of solids emitting electrons under the influence of the energy of light quanta is called the external photoelectric effect or photoelectron emission. In intrinsic semiconductors and dielectrics, photoelectron emission is observed only if hν 0 ≥ΔE g +χ, where ΔE g is the band gap. In addition to knocking out electrons from the valence band, photoelectron emission from donor levels, as well as from surface states filled with electrons, is possible. Of particular interest is photoelectron emission from systems with negative (or close to zero) electron affinity χ, when thermolized electrons can escape into vacuum.

The phenomenon of photoelectron emission is characterized by the number of emitted electrons per absorbed photon on average. This quantity is called quantum yield of the photoelectric effect and are denoted by Y. For emitters with negative electron affinity, the quantum yield reaches the maximum possible values. With an increase in the field strength of the light wave (the density of photons incident on the emitter), the probability of absorption of two or more photons simultaneously by an electron of a solid body can be very noticeable, which corresponds to the multiphoton photoelectric effect. At sufficiently low frequencies, due to the small energy of one quantum (for example, at microwave frequencies hν~10 ‑5 –10 ‑6 eV), the interaction of an electromagnetic wave with electrons of a solid body should be considered purely classically, i.e. as a continuous process of electron acceleration in the field of a microwave wave. This is exactly how the process of emission of “hot” electrons at microwave frequencies from semiconductors and “island” films is described.

By bombarding a solid body with electrons with energy E P >eφ (in metals) or E p ≥ΔE g (in dielectrics and semiconductors), one can observe the emission of secondary electrons, i.e. knocking out electrons from a solid by transferring energy to them from primary electrons incident on the substance.

The phenomenon of emission of electrons by solids when bombarded by a beam of primary electrons is called secondary electron emission. The ratio of the number of secondary electrons emitted by a target over a certain time interval to the number of primary electrons falling on the target over the same interval is called secondary electron emission factor and denoted by σ. The value of σ depends significantly on the energy E P of the primary electrons. Secondary electrons can be emitted both from the front side of the target, bombarded by the primary electron beam, and from its rear side, if the target is shot through by the primary beam. Obviously, the latter is possible only for thin films. In the first case, they talk about secondary electron emission due to reflection, in the second – about secondary electron emission due to cross-section. The coefficient of secondary electron emission per shot is denoted by Σ. The dependence Σ (E P) can differ significantly for the same emitter from the dependence σ (Ep). This is due, first of all, to the fact that up to the values of E P, starting from which the primary electrons shoot through the target, the value of Σ is zero (or negligible).

When a solid body is heated, the vibration amplitudes of the atoms of the crystal lattice increase (in quantum language, this corresponds to an increase in the phonon density). The transfer of energy from phonons to the electron gas leads to an expansion of the energy spectrum of electrons. As the temperature increases, an increasing number of electrons acquire energy sufficient to overcome the work function at the solid-vacuum interface. The phenomenon of electrons being emitted into a vacuum by a heated body is called thermionic emission. In semiconductors at temperatures close to absolute zero, there are no electrons in the conduction band. Heating of the body causes electrons to be thrown into the conduction band from donor levels and from the valence band. When interacting with phonons, electrons are thermolized, and their spectrum acquires a Maxwellian character. Thermionic emission current density j T is determined from the Richardson–Dashman formula: j T =(1– )AT 2 exp(–eφ/kT), where – value of the coefficient of reflection of electrons from the potential threshold averaged over the spectrum of thermionic electrons; A is the thermionic constant equal to 120.4 A/(deg 2 m 2).

2.2. Field emission from metals.

Electrons pass through a potential barrier with a certain probability due to the tunneling effect. A potential step at the metal-vacuum interface turns into a potential barrier due to the application of high voltage between the cathode and anode, the magnitude of which determines the height and width of the barrier. The theory of field emission was first developed by R. Fowler and L. Nordheim (1928–1929).

According to this theory, the basic formula for field emission current density is:

, (10.10)

where J(ξ)=θ(ξ)-(2ξ/3)(dθ(ξ)/dξ), θ(ξ) is the Nordheim function, which is introduced to take into account the reduction in the height of the potential barrier by the amount Δ(eφ), the argument of the function θ(ξ) is a dimensionless quantity representing the ratio of the decrease in work function due to the Schottky effect to the work function of an electron with a given energy Ε x.

The function θ(ξ) is tabulated and can be represented as a graph shown in Fig. 10.3. The approximate expression of the function θ(ξ) is close to a parabola: θ(ξ)≈0.955–1.03ξ 2 . It is valid for those values of the argument where ξ differs noticeably from both zero and one. Thus, in the interval 0.35≤ξ≤0.69, the function θ(ξ) is determined from this expression with an error of less than 1%.

Expressing eφ in electron volts and the electric field strength in V/cm, we obtain the field emission current density in A/cm 2:

For practical calculations, it is convenient to use the following formula for the field emission current density:

. (10.12)

At E=6·10 7 V/cm and еφ=4.5 eV, the current density j A can reach 10 7 A/cm 2 .

For comparison with experimental data, formula (10.11) is usually presented in the form ln(j A / E 2)=f(1/ E). In such coordinates, the dependence of field emission on the electric field strength is a straight line, despite the fact that in the exponent E also depends on the Nordheim function, which varies greatly with changes E. However, the presence of the function θ(ξ) in the exponential does not significantly affect the course of the dependence under consideration, since this function changes weakly within the limits of the experimentally used field strength values. Deviation of dependence ln(j A / E 2)=f(1/ E) from linear in the region of very high electric field strengths is explained by the influence of the space charge of emitted field electrons (Fig. 10.4). A dense negative space charge reduces the field strength at the emitter surface and, therefore, causes a weaker dependence of the current on the applied potential difference V. The dependence of the field emission current on the work function eφ, which follows from the Fowler-Nordheim theory, is also in agreement with experimental data. This dependence is determined mainly by the factor φ 3/2 in the exponent.

The given formulas of the Fowler-Nordheim theory correspond to the case T = 0 K. With increasing temperature, the spectrum of electrons in the metal broadens, which leads to a temperature dependence of the field emission current due to the greater probability of electrons thermally excited to levels above the Fermi level passing through the potential barrier. E. Murphy and R. Goode obtained the following expression for the field emission current density taking into account the emitter temperature:

j A (T)=j A (0)πy/sinπy. (10.13)

At small T, expanding sinπy into a series, we obtain

j A (T)≈j(0). (10.14)

With J(ξ)=J(0.5)=1.044 we have , where eφ is expressed in eV, E- in V/cm, and T - in K. Substituting the value in (10.14), we get

j A (T)/j A (0)≈1+1.40 10 8 (eφ/ E 2)T 2 (10.15)

Thus, to a first approximation, the change in field emission current with temperature follows a quadratic law. Formula (10.15) determines j A (T) with an accuracy of no worse than 10% up to j A (T)/j A (0)=1.6 and 1% up to A (T)/j A (0)=1, 18. Calculation using this formula, for example, at the temperature of liquid nitrogen (77 K) shows that the ratio j A (77)/j A (0) does not exceed 1.01. At room temperature, the addition to j A (0) does not exceed 10% (for eφ≥3 eV and j A ≥10 3 A/cm 2).

In the high-temperature region, the field emission current itself, caused by the tunneling mechanism, is supplemented by thermionic emission current, caused by electrons with energy sufficient to overcome the potential barrier, reduced due to the Schottky effect. For clarity, in Fig. 10.5, the energy spectrum of electrons in a metal is divided into four regions: A, B, C and D. Electrons of group A can be emitted as field electrons at any temperature, including T=0 K. Electrons of group B participate in field emission at T>0 K ( they can be called thermoautoelectrons). The release of group B electrons into vacuum corresponds to an increase in the thermionic current due to the Schottky effect. Finally, group G electrons escape into vacuum due to the thermionic emission mechanism even at E≈0.

Analysis of the energies of electrons leaving the field cathode can be carried out using energy analyzers with a retarding field or with electron deflection in an electric or magnetic field (see Chapter 2). In this case, field electrons are preliminarily accelerated by a certain potential difference in the gap between the emitter and a nearby electrode (for example, a grid), and then are sent to the analyzing system. Measurements show that at low temperatures the energy distribution of field electrons has the form of a curve with a maximum half-width ΔE ½ of several tenths of an electron volt (usually ΔE ½ ~0.15¸0.20 eV), i.e. Most electrons actually tunnel into the vacuum from levels close to the Fermi level. These experimental data are in good agreement with theoretical concepts about the mechanism of field electron emission from clean metal surfaces.

The theory of field emission considered here is based on the use of formulas for barrier transparency obtained by solving the one-dimensional Schrödinger equation. This approximation is valid if: 1) the emitter surface is an ideal homogeneous plane; 2) the free electron model is applicable, for which the Fermi surface in momentum space is a sphere. Real emitters have a step structure with a step height of one or more interatomic distances, and the isoenergetic Fermi surfaces for most metals have a complex structure that is significantly different from a sphere. In addition, an emitter with an adsorbed submonolayer film, the atoms of which tend to assemble into “islands,” has a nonuniformity in work function eφ, which causes the appearance of a so-called spot field at the surface. Taking into account the first two factors leads to some refinements to the theory of field emission from metals. In particular, these refinements concern the spectrum of field electrons and the temperature dependence of the field emission current, but they are not so significant that they require discussion.

Field emission measurements are carried out either in devices with cylindrical symmetry, where the emitter is a very thin metal wire, and the anode is a cylinder surrounding it, or in devices where the emitter has the shape of a tip with a radius of curvature of the order of 0.01-1 μm. In the latter case, the field strength at the cathode surface depends very little on the anode geometry. When calculating the value E the tip is usually approximated as a paraboloid, hyperboloid, cone with a spherical end, etc.

When a monatomic layer of another metal is deposited on the surface of a metal emitter, the nature of the potential barrier does not change, but if the metal surface is covered with a film of non-metallic material, the shape of the surface barrier can change significantly. In the latter case, field electrons must tunnel through an adsorbed atom, which is a potential well with a set of its own discrete levels. This should lead to a change in the energy spectrum of field emission, in particular to the appearance of resonance peaks in it, corresponding to an increase in the probability of the release of those electrons of the metal substrate whose energies coincide with the energies of free levels in the atomic potential well. For example, upon the adsorption of Cs on W, a field electron spectrum with a half-width of 0.05 eV was obtained.

Since real tip emitters differ in shape from the listed idealized models, this inevitably causes an error in the calculated field strength, which can reach 10–30%. In addition, it should be taken into account that the actual surface of the emitter may have microprotrusions with increased field strength. When using single-crystal emitters, local field strength values depend on the cut of the single crystal.

By placing the tip emitter E and the ring anode A adjacent to it in the center of a glass cylinder B, on the inner conducting surface of which a layer of phosphor L is applied, one can observe on the luminescent screen the distribution patterns of the field emission current over the surface of the tip, due to different work functions of the faces of the single crystal eφ, as well as the difference in local electric field strengths at the surface of different faces (Fig. 10.6). The magnification of such an electronic projector, the idea of which belongs to E. Muller, is determined by the ratio R/r, where R is the distance between the emitter and the screen, and r is the radius of the tip. For example, with r=0.1 μm and R=10 cm, the increase reaches 10 6 . In this regard, electronic projectors are used to emit phenomena that occur during the adsorption of films of various substances on the emitter surface. The resolution of such a device, while still insufficient for observing individual atoms, allows one to see on the screen distant atomic complexes with transverse dimensions of ~100 nm, as well as measure field emission currents from individual faces of a single-crystal tip. The brightness of the screen at a certain point is greater for a given V, the higher the emissivity of the elementary section of the tip, which is projected to a given location on the screen.

In 1951, E. Müller proposed an ion projector, which has a resolution of the order of several angstroms and, therefore, allows the observation of individual atoms and molecules on the emitter surface. The operation of an ion projector is based on the phenomenon of surface ionization of atoms, and its higher resolution compared to an electronic projector is determined by the fact that the de Broglie wavelength for ions is much shorter than for electrons moving at the same speed.

Metal field cathodes are used in a number of electric vacuum devices (cathodes in electron guns, “starting” cathodes in microwave devices, etc.).

The advantages of such cathodes are: 1) lack of incandescence, and therefore inertia-free; 2) very high current densities; 3) small dimensions of the cathode, allowing the creation of almost point sources of electrons; 4) small energy spread; 5) high slope of the current-voltage characteristic.

The main disadvantage is the instability of the field emission current, caused by the adsorption of residual gases in insufficiently good vacuum conditions and cathode sputtering of the emitter substance. These factors cause, on the one hand, a change in the work function of the cathode, and on the other, a change in its microrelief. In addition, in strong fields and at a temperature sufficiently high for a given cathode material, a noticeable migration of atoms of the substance itself along the cathode surface is observed, leading to a restructuring of its microgeometry, which changes the field strength at the emitter surface. The transition to ultra-high vacuum, the use of materials that are more resistant to ion bombardment, reducing the ion flow to the cathode using special electron-optical devices - all this makes it possible to achieve fairly stable operation of the field emission cathode.

The formula for the maximum current density j Am of field emission from a metal has the form

(10.16)

where j Am is the maximum field emission current density, A/cm 2 ;

E F =р F 2 /2m e – electron energy at the Fermi level, eV.

Since the energy E F is of the order of several electron volts, the maximum field emission current density can be more than 10 10 A/cm 2 . Such a high current density is, in principle, possible due to the fact that the electron concentration in the conduction band of the metal is 10 22 –10 23 cm -3. The main reason limiting the maximum current density of field emission is the thermal destruction of the emitter by its own current. The value of j Am in practice depends on the duration of the anode voltage pulse and lies in the range of 10 7 –10 9 A/cm 2 .

2.3. Field emission from semiconductors.

Unlike a metal, a semiconductor is a field-field cathode with a significantly limited electron concentration in the conduction band. This determines the characteristics of field emission from semiconductors: 1) the maximum current densities are significantly lower than in metals; 2) nonlinear current-voltage characteristics lgi A =f(1/V); 3) a wider spectrum of emitted electrons compared to metals; 4) dependence of the shape of the current pulse on the amplitude and duration of the anode voltage pulse during pulsed excitation of field emission (relaxation effects); 5) thermal and photosensitivity of field emission current.

An external electric field penetrates the semiconductor to a distance determined by the Debye screening radius, the expression for which has the form r D = (ε r ε 0 kT/2e 2 n) ½ where n is the electron concentration, and leads to band bending. Within this radius, due to band bending, the electron concentration in the conduction band and at donor levels increases. This, in turn, causes the appearance of a near-surface layer of negative space charge. In the case of a strong field, the electron gas in the conduction band near the surface of the semiconductor can become degenerate if, as a result of band bending, the bottom of the conduction band ends up below the Fermi level (Fig. 10.7).

The process of electron tunneling from a space charge layer through a potential barrier into a vacuum is no different from the process of field emission from metals. However, unlike metals, electrons from the valence band can also participate in emission. Another difference is the possibility of “saturation” of the emission current with increasing voltage. This occurs in the case when the rate of electron flow from the volume of the sample to the surface is sufficient only to compensate for the electrons emitted from the surface layer of the space charge into the vacuum.

In this case, a “plateau” will appear on the current-voltage characteristic (Fig. 10.8), i.e. a further increase in the anode voltage will not cause an increase in the field emission current until a new source of electrons “turns on.” Such an additional source of electrons coming from the bulk to the near-surface region can be impact ionization of valence band electrons and autoionization of electrons at donor levels. These strong field effects are responsible for the region of rapid growth of field emission current preceding thermal destruction of the cathode.

Experimentally obtained V.A.C. for p-type semiconductors and high-resistance n-type samples are indeed nonlinear. They have three characteristic sections in coordinates lgi A =f(l/V): 1 – linear, well described by the Fowler–Nordheim formula; 2 – saturation section; 3 – region of a sharp increase in current associated with the multiplication of electrons in the volume of the emitter.

The Fowler–Nordheim field emission theory is essentially a “zero current approximation.” This means that the emission current represents only a small fraction of the total flow of electrons incident on the potential barrier. For metals, this approximation is valid up to the region of very strong fields. In semiconductors, the difference between the drift flow of electrons to the surface and the diffusion flow from the surface can be comparable to the flow of field electrons into a vacuum.

The limited rate of electron flow from the bulk to the surface is the main reason for the appearance of a saturation region in the current-voltage curve. field emission current from semiconductors of the two types indicated. In this case, several interrelated processes are simultaneously observed: 1) the electron concentration in the near-surface layer decreases; 2) the external field penetrates deeper into the emitter; 3) the voltage drop across the volume resistance of the semiconductor increases; 4) the geometry and magnitude of the field strength at the emitter surface change. An increase in the voltage drop across the sample leads, in turn, to an increase in the average electron energy, i.e. to heating the electron gas. If the electron affinity of the crystal is low (χ≤0.5 eV), then with the appearance of “hot” electrons, the transparency of the potential barrier can reach a limiting value and the field emission current will not increase until the process of intensive electron multiplication begins due to impact ionization. For samples with high electron affinity (χ≥3 – 4 eV) and a small band gap (ΔE g ≤1 eV), heating the electron gas by an internal field cannot lead to noticeable “above-barrier” emission, since the electron energy distribution function during the process of impact ionization by “hot” electrons of the valence band, it is not smeared in the energy region E>ΔE g.

An increase in the electron concentration in the volume of a high-resistance semiconductor, for example, due to its irradiation with light, causes an increase in the field emission current. In this case, the addition to the current in the “plateau” region on the V.A.C. proportional to illumination I 0 . The spectral dependence of the field emission current i A (υ) practically coincides with the spectral dependence of photoconductivity. Field emission from a semiconductor irradiated with light corresponds to a combined type of emission - photofield emission.

An increase in cathode temperature usually leads to an increase in emission due to an increase in the electron concentration in the conduction band. Only for low-resistance samples (for example, n-type silicon), when there is strong degeneracy of the electron gas, is the temperature dependence of the field emission current either completely absent or caused by a change in the effective work function of the semiconductor. In such cases, illumination of the samples does not change either the magnitude of the field emission current or the character of the voltage-voltage characteristics. Degeneracy occurs when the Fermi level falls inside the conduction band. The energy gap Δ S (Fig. 10.7) between the bottom of the conduction band and the Fermi level characterizes the degree of degeneracy of the electron gas in the near-surface layer of the semiconductor emitter.

In the absence of degeneracy (the case of weak field penetration), the expression for the current density of field emission from a semiconductor has the form

where n ∞ is the electron concentration in the volume; Δ cs is the energy gap between the position of the bottom of the conduction band in the bulk and on the surface; ε r is the relative dielectric constant of the semiconductor.

This formula includes the mass of a free electron m e , although with a more rigorous approach it is necessary to take into account the complex structure of the bands and operate with the effective mass. However, the corrections due to this uncertainty are usually small.

A study of the energy distribution of field electrons emitted by semiconductors shows that the source of field electron emission can be not only the conduction band, but also the valence band. If the conditions for emission from both bands are approximately the same, then the spectrum of field electrons should consist of two peaks, the distance between which is equal to the band gap ΔE g. In experiments for n-type silicon, “double-humped” spectra were indeed obtained with a distance between maxima ΔE g = 1.1 eV (Fig. 10.10).

In the case of p-type silicon, when field emission comes only from the valence band, the energy distribution curve of field electrons has only one maximum, the width of which, as follows from the theory, increases with increasing anode voltage. When electrons are emitted from the conduction band, the spectrum broadens with increasing field strength E associated with the emission of “hot” electrons. The half-width of the spectrum also increases with increasing temperature, since an increase in temperature leads to a greater probability of electrons occupying energy states lying above the bottom of the conduction band (no degeneracy) or above the Fermi level (presence of degeneracy). A broadening of the energy spectra of field electrons is observed only with a deviation of the current-voltage characteristics. from the linear stroke, and there is a clear relationship between an increase in the half-width of the spectrum and an increase in the voltage drop across the emitter. When the spectrum width ΔΕ exceeds the band gap, a sharp increase in the field emission current is observed (region 3 in the current-voltage curve in Fig. 10.8), associated with impact ionization.

The process of electron tunneling itself is practically inertialess, but the establishment of diffusion-drift equilibrium during the flow of field emission current in a semiconductor is characterized by a finite relaxation time. Therefore, in semiconductor field cathodes there are transient processes when the anode voltage is pulsed in regions 2 and 3 of the current-voltage characteristics, Fig. 10.8. In region 1, the field emission current does not depend on time. In region 2, the current decreases, and in region 3 during the pulse it increases at a constant anode voltage. This behavior of the field emission current is explained by the processes of filling and emptying of electron capture centers in the surface space charge, as well as surface states. The gradual depletion of these centers causes a decrease in the current, and at the moment the field is turned on, the release of electrons from the centers increases the field emission current. Residual effects when turning the field off and on again or illuminating the emitter are associated with the inertia of rearrangement of the space charge region due to the fact that a finite time is required to fill the electron traps. The current relaxation time depends on the concentration of traps in the sample, its temperature and the voltage at the emitter. For high-resistivity Ge and Si samples, depending on the concentration of traps, the relaxation time ranges from τ≤10‑5 s to τ≈10‑3 s.

The practical significance of semiconductor field emission cathodes is that in the electron “depletion” mode (region 2 on the current-voltage curve) it is possible to obtain stationary field emission under not very good vacuum conditions (p ~ 10 -4 Pa) over long time intervals (up to hundreds of hours). For example, for n-type silicon, a stationary field emission current density of up to 10 4 A/cm 2 was obtained.

see also

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