On the Thirtieth Anniversary of Soviet Physics

Soviet Studies on Electronic Semiconductors

B. I. Davydov

The physics of today is the technology of tomorrow. This statement applies to almost all branches of physics. The study of electronic semiconductors is, however, one of those branches of physics which, without losing its purely scientific interest, is already finding important technical applications at the present time. If ten years ago the main interest of researchers working in the field of semiconductors was directed toward clarifying general scientific questions, then already at the present time technical applications—such as, for example, photoelements and rectifiers—have acquired important practical significance, and the study of the phenomena associated with them has come to the forefront. This, to a considerable extent, explains the attention that is being given to semiconductors in our country, in the Soviet Union.

Following the historical course of the research, we shall begin with the purely scientific Soviet works in the field of electronic semiconductors.

The modern development of semiconductor physics is closely connected with the appearance of quantum mechanics and thus belongs to our post-revolutionary period. Indeed, all our ideas about the motion of electrons in solids and, in particular, in nonmetallic solids are based on quantum mechanics.

In studying the electrical conductivity of dielectrics, experimentalists had, of course, already much earlier encountered electronic conductivity. The earlier work of the founder of the Soviet school of semiconductor physics, Academician A. F. Ioffe, carried out partly jointly with W. K. Röntgen in Munich and partly at the Petrograd Polytechnic Institute during the period from 1904 to 1922, was devoted primarily to ionic conductivity. However, already then the authors came to the conclusion that the photoconductivity of naturally or artificially colored rock salt is due to liberated electrons. This conclusion received full

confirmation in the work of P. I. Lukirskii, published soon after the October Revolution, in which he observed the Hall effect.

With the establishment of the general laws of quantum mechanics, the electron theory of solids began to develop broadly (1928–1931). The concepts that had taken shape in the electron theory of metals were transferred to electronic semiconductors. In this way a general theoretical foundation was created for the physics of semiconductors. It is necessary, however, to bear in mind that, on the one hand, the special assumptions of Bloch’s theory of metals are by no means obligatory for the justification of the theory of semiconductors, since everything required here can be obtained from more general considerations. On the other hand, the concepts of the theory of metals are too narrow for interpreting the behavior of electrons in nonmetallic bodies.

Characteristic of semiconductors is their sensitivity to chemical impurities, to deviations from the stoichiometric ratio, and so on. Even the most insignificant impurities, of the order of thousandths of a percent and less, can substantially change all their electrical properties. This applies equally both to crystals with ionic conductivity, investigated in the aforementioned works of Academician A. F. Ioffe, and to electronic semiconductors.

The work of V. P. Zhuze and B. V. Kurchatov (1935), carried out at the LPTI and already belonging to the modern period, clearly showed that in copper oxide at low temperatures the main importance is possessed by the electrical conductivity associated with the presence of impurities. Evidently, the role of such impurities here is played by an excess of oxygen or, more precisely, a deficiency of copper. At high temperatures the intrinsic electrical conductivity of the copper-oxide lattice acquires primary importance. This transition appears in the break of the curve for the logarithm of the electrical conductivity as a function of \(1/T\). Among investigations of the influence of impurities on electrical conductivity at various temperatures, mention should also be made of the work of A. N. Arsen’eva and B. V. Kurchatov, who studied \(MoO_3\), \(VO_3\), and other substances.

Among Soviet works of a general theoretical character on electronic semiconductors, we must note first of all the short but important note by L. D. Landau on the adhesion of free electrons in an ideal crystal lattice.

In the extensive work of Ya. I. Frenkel’ (1936), the mechanical transfer of the theoretical concepts of the Bloch–Peierls electron theory to nonmetallic crystals is thoroughly criticized. In the theory of semiconductors, the approximation which assumes that all valence electrons move throughout the whole crystal independently of one another is hardly reasonable. This assumption, moreover, leads to a completely distorted spectrum of the stationary states of electrons in a nonmetallic crystal, since the possibility is excluded of excited states that do not possess an electric current. These states correspond to the excitation of gas atoms, whereas

during this time as Bloch excited states which possess a current corresponding to their ionization. Owing to the periodicity of the crystal lattice, the excitation can propagate through it in the form of plane waves—excitons.

Modern conceptions of electronic semiconductors are still far from being considered complete. Both theoretical and, especially, experimental study of them under various conditions can clarify many obscure questions that now exist in our views on the structure of solids.

In its purest form the main characteristic of a semiconductor—the number of free electrons—is given by the Hall effect, provided that the picture is not complicated by the presence of free charges of two signs: free electrons and positive holes. Electrical conductivity gives, as is known, a more complex quantity, depending also on the mobility of the electrons. Of the other effects, the thermoelectromotive force has the greatest theoretical significance in semiconductors. At the same time it also has practical significance.

Careful measurements of the Hall effect in cuprous oxide at various temperatures, both in the dark and under illumination, were carried out by I. K. Kikoin and M. N. Noskov (LPhTI, 1932). Because of various impurities, all the properties of semiconductors vary greatly from sample to sample. In order to obtain as complete a picture as possible, all measurements must be made on one and the same sample. Such a comprehensive study of various effects in semiconductors was undertaken at LPhTI by V. A. Davidenko (1939).

Among the investigations of thermoelectric phenomena, it is necessary to mention the experiments of B. M. Gokhberg, M. S. Sominskii, and Yu. P. Maslakovets, carried out at LPhTI from 1935 to 1940. In this work a complex picture emerged, in a number of cases compelling one to assume the presence of mixed conductivity (normal electrons and positive “holes”).

If in the early 1930s the attention of experimentalists was attracted chiefly by those galvanomagnetic and thermoelectric phenomena in semiconductors which had already been studied earlier in metals, then later the main interest shifted to effects characteristic precisely of semiconductors—effects most important from the technical point of view.

Such questions include the behavior of semiconductors in strong electric fields. In a metal a strong electric field is generally impossible, since the conductor in that case simply melts. As a result, throughout the entire range of attainable fields in metals, Ohm’s law remains valid. In semiconductors the range of applicability of Ohm’s law is very limited, and in stronger fields—though still far from the breakdown field—a characteristic increase of electrical conductivity is observed. It is usually described as an exponential increase of electrical conductivity with the field—the so-called Poole law.

Intensive studies were devoted to strong fields by Acad. A. F. Ioffe and A. V. Ioffe, belonging to 1937–1938. Experimentally, it was important here to eliminate heating of the specimen when current was passed through it, which, owing to the positive temperature coefficient of electrical conductivity, can simulate its increase with the field. This makes it necessary to carry out measurements in as short intervals of time as possible. The experiments of Acad. A. F. Ioffe and A. V. Ioffe, who investigated a whole series of substances, showed that the increase in electrical conductivity is a reality: in fields of the order of \(10^3—10^4\ \mathrm{V/cm}\) the electrical conductivity begins to increase. This increase, however, does not fit a simple exponential dependence, and Poole’s law must be regarded rather as a qualitative approximation.

Theoretically, the question of the mobility of electrons in strong fields was posed in the work of L. D. Landau and A. Kompaneets (LFTI, 1934) and by B. I. Davydov (1935–1937), who obtained for a semiconductor with an atomic lattice a decrease of mobility with increasing field. This effect apparently is not observed experimentally; however, sufficiently accurate data are lacking. For semiconductors with an ionic lattice (and such are the majority), the corresponding calculations were carried out by B. I. Davydov and I. M. Shmushkevich (LFTI, 1940), who here already obtained an increase of mobility with strengthening of the electric field.

In experiment, however, the chief role is played not by the change of the mobility of free electrons with the field, but by the increase in their number. This increase is apparently connected with avalanche-like impact ionization by electrons accelerated in a strong electric field. Following the approximate calculations that existed in the above-mentioned works on strong fields, B. I. Davydov showed already in 1942 that taking stepwise impact ionization into account leads not only to an explanation of the sharp increase in the number of free electrons, but also to a consistent theory of breakdown. In this case breakdown appears as a jump-like change of current intensity occurring at a certain critical field, in full agreement with the observed facts.

Besides heating, apparent deviations from Ohm’s law in strong electric fields may also appear as a result of the formation of near-electrode jumps of potential associated with accumulation of space charges. At low temperatures such jumps were encountered by D. N. Nasledov and L. M. Nemenov (LFTI, 1935). Later they were investigated in greater detail by V. I. Lyashchenko and G. A. Fedorus at the Physics Institute of the Academy of Sciences of the Ukrainian SSR (1937–1940).

L. I. Rusinov (LFTI, 1934), measuring the electrical conductivity of silicon carbide by Foucault currents, showed that the low electrical conductivity here is connected with the presence of transition resistances between grains. The true electrical conductivity of the material is considerably higher, of the order of \(1\ \mathrm{cm}^{-1}\). As the rectification theory, to which we shall now turn, shows, such transition resistances are in general characteristic

for semiconductors, especially at low temperatures, and are connected with contact potentials.

Solid (crystalline) rectifiers are one of the most important technical applications of semiconductors. It is therefore natural that in our country, in the Soviet Union, considerable attention was devoted both to the investigation of the physical processes to which rectification is due and to the development and improvement of technical rectifiers.

Although already in 1935 V. P. Zhuse at the LFTI fabricated and investigated artificial rectifiers whose blocking layers were specially made from various insulating substances, even the very mechanism of rectification long remained unclear. The theoretical works dating from 1931–1932, which attributed rectification to the quantum tunneling effect (Ya. I. Frenkel, A. F. Ioffe, and others), proved untenable on close comparison with experiment. They even gave the wrong sign of rectification. On the basis of experimental material A. F. Ioffe came to the conclusion that rectification is connected with the difference in the mechanism of current in the contacting layers of semiconductors.

Such considerations led to the appearance of the diffusion theory of rectification, developed in our country by B. I. Davydov (LFTI) and D. I. Blokhintsev (FIAN), and also by S. I. Pekar (Kiev). It was shown thereby that, owing to the asymmetric accumulation of volume charges at the interface surfaces, rectification can occur, on the one hand, at the boundary between two semiconductors with conductivity of different type (normal electrons and positive holes). In the case of the cuprous-oxide rectifier, which has been studied best of all, it is possible that the layer adjoining the electrode possesses normal electronic conductivity, whereas in the main layer of cuprous oxide the conductivity, as is known, is hole conductivity.

On the other hand, rectification must also be observed in semiconductors with conductivity of one and the same type if there is in them a sufficiently sharp boundary between layers with different electrical conductivity. Rectification of this kind is closely connected with the contact difference of potentials between the semiconductor and the metallic electrode, since, for the appropriate sign of it, a layer with low electrical conductivity appears in the semiconductor automatically.

The basic concepts of the theory of rectification were thus developed. The corresponding works by foreign authors (N. F. Mott, W. Schottky) appeared approximately simultaneously and independently.

A. F. Ioffe and A. V. Ioffe investigated, for a whole series of semiconductors, the relation of rectification to the contact difference of potentials between the metallic electrode and the semiconductor, as well as between various pairs of semiconductors. In doing so they obtained

qualitative agreement with theory. It proved possible to arrange the semiconductors studied in the form of a series, every two members of which give rectification on contact, the sign of which corresponds to their position in the series. In exactly the same way, rectification at a metallic electrode is obtained for normal electronic semiconductors on contact with a more electronegative electrode, and for hole semiconductors—with a more electropositive one. In all these cases, however, rectification is obtained at considerably larger differences of potential than existing theory requires. The conditions at the contact are undoubtedly more complex than the simplest theoretical conceptions.

B. I. Davydov’s assumption about the normal electrical conductivity of the blocking layer in cuprous-oxide rectifiers found experimental confirmation in the elegant work of V. E. Lashkarev (Kiev, 1940), who measured, by means of a thermoprobe, the thermoelectromotive force in the blocking layer of a photoelement and showed that it has the opposite sign.

Subsequently, P. V. Sharevsky (LFTI) succeeded also in directly obtaining cuprous oxide with normal electronic conductivity.

Simultaneously with the theoretical work, experimental work closely connected with technology was also being carried out on the investigation and improvement of existing rectifiers and on the development of new ones. New sulfide rectifiers, giving a large current output, were developed and investigated at LFTI by B. V. Kurchatov with the participation of Yu. A. Dunaev (1937—1940). Here the authors encountered considerable inertia, technically undesirable. This inertia, however, does not differ qualitatively from the inertia observed in other semiconductors, especially at low temperatures, and does not indicate ionic conductivity.

The ordinary cuprous-oxide and selenium rectifiers were also subjected to careful study, partly in scientific institutes (P. V. Sharevsky, A. Z. Levinson—LFTI), partly in factory laboratories (V. T. Renne, T. I. Moldaver, and others).

We turn to investigations of the internal photoeffect in semiconductors. Photoconductivity in various substances and under various, especially low, temperatures was investigated by a number of authors. A. F. Ioffe and A. V. Ioffe explained (1931) the observed distribution of sensitivity over the spectrum by the dependence of the coefficients of absorption and reflection on the frequency of the incident light: if the light is not absorbed at all, then, naturally, there is no internal photoeffect either; but if it is absorbed and reflected too strongly, then photoconductivity is likewise absent, since the light does not penetrate into the depth of the specimen.

The photoelectromotive force arising in nonuniformly illuminated crystals, for example, cuprous oxide—the so-called Dember effect—was also studied in detail by A. F. Ioffe and

A. V. Ioffe. At the same time a rather complex picture was revealed, apparently connected with the presence of free charges of two signs. Works by Ya. I. Frenkel, L. D. Landau and E. M. Lifshitz, and others, were devoted to the theoretical explanation of this phenomenon.

I. K. Kikoin and M. M. Noskov (LPTI, later UFTI in Sverdlovsk), while studying the Hall effect on photoelectrons, encountered in 1934 an entirely new photogalvanomagnetic phenomenon: a considerable electromotive force of the order of 1 V appears in an illuminated cuprous-oxide crystal placed in a transverse magnetic field, even in the absence of current. This electromotive force is perpendicular both to the direction of the incident light and to the direction of the magnetic field. In essence, we have here the Hall effect on a quasi-neutral flow of photoelectrons and positive holes diffusing from the illuminated parts of the specimen into the unilluminated ones.

A number of experimental works, as a natural continuation of the earlier works of A. F. Ioffe, were devoted to the photoconductivity of colored alkali-halide crystals. These questions were studied by P. S. Tartakovskii, who proposed a new scheme of electron levels in the crystal, by Artsibyshev, and others. A. N. Arsen’eva showed that the number of photoelectrons in this case is proportional to the absorbed light energy. The motion of electrons in colored crystals was studied theoretically by Ya. I. Frenkel.

Of great technical significance is the so-called barrier-layer photoeffect in photocells with a blocking layer. A considerable number of works were therefore devoted to the study of these photocells. As early as 1931 Yu. P. Maslakovets (LPTI) proposed an equivalent electrical circuit for such a photocell. Later, on the basis of contemporary theoretical ideas, he gave a scheme for the operation of barrier-layer photocells which qualitatively explains the observed picture.

Whereas in the most widespread cuprous-oxide and selenium photocells the front electrode is charged negatively (in front-wall photocells), in sulfur-thallium photocells developed by B. T. Kolomiets (LPTI, 1938) the front electrode is charged positively. This indicates that the principal role here is played not by ordinary free electrons, but by positive holes. In general, the works of the semiconductor group of the LPTI showed that in many semiconductors, by changing the concentration of various impurities, it is possible, as desired, to obtain both normal electronic and hole conductivity. The photocells of B. T. Kolomiets possess high sensitivity and a favorable spectral distribution of it. They have already found technical application, for example in sound cinema.

At approximately the same time, D. S. Teikhman in Kiev obtained good results with silver-sulfide photocells. These photocells, which likewise possess a positive photoeffect,

approaching B. T. Kolomiits’s photocells in sensitivity, have greater stability.

Interesting experimental investigations of the influence of impurities on the barrier-layer photoeffect in cuprous oxide, connected with modern theoretical conceptions, were carried out by V. E. Lashkarev in Kiev (1940).

In conclusion, mention must also be made of O. V. Losev’s work on the luminescence of crystalline carborundum and on the “reversible” barrier-layer photoeffect in it (1931–1940).

In the postwar years, results of fundamental importance have been obtained at the Physico-Technical Institute in the study of semiconductors of low specific resistance, whose properties represent a combination of semiconductor and metallic phenomena. Many metal alloys have proved to be semiconductors. It has been found that the characteristic properties of semiconductors and, in particular, the hole mechanism of conduction, are also preserved in the molten state, where there is no crystal lattice.

In our review we have not touched upon work on the optical properties of semiconductors, on phosphorescence, etc. These works were included in another review article*).

All the work on electronic semiconductors carried out in the Soviet Union was summed up at conferences convened by the Academy of Sciences of the USSR. The first such conference took place, with the participation of a number of representatives of foreign physics, in Leningrad in 1931. The latest were in 1938 in Kiev and in 1940 in Leningrad. The proceedings of the latest conferences were published in Izvestiya IMEN.

As is clear from our brief review, studies on electronic semiconductors were at first concentrated chiefly in the Leningrad Physico-Technical Institute. This work was carried on there under the direct guidance and with the active participation of Academician A. F. Ioffe. In recent years, however, interesting work on semiconductors has also been carried out in other physics institutes. Particularly noteworthy are the works of the Physics Institute of the Academy of Sciences of the Ukrainian SSR in Kiev.

) T. P. Kravets, “Thirty Years of Soviet Optics,” Uspekhi Fizicheskikh Nauk*, vol. XXXIII, issue 1, p. 23.