Some Experimental Patterns of Electrical Breakdown in Solid Dielectrics

A. A. Vorob'ev

Professor, Doctor of Physico-Mathematical Sciences

Electrical strength of crystalline dielectrics containing impurities

To obtain a dielectric with high electrical strength, one may use the same methods of material treatment that practice and science have developed for obtaining materials with high mechanical strength. These methods are, chiefly: the introduction into the material of various additives and the production of alloys, followed by mechanical and thermal treatment of the materials. Hence it becomes clear why various researchers devote much attention to the study of the influence of impurities on the properties of dielectrics.

Impurities present in the crystal lattice will disturb its inherent regularity and thereby influence the character of the forces acting on the particles. Different authors explain in different ways the influence of impurities on the breakdown voltage of solid dielectrics. In Hippel’s theory [1], according to which the principal process leading to dielectric breakdown is recognized as impact ionization by electrons, the impediments to their motion caused by impurities are taken into account. Hippel developed an original theory of electron motion in solid dielectrics, taking into account possible disturbances in the ideal lattice, and experimental investigations were carried out.

According to Hippel’s ideas, impurities should increase the electrical strength of a dielectric, because their introduction disturbs the regular course of the potential function in the crystal. Distortions of the potential barriers reduce the possibility of free motion of electrons and increase the probability of their capture.

Hippel connects the increase in the probability of electron capture not only with distortion of the lattice, but also with the change in the binding energy between particles that results from such distortion. He considers a “group bond” of an electron with a lattice ion, which consists in the following: an electron moving along a preferred crystallographic direction in the crystal—the diagonal of a face—being delayed in a potential well near a positive ion, converts the ion into an atom of an alkali metal; in this process the dimensions of the particle are approximately doubled. The newly formed particle has such large dimensions that it is practically difficult to speak of localization of the electron at a given center. All twelve positive neighbors interact equally with this charge.

The electron proves to be bound to a group of neighboring ions and receives from it the energy necessary for its further motion. Every

a change in the lattice, similar to a thermal one, will affect the binding energy of the electron in the lattice.

The second type of electron binding in the lattice, according to Hippel, is “atomic binding.” As an example of such binding, Hippel points to the capture of an electron by a copper ion located in the lattice of rock salt. The copper ion, owing to the large value of the ionization potential, binds the electron at a short distance, practically forming a copper atom. In this case the electron proves to be bound to one center, and the acquisition from it of a considerable amount of energy is unlikely. Hence follows the great stability of such formations.

Using the concepts of group and atomic binding, Hippel explains a large number of facts from the field of photochemical reactions in which a solid body participates. These concepts were also used by him to explain the increase in electrical strength in the presence of impurities and lattice disturbances.

If one considers the possible influence of impurities on the breakdown voltage from the point of view of quantum theories of breakdown, it is necessary to note that impurities and other lattice disturbances change its energy spectrum and cause the appearance of discrete levels located in the forbidden energy band [2]. As an example of the formation of such impurity levels one may cite the occurrence of the levels F and F′ in X-rayed rock salt [3]. The level F corresponds to the presence of color centers in the crystal, and the level F′ to lattice disturbances.

The appearance of discrete energy levels located close to the conduction band can considerably facilitate the transition of electrons into this band and thereby lower the breakdown voltage.

From the theoretical arguments presented concerning the possible character of the influence of impurities on the breakdown voltage, we see that they are quite contradictory.

Let us consider the experimental material available for ionic crystals.

Experiments carried out by us [4] on measuring the electrical strength of rock salt containing a colloid of potassium and copper showed that in this case the strength of the crystals, as compared with the strength of specimens not containing a colloid, may be considerably lowered. In explaining this result it must be borne in mind that the presence of a colloid in the crystal will cause a distortion of the field and a decrease in the effective thickness of the dielectric.

Our experiments on measuring breakdown voltages for rock salt containing copper ions or atomic coloration show the absence of any influence of these impurities on the magnitude of the breakdown voltage.

The dependence of electrical strength on chemical composition was investigated by Hippel for the systems KCl—RbCl and KCl—KBr. He showed that in the course of this dependence there is a maximum [5]. The maximum of electrical strength is obtained when both components enter in approximately the same percentage content. The increase in electrical strength observed in this case is relatively small and amounts to about 30%.

A considerably greater strengthening effect on NaCl is exerted by the introduction of AgCl. The addition to NaCl of 15 mol% AgCl doubles the electrical strength.

The electrical strength of a number of solid solutions was also investigated in our laboratory. Student Kanyshin [6] studied the system KI—KBr, which gives a solid solution. He found that with an increase in the content of KBr in KI the electrical strength at first increases and then decreases, i.e., the dependence has the same form as in Hippel. In view of the great hygro-

brittleness and the poor mechanical properties of the resulting solid solutions, these measurements could be carried out only on specimens with additives up to 20%.

Bogdanova [7] studied the electrical strength of the systems KJ—Na and KBr—KJ. With an increase in the impurity content in KJ, she first obtained a decrease in electrical strength, and then an increase.

It is interesting to note that in all these experiments the influence of an impurity of component B on the electrical strength of component A becomes noticeable only when it is introduced in an amount of 5–10%. In general, it should be considered that small impurities do not exert a noticeable influence on the electrical strength of a crystal. It should be noted that small impurities do affect the mechanical characteristics of crystals; for example, coloring rock-salt crystals appreciably raises the yield point, and the salt becomes stronger and less plastic [8].

Influence of Mechanical Deformation on the Electrical Strength of a Dielectric

The different degree of influence of small impurities on the electrical strength and on the mechanical characteristics of a crystal is probably fundamental and may have the following explanation.

Plastic deformation of a specimen is accompanied by slip along certain planes. Even a small disturbance of the lattice, in the form of the replacement of some nodes by foreign particles, creates a disturbance of the regular course of the potential function on these planes and impedes slip.

In breakdown, which develops along some direction, the presence of small disturbances cannot have a substantial influence on the breakdown process, since, if more difficult conditions exist along the given disturbed direction, the discharge will develop along a parallel, unhardened path. Therefore one should expect that the breakdown strength will change appreciably only when such a quantity of impurities is introduced that, along all possible breakdown directions, there is a certain number of foreign ions impeding the development of the discharge.

We studied the influence of chemical composition on the electrical strength of amorphous dielectrics. In particular, the electrical strength of three-component glasses of the system PbSiO₃—Na₂Si₂O₃ was measured. These measurements showed a strong dependence of the electrical strength of glass on chemical composition.

The theoretical considerations presented above do not give an unambiguous answer concerning the possible nature of the influence of impurities on the electrical strength of solid dielectrics. Experimental data show that, for solid solutions, in some cases the introduction of impurities leads to an increase in strength, while in other cases to its decrease.

The influence of impurities on the electrical strength of solid dielectrics will probably depend on the nature of the particles admixed to the given dielectric, just as is observed for semiconductors. Some impurities, being sources of electrons, will promote the development of breakdown; other impurities, on the contrary, being electron traps, will retard the development of breakdown.

Deformation of the crystal lattice under the action of forces will cause the appearance of energetic levels of inhomogeneity that facilitate electronic transitions. On the other hand, disturbance of the regularity of the lattice will hinder the motion of electrons through the crystal and, possibly, will strengthen it. The possibility of strengthening a dielectric by means of appropriate mechanical...

…mechanical or thermal treatment that changes its structure is of great practical interest.

For both practice and theory, it is especially important to determine the possible changes in the electrical strength of a dielectric when a mechanical load acts on it simultaneously, as occurs under service conditions. A mechanical load on a dielectric may cause a number of secondary changes in the dielectric, for example cracking or, conversely, closing of pores, a change in the conditions of contact of the electrodes, etc., which in general will complicate the character of the dependence of the breakdown voltage on the magnitude of the applied force.

We studied the propagation of discharges in crystals in the presence of mechanical stresses in them [9]. The crystal was placed in a polarization apparatus, which made it possible to observe the distribution of stresses in it and the propagation of discharges. These experiments made it possible to assess along which path the discharge would predominantly propagate: through an undisturbed region or through places under mechanical stress.

Figs. 1 and 2 present the characteristic results we observed. The bright regions indicate the mechanically stressed region in the crystal. In Figs. 1 and 2 the discharges are visible; moreover, in Fig. 2 the upper crack is the result of pressing with a point, while the lower one is a discharge.

Fig. 1

Fig. 2

A study of discharges in rock-salt crystals in the presence of mechanical stresses showed that mechanically stressed places in the crystal do not promote the propagation of discharges along them, up to stresses close to destructive ones. In general, discharges proceed along the boundary between stressed and unstressed regions, in the direction of the greatest gradient of mechanical stresses.

Akahira and Gemant [10] investigated the effect of mechanical loading on the magnitude of the breakdown voltage of glass, mica, rubber, celluloid, and cellophane, and established that, when plates of the indicated substances are punctured in a sphere-against-plane field, as the pressure on the sphere is increased, the breakdown voltage increases, reaches a maximum value, and then begins to fall.

Walter and Inge [11] investigated the breakdown of glass, mica, and cable paper in transformer oil and xylol up to a pressure of …

18 atmospheres. They showed that, with poor contact, when there is a layer of liquid between the surface of the dielectric and the electrodes, the breakdown voltage of glass increases with increasing pressure. This change is a secondary effect caused by edge discharges. For glass and mica, in the opinion of these authors, the breakdown voltage cannot depend on the external pressure.

Koch [12], subjecting dielectrics to all-around compression up to pressures of 50 kg/cm², found no change in their electrical strength.

In the breakdown of glass in an electric field, point against plane, a considerable decrease in the breakdown voltage is observed with increasing pressure on the point [13]. With a positive point, a more rapid decrease in breakdown voltage is obtained than with a negative one; thus, as the pressure on the point increases, the polarity effect appears and then increases.

In the breakdown of rock-salt plates in a nonuniform field, a slight lowering of the breakdown voltage with increasing pressure is also observed.

A number of authors [14] investigated the influence of a simultaneous mechanical load on the magnitude of the breakdown voltage of porcelain insulators. The experiments were carried out both at impulse voltage and at alternating voltage. We shall indicate here the results of the experiments of Weicker, who established the following.

1) The mechanical strength of the insulator (tensile strength), when it is under the action of alternating voltage or subjected to the action of electric impulses, remains the same as in the absence of an electric field.

2) If an insulator that is under voltage is loaded mechanically, then it breaks down at a voltage lower than without mechanical load or after mechanical loading. The lowering of the breakdown voltage depends on the magnitude of the simultaneous mechanical load. With increasing mechanical load, the breakdown voltage falls sharply.

3) At impact voltages, after a certain limit of the mechanical load has been reached, a lowering of the breakdown voltage is observed. A further increase of the load is not accompanied by a lowering of the breakdown voltage. The smallest mechanical load at which a lowering of the breakdown voltage on impulses is observed lies considerably above those loads to which the insulator is subjected under its service conditions.

The dependence of the observed effect on the mechanical strength and design of the insulator indicates its complexity and the presence of secondary phenomena. From the standpoint of the problem under consideration by us, it is of interest to elucidate the behavior of porcelain under the simultaneous action of both loads.

Zavadovskaya [15], studying the dependence of the breakdown voltage of porcelain on various factors, points out that, in the breakdown of porcelain plates in a nonuniform field at direct voltage, a decrease in the breakdown voltage is observed with increasing pressure. The lowering of the breakdown voltage is observed after a load approximately equal to 60% of the destructive load has been reached. At a load close to the destructive load, the observed lowering of the breakdown voltage amounts to about 20%.

Comparing the data of these experiments with the data of Weicker and Leckerle, one may conclude that the lowering of the breakdown voltage of insulators under static voltage observed by V. Weicker and others is due to the porcelain.

To resolve the question of the influence of compressive deformation on the breakdown voltage of solid dielectrics, a number of authors carried out experiments in a uniform electric field.

Kobeko and Kurchatov [16] studied the influence of plastic deformation on the magnitude of the electrical strength of rock salt under dc and impulse voltages. For this purpose they compared the values of the electrical strength of previously well-annealed specimens and specimens plastically deformed at high temperature, as well as indefinitely deformed specimens taken immediately after preparation. Plastic deformation of the crystal was produced at a temperature of 700–750°C under a pressure of 5–7 kg/cm² for one hour. In this case the length of the deformed crystal proved to be 70–90% of the initial length. Cleavage of such a piece gave a scaly structure, indicating a strong disturbance of the lattice. Breakdown was produced along the edge of the cube, both in the direction of deformation and perpendicular to it. These experiments revealed no difference between the values of the breakdown voltages of specimens prepared in these different ways.

In our experiments [17] the magnitude of the breakdown voltage was measured, as determined under uniform-field conditions on impulses, for crystals deformed to different degrees; the degree of plastic deformation was assessed by the X-ray method from Laue patterns. These experiments showed that the magnitude of the breakdown strength is practically independent of the degree of disturbance of the crystal lattice under plastic deformation. On the other hand, these same experiments showed that sometimes, for rock-salt crystals, with increasing pressure there is first an increase in the breakdown voltage of the specimens, and then its decrease. It must be noted, however, that in this increase of breakdown voltage observed with increasing pressure, its magnitude does not rise above a certain value characteristic of well-annealed rock salt. These experiments, as well as studies with other dielectrics (ebonite, differently annealed glass), led us to the conclusion that the sometimes observed increase in breakdown voltage with increasing external pressure is a secondary effect, due in origin to the inhomogeneity of the dielectric. With increasing pressure, up to a certain limit, the defects present in the dielectric close up; it improves and raises its electrical strength. Thus, from the character of the dependence of breakdown voltage on the magnitude of the external pressure, one can estimate the degree of defectiveness of plastic insulating materials. For example, in the case of ebonite, when the pressure on the electrodes is increased, an increase in breakdown voltage by almost a factor of four is observed. For rock salt, an increase in breakdown voltage under pressure by a factor of two is observed.

Fig. 3

A violation of the continuity of the dielectric—the formation of cracks and pores—causes a considerable decrease in the breakdown strength of the dielectric.

Figure 3 presents the dependence of breakdown voltage on load for porcelain in a uniform field under dc voltage. As can be seen, at a load equal to 50% of the breaking load, a decrease in breakdown strength begins. At a load close to the breaking load, the magnitude of this decrease reaches 30%.

For porcelain, according to Zavadovskaya’s data [15], a strong dependence of the breakdown voltage on porosity is observed.

Figure 4 shows the dependence of the impulse breakdown voltage on porosity for a P-4.5 type insulator. The porosity of the porcelain was estimated from the length occupied by pores over a distance of 1 mm, measured on a polished section with a microscope.

An increase in the porosity of porcelain is accompanied by a decrease in the breakdown voltage. We observed a similar picture for compound E-3. In the temperature region of cracking of the compound, the breakdown voltage under impulses and alternating voltage drops sharply. This is seen, for example, in Fig. 5, where the dependence of the breakdown voltage on the temperature of compound E-3 is shown for layer thicknesses of 2.5 mm and 1 mm.

In the breakdown of glass with the simultaneous application of mechanical load, beginning with a certain pressure, a considerable decrease in the breakdown voltage is observed. This effect depends on the heat treatment of the glass, becoming considerably stronger for more strongly annealed, more brittle glasses.

Dependence of impulse breakdown voltage on the length occupied by pores over a distance of 1 mm.
Fig. 4

Dependence of the breakdown voltage of compound E-3 on temperature under alternating voltage.
Fig. 5

The main experimental material known at the present time concerning the geometric elements of deformation—slip planes and slip directions—can be explained by means of ideas about translation with rotation or twinning. It is considered that, during deformation of a crystal, translation takes place along definite crystallographic directions, along slip planes; it is accompanied by rotation of the slipping regions about axes perpendicular to the slip directions. As a result of this process, the volume of the crystal is divided into “packets” of planes rotated relative to one another through a certain angle and elastically stressed.

The physical picture of the primary changes in a material under compressive and tensile deformation is the same. However, in view of the practical importance of studying the influence of tensile deformation on the breakdown voltage of solid dielectrics, these investigations have been carried out by a number of authors on various dielectrics.

Gemant [18] studied in detail the influence of a simultaneous mechanical load on the electrical properties of rubber. For his experiments he used—

rubber strips with a thickness from 0.2 to 0.6 mm were used. In his experiments the relative elongations under tension reached 300%; the change in thickness in this case amounted to 30–50%. During breakdown of rubber on alternating current in air and with simultaneous stretching, an increase in breakdown strength by 35% was found. The effect of increasing the breakdown voltage disappeared if the test was carried out under oil, after the rubber had previously been kept in oil for 24 hours.

From these experiments Hemant draws a conclusion regarding the surface origin of the strengthening effect observed by him.

The general conclusion drawn by Hemant on the basis of detailed investigations is that technically important properties of rubber—breakdown strength and dielectric losses under tension—show an improvement of 40%.

Under prolonged loads this effect is masked by the harmful action of ozone.

Akahira and Hemant [19] investigated the influence of various deformations on the breakdown voltage of solid dielectrics. On the basis of experiments with glass, cellophane, rubber, mica, and celluloid, they arrived at the following conclusions.

1. Biaxial plane stretching for materials with a small value of Poisson’s ratio $\sigma$ (for example, glass) is accompanied by a decrease, while biaxial compression by an increase, of the breakdown voltage. Rubber ($\sigma = 0.5$), under biaxial compression, likewise shows an increase in breakdown strength.

2. Uniaxial stretching causes a decrease in breakdown voltage.

3. Bending deformation does not affect the magnitude of the breakdown voltage.

On the basis of their experiments these authors come to the general conclusion that compression increases, while stretching lowers, the breakdown voltage of solid dielectrics. In this connection it is immaterial whether the deformation occurs parallel or perpendicular to the lines of force of the electric field.

We carried out experiments to investigate the influence of uniaxial tensile deformations on the electrical strength of a number of solid dielectrics [13]. Two grades of rubber, mica, and two grades of celluloid were investigated. Breakdown was produced under simultaneous stretching in conditions of a uniform and a nonuniform electric field. The design of the apparatus with which the deformation was imposed in one case ensured constancy of the magnitude of the force under whose action plastic deformation of the specimen occurred. Apparatus of another type ensured a constant magnitude of plastic deformation at a specified force; moreover, owing to elongation of the specimen, the load on the specimen decreased during the process of its deformation.

Figure 6 presents the dependence of the breakdown gradient of rubber on the magnitude of the stretching force (curve b). The measurements were made with impulse voltage. Breakdown occurred between electrodes of the type hemisphere opposite a plane, in transformer oil. In the same figure (curve a) the change in the cross-sectional area of the specimen with change in the stretching force is shown.

The dependence represented by curve a indicates a strong change in the thickness of the specimen.

The increase in electrical strength under uniaxial stretching, observed in these experiments, is a consequence of the decrease in the thickness of the rubber upon stretching, i.e. the well-known effect in measurements in nonuniform fields. If this effect is excluded by carrying out measurements under conditions of a uniform field, for example, in water, or by comparing,

the value of the electric strength for a given specimen thickness, measured under uniform tension, with the value of the electric strength for the same specimen thickness, but measured in the absence of the stretching force, then no influence of mechanical stresses on the electric strength is detected.

Experiments measuring the breakdown voltage of mica under simultaneous unilateral tension showed an increase in its breakdown voltage with increasing load. At a stress of \(1200\ \mathrm{kg/cm^2}\) (the destructive stress is \(4000\ \mathrm{kg/cm^2}\)) the breakdown gradient amounts to 180% of the initial value.

Stretching of rubber: \(a\)—dependence of the cross-sectional area on the force; \(b\)—dependence of the breakdown voltage under pulses on the magnitude of the deforming force.

Fig. 6.

Special measurements of the thickness, carried out with an accuracy up to \(0.001\ \mathrm{mm}\), showed the absence of any noticeable decrease in the thickness of mica under tension. The considerable surface conductivity of mica facilitates equalization of the field before breakdown. Thus, the strengthening effect of mica observed in this case is not connected with the existing nonuniformity of the electric field, but is caused by the inhomogeneity of the dielectric itself—mica. During stretching, a densification of the material probably takes place at the expense of transverse compression—perpendicular to the cleavage planes.

Breakdown of celluloid under direct voltage with simultaneous stretching.

Fig. 7.

Figure 7 presents the results of measurements of the breakdown voltage of celluloid under constant voltage and simultaneous one-sided stretching. As can be seen from the data given in Fig. 7, the breakdown strength of celluloid under stretching, right up to rupture itself, remains unchanged. The small scatter of the points indicates good homogeneity of the material. As for the change in the thickness of the celluloid under stretching, experiments show that it changes hardly at all. For example: the initial thickness is \(d = 0.125\) mm; under a load of 10 kg, when rupture already occurs, the thickness is \(d = 0.123\) mm.

The results of the author’s investigations show that the breakdown strength of solid dielectrics, in the case of microdisturbances of the structure as indicated by changes in Laue diagrams, does not change appreciably. Experiments involving the study of discharges in deformed crystals show that the discharge proceeds along the boundary between stressed and unstressed regions, where the occurrence of discontinuities in the substance is most probable.

Other experiments likewise lead to the conclusion that disturbance of the microstructure of a dielectric causes a considerable decrease in electrical strength.

Dependence of the Breakdown Voltage of Dielectric Crystals on the Electron Binding Energy

One of the essential questions in the theory of breakdown is the question of the origin of the electrons that cause the destruction of the dielectric. If these electrons enter the dielectric from the cathode, then it is of interest to know what influence the concentration of electrons in the electrodes, the potential barrier separating the metal electrons from the dielectric, and the material of the electrodes will have on the electrical strength of the dielectric. Experiments carried out in our laboratory [20] under various conditions provided an answer to the three questions posed above. It turned out that the electrical strength of ebonite and rock salt does not change appreciably when the material of the cathode is changed; in these experiments silver, gold, and lead cathodes were used. Mercury or lead served as the anode. No influence was also found on the breakdown voltage of rock salt from electrons torn from the cathode into the dielectric by the external photoelectric effect.

In breakdown in a nonuniform field of rock salt and mica, no influence was found of the material of the point (silver, platinum, copper, steel, and aluminum) on the breakdown voltage. In other experiments with rock salt and mica, an electron charge, an ionic surface charge (from a gas discharge), silver, lead, and potassium were used as the cathode, and silver or a positive surface charge from a gas discharge was used as the anode; however, the breakdown voltage did not change in this case [21]. These facts allow us to consider that the electrical breakdown of solid dielectrics is a process developing mainly at the expense of the electrons of the dielectric itself, and not of electrons entering the dielectric from the cathode. The study of figures of incomplete breakdown of solid dielectrics also leads to this idea [22]. Experiments carried out in our laboratory [23] showed that incomplete breakdown of crystals, in the presence within them of regions with different concentrations of free electrons, develops mainly in regions with increased concentration. Moreover, the discharge paths in these regions are longer and more branched than in regions with a lower concentration of electrons.

The breakdown process in a dielectric, leading to puncture, may conventionally be divided into three stages.

1. The onset of breakdown. In modern theories of breakdown it is identified with the liberation, by the electric field, of the most weakly bound electrons.

2. The development of breakdown. This is described as the growth of an electron current flowing through the dielectric at high field strength.

3. The completion of breakdown—currently interpreted as the melting of the lattice by the electron current.

The probability that electrons penetrate into the conduction band is connected with the width of the forbidden region [24]. It follows from this that the electric strength depends on the width of the forbidden band—it decreases when this band is reduced. Using literature data [25], we plotted the dependence between the magnitude of the electric strength and the width of the forbidden energy gap for crystals of the alkali-halide series. It is known [24] that the width of the forbidden region in this case is determined by the position of the maximum in the absorption spectrum.

These data are shown in Fig. 8, where along the abscissa is plotted the energy, in electron-volts, corresponding to the maximum of the absorption band, and along the ordinate—the magnitude of the breakdown strength in megavolts (MV/cm). As is seen in Fig. 8, the points corresponding to salts containing one and the same alkali metal lie on one curve. It should be noted that a definite value of the width of the forbidden energy gap does not correspond uniquely to a definite value of the electric strength.

Fig. 8

Volkenstein [25], on the basis of the quantum theory of the solid body, showed that when a dielectric is placed in an external electric field the zones of allowed energy values for the electrons of the dielectric broaden, and the forbidden gap between them decreases. Thus, the work of extracting electrons in strong fields must decrease. The theory of Frenkel leads to the same conclusion.

According to Volkenstein’s assumption, breakdown of a dielectric occurs when the zones of possible energies broaden until they are in complete contact, i.e., the dielectric passes into the conducting state.

Volkenstein’s formulas make it possible to calculate the magnitude of the narrowing of the zones at different field strengths in a dielectric.

Experiments by A. F. Ioffe and A. V. Ioffe [27], carried out by them on semiconductors, showed that in strong fields the dependence of electrical conductivity on field strength is in qualitative agreement with the ideas about a decrease in the width of the forbidden energy gap; however, the temperature dependence of the effect contradicts these ideas.

It was of interest to carry out a corresponding check of the results of Volkenstein’s calculations as applied to dielectrics. These measurements, by means of an optical method, were carried out by us [28]. Measurements of the absorption spectra of dielectrics were performed while crystals of KI, NaCl, CaCO₃, mica, sulfur, and calcite, as well as glass and X-rayed rock salt, were placed in strong electric fields. The electric field in the dielectrics reached a value 10–20% below the breakdown value. No change in the positions of the maxima of intrinsic absorption was detected for any of the dielectrics investigated.

On the basis of the results we have obtained, we come to the conclusion that the work of extracting electrons when a dielectric is placed in a strong electric field does not decrease.

The position of the absorption maximum is almost independent of the metal, but changes when the halide is replaced; therefore it was of interest to compare the magnitude of the electrical strength of the dielectric with the energy of the electron affinity to the halide. In Fig. 9, along the abscissa axis is plotted the value of the electron-affinity energy to the halide, expressed in kcal, and along the ordinate axis—the value of the electrical strength in MV/cm. The character of the dependence obtained is basically the same as in Fig. 8.

Electron affinity of the halide

Dependence of electrical strength on the electron affinity of the halides for crystals of alkali-halide salts.

Fig. 9

Thus, from the data given in Figs. 8 and 9, one may conclude that the electrical strength is connected with the liberation energy of the most weakly bound electrons of the dielectric, but is not determined by it unambiguously.

The polarization properties of the ions constituting the crystal lattice can influence the value of the electrical strength of the dielectric, since for similar ions (alkali, halide, etc.) the polarization of the ion will depend on the displacement of electrons, and the possibility of their detachment in turn depends on the magnitude of the displacement of the electrons.

It was shown above that the magnitude of the electrical strength depends on the affinity of the electron to the halide ion and on the lattice energy. It was of interest to determine how the electrical strength of the crystal depends on the individual components of the lattice energy and, in particular, on the magnitude of the polarization energy. Therefore, graphs were constructed for the dependence of the electrical strength on the magnitude of: 1) the refraction \(R_a = R_k\), taken as the sum of the refractions of the anion and cation, 2) the polarizability of the anion, 3) the polarization energy, and 4) the dielectric constant.

Dependence between the electrical strength of crystals of alkali-halide salts and refraction.

Fig. 10

The dependence between the magnitude of the electrical strength and the refraction, and between the magnitude of the electrical strength and the polarizability of the anion, turned out to be identical. Figure 10 presents the dependence of electrical strength on refraction for crystals of alkali-halide salts. It is seen from Fig. 10 that, with increasing refraction, for fluorides and chlorides the electrical strength of the crystals decreases rapidly; for bromides and iodides there is almost no dependence of strength on refraction. Since the dependence of electrical strength on the polarizability of the anion is exactly the same as ...

shown in Fig. 13, we conclude that the dependence of electrical strength on refraction is determined by the anion.

The dependence of the electrical strength of salts on the polarizability of the anion was also indicated by Hippel (36), who found the rule that electrical strength increases as the polarizability of the anion decreases.

From the data given above it also follows that the magnitude of the width of the forbidden energy band \(W\) is likewise determined by the anion. Therefore the dependence presented in Fig. 10 makes it possible to conclude that electrical breakdown of crystals of alkali-halide salts is associated with the detachment of electrons from the halide; this is also in agreement with the character of the dependence of electrical strength on the electron-affinity energy of the halide (Fig. 9). The dependence of breakdown strength on polarization energy was constructed for chlorides, bromides, and iodides. Three separate curves were obtained. For bromides and iodides the polarization energy in this series changes by 55%. The electrical strength in this case changes hardly at all. For chlorides, at relatively smaller absolute values of the energy, as the polarization energy decreases by 35%, the strength decreases by 80%.

The polarization properties of particles will be manifested especially strongly in the surface layer of a dielectric, owing to the asymmetry of the force field acting on the particles. Therefore the magnitude of the surface energy will be related to the polarization properties of the ions and to the magnitude of the electrical strength of the dielectric. The corresponding constructions made by us showed the presence of a weak dependence between electrical strength and surface energy both for salts in the solid state and for their melts. This dependence is almost absent for bromides and iodides, and only with a further increase in surface energy, on passing to chlorides, does a noticeable increase in strength begin, which corresponds, in general, to the character of the dependence between electrical strength and polarization energy.

In agreement with this is also the high value of the electrical strength of mica (18–25 MV/cm), which correspondingly has a high value of the surface energy, equal to 1500 erg/cm\(^2\).

Dependence of the Breakdown Strength of a Dielectric on Molecular Characteristics

If one consistently develops the conception of breakdown as a process associated only with the liberation and subsequent motion of electrons in the lattice, then the resulting series of consequences is not confirmed by experimental verification. For example, according to the theory of breakdown we should have had an unambiguous relation between the magnitude of the liberation energy of the most weakly bound electrons and the breakdown voltage. Further, the breakdown voltage of a dielectric should change when the lattice is disturbed by deformation, but experiments do not confirm this.

Small impurities of foreign substances, contrary to theoretical expectations, likewise do not exert a noticeable influence on the breakdown voltage. However, the course of the dependence of the breakdown voltage on the magnitude of the electron binding energy basically coincides with that theoretically expected; but it turns out that the breakdown strength changes not only when the halide is replaced, but also the metal (Fig. 8). This latter circumstance indicates that bonds characterizing the given lattice play some role in breakdown.

During breakdown, the dielectric is destroyed, and the bonds between its particles are broken. It is therefore of interest to compare the magnitude of the electrical strength with a quantity characterizing the strength of the bonds of the dielectric particles with one another—the lattice energy. As is known, the lattice energy is understood as the work that must be expended in order to separate the particles constituting the lattice to an infinitely large distance from one another. For crystals of alkali-halide salts, the lattice energy is determined mainly by the Coulomb forces of interaction, and its values are known.

Figure 11 presents the dependence of the electrical strength on the magnitude of the lattice energy for crystals of alkali-halide salts, as constructed by us. From Fig. 11 it is seen that there is an almost linear dependence between these quantities.

One may indicate a number of other dielectrics having a high value of lattice energy and, correspondingly, high values of electrical strength. We give some of them, indicating in parentheses the corresponding value of the lattice energy in kcal/mol: fluorite (612.2), aluminum oxide (3618), quartz (3097), titanium dioxide (2943).

Proceeding from the existence of this dependence [13], one could expect that there would be a certain dependence between electrical strength and a number of other quantities connected with the lattice energy. Such quantities may above all be the activation energy and the melting temperature.

Dependence between the magnitude of the electrical strength of alkali-halide salts and the energy of the crystal lattice.

Fig. 11

Dependence between the electrical strength of crystals of alkali-halide salts and the activation energy.

Fig. 12

The activation energy is the minimum value of energy necessary for transferring a particle across the potential barrier separating two equilibrium positions from one another. Calculations carried out by Zhdanov [29] showed that the activation energy \(Q_a\) is related to the melting temperature of the substance in the following way:

\[ Q_a = \frac{3k}{S}\,TS, \tag{1} \]

where \(S=\frac{1}{S'}\); here \(S'\) determines the fraction of lattice particles in the nonstationary state. The values of \(S'\) for salts of the alkali-halide series are given by Zhdanov. Thus, the magnitude \(Q_a\) can be calculated with allowance for disturbances due to particles in the nonstationary state.

Figure 12 presents the dependence between the magnitude of the electric strength and the activation energy in arbitrary units; a linear dependence was obtained between these quantities. It should be noted that neglecting the correction \(S'\), i.e., neglecting lattice disturbances, gives large deviations from this dependence, especially for crystals having a high value of the strength.

According to expression (1) given above, there is a direct proportionality between the activation energy and the melting temperature of the crystal. Therefore one should expect a linear dependence between the magnitude of the electric strength and the melting temperature. The dependence between these quantities for crystals of alkali-halide salts is shown in Fig. 13, where the magnitude of the electric strength is plotted along the ordinate axis, and the value of the melting temperature in °K along the abscissa axis. Taking into account the scatter of individual tabulated data on the melting temperatures of salts, the linear dependence may be considered to be sufficiently well fulfilled for all salts, with the exception of lithium salts. Among the lithium salts, data on both the electric strength and the melting temperature are available only for LiF; moreover, according to Fig. 11, the values for this salt fall sharply out of the general linear dependence.

Dependence between electric strength and melting temperature for crystals of alkali-halide salts.

Fig. 13

Dependence of electric strength on melting temperature for solid solutions.

Fig. 14

The dependence of electric strength on melting temperature for a number of solid solutions was constructed by Bogdanova [30]; she used data from our laboratory, as well as Hippel’s data. This dependence is presented in Figs. 14, 15, and 16.

The dependence between the magnitude of the electric strength and the melting temperature of solid solutions is also found to be linear. For dielectrics having a melting temperature above \(730^\circ\mathrm{C}\), an inverse dependence is obtained. In this case, as the melting temperature increases, the breakdown strength decreases. Thus, it must be stated that the rule derived by us for ionic crystals, indicating an increase in the breakdown voltage of a crystal with an increase in the melting temperature, is not observed in all cases when applied to solid solutions of the same salts.

Among other factors that can affect the lattice energy and, consequently, the electric strength of a crystal, one may also point to plastic deformation and temperature.

The relationship between the magnitude of the electrical strength and the lattice energy, shown in Fig. 14, indicates that with a decrease in the lattice energy the strength should decrease. Under plastic deformation the lattice energy decreases, which should be accompanied by a lowering of the electrical strength. However, this change in the lattice energy due to latent energy [31] is small and does not exceed 1–2% of the lattice-energy value. The change in the dielectric strength associated with this change in lattice energy will be very small and difficult to determine, as was also observed in our experiments with discharges in crystals in the presence of mechanical stresses [13]. As regards the influence of temperature on electrical strength, it should be small, since the lattice energy changes little with a change in temperature. This consideration is confirmed by experiment.

Fig. 15
Fig. 16
Dependence of electrical strength on melting temperature for solid solutions.

The relation between the magnitude of the electrical strength and the lattice energy leads to a dependence of electrical strength on the physical properties of the dielectric and of the particles forming it, for example, on the lattice constant, the compression coefficient, the radius of the cation and anion, and other quantities.

Conclusion

The materials set forth above show that the breakdown strength of a dielectric is a physical characteristic that changes regularly with changes in its chemical composition. Practically small changes in the chemical composition of a dielectric (of the order of 1–3%) do not cause any noticeable change in its electrical strength. The electrical strength of a dielectric increases with an increase in the binding energy of the most weakly bound electrons and with an increase in the energy of the bonds of the particles forming the lattice. Thermal treatment and mechanical treatment of dielectrics do not exert a noticeable influence on their breakdown strength, probably because of the small change in lattice energy under such action on the dielectric.

A disruption of the continuity of a dielectric (cracks, pores) considerably lowers its electrical strength.

Quantum theories attempt to explain the phenomena of breakdown of solid dielectrics by taking into account only the magnitude of the energy of electron liberation and the subsequent accumulation of energy by the electron during its motion in the lattice.

According to these theories, breakdown is the consequence of a considerable increase in the electronic current and melting of the lattice. The theories do not give sufficient attention to consideration of the last stage of the breakdown process—the destruction of the bonds between the particles forming the crystalline-

crystal lattice, in the breakdown of a dielectric; therefore, in the corresponding formulas the quantities characterizing the binding energy between lattice particles are not reflected.

The experimental regularities we have presented for ionic crystals indicate the necessity of taking into account, in the theory of electrical breakdown, the molecular characteristics of the substance.

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