ELECTRICAL BREAKDOWN OF POLARIZED SOLID DIELECTRICS

E. K. ZAVADOVSKAYA

Associate Professor, Candidate of Physical and Mathematical Sciences

Introduction

Theoretically, the question of the possible role of high-voltage polarization in the breakdown of solid dielectrics does not admit an unequivocal answer. In the opinion of some authors, the electromotive force of polarization will increase the breakdown voltage of solid dielectrics, since in the presence of polarization the potential difference actually acting on the dielectric proves to be smaller by the magnitude of the polarization e.m.f. \[1, 2\].

Fauler’s theory of the breakdown of dielectric crystals \[3\] leads us to the conclusion that the breakdown voltage of polarized dielectrics must be lower than the breakdown voltage of the same dielectrics in the absence of space charges. Finally, it is necessary to take into account one more circumstance that may be significant in considering the phenomenon of breakdown of polarized dielectrics: the considerable potential gradients that are created in the region of the space charge. Estimates of the magnitude of the electric field in the region of the space charge, made by A. F. Ioffe, Sinelnikov \[4\], and Gokhberg \[1\], give a field magnitude of approximately \(10^8\) V/cm. The existence in a dielectric of local fields of such magnitude, exceeding by 10–100 times the mean value of the electric strength, is of great interest for the theory of breakdown of solid dielectrics.

If it is assumed that breakdown is determined by the presence in a solid dielectric of a certain critical potential gradient, just as in gases, then it is clear that the field of the space charge of the magnitude indicated above can lead to the onset of breakdown, which will cause a decrease in the thickness of the dielectric layer and, at a given voltage, will facilitate the development of breakdown. From this point of view, the presence of a space charge should lead to a decrease in the electric strength of the dielectric.

The influence of preliminary electrization of a dielectric on its breakdown voltage was investigated by Groenwald \[5\]. He carried out experiments with Madagascar mica, micanite, and porcelain in a nonuniform electric field. According to this author’s data, the breakdown voltage of the dielectrics indicated above, under short-time application of voltage, when tested by means of high frequency, impulse voltage of various duration, and alternating voltage, is less than under direct voltage. An especially large lowering of the breakdown voltage is observed in impulse breakdown of dielectrics that are under the action of a constant voltage of polarity opposite to that of the impulse. Groenwald explains these results of his experiments by the presence of a “dielectric after-effect” in an inhomogeneous dielectric, i.e., by polarization.

V. D. Kuznetsov, Z. A. Bardakhova, and N. M. Fatykhina \[6\] carried out an investigation of the breakdown voltage and electromotive force

As is seen from Fig. 1, at first, with an increase in the polarizing voltage, the counter-electromotive force of polarization increases, reaches a maximum, and then remains constant. Such a course of the dependence is probably caused by the fact that, at high fields created in the region of space charges, the electrical conductivity of the substance increases considerably and the maintenance of a space charge of high density becomes impossible. In our experiments, with a specimen thickness \(d = 0.38\) mm, the maximum e.m.f. of polarization was 4.6 kV. The obtained dependence of the polarization on voltage coincides with analogous data of other authors (12).

Dependence of the magnitude of the electromotive force of polarization on voltage.

Fig. 1

As a result of the preliminary investigations carried out, we settled on the following experimental conditions, which gave the optimum result: polarizing voltage 5 kV, polarization time 3 minutes, polarization temperature \(20^\circ\)C, experimental temperature \(5^\circ\)C, and duration of the experiment 3–4 minutes.

Breakdown voltage of a dielectric in the presence of space charges in it

To determine the influence of polarization of specimens on their breakdown voltage, comparative determinations were made of the breakdown voltages of unpolarized and polarized specimens. In the latter case, breakdown was produced both with a voltage whose direction coincided with the polarizing voltage and with the opposite one. By testing the specimens with short voltage pulses of duration \(10^{-4}\)—\(10^{-6}\) sec, we could assume that no space charges were thereby created in them. Special experiments showed that, under the action of such pulses, in our conditions no appreciable dissipation of the space charge occurred.

Distribution of the number of specimens according to their electrical strengths.

Fig. 2

The characteristic results obtained by us for rock salt are given in Fig. 2. In this figure, along the abscissa axis is plotted the value of the breakdown strength in kV/cm, and along the ordinate axis—the number of specimens which, on breakdown by pulses, exhibited one or another value of electrical strength.

From consideration of the results presented, it is seen that the greatest number of specimens possesses a definite, most probable value of electrical strength; moreover, the magnitude of this strength proves to be approximately the same for unpolarized specimens and for polarized ones, both for coinciding and for opposite polarities of the steady and pulse voltages. Therefore one must conclude that the presence of a space charge and of an electromotive force of polarization of the order of...

dielectric. According to the data of Wool and Goldman, Venderovich, Vorob'ev, the presence of a space charge in a dielectric lowers its breakdown voltage. None of these works gives quantitative characteristics by which one could be guided in calculating insulation and carrying out tests.

With regard to each of these works, serious objections may be raised against the measurement methods used by the authors [10]. Hence there arose the need to carry out special investigations, under clean experimental conditions, to clarify the influence of a space charge in a dielectric on its breakdown voltage. This question is of practical and theoretical interest.

Experimental Method

The materials investigated in our experiments were rock salt and calcite, which have different distributions of space charge. In rock salt, space charges are created near both electrodes; in calcite, by contrast, a concentrated space charge is obtained in the cathode layer.

Assuming that the space charge in the crystal at low temperature would, owing to the high internal resistance of the crystal, dissipate slowly, we polarized the specimen at a high temperature and then, without removing the voltage, cooled it to a lower temperature, at which breakdown was produced.

For experiments on the breakdown of specimens with a space charge, optimal conditions were selected experimentally under which the space charge obtained was maximal and changed little during the experiment. We also investigated the influence on the breakdown voltage of an electronic space charge, which is created in X-rayed rock salt.

In the experiments with rock salt and calcite, specimens with wells were used, making it possible to obtain a uniform field. According to A. Venderovich and R. Drizina [11], polarization depends strongly on the preliminary annealing of the specimens. The polarization e.m.f. after annealing of the specimens decreases, since annealing causes a redistribution of impurities. In our experiments, when testing a whole series of specimens, it was necessary, in order to obtain comparable results, to normalize the specimens. For the purpose of normalization the specimens were first annealed for 10 hours at a temperature of \(600^\circ\mathrm{C}\); then the flat side of the specimen, by means of spraying in vacuum, was coated with a thin layer of lead or silver. The second electrode was mercury poured into the well, or a layer of metal likewise applied in vacuum by sputtering. We obtained no differences in the experimental results when using electrodes of one kind or another.

The depolarization currents were measured with an Edelmann–Lutz string electrometer by the charging method. The sensitivity of the electrometer in the experiments with ionic space charge was 2 volts/division. The polarized specimen was placed in a glass vessel and filled with transformer oil. As the source of high voltage for polarizing the specimens, an installation assembled according to a single-kenotron circuit was used, stabilized by a capacitance \(C = 0.02\,\mu\mathrm{F}\). The magnitude of the space charge depends on the conditions under which it is formed, and in particular on the magnitude of the applied voltage, temperature, time, and other factors.

Figure 1 presents the dependence of the polarization e.m.f. on the voltage at which polarization was carried out. This dependence was obtained for a rock-salt specimen of thickness \(d = 0.38\) mm at a temperature of \(15^\circ\mathrm{C}\).

polarization in thin layers of rosin and paraffined paper. Their aim was to show the influence of the electromotive force of polarization on the breakdown voltage of rosin and paraffined paper.

The authors carried out breakdown tests of the indicated dielectrics under impact and gradually increasing electrical loading. As a result of the investigations performed, they conclude that there is an influence of the electromotive force of polarization on the breakdown voltage of dielectrics. The investigations of these authors are based on the well-known fact of the accumulation of a volume charge in a dielectric under the action of an applied potential difference, and on the assumption that the electromotive force of polarization must reduce the potential difference acting on the dielectric; therefore the breakdown voltage of the dielectric should increase.

On the basis of their experiments they conclude that the e.m.f. of polarization influences the breakdown voltage of dielectrics, and they consider that the electromotive force of polarization counteracts breakdown and raises the breakdown voltage. When the sign of the voltage applied to the dielectric is reversed, the breakdown voltage falls, since an electromotive force of polarization has already had time to arise in the dielectric. These results are in contradiction with the results of later investigations.

The principal result of these authors is that the breakdown voltage under a short-time action of voltage is lower than under a more prolonged exposure. At the present time it has been firmly established that, owing to statistical lag caused by the formation of the discharge [7], the breakdown voltage of solid dielectrics under pulses is higher than the breakdown voltage under static voltage.

It should be pointed out that there were certain shortcomings in the experiments of the cited authors. Thus, in the breakdown of plates of solid dielectrics in air, surface discharges will necessarily occur; they distort the electric field in the dielectric. In the presence of a low-power energy source, such as the experimenters used, the most indeterminate results will be obtained, since both the shape of the voltage curve and its maximum value will be indeterminate.

A second source of possible errors in this work may lie in the method used for obtaining electrical pulses and measuring them. The method of obtaining short-time electrical voltages employed by the authors did not make it possible to obtain any definite shape of the voltage curve.

The question of the influence of volume charge on the electric strength of dielectrics was also studied by A. M. Venderovich and A. A. Vorob’ev [8]. They investigated the influence of a concentrated volume charge in calcite on its electric strength and found a decrease in the breakdown voltage in the presence of a volume charge.

Wool and Goldman [9], studying the breakdown of X-rayed rock salt under the internal photoelectric effect, observed a lowering of the breakdown voltage under illumination if breakdown was produced under direct and alternating voltage. Carrying out the same experiments under pulse voltage, they did not observe a decrease in the breakdown voltage. They explained the lowering of the breakdown voltage as a consequence of distortion of the electric field in the crystal by volume charges formed by the photocurrent under static voltage.

From this brief survey of known works on the study of the influence of volume charge on the breakdown voltage of solid dielectrics, it is evident that they give mutually exclusive answers to the question posed.

According to the data of Kuznetsov, Bardakhova and Fatykhina, Grünwald, Walter and Inge, a volume charge in a dielectric increases the breakdown voltage—

4 kilovolts, does not exert any noticeable influence on the magnitude of the breakdown voltage of these specimens.

It is known that the volume charge in calcite is concentrated near the cathode in a very thin layer, in which considerable potential gradients arise. Such conditions for the formation of volume charge were of great interest for our purposes. Before proceeding to our main task—the measurement of the electric strength of unpolarized and polarized calcite—we also had to carry out preliminary investigations to select the optimum conditions for the formation of volume charge.

As a result of the preliminary investigations we settled on the following experimental conditions. For specimens 150–400 microns thick, the voltage at which the specimens were polarized was taken to be 5 kV, the polarization time 5 minutes, and the temperature 80°C. During breakdown the temperature was maintained at 6°C. For thinner specimens, up to 100 microns thick, the voltage used during polarization was 3 kV.

Legend:
× — unpolarized specimens
△ — specimens polarized in a field of polarity opposite to that of the breakdown field
● — specimens polarized in a field of the same polarity as the breakdown field

Fig. 3. Dependence of the breakdown voltage (mean values) of calcite on specimen thickness.

Figure 3 presents the dependence of the breakdown voltage of calcite on thickness—for unpolarized specimens (indicated by crosses), broken down under a voltage of polarity opposite to that at which polarization took place. From Fig. 3 it is seen that the electric strength of polarized calcite differs somewhat from the strength of unpolarized calcite. As in the experiments of Vorob'ev and Venderovich, the breakdown strength of polarized calcite, broken down upon application of a voltage of opposite polarity, proved to be higher, while the breakdown strength upon application of pulses of the same polarity was lower than the breakdown strength of unpolarized calcite.

However, it must be emphasized that the difference obtained in the breakdown strengths of polarized calcite is insignificant. This indicates that the polarization phenomena, which are most strongly expressed in calcite, do not have any substantial influence on breakdown.

As the material for experiments with electronic volume charge, X-rayed rock salt was chosen, whose photoconductivity has been well studied [13].

The coloring of the specimens was carried out with the aid of a Coolidge tube. Prolonged irradiation with X-rays and frequent stirring of the specimens during this process gave an apparently uniform coloration.

The vessel in which the experiments were carried out was well darkened. The insulation of the electrometric circuit was made with the aid of amber and thick layers of paraffin. Illumination of the specimen was produced by a carbon arc through a focusing optical system.

Photoconductivity depends strongly on the intensity of light [14]. In our experiments it was shown that, with prolonged polarization of the specimens, small fluctuations in the intensity of illumination have little influence on the magnitude of the polarization. It proved possible to select such experimental conditions under which the polarization of the specimens was identical.

It is seen from Fig. 4 that the maximum values of the electric strength of specimens that are unpolarized, polarized, and broken down under voltages of opposite and identical polarity coincide. These experiments make it possible to conclude that no appreciable influence of space charge on the electric strength under pulses of X-rayed rock salt is observed.

Dependence of the breakdown voltage of X-rayed polarized NaCl on the thickness of the specimens.

Fig. 4

Conclusion

The theoretical assumptions concerning the possible role of space charges in breakdown are based on two premises: 1—the existence, in the region of space charge, of a field of high intensity, and 2—the influence of the electromotive force of polarization on the breakdown voltage.

Our experimental investigations have shown that the breakdown voltage of calcite and rock salt under pulses, in the presence of a space charge, does not change appreciably. These results have the following probable explanation. Even with a more or less uniform distribution of the space charge over the thickness of the crystal, the greatest potential drop occurs near the electrodes in thin layers. It is difficult to admit the formation of electric fields of high intensity in the region of the space charge, since already at fields of the order of \(10^5\) V/cm a strong increase in electrical conductivity begins.

In the opinion of Walter and Inge [15], the growth of dark electrical conductivity in strong fields in rock-salt crystals can be explained only by a real increase in ionic electrical conductivity or by the superposition upon the ionic currents of additional currents caused by the motion of free electrons released directly by the field.

The electrical conductivity of the crystal, increasing with increasing field, will retard the further growth of the field and will lead to an equalization of the potential distribution over the specimen and to an averaging of the fields.

In Vorob’ev’s work [16] it was shown that small local disturbances of the homogeneity of a dielectric upon the introduction into it of impurities or deformation do not exert a noticeable influence on the breakdown strength.

In the presence of a space charge in the dielectric, deviations from the regime average for the dielectric will occur in layers with thicknesses of the order of microns. We dealt with dielectrics with a layer thickness of several hundred microns. It may be thought that the phenomena occurring in these thin layers do not exert a significant influence on the breakdown strength of the dielectric.

If one takes into account the various secondary phenomena that arise during breakdown, then the volume charge has no noticeable effect on the magnitude of the breakdown voltage of solid dielectrics. We arrive at this conclusion on the basis of an analysis of the results of our experiments and a critical consideration of the works of preceding authors.

References

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