Exithons - artificial atoms in crystals

It would seem that an unusual one can happen if the light falls on the crystal? However, the scientist’s inquisitive look will find a real miracle resembling the computer game The Escapists , where the prisoner eventually breaks out, breaking a prison fence or arranging a digging.

If the energy of the photon falling on the crystal is equal to the width of the prohibited zone ( see our insertion with explanations ) or it exceeds it, then the electron under the influence of light can receive additional energy, overcome the prohibited zone, be in the conductivity zone and begin to conduct current. In the valence zone there remains an incomplete state - a hole, therefore, in the valence zone, electrons can begin movement.

This is a phenomenon of photo -leading, also called an internal photo effect (it was for the photo effect that Albert Einstein in 1921 received the Nobel Prize in Physics); It is observed in many crystals, as schematically shown in Fig. 1b.

Some details

Due to the interaction of the electron with the ions forming the crystal, permitted and prohibited energy zones are formed. If the energy of the electron enters the permitted zone, then its movement is largely similar to the movement of the free particle, and the presence of a crystal lattice leads, for example, to the fact that the “effective” mass of the electron in the crystal differs from the mass of free electron in vacuum.

In the quantum language, the wave function of the electron in the permitted zone is a flat wave modulated by a function of a crystal lattice (intermediary distance). The permitted zones are separated by gaps - prohibited zones. If the energy of the electron enters the prohibited zone, its distribution in the crystal is impossible, and the wave function exponentially fades in space.

In equilibrium conditions, electrons fill the energy zones - to the most deep with the lowest energies. In the semiconductors, it turns out that the last full state corresponds to the top of one of the permitted zones - Valentine. Electrons - Fermiones; Two electrons cannot occupy the same quantum state. Therefore, the valence zone fully occupied by electrons cannot conduct electric current, because the electrons have no free places where they can go.

The transition to the nearest incomplete zone - the conduction zone requires overcoming the energy gap, the prohibited zone (its width, E G in Fig. 1A, depends on the material, typical - on the shares to units of electron -volts). Thus, at low temperatures (when the electrons are not “thrown into the permitted zone) in clean semiconductors (they are also called their own - impurities that can add electrons to the conductivity zone or select electrons from the valence zone are not added to such semiconductors). Electrical conductivity is not observed. Semic conductors are insulators.

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In the early 1930s, Yakov Ilyich Frenkel thought about the question: can the crystal absorb the light, but so that photography does not arise, despite the presence of electrons and holes? The answer to this, at first glance, the paradoxical question was positive [1]. Indeed, the electron and hole are charges of the opposite sign, so they are attracted to each other and can form a related state. Such a related state of electron and holes is called an exciton - a quantum of “excitation” of a semiconductor crystal. Exithon is an electrically neutral quasi -player, so it cannot transfer the electric current.

In the model of Frenkel, the electron and the hole were at a distance of the intermediary order in the crystal - in fact on neighboring ions. Such excitons are called excitons of frenkel or small radius excitons.

A few years later, Gregory Vanya and Neville Mott [2] realized that in many semiconductors a characteristic distance between the electron and the hole can be a significant number of inter -stitched distances.

Such an exciton - it is called an exciton vany - Mott - is an analogue of the hydrogen atom (see diagram in Fig. 2A), with the only difference being that the effective mass of the exciton “proton” - holes - is significantly different (to the smaller direction) from the mass of the real proton. In addition, the interacting electron and hole are in a crystal, where the Kulon interaction is weakened compared to free space due to the shielding effect. However, these differences are quantitative - as well as for the hydrogen atom, the exiton has a series of conditions corresponding to the fulfillment of the conditions of quantization of orbit.

The energy of such a series is described by the atomic formula

E n = e g - ry*/ n 2, (1)

Where n = 1, 2, 3 ... is the main quantum number, and Ry* is an effective constant Reidberg, which depends on the crystal parameters. It is significantly smaller than the atomic Reidberg and is, depending on the semiconductor, from thousandths to the tenth of the sector of the electron -water. The energy of the exciton is less than the width of the prohibited zone E G , because Kulonov’s interaction attracts an electron and hole, lowering the energy of a related state compared to the energy of a non -current -appropriate pair.

The history of the experimental detection of exciton is very dramatic. It was opened in the very beginning of the 1950s by the domestic scientist Evgeny Gross, a brilliant spectroscopist, and his graduate student Nuri Karryev.

Gross and Karryev studied the spectra of the passage of light of crystals of the crystal of copper - CU2O (see photo of crystals in Fig. 2b) and found slightly below the edge of fundamental absorption (corresponding to the transitions from the valence zone to the conduct of the above) a series of narrow lines, the provisions of which were well described by the formula (1). The corresponding spectrum is shown in Fig. 2v.

The presence of absorption on discrete energies was interpreted as a manifestation of an exciton. At first, GRSS ran into great distrust of his discovery; Its opponents tried to attribute these lines to absorption due to impurities or defects in crystals. Moreover, in the spectrum, lines corresponding to levels from N from 2 to 6 or 7 were observed (depending on the quality of the sample), and the lower condition with N = 1 could not be detected. However, it soon became clear what it should be: the main state with n = 1 in the oxide of copper does not contribute to the absorption of light due to the features of the rules of selection. E.F. Gross and N. A. Karryev encountered difficulties in publishing work (a note that reports on the opening was published in 1952 in the reports of the USSR Academy of Sciences [3]). They say that for his discovery, the gross was even reduced for a while.

Subsequent studies, performed by both Eugene Gross with students and other groups in the Soviet Union and abroad, fully confirmed the discovery of exciton. Exiton behavior was examined in detail when the external fields were applied to the crystal - electric and magnetic, elastic deformations; The features of the subtle structure of the exciton spectrum were investigated. Subsequently, in the oxide of copper, with the help of special cunning experiments, an “lost” exciton was also found in the main state with the main quantum number equal to one.

After the work of the Gross, the excitons were found in almost all semiconductors. All these facts fully confirmed the theories of Frenkel, Vanya and Mott. The concept of exciton has received recognition. In the late 1960s, E.F. Gross, addressing the participants of the All-Union Seminar “Exitons in Crystals”, gladly noted that the distrust of the exciton was gone and more and more physicists are connected to the study of this unusual quasi-player [5].

Since then, the exciton effects in semiconductors and semiconductor nanostructures are actively examined experimentally and theoretically, because it is the exitons that largely determine the optical properties of semiconductors. Exithons are also important in many organic compounds; Strong exciton absorption of light opens up the prospects for creating devices for photovoltaic, effectively producing solar energy.

For almost seventy years that have passed since the opening of an exciton in the oxide of copper, interest has shifted to other semiconductors. Mopy oxide is a fragile material, therefore its use is very limited (despite the beauty of crystals, they cannot be used in the jewelry industry, and detector receivers of radio waves on CU2O were supplanted by other models).

In the oxide of copper with varying success, the search was conducted by Bose-Einstein condensate of excitons-the collective state of many quasi-players occupying one quantum state; For this, the main condition with n = 1, which is difficult to find in the spectrum, was investigated, but such an exciton lives for a long time, since it almost does not radiate light.

However, recently, in 2014, Exiton in the oxide of copper proved himself from an unexpected side. Experimenters from the Technical University of Dortmund (Germany) were able to significantly extend the series of exciton states and found excitons with the main quantum number up to 25 (Fig. 3) [6].

With the growth of n, the kinetic energy of the relative movement of the electron and holes grows, so they can disperse a greater distance. The size of the exciton thereby increases with the growth of the main quantum number. In Exiton with N = 25, the characteristic size is about a micron (and in an exciton n = 1 - only a few nanometers), which is a lot by the standards of semiconductor physics.

Exitons with large quantum numbers are analogues of Ridberg atoms (where the electron is in highly excited orbit). Such states of matter are very interesting for researchers, because, in fact, macroscopic quantum objects that effectively interact with each other, and are also largely subject to external fields. On Ridberg atoms, precision experiments in quantum physics are possible.

Now, after the discovery of the Reidberg states of excitons, it became possible to study the analogues of Reidberg atoms in semiconductors, which greatly facilitates the research in this area of ​​quantum physics. For example, due to the presence of a crystal lattice, the selection rules for optical transitions associated with exciton excitement differ from the atomic ones, so there are more lines in the spectrum of the Ridberg exciton-you can simultaneously study more conditions.

There are new effects that are not in the physics of atoms: for example, the excited states of an exciton with an angular moment of 3 (the state of the F -series by analogy with atoms physics) are observed in spectra in the form of weak triplets on the high -energy edge of the absorption peaks [7]. For excitons, the “Reidberg” blockade was found in the oxide of copper-due to effective repulsion next to one exciton, the second cannot be excited.

Compared to the Ridberg atoms of the energy of the Ridberg states of the exciton are small, so the excitons are even more sensitive to external fields. For example, by placing a sample of copper oxide into a flat capacitor, one can observe not only the variety of shifts, intersections and anti -excess levels under the influence of an external electric field, but also to ionize exciton by pulling an electron and a hole with an electric field in opposite directions.

It turns out that here the excitons do not behave like it was expected - conditions with a large angular moment are destroyed in large electric fields compared to the fields of ionization of conditions with a lesser moment and the same main quantum number, although in the zero field of their communication energy is less [8]. And in the external magnetic field, the Ridberg Exiton in Cu2O can demonstrate chaotic behavior [9].

So, despite his almost 70-year age, Exito in the oxide of copper sets up new tasks for scientists. The prospects of further research can be listed for a very long time; For example, the possibilities of the formation of spatial lattices from Ridberg excitons are discussed [10].

Such lattices can be used to manage the spread of radiation in the oxide of copper, and in a very distant perspective - to build “quantum simulators”: systems for modeling other quantum systems that cannot be implemented in laboratory conditions. We are waiting for new discoveries.

Mikhail Glazov, Marina Semina
(FTI named after A.F. Ioffe, St. Petersburg)

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