ON THE PROBLEM OF BREAKDOWN OF SOLID DIELECTRICS IN A NONUNIFORM FIELD

G. A. VOROB'EV

Experimental Method

Experiments on the breakdown of solid dielectrics in a nonuniform field are often carried out with specimens in the form of plates, on whose surface electrodes—a point and a plane—are placed opposite one another. This method has the essential shortcoming that, as a result of the experiment, one obtains the breakdown voltage not of the solid dielectric, but of the combination of the solid dielectric and the surrounding medium. Breakdown of the solid dielectric with this method is, as a rule, preceded by discharges along the surface of the specimen, which substantially affect the breakdown of the solid dielectric itself [1].

In order to obtain regularities characterizing the solid dielectric, it is necessary to eliminate the influence of the surrounding medium. Experiments with elimination of the influence of the surrounding medium were carried out by A. F. Val'ter and

Fig. 1-a—Calibration oscillations with a frequency of 100 kHz.

L. D. Inge (embedding electrodes inside sulfur, glass) [2], by A. A. Vorob'ev and N. A. Prikhod'ko (pressing electrodes into ice), [1] and others. A. A. Vorob'ev and V. D. Kuchin [3], in experiments on phosphorescence in rock salt,

to avoid discharges along the surface, specimens with one deeply drilled electrode were used.

Fig. 1-b—Calibration oscillations with a frequency of
1 MHz.

We propose, for the investigation of the breakdown of solid dielectrics in a nonuniform field, to use specimens of the form indicated in Fig. 1 [7]. Specimens of solid dielectrics of the indicated form can be obtained by drilling out cavities, casting, pressing, and other methods.

Fig. 1-c—Calibration oscillations with a frequency of
10 MHz.

We carried out an experimental investigation of breakdown in a nonuniform field in rock salt (NaCl), single crystals of KCl, KBr, and KJ grown from the melt, and organic glass. The dielectrics were broken down on the front of a single pulse, while the rock-salt specimens were pro-

were also broken down under a dc voltage of both polarities. Experiments on the breakdown of rock salt under dc voltage were carried out by students of the Tomsk Polytechnic Institute T. V. Shushkalova, Z. I. Druzhinina, and Zh. I. Kalyannikova. The high voltage was applied to an electrode in the form of a point; the plane electrode was grounded. For breakdown under impulse voltage, an electronic oscilloscope was used as the recording and measuring instrument. Fig. 1 shows oscillograms for the breakdown of the dielectrics studied at different durations of voltage application.

Fig. 1г—Duration of voltage application \(1.7 \cdot 10^{-7}\) sec.

Breakdown of Rock Salt

Volt-second characteristics were obtained for specimens \(0.7 \pm 0.02\) mm thick for both polarities of the point electrode. For each point, 20–30 specimens were taken. The experimental data were statistically processed. Fig. 2 presents the volt-second characteristics for a breakdown probability \(\psi = 90\%\). The general form of the curves is similar to the analogous curves for NaCl, KCl, KBr, and KJ in the case of a uniform field [4].

The rise of the curves at the very shortest times is explained by the delay of the discharge; at a time of \(2 \div 3 \cdot 10^{-5}\) sec it is due to the influence of the space charge, which has time to form in the crystal during this interval.

The delay of the discharge in the present case should not be explained by the absence of electrons during the application of the voltage. In solid dielectrics with high electric strength, at field intensities approaching the static breakdown values, considerable electrostatic ionization takes place, which is a good supplier of electrons that must participate in the formation of the discharge. In the case of a nonuniform field, near an electrode with large curvature, at voltages approaching breakdown values, the field intensity is significantly

exceeds the electric strength of the dielectric. Consequently, in this case there must be still more free electrons.

Therefore it should be assumed that the time elapsed from the moment when the voltage reached the breakdown-static value until breakdown is the time of discharge formation under the given conditions of voltage action. The discharge-formation time was determined from the breakdown oscillogram [4]. In the case

Fig. 2.— Volt-time characteristics of rock salt at breakdown in a nonuniform field. Specimen thickness \(d = 0.7\) mm.
1—point negative; 2—point positive.

when the point was negative, the discharge-formation time was found to be \(5.1 \cdot 10^{-8}\) sec; when the point was positive, \(0.9 \cdot 10^{-8}\) sec. Accordingly, the velocities of discharge propagation are \(1.37 \cdot 10^{6}\) cm/sec and \(7.77 \cdot 10^{6}\) cm/sec. The velocity of discharge propagation for positive po-

Fig. 3.— Microphotographs of discharge paths in rock salt (time of voltage action \(5 \div 6 \cdot 10^{-7}\) sec, magnification 80 times).

a) negative polarity of the point.

the polarity of the point is 5.67 times greater than with negative polarity of the point.

These results are analogous to those observed in air. Probably, in the case of rock salt as well, near the point, as a result of ionization processes, a positive space charge is formed, which, with positive polarity of the point, facilitates the discharge, and with negative polarity retards the discharge. The polarity effect is clearly manifested for short times of voltage application and is weak for long times. Evidently, at long times the positive space charge has time to spread out considerably under the action of the high field strength at the boundaries of the space charge. This should lead to a smoothing of the polarity effect.

b)—positive polarity of the point.

Characteristic is the direction of the discharge path. With negative polarity of the point, the discharge proceeds along the shortest distance between the electrodes—along the edge of the lattice cube \([100]\). With positive polarity of the point, the discharge proceeds, as a rule, along the diagonal of the cube face \([110]\) and rarely along the diagonal of the cube \([111]\). For a voltage application time of \(1 \div 2 \cdot 10^{-7}\) sec, deviations from the indicated regularity were observed for both polarities of the point; the discharge channel was often curved. At the same time, a large number of discharge channels (up to 6) were often observed in one specimen, whereas at longer times specimens with two discharge channels were encountered only rarely (with positive polarity of the point). Fig. 3 presents microphotographs of discharges for a voltage application time of \(5 \div 6 \cdot 10^{-7}\) sec.

Breakdown of KCl, KBr, and KJ Single Crystals

Breakdown of KCl, KBr, and KJ single crystals was carried out for both polarities of the point and for two voltage application times: \(9 \cdot 10^{-8} \div 1.3 \cdot 10^{-7}\) sec and \(1 \div 3 \cdot 10^{-6}\) sec. Fig. 4 presents the results of the experiments. The voltages correspond to a breakdown probability \(\psi = 90\%\). Each

point is the result of processing 4–7 oscillograms. The character of the dependence is the same as for rock salt.

Figure 3 [7] presents the dependences of the breakdown voltage on the lattice energy for the crystals investigated. With increasing lattice energy the breakdown voltage also increases, as in the case of a uniform field [4, 5]. Consequently, the breakdown voltages of crystals punctured in a nonuniform field, when the influence of the surrounding medium is excluded, are determined by the material of the crystal, as in a uniform field. In those cases where it is difficult to carry out the breakdown of solid dielectrics in a uniform field, experiments for comparing dielectrics may be carried out in a nonuniform field.

Fig. 4.—Voltage-time characteristics in the breakdown of KCl, KBr, and KI single crystals in a nonuniform field.

Fig. 5.—Voltage-time characteristics in the breakdown of organic glass in a nonuniform field.

Experiments were carried out on the breakdown in a nonuniform field of NaCl and KBr plates of thickness \(0.7 \pm 0.02\) mm at a voltage exposure time of \(1.1 \div 1.7 \cdot 10^{-6}\) sec. Figure 2 [7] presents the results of the experiments and, for comparison, data on the breakdown of NaCl and KBr using specimens with a conical recess. The voltages are taken at a breakdown probability \(\psi = 90\%\). The results of the experiments on the breakdown of plates do not characterize the dielectric.

Walter and Inge [6] recorded volt-second characteristics during the breakdown of rock-salt plates 2.7 mm thick in the field of point–plane electrodes. The specimens were immersed in transformer oil. They obtained a static breakdown voltage of 30 kV for positive polarity of the point and 36 kV for negative polarity of the point. In our experiments with specimens having a conical recess, at an average specimen thickness of 0.7 mm, i.e., almost 4 times smaller, the breakdown voltage at a voltage exposure time of the order of \(10^{-6}\) sec, when there is still no discharge lag, was 40 kV for positive polarity of the point and 43 kV for negative polarity of the point. In experiments with plates of average thickness 0.7 mm, we also obtained a low breakdown voltage: 18 kV for positive polarity of the point and 21 kV for negative

polarity of the point. Apparently, surface discharges considerably reduce the breakdown voltage of a solid dielectric.

The authors of [6] indicate that breakdowns were often observed on the tail of the pulse, and the same cases were observed in the breakdown of one transformer oil. In our experiments with specimens having a conical projection, no such cases were observed. Walter and Inge [6] obtained discharge delay times quite different from our data. In their experiments, the increase in breakdown voltage begins at a voltage action time of \(3 \div 7 \cdot 10^{-6}\) sec; in our experiments, at a voltage action time of \(2.5 \div 6 \cdot 10^{-7}\) sec, that is, an order of magnitude smaller.

Examination of the discharge paths in KCl specimens showed that the discharge, both for negative polarity of the point and for positive polarity, goes along the shortest path—in the direction [100]. For KBr and KJ it was not possible to examine the discharge paths.

Breakdown of Organic Glass

Specimens of organic glass of thickness \(0.12 \pm 0.02\) mm were broken down for both polarities of the point and two voltage action times. Fig. 5 presents the experimental results. The voltages are taken at a breakdown probability \(\psi = 90\%\). Each point is the result of processing 7–13 oscillograms. The same regularities are observed as for crystalline dielectrics.

Conclusions

1. The method of breakdown testing of specimens with a conical projection eliminates the influence of the surrounding medium on the breakdown voltage of a solid dielectric.

2. At short voltage action times \((6 \cdot 10^{-8} \div 2 \cdot 10^{-7}\ \text{sec})\), a delay of the discharge is observed.

3. At short voltage action times \((6 \cdot 10^{-8} \div 2 \cdot 10^{-7}\ \text{sec})\), the polarity effect is clearly manifested, similar to the polarity effect in air. This indicates the presence of ionization processes in the dielectrics studied, beginning near the point. This regularity holds for crystalline dielectrics and for an amorphous dielectric (organic glass).

4. In a nonuniform field, the breakdown voltage is also a characteristic of the material. For alkali-halide crystals in a nonuniform field, an increase in breakdown voltage occurs with increasing lattice energy.

The present work was carried out at the suggestion and under the scientific supervision of Professor-Doctor A. A. Vorob’ev, to whom the author expresses sincere gratitude.

References

1. A. Vorob’ev and N. Prikhod’ko, Proceedings of SFTI, vol. 4, no. 3, 112–126, 1936.
2. A. P. Aleksandrov, A. F. Walter et al., Physics of Dielectrics, GTTI, Moscow—Leningrad, 1932.
3. A. A. Vorob’ev and V. D. Kuchin, ZhTF, in press.
4. G. A. Vorob’ev, ZhETF, vol. 30, no. 2, 256–261, 1956.
5. A. A. Vorob’ev, ZhTF, 10, 183, 1940.
6. A. F. Walter and L. D. Inge, ZhTF, vol. III, no. 6, 840–849, 1933.
7. A. A. Vorob’ev, G. A. Vorob’ev and V. D. Kuchin—present issue, p. 193.

Tomsk Polytechnic Institute