F6. Tunnel effect (physics)

There is a possibility that a quantum particle will penetrate a barrier that is insurmountable for a classical elementary particle.

Imagine a ball rolling inside a spherical hole dug in the ground. At any moment of time, the energy of the ball is distributed between its kinetic energy and the potential energy of gravity in a proportion depending on how high the ball is relative to the bottom of the hole (according to the first law of thermodynamics). When the ball reaches the side of the hole, two scenarios are possible. If its total energy exceeds the potential energy of the gravitational field, determined by the height of the ball's location, it will jump out of the hole. If the total energy of the ball is less than the potential energy of gravity at the level of the side of the hole, the ball will roll down, back into the hole, towards the opposite side; at the moment when the potential energy is equal to the total energy of the ball, it will stop and roll back. In the second case, the ball will never roll out of the hole unless additional kinetic energy is given to it - for example, by pushing it. According to Newton's laws of mechanics, the ball will never leave the hole without giving it additional momentum if it does not have enough of its own energy to roll overboard.

Now imagine that the sides of the pit rise above the surface of the earth (like lunar craters). If the ball manages to fall over the raised side of such a hole, it will roll further. It is important to remember that in the Newtonian world of the ball and the hole, the fact that the ball will roll further over the side of the hole has no meaning if the ball does not have enough kinetic energy to reach the top edge. If it does not reach the edge, it simply will not get out of the hole and, accordingly, under no conditions, at any speed and will not roll anywhere further, no matter how high above the surface the edge of the side is located outside.

In the world of quantum mechanics, things are different. Let's imagine that there is a quantum particle in something like such a hole. In this case, we are no longer talking about a real physical hole, but about a conditional situation when a particle requires a certain supply of energy necessary to overcome the barrier that prevents it from breaking out of what physicists have agreed to call "potential hole". This pit also has an energy analogue of the side - the so-called "potential barrier". So, if outside the potential barrier the level of tension energy field lower than the energy possessed by the particle, it has a chance to be “overboard”, even if the real kinetic energy of this particle is not enough to “go overboard” in the Newtonian sense. This mechanism of a particle passing through a potential barrier is called the quantum tunneling effect.

It works like this: in quantum mechanics, a particle is described through a wave function, which is related to the probability of the particle being located in a given place in this moment time. If a particle collides with a potential barrier, Schrödinger's equation allows us to calculate the probability of the particle penetrating through it, since the wave function is not just energetically absorbed by the barrier, but is extinguished very quickly - exponentially. In other words, the potential barrier in the world of quantum mechanics is blurred. It, of course, prevents the movement of the particle, but is not a solid, impenetrable boundary, as is the case in classical mechanics Newton.

If the barrier is low enough or if the total energy of the particle is close to the threshold, the wave function, although it decreases rapidly as the particle approaches the edge of the barrier, leaves it a chance to overcome it. That is, there is a certain probability that the particle will be detected on the other side of the potential barrier - in the world of Newtonian mechanics this would be impossible. And once the particle has crossed the edge of the barrier (let it have the shape of a lunar crater), it will freely roll down its outer slope away from the hole from which it emerged.

A quantum tunnel junction can be thought of as a kind of "leakage" or "percolation" of a particle through a potential barrier, after which the particle moves away from the barrier. There are plenty of examples of this kind of phenomena in nature, as well as in modern technologies. Take a typical radioactive decay: a heavy nucleus emits an alpha particle consisting of two protons and two neutrons. On the one hand, one can imagine this process in such a way that a heavy nucleus holds an alpha particle inside itself through intranuclear binding forces, just as the ball was held in the hole in our example. However, even if an alpha particle does not have enough free energy to overcome the barrier of intranuclear bonds, there is still a possibility of its separation from the nucleus. And by observing spontaneous alpha emission, we receive experimental confirmation of the reality of the tunnel effect.

Another important example tunnel effect - the process of thermonuclear fusion that supplies energy to stars (see Evolution of stars). One of the stages of thermonuclear fusion is the collision of two deuterium nuclei (one proton and one neutron each), resulting in the formation of a helium-3 nucleus (two protons and one neutron) and the emission of one neutron. According to Coulomb's law, between two particles with the same charge (in this case, protons that are part of deuterium nuclei) there is a powerful force of mutual repulsion - that is, there is a powerful potential barrier. In Newton's world, deuterium nuclei simply could not come close enough to synthesize a helium nucleus. However, in the depths of stars, the temperature and pressure are so high that the energy of the nuclei approaches the threshold of their fusion (in our sense, the nuclei are almost at the edge of the barrier), as a result of which the tunnel effect begins to operate, thermonuclear fusion occurs - and the stars shine.

Finally, the tunnel effect is already used in practice in electron microscope technology. The action of this tool is based on the fact that the metal tip of the probe approaches the surface under study at an extremely short distance. In this case, the potential barrier prevents electrons from metal atoms from flowing to the surface under study. When moving the probe at an extremely close distance along the surface under study, it seems to be moving atom by atom. When the probe is in close proximity to atoms, the barrier is lower than when the probe passes between them. Accordingly, when the device “gropes” for an atom, the current increases due to increased electron leakage as a result of the tunneling effect, and in the spaces between the atoms the current decreases. This allows for a detailed study of the atomic structures of surfaces, literally “mapping” them. By the way, electron microscopes they provide the final confirmation of the atomic theory of the structure of matter.

Translation

I'll start with two simple questions with fairly intuitive answers. Let's take a bowl and a ball (Fig. 1). If I need to:

The ball remained motionless after I placed it in the bowl, and
it remained in approximately the same position when moving the bowl,

So where should I put it?

Rice. 1

Of course, I need to put it in the center, at the very bottom. Why? Intuitively, if I put it somewhere else, it will roll to the bottom and flop back and forth. As a result, friction will reduce the height of the dangling and slow it down below.

In principle, you can try to balance the ball on the edge of the bowl. But if I shake it a little, the ball will lose its balance and fall. So this place doesn't meet the second criterion in my question.

Let us call the position in which the ball remains motionless, and from which it does not deviate much with small movements of the bowl or ball, “stable position of the ball.” The bottom of the bowl is such a stable position.

Another question. If I have two bowls like in fig. 2, where will be the stable positions for the ball? This is also simple: there are two such places, namely, at the bottom of each of the bowls.

Rice. 2

Finally, another question with an intuitive answer. If I place a ball at the bottom of bowl 1, and then leave the room, close it, ensure that no one goes in there, check that there have been no earthquakes or other shocks in this place, then what are the chances that in ten years when I If I open the room again, I will find a ball at the bottom of bowl 2? Of course, zero. In order for the ball to move from the bottom of bowl 1 to the bottom of bowl 2, someone or something must take the ball and move it from place to place, over the edge of bowl 1, towards bowl 2 and then over the edge of bowl 2. Obviously, the ball will remain at the bottom of the bowl 1.

Obviously and essentially true. And yet, in quantum world, in which we live, no object remains truly motionless, and its position is precisely unknown. So none of these answers are 100% correct.

Tunneling

Rice. 3

If I place an elementary particle like an electron in a magnetic trap (Fig. 3) that works like a bowl, tending to push the electron towards the center in the same way that gravity and the walls of the bowl push the ball towards the center of the bowl in Fig. 1, then what will be the stable position of the electron? As one would intuitively expect, the average position of the electron will be stationary only if it is placed at the center of the trap.

But quantum mechanics adds one nuance. The electron cannot remain stationary; its position is subject to "quantum jitter". Because of this, its position and movement are constantly changing, or even have a certain amount of uncertainty (this is the famous “uncertainty principle”). Only the average position of the electron is at the center of the trap; if you look at the electron, it will be somewhere else in the trap, close to the center, but not quite there. An electron is stationary only in this sense: it usually moves, but its movement is random, and since it is trapped, on average it does not move anywhere.

This is a little strange, but it just reflects the fact that an electron is not what you think it is and does not behave like any object you have seen.

This, by the way, also ensures that the electron cannot be balanced at the edge of the trap, unlike the ball at the edge of the bowl (as below in Fig. 1). The electron's position is not precisely defined, so it cannot be precisely balanced; therefore, even without shaking the trap, the electron will lose its balance and fall off almost immediately.

But what's weirder is the case where I'll have two traps separated from each other, and I'll place an electron in one of them. Yes, the center of one of the traps is a good, stable position for the electron. This is true in the sense that the electron can remain there and will not escape if the trap is shaken.

However, if I place an electron in trap No. 1 and leave, close the room, etc., there is a certain probability (Fig. 4) that when I return the electron will be in trap No. 2.

Rice. 4

How did he do it? If you imagine electrons as balls, you won't understand this. But electrons are not like marbles (or at least not like your intuitive idea of marbles), and their quantum jitter gives them an extremely small but non-zero chance of "walking through walls" - the seemingly impossible possibility of moving to the other side. This is called tunneling - but don't think of the electron as digging a hole in the wall. And you will never be able to catch him in the wall - red-handed, so to speak. It's just that the wall isn't completely impenetrable to things like electrons; electrons cannot be trapped so easily.

In fact, it's even crazier: since it's true for an electron, it's also true for a ball in a vase. The ball may end up in vase 2 if you wait long enough. But the likelihood of this is extremely low. So small that even if you wait a billion years, or even billions of billions of billions of years, it won’t be enough. From a practical point of view, this will “never” happen.

Our world is quantum, and all objects consist of elementary particles and obey the rules quantum physics. Quantum jitter is always present. But most of objects whose mass is large compared to the mass of elementary particles - a ball, for example, or even a speck of dust - this quantum jitter is too small to be detected, except in specially designed experiments. And the resulting possibility of tunneling through walls is also not observed in ordinary life.

In other words: any object can tunnel through a wall, but the likelihood of this usually decreases sharply if:

The object has a large mass,
the wall is thick (large distance between two sides),
the wall is difficult to overcome (it takes a lot of energy to break through a wall).

In principle the ball can get over the edge of the bowl, but in practice this may not be possible. It can be easy for an electron to escape from a trap if the traps are close and not very deep, but it can be very difficult if they are far away and very deep.

Is tunneling really happening?

Rice. 5

Or maybe this tunneling is just a theory? Absolutely not. It is fundamental to chemistry, occurs in many materials, plays a role in biology, and is the principle used in our most sophisticated and powerful microscopes.

For the sake of brevity, let me focus on the microscope. In Fig. Figure 5 shows an image of atoms taken using a scanning tunneling microscope. Such a microscope has a narrow needle, the tip of which moves in close proximity to the material being studied (see Fig. 6). The material and the needle are, of course, made of atoms; and at the back of the atoms are electrons. Roughly speaking, electrons are trapped inside the material being studied or at the tip of the microscope. But the closer the tip is to the surface, the more likely the tunneling transition of electrons between them is. A simple device (a potential difference is maintained between the material and the needle) ensures that electrons will prefer to jump from the surface to the needle, and this flow - electricity, measurable. The needle moves over the surface, and the surface appears closer or further from the tip, and the current changes - it becomes stronger as the distance decreases and weaker as it increases. By monitoring the current (or, conversely, moving the needle up and down to maintain direct current) when scanning a surface, the microscope makes a conclusion about the shape of this surface, and often the detail is enough to make out individual atoms.

Rice. 6

Tunneling plays many other roles in nature and modern technology.

Tunneling between traps of different depths

In Fig. 4 I meant that both traps had the same depth - just like both bowls in fig. 2 are the same shape. This means that an electron, being in any of the traps, is equally likely to jump to the other.

Now let us assume that one electron trap in Fig. 4 deeper than the other - exactly the same as if one bowl in fig. 2 was deeper than the other (see Fig. 7). Although an electron can tunnel in any direction, it will be much easier for it to tunnel from a shallower to a deeper trap than vice versa. Accordingly, if we wait long enough for the electron to have enough time to tunnel in either direction and return, and then start taking measurements to determine its location, we will most often find it deeply trapped. (In fact, there are some nuances here too; everything also depends on the shape of the trap). Moreover, the difference in depth does not have to be large for tunneling from a deeper to a shallower trap to become extremely rare.

In short, tunneling will generally occur in both directions, but the probability of going from a shallow to a deep trap is much greater.

Rice. 7

It is this feature that a scanning tunneling microscope uses to ensure that electrons only travel in one direction. Essentially, the tip of the microscope needle is trapped deeper than the surface being studied, so electrons prefer to tunnel from the surface to the needle rather than vice versa. But the microscope will work in the opposite case. The traps are made deeper or shallower by using a power source that creates a potential difference between the tip and the surface, which creates a difference in energy between the electrons on the tip and the electrons on the surface. Since it is quite easy to make electrons tunnel more often in one direction than another, this tunneling becomes practically useful for use in electronics.

There is a possibility that a quantum particle will penetrate a barrier that is insurmountable for a classical elementary particle.

Imagine a ball rolling inside a spherical hole dug in the ground. At any moment of time, the energy of the ball is distributed between its kinetic energy and the potential energy of gravity in a proportion depending on how high the ball is relative to the bottom of the hole (according to the first law of thermodynamics) . When the ball reaches the side of the hole, two scenarios are possible. If its total energy exceeds the potential energy of the gravitational field, determined by the height of the ball's location, it will jump out of the hole. If the total energy of the ball is less than the potential energy of gravity at the level of the side of the hole, the ball will roll down, back into the hole, towards the opposite side; at the moment when the potential energy is equal to the total energy of the ball, it will stop and roll back. In the second case, the ball will never roll out of the hole unless additional kinetic energy is given to it - for example, by pushing it. According to Newton's laws of mechanics , the ball will never leave the hole without giving it additional momentum if it does not have enough of its own energy to roll overboard.

In the world of quantum mechanics, things are different. Let's imagine that there is a quantum particle in something like such a hole. In this case, we are no longer talking about a real physical hole, but about a conditional situation when a particle requires a certain supply of energy necessary to overcome the barrier that prevents it from breaking out of what physicists have agreed to call "potential hole". This pit also has an energy analogue of the side - the so-called "potential barrier". So, if outside the potential barrier the level of energy field intensity is lower , than the energy that a particle possesses, it has a chance to be “overboard”, even if the real kinetic energy of this particle is not enough to “go over” the edge of the board in the Newtonian sense. This mechanism of a particle passing through a potential barrier is called the quantum tunneling effect.

It works like this: in quantum mechanics, a particle is described through a wave function, which is related to the probability of the particle being located in a given place at a given moment in time. If a particle collides with a potential barrier, Schrödinger's equation allows one to calculate the probability of a particle penetrating through it, since the wave function is not just energetically absorbed by the barrier, but is extinguished very quickly - exponentially. In other words, the potential barrier in the world of quantum mechanics is blurred. It, of course, prevents the particle from moving, but is not a solid, impenetrable boundary, as is the case in classical Newtonian mechanics.

Another important example of the tunnel effect is the process of thermonuclear fusion, which supplies energy to stars ( cm. Evolution of stars). One of the stages of thermonuclear fusion is the collision of two deuterium nuclei (one proton and one neutron each), resulting in the formation of a helium-3 nucleus (two protons and one neutron) and the emission of one neutron. According to Coulomb's law, between two particles with the same charge (in this case, protons that are part of deuterium nuclei) there is a powerful force of mutual repulsion - that is, there is a powerful potential barrier. In Newton's world, deuterium nuclei simply could not come close enough to synthesize a helium nucleus. However, in the depths of stars, the temperature and pressure are so high that the energy of the nuclei approaches the threshold of their fusion (in our sense, the nuclei are almost at the edge of the barrier), as a result of which the tunnel effect begins to operate, thermonuclear fusion occurs - and the stars shine.

Finally, the tunnel effect is already used in practice in electron microscope technology. The action of this tool is based on the fact that the metal tip of the probe approaches the surface under study at an extremely short distance. In this case, the potential barrier prevents electrons from metal atoms from flowing to the surface under study. When moving the probe at an extremely close distance along the surface being examined, he sorts it out atom by atom. When the probe is in close proximity to atoms, the barrier is lower , than when the probe passes in the spaces between them. Accordingly, when the device “gropes” for an atom, the current increases due to increased electron leakage as a result of the tunneling effect, and in the spaces between the atoms the current decreases. This allows for a detailed study of the atomic structures of surfaces, literally “mapping” them. By the way, electron microscopes provide the final confirmation of the atomic theory of the structure of matter.

> Quantum tunneling

Explore quantum tunnel effect. Find out under what conditions the tunnel vision effect occurs, Schrödinger's formula, probability theory, atomic orbitals.

If an object does not have enough energy to break through the barrier, then it is able to tunnel through an imaginary space on the other side.

Learning Objective

Identify factors influencing the probability of tunneling.

Main points

Quantum tunneling is used for any objects in front of the barrier. But for macroscopic purposes the probability of occurrence is small.
The tunnel effect arises from Schrödinger's imaginary component formula. Since it is present in the wave function of any object, it can exist in imaginary space.
Tunneling decreases as the body mass increases and the gap between the energies of the object and the barrier increases.

Term

Tunneling is the quantum mechanical passage of a particle through an energy barrier.

How does the tunnel effect occur? Imagine throwing a ball, but it disappears instantly without ever touching the wall, and appears on the other side. The wall here will remain intact. Surprisingly, there is a finite probability that this event will come to fruition. The phenomenon is called the quantum tunneling effect.

At the macroscopic level, the possibility of tunneling remains negligible, but is consistently observed at the nanoscale. Let's look at an atom with a p orbital. Between the two lobes there is a nodal plane. There is a possibility that an electron can be found at any point. However, electrons move from one lobe to another by quantum tunneling. They simply cannot be in the hub area, and they travel through an imaginary space.

The red and blue lobes show volumes where there is a 90% probability of finding an electron at any time interval if the orbital zone is occupied

Temporal space does not appear to be real, but it actively participates in Schrödinger’s formula:

All matter has a wave component and can exist in imaginary space. A combination of the object's mass, energy, and energy height will help understand the difference in tunneling probability.

As the object approaches the barrier, the wave function changes from sine wave to exponentially contracting. Schrödinger formula:

The probability of tunneling becomes less as the mass of the object increases and the gap between energies increases. The wave function never approaches 0, which is why tunneling is so common at nanoscales.

TUNNEL EFFECT

(tunneling), the overcoming of a potential barrier by a microparticle in the case when its total (remaining mostly unchanged at T.E.) is less than the height of the barrier. That is, the phenomenon is essentially quantum. nature, impossible in classical. mechanics; analogue of T. e. in waves optics can be served by the penetration of light into the reflecting medium (at distances of the order of the light wavelength) in conditions where, from the point of view of geom. optics is happening. T. e. underlies plural important processes in at. and they say physics, in physics at. cores, TV bodies, etc.

T. e. interpreted on the basis of (see QUANTUM MECHANICS). Classic ch-tsa cannot be inside the potential. barrier height V, if its energy? impulse p - imaginary quantity (m - h-tsy). However, for a microparticle this conclusion is unfair: due to the uncertainty relationship, the particle is fixed in space. area inside the barrier makes its momentum uncertain. Therefore, there is a non-zero probability of detecting a microparticle inside a particle that is forbidden from the classical point of view. mechanics area. Accordingly, a definition appears. probability of passage through the potential. barrier, which corresponds to T. e. This probability is greater, the smaller the mass of the substance, the narrower the potential. barrier and the less energy is missing to reach the height of the barrier (the smaller the difference V-?). Probability of passing through a barrier - Ch. factor determining physical characteristics T. e. In the case of one-dimensional potential. such a characteristic of the barrier is the coefficient. barrier transparency, equal to the ratio of the flow of particles passing through it to the flow incident on the barrier. In the case of a three-dimensional barrier limiting a closed area of production from lower. potential energy (potential well), i.e. characterized by the probability w of an individual leaving this area in units. time; the value of w is equal to the product of the frequency of oscillations inside the potential. pits on the probability of passing through the barrier. The possibility of “leakage” out of the tea that was originally in the potential. well, leads to the fact that the corresponding particles acquire a finite width of the order of ћw, and these themselves become quasi-stationary.

An example of the manifestation of T. e. in at. physics can serve atoms in strong electric. and ionization of an atom in a strong electromagnetic field. waves. T. e. underlies the alpha decay of radioactive nuclei. Without T. e. it would be impossible for thermonuclear reactions to occur: Coulomb potential. the barrier that prevents the convergence of reactant nuclei necessary for fusion is overcome partly due to the high speed (high temperature) of such nuclei, and partly due to thermal energy. There are especially numerous examples of the manifestation of T. e. in physics TV. bodies: field emission, phenomena in the contact layer at the boundary of two PPs, Josephson effect, etc.

Physical encyclopedic Dictionary. - M.: Soviet Encyclopedia. . 1983 .

TUNNEL EFFECT

(tunneling) - systems through a movement area prohibited by classical mechanics. A typical example of such a process is the passage of a particle through potential barrier when her energy less than the height of the barrier. Particle momentum R in this case, determined from the relation Where U(x)- potential particle energy ( T - mass), would be in the region inside the barrier, an imaginary quantity. IN quantum mechanics thanks to uncertainty relationship between the impulse and the coordinate, the subbarrier turns out to be possible. The wave function of a particle in this region decays exponentially, and in the quasiclassical case (see Semiclassical approximation)its amplitude at the point of exit from under the barrier is small.

One of the formulations of problems about the passage of potential. barrier corresponds to the case when a stationary flow of particles falls on the barrier and it is necessary to find the value of the transmitted flow. For such problems, a coefficient is introduced. barrier transparency (tunnel transition coefficient) D, equal to the ratio of the intensities of the transmitted and incident flows. From the time reversibility it follows that the coefficient. Transparencies for transitions in the "forward" and reverse directions are the same. In the one-dimensional case, coefficient. transparency can be written as

integration is carried out over a classically inaccessible region, X 1,2 - turning points determined from the condition At turning points in the classical limit. mechanics, the momentum of the particle becomes zero. Coef. D 0 requires for its definition an exact solution of quantum mechanics. tasks.

If the condition of quasiclassicality is satisfied

along the entire length of the barrier, with the exception of the immediate neighborhoods of turning points x 1,2 . coefficient D 0 is slightly different from one. Creatures difference D 0 from unity can be, for example, in cases where the potential curve. energy from one side of the barrier goes so steeply that the quasi-classical not applicable there, or when the energy is close to the barrier height (i.e., the exponent expression is small). For a rectangular barrier height U o and width A coefficient transparency is determined by the file
Where

The base of the barrier corresponds to zero energy. In quasiclassical case D small compared to unity.

Dr. The formulation of the problem of the passage of a particle through a barrier is as follows. Let the particle in the beginning moment in time is in a state close to the so-called. stationary state, which would happen with an impenetrable barrier (for example, with a barrier raised away from potential well to a height greater than the energy of the emitted particle). This state is called quasi-stationary. Similar to stationary states, the dependence of the wave function of a particle on time is given in this case by the factor The complex quantity appears here as energy E, the imaginary part determines the probability of decay of a quasi-stationary state per unit time due to T. e.:

In quasiclassical When approaching, the probability given by f-loy (3) contains an exponential. factor of the same type as in-f-le (1). In the case of a spherically symmetric potential. barrier is the probability of decay of a quasi-stationary state from orbits. quantum number l determined by f-loy

Here r 1,2 are radial turning points, the integrand in which is equal to zero. Factor w 0 depends on the nature of the movement in the classically allowed part of the potential, for example. he is proportional. classic frequency of particle oscillations between the walls of the barrier.

T. e. allows us to understand the mechanism of a-decay of heavy nuclei. Between the -particle and the daughter nucleus there is an electrostatic force. repulsion determined by f-loy At small distances of the order of size A the nuclei are such that eff. can be considered negative: As a result, the probability A-decay is given by the relation

Here is the energy of the emitted a-particle.

T. e. determines the possibility of thermonuclear reactions occurring in the Sun and stars at temperatures of tens and hundreds of millions of degrees (see. Evolution of stars), and also in terrestrial conditions in the form of thermonuclear explosions or CTS.

In a symmetric potential, consisting of two identical wells separated by a weakly permeable barrier, i.e. leads to interference of states in wells, which leads to weak double splitting of discrete energy levels (so-called inversion splitting; see Molecular spectra). For an infinitely periodic set of holes in space, each level turns into a zone of energies. This is the mechanism for the formation of narrow electron energies. zones in crystals with strong coupling of electrons to lattice sites.

If an electric current is applied to a semiconductor crystal. field, then the zones of allowed electron energies become inclined in space. Thus, the post level electron energy crosses all zones. Under these conditions it becomes possible transition electron from one energy. zones to another due to T. e. The classically inaccessible area is the zone of forbidden energies. This phenomenon is called. Zener breakdown. Quasiclassical the approximation corresponds here to a small value of electrical intensity. fields. In this limit, the probability of a Zener breakdown is determined basically. exponential, in the cut indicator there is a large negative. a value proportional to the ratio of the width of the forbidden energy. zone to the energy gained by an electron in an applied field at a distance equal to the size of the unit cell.

A similar effect appears in tunnel diodes, in which the zones are inclined due to semiconductors R- And n-type on both sides of the border of their contact. Tunneling occurs due to the fact that in the zone where the charge carrier goes there is a finite amount of unoccupied states.

Thanks to T. e. electric possible between two metals separated by a thin dielectric. partition. These can be in both normal and superconducting states. In the latter case there may be Josephson effect.

T. e. Such phenomena occurring in strong electric currents are due. fields, such as autoionization of atoms (see Field ionization)And auto-electronic emissions from metals. In both cases, electric the field forms a barrier of finite transparency. The stronger the electric field, the more transparent the barrier and the stronger the electron current from the metal. Based on this principle scanning tunneling microscope - a device that measures tunnel current from different points of the surface under study and provides information about the nature of its heterogeneity.

T. e. is possible not only in quantum systems consisting of a single particle. So, for example, the low-temperature movement of dislocations in crystals can be associated with tunneling of the final part, consisting of many particles. In problems of this kind, a linear dislocation can be represented as an elastic string, initially lying along the axis at in one of the local minima of the potential V(x, y). This potential does not depend on y, and its relief along the axis X is a sequence of local minima, each of which is lower than the other by an amount depending on the mechanical force applied to the crystal. voltage. The movement of a dislocation under the influence of this stress is reduced to tunneling into an adjacent minimum defined. segment of a dislocation with subsequent pulling of its remaining part there. The same kind of tunnel mechanism may be responsible for the movement charge density waves in the Peierls dielectric (see Peierls transition).

To calculate the tunneling effects of such multidimensional quantum systems, it is convenient to use semiclassical methods. representation of the wave function in the form Where S- classic systems. For T. e. the imaginary part is significant S, determining the attenuation of the wave function in a classically inaccessible region. To calculate it, the method of complex trajectories is used.

Quantum particle overcoming potential. barrier may be connected to the thermostat. In classic Mechanically, this corresponds to motion with friction. Thus, to describe tunneling it is necessary to use a theory called dissipative quantum mechanics. Considerations of this kind must be used to explain the finite lifetime of current states of Josephson contacts. In this case, tunneling occurs. quantum particle through the barrier, and the role of a thermostat is played by electrons.

Lit.: Landau L. D., Lifshits E. M., Quantum, 4th ed., M., 1989; Ziman J., Principles of Solid State Theory, trans. from English, 2nd ed., M., 1974; Baz A. I., Zeldovich Ya. B., Perelomov A. M., Scattering, reactions and decays in nonrelativistic quantum mechanics, 2nd ed., M., 1971; Tunnel phenomena in solids, trans. from English, M., 1973; Likharev K.K., Introduction to the dynamics of Josephson junctions, M., 1985. B. I. Ivlev.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Editor-in-chief A. M. Prokhorov. 1988 .

See what the "TUNNEL EFFECT" is in other dictionaries:

Modern encyclopedia

Passage of a microparticle whose energy is less than the height of the barrier through a potential barrier; quantum effect, clearly explained by the spread of momenta (and energies) of the particle in the barrier region (see Uncertainty principle). As a result of the tunnel... ... Big Encyclopedic Dictionary

Tunnel effect- TUNNEL EFFECT, the passage through a potential barrier of a microparticle whose energy is less than the height of the barrier; quantum effect, clearly explained by the scatter of momenta (and energies) of the particle in the barrier region (due to the uncertainty of the principle) ... Illustrated Encyclopedic Dictionary

tunnel effect- - [Ya.N.Luginsky, M.S.Fezi Zhilinskaya, Yu.S.Kabirov. English-Russian dictionary of electrical engineering and power engineering, Moscow, 1999] Topics of electrical engineering, basic concepts EN tunnel effect ... Technical Translator's Guide

TUNNEL EFFECT- (tunneling) a quantum mechanical phenomenon that consists in overcoming a potential potential (see) by a microparticle when its total energy is less than the height of the barrier. T. e. is caused by the wave properties of microparticles and affects the flow of thermonuclear... ... Big Polytechnic Encyclopedia

Quantum mechanics ... Wikipedia