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By Academician Boris ZAKHARCHENYA, RAS Physico-Technical Institute named after A. Joffe

When a ray of light strikes a crystal the glitter and sparkle thus produced, can often be quite a remarkable sight. The range of the resulting phenomena are of importance not only from the point of view of pure physics, which broadens our understanding of nature, but also for dealing with applied problems. Among them are photogalvanic processes; discrete light scatter on oscillations of crystal lattice; laser emissions, first observed with a ruby crystal transformation of an avalanche of electrons in semiconductors and semiconductor microstructures into a flux of a coherent "laser" beam; the ability of polarized light to magnetize electrons and nuclei in crystal... In the article which follows we take a closer look at one of these phenomena.

Light hitting a crystal generates the quasiparticles-excitons. And why are they not real, but only "quasi", or "apparent", or "looking like" particles? Because they exist only there and then, and not in vacuum, moving in a periodically changing field produced by the atoms (ions) of its lattice. In crystal medium an electron is also a quasiparticle.

It was back in 1931 that the idea of exciton first struck the prominent Leningrad researcher from the Physico-Technical Institute, RAS Corresponding Member, Prof. Ya. Frenkel. Bypassing the details which call not only for the knowledge of quantum physics, but also of the history of its development, let me just say that Frenkel's exciton is an exited state of crystal. Lattice, produced, for example, by light. Originating in one of its cells, which differ in absolutely no way one from the other, the effect spreads out across the whole structure. Physicists call this translation symmetry.

The term "exciton" was derived by Prof. Frenkel, from the Greek "exito"-"to exite". The scientist was fond of giving names to new particles, and even suggested a term for the oscillator quantum of crystal grid, calling it phonon (incidentally, few experts are aware of the fact that this physical term is his invention). When Prof. Frenkel was presenting his report on the exciton in his "beloved" Physico-Technical Institute, one of the younger staff could not resist the temptation and asked as a joke: "And why not call it the Russian way- "vozbudon" (exiter)?"

The difference between an electron, which can also be "generated" in a crystal by light, and an exciton consists in the fact that the latter is electrically neutral. That is why, when moving, it carries energy and not a charge. In this respect it is similar to the atom, apart from the fact that it is generated by light within a crystal. The model of such a quasiatom is especially vivid in semiconductors, where it can be represented as an electron and a positively charged hole, bound together by the coulomb interaction. This looks very much like the Dirac's electron-positron pair whose existence follows from the equation of the 1933 Nobel Prize winner and Foreign Member of the USSR Academy of Sciences, Paul Dirac. It took into account the relativistic invariance and revealed to mankind the existence of antiparticles. My own feeling is that it was under the influence of the ideas of this great physicist that the British researcher Prof. N. Mott (1977 Nobel Prize winner) and his American counterpart Prof. G. Wannier suggested a

Pages. 17


Hydrogen-like exciton series in cuprous oxide. Lines of absorption-white-on the visible spectrum background.

model of exciton similar to the atom of positronium (electron and positron, held together by coulomb forces). This exciton is usually described as "water-like", bearing in mind its likeness to a hydrogen atom (positively charged nucleus and an electron spinning around). But a hole is still not a nucleus, and its mass is scores of times smaller than that of a proton.

Wannier and Mott invented their model even before the Second World War, when the concept of a hole was introduced into the semiconductor physics from electrical measurements which were not very accurate at that time. By the mid-1950s two teams of researchers-from Berkeley and the Massachusetts Institute of Technology (USA)- had proved by their fine cyclotron resonance experiments the existence of holes of several types, with complex energy spectra in the crystal; accordingly, there are also different excitons. They can be bound either with a light, or a heavy hole, as was observed later.

By their technical implementation, or arrangement, cyclotron resonance experiments looks very much like the experiments of Acad. E. Zavoysky of the Kazan University who discovered, at the end of Russia's Great Patriotic Warwith Nazi Germany, the famous physical phenomenon of "paramagnetic resonance".

As has already been said, the electron and the hole are bound together by coulomb interaction which physicists describe as "long-range". Since its potential is inversely proportional to the first degree of the distance between the interacting particles, this pair produces an exciton of a very large size. And all this is taking place in crystals where the medium is characterized by rather strong dielectric permeability (e). And that means that the interaction in crystal is weaker by e times as compared with vacuum. The exciton is "swollen", and its orbit spinning around which are the bound together electron and hole, covers many cells, thus producing what one could call a megaatom.

So, how can one see this structure in a crystal? It seems it would be enough to "fix" the corresponding spectrum of an exciton: according to the laws of behavior of a water-like atom in the coulomb potential hole, there appears therein a series of levels, which gravitate in a characteristic way towards the border of total absorption where the movement of the electron and the hole is already free. Within this pace the exciton is ionized. Consequently, at the edge of absorption, corresponding to the transport of electron by light to the zone of conductivity, there should be observed a series of narrow levels of the exciton-megaatom in crystal, which looks, for example, like the Balmer series for hydrogen atoms-well familiar from school textbooks.

At first sight-everything is simple. But no one has ever observed anything of this kind. The spectrum of semiconductors looked really banal. Neither more nor less that a light filter spectrum: transparent on the long-wave side (low energy light quanta) with a rather intensive absorption in the short-wave band. The energy of "red" photons is not enough to transport the electron into the zone of conductivity, and when it increases, the electron transfer into that zone takes place, and light is strongly absorbed by crystal.

But why, while observing this brink of absorption, and the flash of photoflux associated with it, no one has seen any traces of an exciton? The answer is simple-and the best one was suggested by Alexander Pushkin: "We are lazy and incurious".

It was Prof. E. Gross, Corresponding Member of the USSR Academy of Sciences, who had the luck of seeing that very series of hydrogen-like lines. All he did was take a thin plate of cuprous oxide (semiconductor of ruby-red color), cool it down to -196C in liquid nitrogen and, most important of all, use a high-dispersion spectral instrument. Of course he had the luck of picking on a cuprous oxide crystal where all of these events were taking place in the visible band of the spectrum which is easily accessible for spectroscopy, and the parameters of zonal structure of the crystal made it possible to observe not just one or two, but a multitude of exciton lines. And myself, one of the first pupils of Gross, have also been lucky enough: I saw before me a giant virgin field of semiconductor spectroscopy, a science which yielded later on some invaluable knowledge about light interactions with electrons and even with nuclei in semiconductors. I remember how, having cooled down a crystal of cuprous oxide to the liquid helium temperature (-269C) I saw more than a score of narrow exciton lines. As a man of emotions, Gross could not restrain his excitement:

- Boris! This is a miracle. A series of narrow lines in a crystal! Our exciton studies shall make us famous! I am sure this is a common phenomenon for all semiconductors and it will help us understand the details of both-photoconductivity and luminescence, and of other things we still know nothing about!

Resounding in the soul of my teacher were the jubilant trumpets from all of the operas of his beloved Wagner. It was to him, Gross, that gods sent the "Gold of the Rhine" with the Walgalla shining up in front with all the colors of a rainbow-the place of the eternal scientific pursuits and glory of my teacher. And my saying that is hardly an exaggeration, knowing as I do, his ecstatic-belligerent temper. His father, a German, held the

Pages. 18


rank of General-Lieutenant and the post (before the October Revolution)- of the manager of the Izhora Plant (near St. Petersburg), and his mother was Danish. I remember how, on more than one occasion, Yevgeny Fyodorovich, a short and fat man, wearing a short jacket and an old-fashioned cap, would turn to me and say:- Boris, I am a Viking. I enjoy having enemies and fighting with them!

But he was most of all fond of science, music and painting. In all creative pursuits he treasured most of all daring innovations and dramatic discoveries.

Discoveries of new physical effects in Prof. Gross's small lab at the Physico- Technical Institute poured out as from a horn of plenty. In 1952 they observed two exciton series. One-an electron and a light hole, and the other-electron and a heavy hole. This pointed to the existence of a fundamental phenomenon in semiconductors- spin-orbital split of energy zones. Discovered shortly after was the effect of external electric fields on exciton (something like the Stark effect* for atoms). This seemed to be a miracle. Never before could any one observe the effect of electric fields on crystal spectra because their internal field is many times greater than the external which we can create. But, as has been said before, exciton is a large-size megaatom. It is easily polarized in small external fields. I remember how shocked with this experiment was the director of our Institute, Acad. A. Joffe. Slapping me in a friendly way on the shoulder, he kept saying in an astounded voice: "How wonderful you manage all these things". The father of Soviet physics research was then 73.

The great range of exciton orbits made it possible to easily watch, under the effect of a magnetic field, the diamagnetic shift of the energy states of the exciton-the relativistic effect which had been hitherto noticed only for the excitation states of free atoms in a very clumsy experiment.

And even despite this firework of phenomena only few believed in the exciton. They said that what Prof. Gross was really observing was some trivial admixture spectrum. I remember one seminar when our highly respected scientist, Acad. A. Terenin, came to me and said: "Young man, place no confidence into Gross's whims!" He said exciton was another phlogiston (a hypothetic substance, also called "heat-generator" ('teplorod' in Russian) which was "buried" by the experiments of Lomonosov- Lavoisier some two and a half centuries ago.

Many, however, were impressed with the fact of observation in a semiconductor crystal of narrow spectral lines, producing a hydrogen-like series. In the mid-1950s at our lab Acad. L. Landau (1962 Nobel Prize laureate) told Prof. Gross and myself he had no doubts about the exciton nature of the observed spectrum, because immobile admixture cannot produce narrow lines in optical transitions of admixture-zone type. In these considerations he relied on the indeterminacy principle of the German scientist W. Geizenberg (1932 Nobel Prize winner). Years later one of the American physicists developed and published an idea similar to that expressed by Acad. Landau.

I remember making a report on exciton effects at the Department of Physics of the USSR Academy of Sciences in Moscow before a select audience which included academicians I. Kurchatov, Ya. Zeldovich, N. Semenov, P. Kapitsa, L. Artsimovich and the Lifshits brothers... The session was chaired by Acad. A. Joffe. I was "in jitters" before this abundance of stars of our physical science. The exciton idea was sharply criticized by our opponents. But in conclusion of it all Acad. Joffe said in reply to one especially aggressive lady professor:

- In the final analysis, and no matter what it could be-admixture or particle in crystal, one can say with confidence that observations of a series of narrow lines in a semiconductor is the starting point of the optics and spectroscopy of these crystals.

His words were prophetic! Soon after a series of experiments proved the movement of excitons and even assessed their velocity distribution. These experiments


* German physicist, Johannes Stark, discovered in 1913 the effect of splitting (cleavage) of spectral lines in an electric field. The effect bears his name.- Ed.

Pages. 19


and their theoretical foundations were performed mainly by Soviet and American physicists. In connection with this and many other achievements in the spectroscopy of excitons in semiconductors one can mention many names-something I am not going to do in order not to overlook some name and thus offend that person. But I cannot help remembering our American colleagues and brilliant scientists Prof. D. Thomas and Prof. J. Hopefield.

Remarkable theorists and experimenters took part in developing the concept of what are called polarytons in semiconductors-mixed states when a corpuscule-exciton-is mixed up with a lightwave. Among the scientists who provided the greatest contributions to the elaboration of this problem are our Kiev colleagues Prof. Pekar and Rashba, Moscow scientists Ginzburg and Agranovich, our Leningrad colleagues Kaplyansky, Razbirin and Uraltsev as well as the aforesaid American researchers.

As I recall the exciton crystals physics of the 1950s-1960s, and Mowing the example of Goethe and Schiller, I call it the epoch of "storm und drang". But the stormy waves of exciton spectroscopy kept foaming even later. The advent of lasers made it possible for Prof. Ya. Pokrovsky of the Moscow Institute of Electronics to observe the superfine structure of exciton admixture complexes. Powerful light sources were also used for observations of electron-hole condensate in semiconductors. But the original idea of these studies was stimulated by the existence of excitons and attempts to observe their condensation. Considerable efforts to solving this problem were contributed by Acad. L. Keldysh, Prof. A. Rogachev and many other Russian and foreign researchers. The results of experiments of my friend, physicist and painter from Berkley, Prof. K. Jeffrice, who studied a "giant"-one millimeter in size-electron- hole drop in a germanium crystal, were even published in the New York Times.

The exciton tide has swept the whole world, but its "birthplace" was a small lab of Prof. Gross at the Physico-Technical Institute of the Russian Academy. And it is really very uncomfortable, to say the least, when one finds many Astern manuals on solid state physics saying that exciton in cuprous oxide was originally observed by a Strasbourg researcher, Prof. S. Nikitin. As a matter of fact, nothing can be further from the truth. It was back in 1951 that Prof. Gross discovered the hydrogen-like series in a semiconductor and published his findings in 1952 in the journal Doklady AN SSSR (Proceedings of the USSR Academy of Sciences). As for Prof. S. Nikitin, he knew Russian and, having read the article of Prof. Gross, he repeated his experiment and published his results, much later, in European science journals.

Another surprise have been the references to a short article (1951) of Japanese physicists from Hokkaido, which, probably without reading it, is being referred to as the first observation of exciton. Yes, the article does speak of identification of certain rims of absorption at the fundamental boundary of absorption. But there is not a word there about the aforesaid lines, "hydrogen-like" properties or the exciton!

On more than one occasion young researchers from our Institute who came to our lab asked me: "What would happen to exciton if it appears in a microcrystal whose size is comparable with the exciton orbit radius?" And I knew the answer to that question, having studied exciton behavior in magnetic fields a long time ago. In such circumstances the orbits of electrons and the holes, which it consists of, shrink, and, under the effect of a strong magnetic field, the movement comes close to unidimensional. This situation is similar to that which exists in the structure which is now called quantum wire (one of the semiconductor microstructures). But in this kind of a quasi-unidimensional potential pit the exciton bond energy is increased (actually, this is already what we call magneto-exciton).

In actual fact, in present-day semiconductor microstructures (quantum pits, wires, points superlattices) the exciton bond energy is increased, and in a number of cases it can be observed at room temperature.

Today no conference on nanostructures can do without the exciton optics.

There is no end to the list of studies and discoveries made in this field thanks to exciton spectroscopy, which is important for microelectronics. Let me just mention the discovery of the trion, where the hole interacts already not with one (or the other way round), but with two electrons. The existence of trions gives grounds for hopes of developing quantum computers. As for myself, I can not count myself with the ardent champions of this idea. But then, who knows?!

Exciton spectra are observed not only in semiconductors, but also in crystals of ionic salts (NaCl), molecular ones (anthracene, naphthalene, etc.), salts of rare earths and actinides and in polymers, including biological ones. But the awareness of the fact that these are exciton quasiparticle spectra (in such cases of the so-called small-radius exciton, when the wave function of a particle is localized within the bounds of the elementary cell of the crystal) reached the experimenters only after the works of Prof. Gross and his co-workers. And for the very first time the theory of such excitons was developed back in the early 1940s by the Kiev researcher A. Davydov.

To make the long story short, let me recall Prof. Gross once again. It was he who taught me to be fond of not only science, but also music and painting. In that latter field he especially valued innovations and creative search. On my visits to New York I go to the Museum of Modern Art and often look with Gross's eyes on the unexpected "moves" of the Vanguardists. And I have been particularly impressed with our compatriot A. Rodchenko (1891 -1956). Back in the 1920s he produced his composition "Planes, organizing light". This is a volumetric creation, made of strips of metal and cardboard, which conveys our notion of a planetary model of the atom. Beaming out from it, like radiant butterflies, are light quanta. How could the artist sense the structure of the microworld even before many physicists?

...Wonderful is the world of human knowledge! And, as often as not, an artistic image anticipates the achievements of scientific thought.

Illustrations supplied by the author.


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