Bibliography

A. F. Ioffe. Semiconductors in Modern Physics. Publishing House of the USSR Academy of Sciences, Moscow–Leningrad, 1954, 355 pp. Price 17 rubles 60 kopecks. 7000 copies.

A. F. Ioffe. Semiconductors. Publishing House of the USSR Academy of Sciences. Popular-science series. Moscow–Leningrad, 1955, 94 pp. Price 1 ruble 45 kopecks. 10,000 copies.

These books are intended for different readers. The first book is a scientific monograph written for a prepared reader: a physicist, chemist, or qualified engineer. The second is a popular-science book, written for broader circles of readers interested in the modern development of science and technology.

It is necessary, first of all, to draw attention to the following circumstance. The author of these books is a scientist who has devoted many years to a comprehensive and profound study of semiconductors. Academician A. F. Ioffe, the founder of the largest school in the field of semiconductor physics in the USSR, is the author of many concepts and ideas that have now become generally accepted in the science of semiconductors. The investigations of A. F. Ioffe himself and of his collaborators have, in many directions, determined the development of the theory of semiconductors and the progress of semiconductor technology in our country.

The works under review are to a considerable degree the author’s creative report on his many years of work. At the same time, unlike many monographs of this kind, the author has not confined himself to presenting the work of his own school alone, but has encompassed the theory of semiconductors as a whole. As far as is known to the reviewer, there is no other similar monograph on semiconductors in the world literature in terms of breadth of coverage and depth of exposition of the subject.

The monograph Semiconductors in Modern Physics consists of an introduction and six chapters.

In the introduction, after a very brief outline of the main stages in the development of the theory of semiconductors, the author points out that the fields of technical application of semiconductors are already very significant, and gives 16 examples of the use of semiconductors in such areas of technology as automation, high-frequency radio engineering, current conversion, power engineering, heat engineering, and refrigeration engineering. On the other hand, it is emphasized that the theory of semiconductors is a key problem of solid-state physics as a whole. Many questions both in the physics of dielectrics and in the physics of metals were resolved in connection with the study of semiconductors. Noting that three types of solid conductors—solid electrolytes, metals, and electronic semiconductors—have much in common both in the mechanism of current flow and in the laws governing them, the author points out that a complete understanding of physical phenomena in semiconductors can be achieved only by comparing the properties of these three types of solids. This idea permeates the entire book and explains why

...is the introduction into it of a chapter devoted to solid electrolytes, and a chapter devoted to metals.

In Chapter I, “Solid Electrolytes,” the mechanism of conductivity in solid electrolytes is elucidated. Numerous studies in this field belong to A. F. Ioffe himself and his collaborators, and these studies date from the early period of the author’s scientific activity. Here proof is given of the ionic conductivity of solid electrolytes; the mechanism of the occurrence of mobile ions through the formation of defects in the lattice according to Frenkel and Schottky is discussed in detail, as are the temperature dependence of electrical conductivity, the role of distortion of the crystal lattice and of impurities, and the chemical nature of the current carriers (anion and cation conductivity). At the same time, examples are given of mixed ionic and electronic conductivity. The latter usually appears under the action of ionizing radiation or strong electric fields.

The chapter concludes with a discussion of high-voltage polarization. The significance of this chapter for the subsequent material lies in the fact that many regularities established for solid electrolytes also apply, to varying degrees, to the electrical properties of semiconductors. In the case of solid electrolytes, however, the physical meaning of these regularities can be more easily disclosed, since, in contrast to electrons, the motion of ions is complicated by quantum-mechanical effects.

Chapter II, “Metals,” is devoted to a survey of modern physical conceptions of the nature of electric current in metals. First a physical picture is given of the motion of electrons in a metal, together with an elementary derivation of the formulas for electrical conductivity, thermal conductivity, and the Wiedemann–Franz relation. Discussing the temperature dependence of the electrical resistance in metals, the author points out that the latter (in the case of pure metals) is in fact proportional to the thermal energy of the metal—

\[ \int_0^T c\,dT. \]

The author then substantiates the necessity of introducing quantum statistics to describe the properties of the electron system in a metal, and briefly sets forth the foundations of Fermi–Dirac statistics for electrons in a metal. The genesis of energy bands in a metal is also presented as the result of the displacement, splitting, and broadening of the levels of isolated atoms, as well as methods for investigating the energy spectrum of electrons in a metal by studying the emission X-ray spectra of metals. The distortion of the velocity distribution of electrons in an electric field, thermionic emission, and the thermoelectric and magnetic properties of electrons in a metal are also briefly considered.

The significance of this chapter lies in the fact that a number of features inherent in the system of electrons in a metal also occur in the system of electrons in a semiconductor. This includes, above all, the mechanism of scattering of electrons by thermal vibrations of the lattice and the degeneracy of the electron system. It should also be noted that the modern theory of semiconductors arose as a generalization of the quantum theory of metals.

Chapter III, “Electronic Semiconductors,” contains a general survey of the properties of the latter. The chapter begins by comparing electronic semiconductors with metals and solid electrolytes. Electronic semiconductors are brought closer to metals by the fact that, in both cases, the passage of current is associated with the motion of electrons and there is a common mechanism of scattering of current carriers by thermal vibrations of the lattice. The fundamental distinction lies in the much smaller concentration of free electrons in semiconductors and, most importantly, in the fact that the concentration of free electrons in a semiconductor depends on temperature, illumination, and other external conditions, whereas in metals the concentration of free electrons is a constant quantity and is determined by the nature of the metal.

With solid electrolytes, electronic semiconductors are similar in the sense that in both cases the current carriers are released by thermal fluctuations. However, the nature of the current carriers in electronic semiconductors (electrons) and in solid electrolytes (ions), as well as the mechanism of their motion in the crystal lattice, are completely different. Further, in this chapter the basic properties of semiconductors and the laws observed in them are set forth: electron and hole conductivity, the Hall effect, the temperature dependence of electrical conductivity, the influence of impurities on electrical conductivity, and so on.

The main conclusion at which the author arrives in this chapter is that, for a full understanding of the physical processes occurring in semiconductors, and in order to be able to control them, it is necessary to invoke the concepts of quantum mechanics.

The following chapter, Chapter IV, is devoted precisely to the fundamentals of the quantum theory of semiconductors. This chapter is written in a very interesting and distinctive way. Here all mathematical derivations are almost completely omitted. Instead, a clear and profound discussion is given of all questions of the modern quantum theory of semiconductors. In this chapter the basic concepts of band theory and the concept of the effective mass of a hole are discussed in detail. The author analyzes the latter two concepts at length. In A. F. Ioffe’s opinion, these concepts have a conditional character, since they are applicable only insofar as, in certain limiting cases, the laws of motion of electrons in a crystal lattice can be approximately reduced to the laws of motion of free electrons in a vacuum. It should be noted, however, that there is no unanimous opinion on this question among physicists. It is beyond doubt that holes in semiconductors are no less real than positrons. Therefore, if the mass of a hole is a conditional concept, then by the same token the mass of the positron must also be a conditional concept. In any case, these fundamental questions ought to be subjected to broad discussion at some scientific conference.

Further in this chapter, the application of quantum statistics to semiconductors, the X-ray spectra of semiconductors, the mechanism of formation of impurity levels, and the surface levels of I. E. Tamm are considered. The basic ideas of polaron theory and exciton theory are also briefly set forth.

The chapter ends with a survey of the present state of the theory of semiconductors. Here a critique of band theory is given, and the difficulties faced by the modern theory of semiconductors are indicated. These include the difficulties of explaining the temperature dependence of mobility observed in a number of cases, the difficulties of introducing the concept of the mean free path in semiconductors, and a number of other questions.

It should be noted that the study of A. F. Ioffe’s monograph gives a clear idea of what a major role is played by theory in the physics of semiconductors, and that the new semiconductor technology can develop only in close unity between theory and practice.

A central place in the book, both in content and in volume, is occupied by Chapter V, “Physical Phenomena in Semiconductors.” In this chapter, on the basis of theoretical conceptions, the mechanisms of all the principal phenomena in semiconductors are analyzed, phenomena important both from the standpoint of science and from the standpoint of their use in technology. The material considered in this chapter is extraordinarily broad. In almost every section the author has his own important investigations. The main sections of the chapter are as follows: the mechanism of electron and hole scattering, semiconductors in electric and magnetic fields, thermoelectricity, the emission of charges from a semiconductor, electrization by contact, phenomena in the boundary layers of semiconductors, the thermal conductivity of semiconductors, and methods of measuring the basic quantities characterizing the properties of semiconductors. Let us dwell on some of these sections.

Of great interest is the section devoted to thermoelectricity. Usually these questions are presented somewhat formally and behind mathematical conclusions the physical essence of the matter is not visible. Here the mechanism of thermoelectric phenomena is examined in very great detail. The author connects the release of Peltier heat with the transport of entropy by electrons when passing through the junction of two conductors. However, it seems to the reviewer that the question of how the transported entropy should be calculated has been worked out insufficiently fully. There are some ambiguities here. In the same section are set forth the methods developed by the author for calculating the efficiency of thermoelements and the theory of thermoelectric refrigerators.

The section on phenomena in boundary layers is written briefly but clearly. This section considers the principal effects that occur at the boundaries metal—semiconductor and semiconductor—semiconductor: rectification and amplification of electric currents.

In the section “Thermal Conductivity of Semiconductors,” as far as the reviewer knows, this important subject, of theoretical and practical significance, is for the first time treated systematically and comprehensively in the literature. Here there are many original considerations by the author, arising from his own investigations and those of his collaborators.

The chapter ends with the section “Methods for Measuring the Basic Quantities Characterizing the Properties of Semiconductors.” Methods are considered for measuring electrical conductivity, mobility, concentration of charge carriers, effective mass, activation energy, thermo-emf, thermal conductivity, contact potential, photoconductivity, and dielectric constant. Despite the conciseness of the exposition, this section contains many important indications, and it is of great value for persons beginning experimental research in the field of semiconductors.

The last, sixth chapter, “Experimental Data,” treats questions concerning the state of knowledge of semiconductor compounds, their classification, and gives a survey of various classes of semiconductors.

In drawing general conclusions, the author arrives at the conclusion that it is necessary to broaden and deepen the study of various classes of semiconductors. The author concludes that there is very direct correlation between the electrical properties of semiconductors and the character of the chemical bonds in them. However, only fragmentary data are available on this correlation. The theory of semiconductors is also insufficiently developed to serve as a guiding thread in these questions.

The popular-science work by Academician A. F. Ioffe, Semiconductors, consists of an introduction and three chapters.

In the introduction the author points out the importance of studying semiconductors, gives 17 examples of the practical use of semiconductors in various fields of science and technology, and also sketches a picture of possible applications of them in the near future.

Chapter I, “Electrical Properties of Semiconductors,” in a popular, accessible form treats the question of the connection between the electrical properties of semiconductors and the structure of atoms and crystals. Here the concept is given of the wave properties of electrons, of the quantum theory of atomic structure, of the nature of the forces binding atoms in crystals, of the formation of energy bands in crystals, and of the mechanism of motion of electrons in crystalline bodies. Here also the concept of holes is introduced and the energy spectrum of semiconductors is explained. This chapter, like the whole book as a whole, is written in simple, clear language and is accessible to all who are familiar with the elements of physics.

The chief place in the book is occupied by Chapter II—the application of semiconductors in industry and everyday life. Here all the principal directions of the practical use of semiconductors are considered: rectifiers

direct current, photoresistance, photocells, luminescent materials, thermoelements, refrigerators, ferrites, ferroelectrics, piezoelectrics, thermistors, and strong electric fields. In connection with each of these questions, the discussion concerns not only how semiconductors are used, but also describes in detail the physical principles of operation of the corresponding devices, instruments, etc. This chapter will be read with great interest also by those readers who have studied A. F. Ioffe’s monograph Semiconductors in Modern Physics.

In Chapter III, “The Present State of the Theory of Semiconductors,” the author dwells on questions that are being developed at the present time, and on problems that must be solved by science in the very near future.

There is no doubt that the works of A. F. Ioffe reviewed here will give a new impetus to the development of the science of semiconductors and will inspire many to undertake new research in this important field of modern physics and technology. It seems to us that this is precisely what the author sought in working on these books.

A. G. Samoilovich