BIBLIOGRAPHY

A. F. Ioffe. Semiconductor Thermoelements. Publishing House of the Academy of Sciences of the USSR, Moscow–Leningrad, 1956, 103 pp., price 3 rubles 80 kopecks, 20,000 copies.

A. F. Ioffe, L. S. Stilbans, E. K. Iordanishvili, T. S. Stavitskaya. Thermoelectric Cooling. Publishing House of the Academy of Sciences of the USSR, Moscow–Leningrad, 1956, 108 pp., price 3 rubles 70 kopecks, 15,000 copies.

The broad and highly successful application of semiconductors in radio engineering, where they are the sole means of solving many urgent technical problems, has somewhat overshadowed, I would say, other important uses of semiconductors in technology. Meanwhile, the use of semiconductors makes it possible to solve many important problems of science and the national economy. Among the latter is so-called small-scale power engineering, i.e., the problem of generating and using energy (especially electrical energy) up to 100 kW. Small-scale power engineering is of enormous importance in everyday life, communications engineering, measuring technology, etc.

The monographs under review are devoted to the theory and practice of the use of thermoelectric phenomena in small-scale power engineering. Why is this important? The point is that the usual methods of converting thermal energy into electrical energy have, as an intermediate stage, the conversion of thermal energy into mechanical energy, which leads to excess losses. The use of thermoelectric phenomena makes it possible to convert thermal energy into electrical energy directly. Moreover, the laws governing thermoelectric phenomena are such that here one should expect the highest efficiency.

It should also be emphasized that the practically important question of applying thermoelectric phenomena in the field of small-scale power engineering could arise only in connection with the development of semiconductor physics. This is explained by the fact that in thermoelectric processes the working substance is an electron gas. But the electron gas is always found in some substance, in a definite medium, which in a definite way influences its properties. It turns out that precisely in semiconductors the properties of the electron gas are such that they make it possible to carry out the direct conversion of thermal energy into electrical energy in the most effective way.

What aims do the monographs under review pursue? Above all, they sum up the results obtained by a team of scientists headed by Academician A. F. Ioffe in developing questions of the application of thermoelectric phenomena in power engineering and the experience of their practical use accumulated by 1954–1955. As A. F. Ioffe states in the preface to his monograph, the further development of this important field requires the collaboration of physicists, chemists, and engineers. It is therefore necessary to place in the hands of chemists and engineers the necessary knowledge and accumulated experience. This also explains the style in which both monographs are written, distinguished by great clarity, a detailed discussion of the physical mechanisms of the processes considered, minimal use of mathematical apparatus, and, at the same time, a high scientific level of exposition.

Academician A. F. Ioffe’s monograph Semiconductor Thermoelements consists of three chapters.

Chapter 1, “Introduction,” first of all presents a very interesting historical sketch of the discovery of thermoelectric phenomena, a description of the latter, and the introduction of the quantities that characterize them. Analyzing the development of the theory of thermoelectricity from its origin 125 years ago to the present day, and considering recent work carried out abroad, the author comes to the conclusion that the shortcomings present in these works in the theoretical treatment of the problems, as well as the inadequacy of the experimental investigations, do not make it possible to reveal all the actually existing possibilities in this field.

Further in this chapter the author establishes the thermodynamic relations between the various coefficients characterizing thermoelectric phenomena, and explains in detail and very clearly the connection between Peltier heat and the flow of

entropy through contact and shows why, for calculating thermoelectric phenomena, it is necessary to bring in statistical theory. In the next paragraph of the same chapter the foundations of the statistical theory of thermoelectric phenomena are set forth; the mechanisms by which thermoelectromotive force arises are examined in detail, both in the case of carriers of only one sign and in the case of bipolar diffusion. Here, too, the most important concepts in semiconductor physics are analyzed: the concept of effective mass and of the hole.

The chapter ends with a summary of calculation formulas and a general review of experimental facts relating to the temperature dependence of thermo-emf. The author points out that, basically, within the temperature ranges with which one has had to deal, the stated theory of thermoelectric phenomena gives values of the thermo-emf that are quite close to those obtained from experiment and therefore can be used as the basis for calculations of thermoelectric generators.

Central to the book is Chapter 2—“Thermoelectric Generators.” Here the author presents above all the theory of thermoelectric generators that he developed in 1950 and that was subsequently confirmed experimentally; in this theory, for the first time, a correct derivation is given of the efficiency of a thermoelectric generator. The main physical problem confronting the author here is the following. Although thermoelectric phenomena themselves are, in a certain sense, reversible, they are always inevitably accompanied by irreversible processes, the most important of which are heat transfer from the hot junction to the cold one owing to thermal conductivity, and the evolution of Joule heat. Therefore, even if an “ideal” thermoelectric generator were constructed, in which all losses caused by the design of the device were eliminated (imperfection of thermal and electrical contacts, etc.), even in that case the efficiency of such a generator would be less than the efficiency of Carnot’s ideal cycle. Thus, the chief task of the theory of thermoelectric generators is to establish the influence of the above-listed factors on the efficiency of a thermoelectric generator. It is precisely this problem that A. F. Ioffe solves in the first section of Chapter 2, using very elementary means. In doing so A. F. Ioffe obtains a most important result, namely that the effectiveness of a thermoelectric generator is determined by the quantity

\[ z=\frac{\alpha^{2}\sigma}{\varkappa}, \]

where \(\alpha\) is the differential thermo-emf, \(\sigma\) is the specific electrical conductivity, and \(\varkappa\) is the coefficient of thermal conductivity. The larger \(z\) is, the greater the efficiency of the thermoelement.

In the concluding part of this section the author gives graphs, tables, and approximate formulas for the rapid calculation of the efficiency of thermoelements.

The main result obtained by A. F. Ioffe—the determining value of the quantity \(z\)—makes it possible to approach scientifically the selection of substances most suitable for thermoelectric generators. In fact, the quantities \(\alpha\) and \(\sigma\) depend on the concentration of current carriers and on their mobility. There are classes of semiconductors in which the temperature dependences of the mobility of current carriers have been well studied experimentally, and for some of them there also exists a rigorous theoretical basis. This makes it possible to select the most effective semiconductor substances from among the known ones and to pose the question of synthesizing new semiconductors with properties most suitable for the creation of thermoelectric generators. The situation is somewhat worse with the coefficient of thermal conductivity \(\varkappa\). A complete theory of thermal conductivity does not yet exist. At the same time, the principal losses in a thermoelement occur precisely as a result of heat transfer from the hot junction to the cold one as a consequence of thermal conductivity. Therefore A. F. Ioffe and A. V. Ioffe have undertaken, in recent years, special investigations of the thermal conductivity of semiconductors.

In order to reduce losses due to thermal conductivity, it is necessary to choose materials with smaller \(\varkappa\). But, as is known, the thermal conductivity of semiconductors (and metals) consists of two parts: \(\varkappa=\varkappa_{\mathrm{phon.}}+\varkappa_{\mathrm{el.}}\), where \(\varkappa_{\mathrm{phon.}}\) is the thermal conductivity due to phonons, and \(\varkappa_{\mathrm{el.}}\) is the thermal conductivity due to electrons. As is known, the final value of the thermal conductivity is due to the scattering of both phonons and electrons. Experiments by A. F. Ioffe and his collaborators in recent years have established that the conditions for the scattering of phonons and electrons in a semiconductor are different. They can be varied by introducing certain impurities and thereby changing the ratio between \(\varkappa_{\mathrm{phon.}}\) and \(\varkappa_{\mathrm{el.}}\) in the desired direction. In particular, one can introduce such impurities as strongly scatter phonons and have almost no effect on electrons. This is achieved, for example, by synthesizing ternary systems from two isomorphous compounds, say, \(\mathrm{PbSe}+\mathrm{PbTe}\), as is described in detail in the second of the monographs reviewed here. Thus, theory truly makes it possible to raise the question of creating special materials for thermoelectric generators. As the author points out, real semiconductor thermoelements have

Bibliography

…now reaches efficiencies on the order of 10%. The seriousness of this achievement can be clearly understood if one takes into account that in metallic thermoelements the efficiency is of the order of 0.2%. The section of the monograph under consideration ends with a formulation of the general conditions necessary for attaining the highest possible efficiencies.

At the conclusion of Chapter 2 the author considers the question of the efficiency of vacuum thermoelements, in which there are no losses due to thermal conductivity, but there are losses due to work-function losses. It is shown that in the range of high temperatures the efficiency of such a thermoelement may also amount to 10%, and in combination with a semiconductor thermoelement the efficiency of the battery can be brought up to 20%. The possibility of practical use of such a type of complex thermoelectric generator is ultimately determined by the attainable density of the emission current.

In Chapter 3—“Other Applications of Thermoelements”—other applications of thermoelements are briefly described. First the question of obtaining cold by means of thermoelements is analyzed. Here an expression for the refrigeration coefficient is obtained and analyzed. It is shown that, for the efficiency of a refrigeration device, the conditions of heat transfer from the junctions of the thermoelements to the surrounding medium are of decisive importance.

In the following sections thermoelectric heating is briefly considered (which proves more advantageous than direct heating by Joule heat for small temperature differences), the possibility of more effective use of semiconductors in measuring technology is discussed (rational choice of materials for thermopiles), the use of thermal stresses in semiconductors for constructing sound generators, and, finally, the influence of Peltier heat on the crystallization process. It is pointed out that the zone melting can be carried out not by mutual displacement of the specimen and the furnace, but by passing a current.

The appendix gives a summary of the basic formulas for calculating the thermoelectric properties of semiconductors when an expression for the electron gas is available, and a summary table of Fermi functions.

The collective work of A. F. Ioffe, L. S. Stil’bans, E. K. Iordanishvili, and T. S. Stavitskaya is devoted to a question that in the monograph reviewed above was considered only briefly—thermoelectric cooling. The monograph consists of three chapters.

Chapter 1 is devoted to the theory of thermoelectric cooling. After a brief exposition of the thermodynamic theory of thermoelectric phenomena, the authors proceed to a detailed study of the efficiency of thermoelements on the basis of statistical theory and to a discussion of the rational selection of semiconductors for a refrigeration device. As a result of the analysis the authors arrive at the conclusion that the most promising for refrigeration devices are thermoelements made of semiconductors with a degenerate electron gas or of semimetals. A detailed study of the influence of Thomson heat on the energy balance of the thermoelement is given, and it is shown how the formula for the efficiency must be modified in order to take account of Thomson heat.

In the next section the efficiency of a multistage battery is calculated, and it is shown that increasing the number of stages beyond two makes no sense. In the concluding section of Chapter 1 the fundamentals of the theory of thermoelectric batteries are given: the rational choice of the ratios of the cross sections of the thermoelement branches is discussed, the calculation of a single-stage battery is given, and the influence of deviations from optimal conditions is investigated.

In Chapter 2—“Experimental Investigations of the Thermoelectric Properties of Semiconductors”—the methods for measuring the Peltier and Thomson coefficients, thermo-e.m.f., electrical conductivity, mobility, and concentration of carriers are considered first of all. Methods for measuring electrical conductivity and the Hall effect with direct and alternating current are examined. This section will be of great interest to those readers who wish independently to undertake the corresponding experimental investigations.

After this the authors proceed to a discussion of the results of experimental investigations of the thermoelectric properties of semiconductors. First the results of measurements of the Peltier and Thomson phenomena for ZnSb and PbTe are considered, and the extent to which the thermodynamic relations between the thermoelectric coefficients are fulfilled is clarified. It may be regarded as established that, within the limits of experimental error, the thermodynamic relations are fulfilled. We note that the latter circumstance is not trivial, since in deriving the thermodynamic relations between the thermoelectric coefficients, in addition to the laws of classical thermodynamics, the principle of symmetry of Onsager’s kinetic coefficients is also used. Next follow detailed investigations of the thermoelectric properties of lead telluride and selenide and of the solid solution PbTe–PbSe, since until recently these substances were the best material for thermoelements. In these substances the temperature dependence of the mobility…

... has the form \(u \sim aT^{-s}\), \(s = 2.5;\ 3\). This temperature dependence finds no explanation in the modern theory of semiconductors. However, if it is accepted, then the experimental and theoretical values of the thermoelectric coefficients will coincide, while simultaneously taking into account the degeneracy of the electron gas. The last section of Chapter 2 is devoted to comparing the theory of thermoelectric cooling with experiment and is of special interest because, as far as the reviewer knows, such a verification is being carried out for the first time. Here, above all, the temperature dependence of the product \(\alpha^{2}\sigma\), which enters into the numerator of the quantity \(z\) that chiefly determines the efficiency of a thermoelement, is analyzed. A comparison of experimental and theoretical data indicates qualitative agreement between them and, at the same time, certain discrepancies, the nature of which requires further investigation. Next, the apparatus for measuring the cooling coefficient and the maximum temperature decrease is described. If the temperature dependence of the quantity \(z\) observed experimentally is accepted, it turns out that the theory of thermoelectric cooling set forth in Chapter 1 agrees well with experiment.

Chapter 3 is devoted to the application of thermoelectric cooling. This chapter contains the following sections:

1. Domestic refrigerators. In this section the designs of thermobatteries, thermal contacts between radiators and thermoelements, the design of radiators, calculation of a thermobattery and testing of a refrigerator are considered in detail; the latest models of thermoelectric refrigerators, created in 1954, are also described. At the present time it may be asserted that thermoelectric refrigerators can already be more economical than absorption-type refrigerators, although still less economical than compressor refrigerators, whose cooling coefficient reaches 80–100%. To achieve such a cooling coefficient in thermoelectric refrigerators it is necessary to improve the thermoelectric properties of the material of the thermoelements (to increase \(z\)).

2. Other applications of thermoelectric cooling. Even now one can point to areas where thermoelectric refrigerators have an indisputable advantage over all other methods of cooling. This is the case when it is necessary to cool small objects, in particular, for example, to thermostat semiconductor units of radio receivers. This section considers various applications of this kind: the use of cooling thermoelements in meteorology; deep cooling by means of a three-stage battery (a temperature decrease from \(+20^\circ\) C to \(-40^\circ\) C was achieved); combined cooling—when, as the first cascade, the refrigerating unit of the “ZIL—MOSCOW” electric refrigerator was used, which produced a decrease to \(-30 \div -32^\circ\) C, and a two-stage thermoelectric battery, which gave a further decrease to \(-63^\circ\) C at a room temperature of \(+23^\circ\) C. Subsequently, as the last cascade, a thermoelement with improved negative branch was used, which gave a decrease to \(-78^\circ\) C at an overall temperature drop of \(102^\circ\) C. The thermostating of radio-engineering instruments and units is then considered. In the section “Data from foreign literature” it is noted that, according to foreign literature, in the spring of 1955 the maximum temperature decrease achieved by English scientists was \(37^\circ\) C.

In conclusion it is pointed out that the data presented in the monograph are based on results obtained 1.5 years earlier, and that at present the authors have at their disposal thermoelements possessing considerably better characteristics. There is every reason to suppose that in the near future the economy of thermoelectric refrigerators will surpass that of compressor ones, and the range of applications of thermoelectric cooling, where even now the latter has an indisputable advantage over other methods of cooling, will expand considerably.

It must be emphasized that the monographs under review are of interest not only from the standpoint of the special questions considered in them. Not to mention the fact that the application of semiconductor theory to the solution of purely applied problems is set forth in them in a very instructive way, of great interest to anyone engaged in semiconductor physics are the theory of energy transformations in semiconductors developed in them, a number of new experimental results, and new ideas expressed in them.

The monographs will undoubtedly be read with interest by physicists, chemists, and engineers.

A. G. Samoilovich