Physics – Optics
Scientific paper
Nov 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008sesct..23k0302z&link_type=abstract
Semiconductor Science and Technology, Volume 23, Issue 11, pp. 110302 (2008).
Physics
Optics
Scientific paper
And God said: 'Let there be light', and there was light. Genesis 1 3
When trapped in a crystal, light interacts with electrons, phonons (crystal lattice vibrations) and defects, generating many effects which are important not only for pure physics, by broadening our comprehension of nature, but also for practical applications. These include: photo-galvanic effects; discrete light scattering on lattice vibrations; laser radiation, first observed in ruby crystals; nonlinear effects resulting in generation of harmonics, so that under incidence of an intense coherent light beam onto a crystal it emits (or reflects) light of different wavelengths; transformation of the electron avalanche in semiconductors and semiconductor microstructures into the flow of coherent 'laser' light; and the capability of polarized light to magnetize electrons and nuclei in a crystal. This is far from being a complete list of the remarkable optical effects that scientists have observed and studied in crystals. Countless scientific papers and monographs have been devoted to these investigations, with quite a number of them leading to the award of Nobel Prizes.
Here I'm going to speak very briefly, simplifying the problem as best I can, about a remarkable optical phenomenon in crystals: the generation by light of a quasiparticle called an 'exciton'. Why is it a 'quasiparticle', i.e. 'as if' a particle, and not a true particle? Because it exists in a crystal and not in vacuum and moves in a periodically changing field created by the atoms (ions) of the crystal lattice. In this respect, an electron in a crystal is also a quasiparticle.
The idea of the exciton dawned upon Yakov Ilyich Frenkel, the well-known physicist of the Physico-Technical Institute (PhysTech), in 1931. Omitting the details that would require knowledge not only of quantum physics, but also of the history of its development, I'll say only that the Frenkel exciton is the excited state of the crystal, which is created, for instance, by light and which, arising in one of the crystal cells, spreads over the whole crystal, because the cells differ absolutely in no way from one another. Physicists call such a situation translation symmetry. Without going into the mechanism of the energy transfer from cell to cell, note only that the whole crystal, like a gigantic molecule, assumes in the excited exciton state. The word 'exciton' was coined by Frenkel himself, who had formed it from old Greek exito, meaning 'I excite'. Yakov Ilyich liked to give names to newly-discovered particles, and it was he who invented the name 'phonon' for the vibrational quantum of the crystal lattice. Few physicists know that the godfather of this term, forever established in physics, was Frenkel. When Frenkel reported his study on the exciton at PhysTech, one of his young colleagues couldn't help joking: 'Yasha, why didn't you name this particle in Russian---vozbudon'? (From the Russian vozbudit, meaning 'to excite'.)
In contrast to the electron, which can also be excited by light in a crystal, the exciton is electrically neutral. Moving in the crystal it transfers energy, but not a charge. A neutral exciton is very much like an atom. But this 'atom' is generated by light within a crystal. The model of such a quasi-atom is particularly obvious in semiconductor crystals, where it can be conceived as an electron and a positively charged hole bound by Coulomb interaction. It is very much like the Dirac electron--positron pair, whose existence ensues from the well-known Dirac equation taking into account relativistic invariance---the same equation that has revealed to mankind the existence of antimatter. I think that it was under the influence of Dirac's ideas that the Englishman Mott and the American Wannier suggested an exciton model analogous to the positronium atom (an electron and a positron bound to each other by Coulomb interaction). It should be noted that both Mott and Wannier worked at Bristol University where Dirac had worked. Usually, the Wannier--Mott exciton is called hydrogen-like, bearing in mind its similarity to the hydrogen atom (a positively charged nucleus and an electron rotating around it). Yet a hole is not the same as a nucleus: its effective mass is a factor of thousands less than the mass of a proton. Wannier and Mott had conceived their model before the Second World War, when the concept of the hole was introduced into semiconductor physics from electrical measurements, which were really not very precise at that time. In the mid-1950s, two groups of Americans, at Berkeley and Massachusetts Institute of Technology, proved by beautiful experiments the existence of different types of holes, due to their complex energy spectrum in the crystal; accordingly, excitons can be different, too. An electron may be bound either to a light or a heavy hole, which subsequently was indeed observed. The experiments on cyclotron resonance are technically very similar to the experiments of the physicist Zavoysky of Kazan University, who discovered right after the war the remarkable physical phenomenon of paramagnetic resonance. Strange as it may seem, the war had favoured the discovery since it had encouraged the rapid development of radar, which generated the technology of very high radio frequencies, and which was used brilliantly in those experiments.
As has been mentioned, an electron and a hole are bound by Coulomb interaction, which physicists call a long-range interaction. As the force is proportional to the inverse square of the distance between interacting particles, 1/r^2, an electron and a hole become bound into a pair, i.e. an exciton, at very long distances. Yet all this occurs in crystals, and the crystalline medium is characterized by a rather high dielectric constant ɛ. Thus interaction in a crystal is a factor of ɛ weaker compared with that in vacuum. The exciton is enlarged, the orbit in which the electron--hole pair is moving encompasses a great number of crystal cells, and such an exciton may be called a mega-atom.
How can we observe this mega-atom in a crystal? One might think we could do so simply by observing the hydrogen-like exciton spectrum. By virtue of the well-known behaviour of a hydrogen-like atom in a Coulomb potential well, the exciton is expected to show a series of lines, getting characteristically closer and closer towards the continuous absorption boundary where the motion of electrons and holes has become free. In this region the exciton is ionized. So a series of narrow lines of the spectrum of the exciton (mega-atom in a crystal) must be observed at the absorption edge, which corresponds to electron transfer into the conduction band by light. This series should be similar, for instance, to the Balmer series of the hydrogen atom---well known from school textbooks.
One might think all this is simple. But nobody had ever observed anything like it. The semiconductor spectra looked very trivial---exactly the same as the spectrum of a light filter, transparent on the long wavelength side (low-energy light quanta) and having rather intense absorption in the short-wavelength region. It is simple: at first the energy of photons is insufficient for electron transfer into the conduction band, but eventually their energy becomes high enough for such a transfer and the crystal absorbs light strongly. But why, when observing an absorption edge and the photo-current associated with it, did nobody see the hydrogen-like lines of the exciton? The answer is simple and cannot be expressed better than in Pushkin's words: 'We all are lazy and incurious.'
As soon as Evgeny Feodorovich Gross, of the Physico-Technical Institute of Leningrad, took a thin plate of cuprous oxide (a ruby-coloured semiconductor), cooled it down to liquid nitrogen temperature (-196 °C) and, above all, used a spectral device with great dispersion, he saw at once a series of hydrogen-like exciton lines. Of course, Gross was lucky that it was a cuprous oxide crystal that had fallen into his hands, because in that crystal everything occurs in the visible region, easily amenable to
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