DISCUSSION OF THE PAPERS

G. I. Skanavi says:

Those present get the impression that there exist two directions in the study of electrical breakdown, one of which is being developed at the Tomsk Polytechnic Institute and the other at FIAN; but one cannot speak of the existence of two directions, since they do not exist.

In recent years the study of electrical breakdown has been pursued much less than it should have been. A number of theories of electrical breakdown have arisen, and a number of studies have been carried out that cannot be ignored (the work of Hippel and others). In undertaking the study of electrical breakdown it is necessary to understand the present state of the question. From the many existing theories one must select those that are more correct, more probable. It is apparently beyond doubt that breakdown begins with impact ionization, but this is only an intuitive conviction. There is no experimental proof that breakdown begins with impact ionization in a solid dielectric, as it does in a gas. Proof of the existence of impact ionization could be an experimentally obtained curve of the dependence of current on the thickness of the dielectric. Not every electron avalanche leads to breakdown. How does the current change before breakdown? Do pre-breakdown avalanches exist? It is necessary to carry out a cycle of work with the aim of demonstrating by direct experiments the presence of impact ionization.

There are assumptions that such mechanisms as cold electron emission, thermal ionization, and the tunnel effect exist; one cannot simply discard these mechanisms without proving their invalidity. To what extent are these processes probable? The probability of these mechanisms must be checked experimentally, just as the dependence of \(E_{pr}\) on temperature and thickness must be clarified.

In setting up the investigation of the dependence of the electrical strength of glass and mica on the thickness of the dielectric and on the time of application of the voltage (pulse duration), the aim was to study the beginning of the process of ionization and breakdown.

The works of A. A. Vorob’ev and his coworkers are interesting, but they do not resolve the question of electrical breakdown. What is the sense in comparing \(E_{pr}\) with characteristics of a substance that are likewise interconnected? The dependence of \(E_{pr}\) on all sorts of physicochemical properties exists, but for its physical justification it is first necessary to gain a firm understanding of the conditions under which breakdown arises, of the mechanism of breakdown, and of the very beginning of breakdown.

Thermal breakdown is characterized by the expended energy, which is easy to calculate. In the case of electrical breakdown, the initial stage is impact ionization. The energy necessary for the ionization of atoms in the volume of the channel is determined by the number of atoms in this volume and by the energy necessary to ionize each atom. The energy necessary for the second stage of breakdown is determined in some way by the lattice energy, but is not equal to it. One cannot judge the relation between these energies until the first stage of breakdown has been studied in detail. The formulation of the question of breakdown energy is important and interesting, but experimentally difficult to resolve. Of great significance would be even a rough estimate of the mechanism of the second stage of breakdown, clarification of the role of the electron avalanche and of the role of defects, which are always present in a real crystal.

V. D. Kuznetsov says that earlier he had not assumed the existence of a connection among such quantities as electrical strength, mechanical strength, and the surface energy of dielectric crystals. However, experiments have shown the presence of such a connection. A. A. Vorob’ev, who had previously studied mechani-

...the mechanical properties of materials, now studies electrical properties, linking them with mechanical ones. K. A. Vodop’yanov studies dielectric losses in dielectrics and also discovers a connection between losses and the mechanical properties of the crystal lattice. Energy is expended in destroying the crystal lattice, but energy is proportional to surface energy; consequently, comparing electrical strength with surface energy is meaningful. In studying the question of lattice destruction it is necessary to investigate experimentally many aspects of the phenomenon, but at the same time the problem must also be solved theoretically.

The calculation of lattice energy has been carried out for ideal crystals, whereas researchers work with real crystals, whose properties differ from those of ideal ones. It is necessary to take into account the defects present in real crystals.

On the basis of experimental data on the electrical and mechanical strength of alkali-halide crystals, data must be obtained for constructing a correct theory of the crystal lattice. It is impossible to build a theory of the crystal lattice only for the mechanical or only for the electrical properties of crystals. In electrical and mechanical destruction new surfaces are formed, whose nature is the same; consequently, the problem of mechanical destruction and electrical breakdown must be approached from common positions.

Previously, all unclear phenomena were explained by the presence of impurities, which proved to be undetectable. The role of impurities really must be clarified. Thus, A. M. Trubitsin introduced a definite impurity and thereby changed both the electrical and the mechanical strength of mixed alkali-halide crystals. This is important for elucidating the ways of obtaining substances with specified properties.

The general task for the future should be: to obtain perfectly pure crystals without defects and, on the basis of an experimental study of their properties, to determine the lattice energy, and then to construct the entire theory of the crystal lattice.

Researchers of the electrical properties of dielectrics devote insufficient attention to the theory of the crystal lattice, and this makes it difficult to solve the problem of electrical breakdown. Electrical properties must be linked with the theory of the crystal lattice. The theory of the crystal lattice ought to be introduced as a compulsory academic discipline in certain specialties of the Tomsk Polytechnic Institute and Tomsk State University.

A. A. Vorob’ev. Konorova E. A.’s work has introduced experimental clarity with regard to the electrical properties of mica in a thin layer (the dependence of $E_{\text{pr}}$ on $d$ is absent at constant voltage, but exists at pulse voltage).

The study of the electrical strength of materials in a thin layer gives contradictory data. In some works the presence of strengthening in a thin layer is established; other investigators establish the absence of strengthening.

Obviously, the phenomenon of breakdown in a thin dielectric layer is complex; there is no reason not to believe the experimental data. It is indeed possible that strengthening of the material exists in one case and is absent in another. Such contradictory data may possibly be obtained because such phenomena as emission from the cathode, secondary electrical emission, and polarization manifest themselves to a greater or lesser degree. For example, NaCl withstands enormous electron currents without destruction. In studying dielectrics in a thin layer it is necessary to take into account and keep in mind not only the processes of impact ionization, but also emission from...

the cathode, secondary electric emission, and polarization. In studying the electric strength of a material in a thin layer, it is necessary to measure the currents as well.

G. A. Vorob'ev, in the laboratory of the Tomsk Polytechnic Institute, has recorded reliable current-voltage characteristics at constant and pulsed voltages, and obtained a family of curves over a large time interval for 4 salts. These curves provide firm evidence for the existence of a connection between electric strength and the energy of the crystal lattice.

G. I. Skanavi says that the new correlations we are seeking (the relation of \(E_{pr}\) to lattice energy and other characteristics of the substance) will hardly provide new material for solving the question of the electrical breakdown of dielectrics. One cannot agree with this assertion, since lattice energy is a universal quantity expressed through the charge of the particles of which the lattice is built, through the valence of the ions, and other quantities determining the chemical bonds of the particles and the electrical and mechanical strength of the material.

The connections between thermodynamic characteristics and the properties of a substance must be sought out and revealed. G. I. Skanavi believes that the phenomenon of electrical breakdown must be studied from the beginning of the process of impact ionization. However, there are no direct experimental data showing that breakdown begins with impact ionization. There are no experimental data on the onset of electrical breakdown. All theories consider the growth of electrical conductivity, the loss of electric strength, but not destruction. On the end of the breakdown phenomenon there exist actually measured data (electric strength \(E_{pr}\)). The picture of the initial stage of destruction, of the beginning of breakdown, may become clear later, after a sufficient number of data have been obtained on the end of the breakdown process.

The idea of a connection between electric strength and lattice energy is only just beginning to be developed by us and may prove useful; we shall continue work in this direction.

In considering the phenomenon of breakdown in liquids and gases, it is necessary to take intermolecular and intramolecular bonds into account. Which bonds are broken during breakdown? The work of A. F. Kalganov has shown that intermolecular bonds are broken.

In the phenomenon of gas breakdown, impact ionization is of primary importance. In a compressed gas the phenomena become more complicated; the picture of breakdown in them must be drawn necessarily with chemical interactions taken into account. Intermolecular bonds may have decisive significance.

Since intermolecular bonds are broken during electrical breakdown, it is necessary to seek materials with strong intermolecular bonds. These materials must possess high electric strength.

The search for substances with strong intermolecular bonds is an important technical task.

V. A. Presnov says the following: G. I. Skanavi believes that there are not two directions in the study of the breakdown phenomenon; however, the impression is otherwise. Among workers of the Physics Institute of the Academy of Sciences of the USSR there is a firm conviction that breakdown begins with impact ionization. The Tomsk researchers believe that this is not a firmly established experimental fact, that there is no clarity in the mechanism of breakdown, but that the connection of \(E_{pr}\) with lattice energy is firmly established.

The theory of impact ionization is not a new theory. From A. F. Ioffe’s theory of impact ionization developed Hippel’s theory. Ioffe’s experiments showed that electric strength does not depend on the concentration of initial electrons, that photoelectrons apparently do not participate in the breakdown phenomenon and

then it is doubtful that breakdown is caused by impact ionization by conduction electrons.

A weak point in the work of the Tomsk Polytechnic Institute is that there is no picture of the breakdown mechanism. The question has not been resolved as to as a result of what act the destruction of the dielectric occurs. Perhaps not only electrons but also ions are responsible for breakdown; these ions may be in both stable and metastable states, differing in the depth of the potential well. The activation energy of the ions is the difference between energy levels. By applying an electric field, we reduce the activation energy, i.e., we create conditions for a change in the concentration of ions in the stable and metastable states; statistical equilibrium is disturbed, and disturbances arise in the lattice. Destruction of the dielectric may occur through the departure of ions from stable states. Such a mechanism of disturbance is necessarily connected with the energy of the lattice.

A correct theory of electrical breakdown cannot consider only the behavior of electrons; it is necessary to consider the behavior of ions as well.

E. A. Konorova says that the theory of impact ionization is not refuted by the experimentally established independence of the electric strength from the concentration of initial electrons. The impression held by some that the theory of impact ionization is being developed in isolation from the theory of the structure of the crystal lattice is incorrect. Theories of impact ionization, on the contrary, are based on the theory of the structure of the crystal lattice (Seitz, Hippel). Electrical phenomena in dielectrics must be studied on the basis of solid-state physics, in connection with lattice energy.

The results of the work on determining breakdown energies are very interesting, although they do not seem very convincing. The report states that the diameter of the breakdown channel depends on the thickness of the specimen, whereas the energy does not. This seems strange. The resistance of the breakdown channel is finite. If the channel length is greater, then the resistance is greater and the conductivity smaller. Why, then, does the breakdown energy not depend on the dimensions of the channel? The relationship between the channel dimensions and the measured energy must be specially studied. Microscopic examination of the breakdown channel is insufficient. It is possible that there is a difference in the magnitude of the channel and a difference in energy, but that this difference was not detected because of the large scatter of the values obtained.

V. A. Chuenkov notes the following:

1. A. K. Krasin’s experiments, which showed the independence of the breakdown voltage from the cathode material, indicate, as it seems to us, that cathode emission does not exert a significant influence on the electrical breakdown of solid dielectrics.

2. The development of the breakdown channel is substantially influenced by the space charge of positive ions formed as a result of the development of the electron avalanche. Without taking into account the retarding action of the space charge of positive ions, the electron density at the head of the avalanche would reach a value greater than \(10^{23}\ \mathrm{cm}^{-3}\), which is meaningless.

3. A number of comrades expressed doubt about the advisability of studying the first stage of electrical breakdown, i.e., the stage at which electric strength is lost. It is difficult to agree with this. The magnitude of the electric-field strength at which electric strength is lost is an important characteristic of a dielectric, since at \(E = E_{\mathrm{pr}}\) the electrical conductivity increases abruptly to very large values and the dielectric loses its dielectric properties.

Without studying the phenomenon of loss of electric strength, which is the beginning of breakdown and at the same time the cause determining the course of all subsequent processes, it is impossible to understand the mechanism of destruction of a dielectric under electrical breakdown.

M. P. Tonkonogov says that the theory of electrical breakdown lags far behind the experimental data. Theories of electrical breakdown encompass only individual aspects of the process. Chuenkov’s work is valuable in that it considers the general kinetic equation. Solving the general kinetic equation is the correct path toward solving the problem of electrical breakdown. But this equation should be solved for a specific structure. Knowing the dependence of electrical conductivity on the field strength, one must find the conditions for the disruption of the steady regime. The dependence of the current on the field strength does not exhaust the mechanism of electrical breakdown. Krasin’s idea that the bond of ions is weakened as a result of the growth of the electron avalanche deserves attention.

However, the fact that ionic bonds may be weakened by an electronic current is not considered in a broad formulation of the question.

A large amount of experimental data obtained at the Tomsk Polytechnic Institute can provide a basis for calculating the theory of electrical breakdown, for determining the constants entering into the theory.

A. A. Vorob'ev says that the work of A. F. Kalganov is of interest for practice.

Electrical breakdown is accompanied by destruction of the material. Powerful electric sparks are used for destruction (for example, they may be applied in prospecting for minerals). What power source is required for this? A. F. Kalganov’s work shows that, with the electrical method of destruction, less energy is expended than with mechanical destruction, when a large part of the energy is spent outside the region subjected to destruction. The work is exploratory in character; the investigation will be supplemented by oscillography.

Regarding the mechanism of interaction of electrons with the lattice, we can say nothing definite; this mechanism has not been revealed and is unknown.

V. I. Odelevskii says that, having established the connection between electric strength and lattice energy, one should not consider the connection of \(E_{\mathrm{pr}}\) with many quantities. The lattice energy is in direct relation to the quantity \(h\nu\); this relation indicates the physical mechanism of the interaction and is fundamental, while the others are derivative and inessential.

It is incorrect to suppose that the breakdown criterion should be transferred from the first stage of breakdown to the second. The breakdown criterion must be in the first stage, since in this stage the loss of electric strength and the disruption of the stationary regime occur.

ERRATA