DEPENDENCE OF THE ELECTRIC STRENGTH OF SOME SOLID DIELECTRICS ON THE DURATION OF VOLTAGE APPLICATION

G. A. VOROB'EV

Introduction

The question of the dependence of the electric strength of a dielectric on the duration of voltage application is of great importance for the physics of dielectrics. Knowledge of these dependences brings us closer to elucidating the breakdown process and to determining the role of various factors in the mechanism of dielectric breakdown.

Since breakdown of solid dielectrics is a material process and, consequently, takes place in space and time, all theories of breakdown of solid dielectrics must predict an increased electric strength of the dielectric for short durations of voltage application, comparable with the duration of the breakdown process. If a dielectric is subjected to a low voltage of short duration, breakdown may not occur—there will not be enough time for the breakdown to be completed. In order for breakdown to occur during the time of voltage application, an increased voltage must be applied to the dielectric, at which the breakdown process proceeds more rapidly. However, in most theories of breakdown of solid dielectrics this question has not been developed.

Whitehead [1] calculated, on the basis of Fröhlich’s theory, the time required to accelerate an electron to the ionization energy. This time was found to be of the order of \(10^{-10}\) sec.

Seitz [2] took into account the role of individual electrons in the breakdown process. He points out that individual electrons can produce ionization at an electric-field strength at which electrons with average energy cannot produce ionization. Seitz then calculates the probability of the formation of an electron avalanche during its passage through the thickness of a specimen, which would lead to destruction of the solid dielectric. This probability, according to Seitz, is the greater, the greater the strength of the applied field. The quantity reciprocal to this probability will be the mean time between two destructive avalanches and was called by Seitz the statistical time lag of the discharge. Consequently, this time is the smaller, the greater the strength of the applied field.

The available experimental data on the influence of the duration of voltage application on the magnitude of the electric strength of solid dielectrics are few and contradictory. Many experimental studies have major methodological shortcomings: the uniformity of the field was disturbed by edge discharges; an electronic oscilloscope was not used to record the time and breakdown voltage. Such studies include the works of Yost and Schriel.

In a number of other works (those of Keller and Plesner) the dependence of the electric strength of a solid dielectric on time is due not

by discharge lag, which is of greatest interest to us, but by thermal, polarization, and other phenomena.

The works of Walter and Inge [3], Dittert [4], and Hippel and Alger [5] deserve consideration.

A. F. Walter and L. D. Inge [3] found the electric strength of glass to be independent of the duration of voltage application over the range from \(10^{-7}\) to \(1\) sec.

Analogous results for Bakelized paper over the time range from \(10^{-8}\) to \(10^{-1}\) sec are reported by Dittert [4].

Hippel and Alger [5] obtained an interesting dependence for KBr single crystals. As the duration of voltage application is decreased, the electric strength remains constant from long times down to \(10^{-4}\) sec, then decreases and, at a time of \(5 \cdot 10^{-5}\) sec, reaches a minimum, then increases. At a time of \(1\ \mu\)sec the electric strength reaches its initial value, and at a time of \(1.7 \cdot 10^{-8}\) sec it exceeds the initial value by 33%.

Japanese investigators Kawamura, Okura, and Kikuchi [6] attempted to test experimentally Seitz’s theory of statistical lag time. They did not find discharge lag for glass and KCl (the discharge lag time, according to their data, was no more than \(3 \cdot 10^{-8}\) sec), but for mica the lag time obtained at a 10% overvoltage was of the order of \(10^{-4}\) sec. This time is too large and, evidently, is due to defects in the method.

Thus, there are no reliable data on the discharge lag time or on the rates of discharge development for various solid dielectrics. Systematic investigations are required. We investigated the dependences of the electric strength of single crystals of NaCl, KCl, KBr, and KJ, as well as of organic glass, on the duration of voltage application in a uniform field.

Experimental Method

Natural rock salt was used for the experiments. Single crystals of KCl, KBr, and KJ were grown from the melt. In the specimens of the dielectrics studied, a spherical recess was drilled out. The surfaces of the specimen were polished, after which they were coated with a layer of tin by spraying the latter in vacuum.

Fig. 1. Diagram of the setup for testing dielectrics for breakdown at voltage-application times from \(10^{-7}\) sec to \(10^{-4}\) sec. \(T_p\)—transformer, \(R_3\)—protective resistance; \(B\)—rectifier, \(P\)—trigatron, \(R_B\) and \(C_B\)—resistance and capacitance of the time delay, \(C_1\), \(R_1\), \(C_2\), \(R_2\)—parameters of the generator circuit, \(r_0\) and \(R_0\)—current-limiting resistances; Д. Н.—voltage divider; И. О.—test object. П. Я.—plates of the oscilloscope tube; П—switch for connecting the test object.

The thickness of the samples of NaCl, KCl, KBr, and KJ single crystals at the thinnest point, where breakdown occurs, was usually \(150 \pm 10\ \mu\text{m}\). For a voltage-application time of \(2 \div 3 \cdot 10^{-8}\) sec, the thickness of the NaCl samples was \(100 \pm 10\ \mu\text{m}\), and that of the KCl samples was \(120 \pm 10\ \mu\text{m}\). The thickness of the organic-glass samples was \(50 \pm 10\ \mu\text{m}\).

Fig. 2. Circuit diagram of the setup for breakdown testing of dielectrics with voltage-application times of the order of \(10^{-8}\) sec.
Tr — transformer; \(R_{\text{з}}\) — protective resistance; B — rectifier; P — trigatron; \(R_0\) — current-limiting resistance; Π — switch for connecting the test object, I. O.; I. O. — test object; P. Ya — oscilloscope phenomenon plates; \(C_1\) — generating capacitance; \(L\) — parasitic inductance of the generator circuit; \(R_1\) and \(R_2\) — resistances (discharge) of the voltage divider (D. \(H_1\)) for the time circuit; \(r_{\text{в}}\) and \(C_{\text{в}}\) — resistance and capacitance of the time circuit; D. \(H_2\) — voltage divider for P. Ya; P. V — time plates.

In experiments with impulse voltage, an electronic oscillograph was used as the measuring and recording instrument.

For voltage-application times of \(10^{-7} \div 10^{-4}\) sec, the ordinary circuit of an impulse generator was used (Fig. 1), producing a voltage pulse whose mathematical expression is \(U = A(e^{p_1 t} - e^{p_2 t})\). A trigatron was used as the switching element.

Fig. 3. Circuit diagram of the setup for breakdown testing of dielectrics with voltage-application times of the order of \(10^{-1}\) sec.
Tr — transformer; \(R_{\text{з}}\) — protective resistance; B — rectifier; C — generating capacitance; R — current-limiting resistance; I. O. — test object; P. Ya — oscilloscope phenomenon plates; P. V — time plates; \(R_{\text{в}}\), \(C_{\text{в}1}\), \(C_{\text{в}2}\) — parameters of the time circuit; \(R_{\text{я}}\), \(C_{\text{я}1}\), \(C_{\text{я}2}\) — parameters of the phenomenon circuit; P — mechanical switch; Π — switch.

For synchronization of the operation of the impulse generator and the electronic oscillograph, a time-delay circuit \((R_{\text{в}}, C_{\text{в}})\) and a spark relay were used.

For voltage application times of \(2 \div 3 \cdot 10^{-8}\) sec, a generator consisting of a capacitance and a resistance was used (Fig. 2). In this case the length of the pulse front was determined by the parasitic inductance of the condenser and of the generating circuit, and by the parasitic capacitance.

Fig. 4-a. Calibration oscillations with a frequency of 50 Mc,

Considerable difficulty at short times is presented by synchronizing the triggering of the pulse generator and the time sweep of the oscillograph. In order that the impulse would always appear on the oscillograph screen, triggering of the sweep from the phenomenon under investigation was used.

Fig. 4-b. Calibration oscillations with frequency \(f = 100\) kc,

For a voltage application time on the order of \(10^{-1}\) sec, a mechanical switch designed by A. F. Kalganov was used as the commutating element. The transition from an arc to mechanical switching was made because it is difficult to count on the stability of an arc over a long period at its low power, which occurs in the present case. When the mechanical switch is closed, the generating capacitance charges, through high-ohmic resistances, two other capacitances. The voltage on one capacitance is used for breakdown of the specimen; the voltage on the other capacitance—for the time sweep (Fig. 3).

Fig. 4-v. Calibration oscillations with a frequency of
\(1\) Mc/s.

For breakdown at constant voltage, a high-voltage electrostatic voltmeter of type S 96 was used as the measuring instrument.

Fig. 4-g. Voltage application time on the order of \(10^{-7}\) sec.

Figure 4 presents oscillograms of breakdown for different durations of voltage application.

Experimental Results

In breakdown tests of single crystals of NaCl, KCl, KBr, and KJ, for each duration of voltage application, as a rule, 20–30 specimens were taken. Statistical processing of the experimental points was carried out according to the probability of breakdown. Taking into account that the greatest strength is found in the cleanest and most defect-free specimens, we took as the principal values the electric strength at a breakdown probability \(\psi = 90\%\). In Fig. 5—

Fig. 5. Dependence of the electric strength of single crystals of NaCl, KCl, KBr, and KJ on the duration of voltage application.

Fig. 6. Dependence of the electric strength of organic glass on the duration of voltage application.

—the experimentally obtained dependences of the electric strength of single crystals of NaCl, KCl, KBr, and KJ on the duration of voltage application are presented, for a breakdown probability \(\psi = 90\%\). Figure 6 presents an analogous dependence for organic glass, for which from 9 to 13 specimens were taken for each point. Data were obtained for breakdown of X-rayed rock salt under illumination and in the dark, for voltage-application times of \(2 \div 3 \cdot 10^{-8}\) sec. At a breakdown probability \(\psi = 90\%\), we have the following data:

Unirradiated rock salt
\[ E_{\mathrm{br}} = 2740\ \text{kV/cm}. \]

X-rayed rock salt
broken down in the dark
\[ E_{\mathrm{br}} = 2690\ \text{kV/cm}. \]

X-rayed rock salt
broken down under illumination
\[ E_{\mathrm{br}} = 2800\ \text{kV/cm}. \]

The difference in the cited values of electric strength is small, and it may be considered that the electric strength of unirradiated rock salt and of X-rayed rock salt, broken down in the dark and under illumination, is practically one and the same.

For all the solid dielectrics investigated by us, an increase in electric strength was obtained at short durations of voltage application. For single crystals of NaCl, KCl, KBr, and KJ, a certain increase in electric strength was obtained for voltage-application times

on the order of \(10^{-5}\) sec. The rock-salt specimens also broke down under dc voltage and pulsed voltage with voltage-application times on the order of \(10^{-4}\) and \(10^{-1}\) sec. The electric strength obtained in these experiments practically coincides with the electric strength for a voltage-application time on the order of \(10^{-5}\) sec.

Discussion of the Results

A higher electric strength of ionic crystals under dc voltage, as compared with pulsed voltage, has been obtained by many investigators. This effect is attributed to the influence of space-charge formation.

B. M. Gokhberg and A. V. Ioffe [7] believe that the space charge creates in the dielectric a field opposite to the applied one, and that a higher applied voltage is required for breakdown of the dielectric.

Evidently, in our experiments with a voltage-application time on the order of \(10^{-5}\) sec, a space charge had time to form, which led to an increase in electric strength.

The increase in the electric strength of the dielectrics studied for a voltage-application time of \(1 \cdot 10^{-7}\) sec and less is caused by the delay of the discharge. The delay of the discharge may be associated with two circumstances: during the short time in which the voltage acts, there may be no free effective electrons; or the time of formation of the discharge is comparable with the time of voltage application. In our opinion, the first circumstance does not apply to solid dielectrics with high electric strength.

In solid dielectrics, at electric-field strengths close to breakdown, significant electrostatic ionization takes place, which supplies electrons. The fact, indicated above, of the equal electric strength of non-X-irradiated and X-irradiated rock salt supports the argument that free electrons exist in a solid dielectric at high field strengths.

If, in X-irradiated rock salt, at high field strengths, at least one electron is produced in the volume during the discharge delay time under intense illumination, this will prove that free electrons also appear in non-X-irradiated rock salt at high field strengths.

Let us make a rough calculation. Take an electrode area with a diameter of \(0.5\) mm. The electric-field strengths under this area may differ by at most 6% (for a specimen thickness of \(0.1\) mm and a curvature radius of the point of 10 mm), which is within the limits of measurement accuracy. When X-irradiated rock salt is illuminated, as Walter and Inge [8] indicate, \(10^{14}\) free electrons are formed in \(1\ \mathrm{cm}^3\) in 1 sec. In the volume of X-irradiated rock salt between the electrodes, with their diameter \(0.5\) mm and a thickness of \(0.1\) mm, during \(10^{-8}\) sec\(^1\) there are formed

\[ 10^{14}\cdot \frac{\pi \cdot 0.5^2 10^{-2}}{4}\,10^{-1}\cdot 10^{-8}=19 \]

free electrons. Consequently, the delay of the discharge in the solid dielectrics studied is due not to the absence of free electrons, but to the duration of the process of discharge formation. Therefore, the discharge-delay time in the dielectrics studied is the time of discharge formation under the given conditions of voltage application.

\(^1\) It will be shown below that the time of discharge formation in the dielectrics studied is \((1\text{–}3)\,10^{-8}\) sec.

Seitz’s theory of the statistical time lag, in our opinion, is not applicable to “thick” layers with a thickness of 100 microns or more. At such a thickness, an electron avalanche that has begun, after passing through the dielectric thickness, under any conditions—if it does not die out—will reach a magnitude sufficient to destroy the dielectric. However, Seitz’s idea concerning the role of individual electrons is interesting and worthy of attention. The development of the discharge may take place under more or less favorable conditions. Favorable conditions for breakdown are created in the dielectric with some statistical probability. For long times of voltage application, breakdown occurs in the overwhelming majority of cases under favorable conditions, and the scatter in the values of the electric strength of solid dielectrics is due to particular differences in the structure (microcracks, defects in specimen preparation, impurities, etc.) of different specimens. At short times of application, to this cause of scatter there is added scatter due to differences in the time of discharge formation in different specimens. Therefore, in the general case, the scatter in the values of electric strength at short times of voltage application is greater than at long times. This is known for air and is confirmed for the solid dielectrics we investigated, as shown by the data in Table 1.

Table 1

Consequently, the time of discharge formation in the dielectrics investigated is statistical in character, as has long been established for air.

Table 2 gives the calculated values of the discharge formation time and the mean velocity of discharge development for the dielectrics investigated. The calculations refer to the values of electric strength at a breakdown probability $\psi = 90\%$. The discharge formation time was determined from the graph, as shown in Fig. 7. The curves of voltage variation used in the calculation were taken from the oscillogram. Assuming that, during formation, the discharge passes through the entire thickness of the dielectric, one can calculate the mean velocity of discharge development

$$ V_{\mathrm{av}} = \frac{d}{t_{\phi}}. $$

The data of Table 2 show that, with increasing overvoltage, the discharge formation time decreases, and the mean velocity of discharge development increases, as was to be expected.

For a voltage application time of $2 \div 3 \cdot 10^{-8}$ sec, the discharge formation time decreases and the mean velocity of discharge development increases in going from NaCl to KJ, i.e., with decreasing lattice energy and increasing lattice constant (Fig. 8). For a voltage application time of $6 \div 9 \cdot 10^{-8}$ sec, no definite pattern was obtained.

The velocities of discharge development in the dielectrics investigated are of the order of $10^{6}$ cm/sec, while the velocity of electron avalanches in air is about $10^{7}$ cm/sec, although the field strength in the latter case is several tens of times ...

Table 2

Notes: 1. The time \(t_{\phi}\) is reduced to the thickness \(d = 150\ \mu\) by the formula

\[ t_{\phi} = t_{\phi\,\mathrm{act.}} \frac{150}{d}. \tag{2} \]

1. Since, during the formation of the discharge, in the present case the voltage did not remain constant but was increasing, the mean overvoltage indicated in Table 2 was adopted and calculated from the formula

\[ \eta = \frac{U_t - U_{\mathrm{stat}}}{2U_{\mathrm{stat}}}\,100\%. \]

Fig. 7. Graph for determining the time of discharge formation \((t_{\phi})\).

Fig. 8. Dependence of the time of discharge formation \((t_{\phi})\) and the average rate of discharge development \((V_{\mathrm{av}})\) on the lattice energy of crystals NaCl (○ ○), KCl (● ●), KBr (× ×), and KJ (△ △).

smaller. Evidently, the motion of an electron in a solid dielectric is strongly hindered by frequent collisions with ions (or atoms) and by their strong electrostatic influence. On the basis of the data on the rate of development, it may be stated that the discharge time in a solid dielectric is approximately an order of magnitude greater than in air for the same distance between the electrodes.

As oscillograms show, for short times of voltage application the voltage drop across the specimen during breakdown has a certain duration. For the dielectrics investigated, this duration lies in the range from \(2 \cdot 10^{-9}\) to \(1.5 \cdot 10^{-8}\) sec and averages \(7 \cdot 10^{-9}\) sec. Thus, the process of breakdown of a solid dielectric may be divided into 2 stages: the stage of discharge formation, at the end of which high electrical conductivity is created, and the stage of completion of breakdown, when the resistance of the breakdown channel falls practically to zero and the voltage across the specimen decreases to zero.

A. A. Vorob’ev [9] noted a proportionality between the electric strength and the lattice energy of alkali-halide salts. The curves in Fig. 5 show that the indicated dependence also holds in the present case over the entire investigated time interval from \(10^{-5}\) to \((2 \div 3) 10^{-8}\) sec.

Conclusions

1. For single crystals of NaCl, KCl, KBr, and KJ, a certain increase in electric strength was observed at a voltage-application time of the order of \(10^{-5}\) sec, which is evidently connected with the formation of a space charge in the specimen.

2. For all the dielectrics investigated, at a voltage-application time of \(1 \cdot 10^{-7}\) sec and less, an increase in electric strength was obtained, associated with the delay of the discharge.

3. The discharge-delay time, determined by calculation, proved to be of the order of \(10^{-8}\) sec. The discharge-formation time
   a) decreases with increasing overvoltage;
   b) at a voltage-application time of \((2 \div 3) 10^{-8}\) sec decreases with decreasing lattice energy and with increasing lattice constant;
   c) is statistical in character.

4. The average rate of discharge development in the dielectrics investigated is of the order of \(10^{6}\) cm/sec.

5. The time of voltage drop across the specimen during breakdown for the dielectrics investigated averages \(7 \cdot 10^{-9}\) sec.

6. The breakdown of the solid dielectrics investigated may be divided into 2 stages: the stage of discharge formation and the stage of completion of breakdown.

7. The electric strength of single crystals of NaCl, KCl, KBr, and KJ over the entire investigated time interval is proportional to the lattice energy.

The present work was carried out under the scientific supervision of A. A. Vorob’ev, to whom the author expresses sincere gratitude.

References

1. S. Whitehead, The Dielectric Breakdown of Solids, Oxford, Clarendon Press, London, 1951.

2. F. Seitz, Phys Rev., 76, 1376, 1949.

3. A. F. Walther and L. D. Inge, ZhRF, 6, 3, 1929.

4. Dittert, Dissertation, Dresden, 1930.

5. A. von Hippel and R. S. Alger, Phys. Rev., 76, No. 1, 127—133, 1949.

6. H. Kawamura, H. Ohkura and T. Kikuchi, Journ. Phys. Soc. Japan, 9, No. 4, 541—545, 1954.

7. B. M. Gokhberg and A. V. Ioffe, ZhETF, 1, 1264, 1931.

8. A. F. Walther and L. D. Inge, DAN SSSR, 2, No. 2, 65—71, 1934.

9. A. A. Vorob’ev, ZhTF, 10, 183, 1940.

Tomsk Polytechnic Institute

Errata