TEMPERATURE DEPENDENCE OF THE PROCESSES OCCURRING DURING ELECTRICAL BREAKDOWN OF IONIC CRYSTALS

V. D. Kuchin

(Presented by Professor, Doctor A. A. Vorob’ev)

Theories of the breakdown of ionic crystals still provide only very limited and highly approximate data on certain physical processes occurring during breakdown (for example, the time and rate of development of the discharge, etc.), and still more limited data on their variation as the external conditions with respect to the crystal change (temperature, degree of overvoltage, etc.). Experimental data on these processes are few in number because of the difficulties in carrying out the experiment, since breakdown proceeds in an insignificant volume of the crystal (\(10^{-4}\ \mathrm{cm}^3\)) and over ultrashort times (of the order of \(10^{-8}\)—\(10^{-9}\ \mathrm{sec}\)).

It is customary to regard the electrical breakdown of solid dielectrics as an electronic process. Therefore, some authors believe that the delay time of the discharge in the general case is made up of two components: the statistical delay time and the time of formation of the discharge.

Thus, Strigel [1], Inushi and Suita [2], without proof, by analogy with gases divide the delay time of the discharge in solid dielectrics into two components. Seitz [3] pointed out that in each individual case an electron avalanche of a definite magnitude is needed for the destruction of a dielectric. For the destruction of a NaCl crystal \(1\ \mathrm{cm}\) thick, according to Seitz, \(10^{12}\) electrons are required. The appearance of such an avalanche in a given field \(F\) has a certain probability \(\beta\). Seitz considers the quantity \(1/\beta\) to be the statistical delay time of the discharge. The probability of the appearance of an avalanche \(\beta\) depends on the probability of the appearance of a free electron \(\nu\). Since the value of \(\nu\) is at present unknown, Seitz does not indicate the magnitude of the statistical delay time.

The existence of a statistical delay time of the discharge in solid dielectrics is questioned by some investigators. Unfortunately, there are as yet no data that would make it possible to mark the beginning of discharge formation. Whitehead [4] believes that in real ionic crystals there is always a certain number of free electrons due to the absorption of various radiations, thermal vibrations, and the presence of defects in the crystals. Confirmation of this may be seen in the experiments of Walter and Inge [5] and Vorob’ev [6], who obtained the same strength for X-rayed and non-X-rayed rock salt at short times. These experiments show that the number of electrons before breakdown should not have a large influence on the process of discharge formation.

Crowe [7] points out that during breakdown of highly purified liquids (hexane, heptane, octane, etc.) there is no statistical delay time of the discharge, because at fields above \(1 \cdot 10^5\ \mathrm{V/cm}\) cold emission from the cathode is a good supplier of electrons. In [8] it is indicated that for cold emission from the cathode a field strength of \(300\ \mathrm{kV/cm}\) is required. It may be assumed that at fields of \(1 \cdot 10^6\ \mathrm{V/cm}\) and above it

should also be present. It is also possible that, at these fields, electrostatic ionization occurs. Both types of ionization are the cause of the appearance of free electrons in the dielectric.

Consequently, in ionic crystals the statistical lag time is practically absent, and the discharge time may be taken to be the time of formation of the discharge.

Whitehead [4] determined the electron velocity before the act of ionization at \(E = I = 10\) eV to be \(v = 1.88 \cdot 10^8\) cm/sec, and the time required to attain this velocity in a field \(F\) to be \(t_1 = 1.07 \cdot 10^{-7}/F\) sec. For fields \(F^* = 10^7\) V/cm, \(t_1 = 10^{-14}\) sec. In this case the electron mean free path is \(\lambda > 10^{-6}\) cm. According to Fröhlich, the time during which the average electron has the smallest mean free path (during breakdown) is \(t_p = t_1 e^{t/\tau}\), where \(\tau\) is the time between two electron collisions. If \(\tau = (10^{-13}—10^{-15})\) sec, then \(t_p \cong 2 \cdot 10^{-10}\) sec. According to Simpson’s calculations [9], which likewise do not take into account the statistical discharge time, \(t_p = (5 \cdot 10^{-10}—5 \cdot 10^{-12})\) sec. From oscillograms Walter and Inge [10] found that the time of development of the discharge in ionic crystals is \(3 \cdot 10^{-8}\) sec.

Knowing the time of discharge formation, one can determine the average velocity of propagation of the discharge as \(\bar v = \bar d/t_p\), where \(\bar d\) is the average thickness of the specimens at the breakdown site. Thus, according to Simpson’s calculations [9], for \(d = 10^{-2}\) cm we have \(v = (5 \cdot 10^8—5 \cdot 10^{10})\) cm/sec. According to Fröhlich’s theory [11], the average velocity of free electrons is \(v = EF\tau/2m \cong 0.9 \cdot 10^{15}F\tau\). For the values of \(F^*\) and \(\tau\) adopted above, \(v = (10^7—10^9)\) cm/sec, which gives \(t_p = (10^{-9}—10^{-10})\) sec. In reality, the discharge time in ionic crystals is greater, since the theoretical calculations do not take into account the time required for the electron avalanche to propagate through the thickness of the dielectric.

Hippel and Alger [12], Vorob’ev [6], Kuchin [13], and Vorob’ev and Kuchin [14] obtained an increase in the electric strength of ionic crystals at voltage exposure times shorter than \(10^{-7}\) sec. We consider that the statistical lag time of the discharge in ionic crystals is absent, and that the increase in \(F^*\) for pulses shorter than \(10^{-7}\) sec is explained by the lag of the discharge. The experiments of Inushi and Suita [15] and of Sonchik [16] on the breakdown of solid dielectrics by rectangular pulses convincingly showed that, in solid dielectrics, a discharge lag time exists.

Vorob’ev [6] calculated the time and velocity of discharge formation for alkali-halide crystals under the assumption that the statistical lag time of the discharge is absent.

The time of discharge development was determined from oscillograms as the time during which the intensity of the external electric field on the specimen changes from \(F_0^*\) to \(F_t^*\), where \(F_0^*\) is the electric strength of the given dielectric at such a voltage exposure time for which no discharge lag is yet observed (in our case, as \(F_0^*\) we took the electric strength at a voltage exposure time of the order of \((10^{-6}—10^{-7})\) sec), and \(F_t^*\) is the electric strength of the same dielectric at a voltage exposure time \((1.2—3.1) \times 10^{-8}\) sec. It was assumed here that discharge formation begins when the field intensity in the dielectric reaches the breakdown value for a voltage exposure time of the order of \((10^{-6}—10^{-7})\) sec.

Using the data obtained on the time dependence of the electric strength of NaCl, KCl, KBr, and KJ [13], let us determine the time and velocity of development of the discharge and their changes with temperature.

Figure 1 shows the change in time, and Fig. 2 the change in the velocity of discharge formation as a function of temperature for NaCl, KCl, KBr, and KJ crystals. If one takes into account the approximate nature of the calcu-

then the agreement of the obtained data \(t_p\) and \(v\) with the conclusions from Fröhlich’s theory should be considered satisfactory.

The values of \(v\) also agree with the data of Vorob’ev and Sonchik. The value found for \(v\) for KCl is considerably higher than that of Inuishi and Suita. For a voltage application time of \((1.2—3.1)\cdot 10^{-8}\) sec, the discharge-development time decreases, while the average discharge velocity increases with decreasing crystal-lattice energy over the entire temperature interval investigated. As in [6, 13], for KCl a certain deviation from direct proportionality is observed: the values of \(F^*\) and \(t\) are obtained somewhat too high.

The dependences shown in Fig. 2 can be given the following explanation. With increasing temperature the crystal-lattice constant increases,

Fig. 1. Dependence of the discharge-formation time in NaCl, KCl, KBr, and KJ crystals on temperature.

Fig. 2. Dependence of the discharge-formation velocity in NaCl, KCl, KBr, and KJ crystals on temperature.

and consequently the electron mean free path also increases. Therefore, with increasing temperature the rate of discharge development should increase, which is indeed observed. However, as the temperature increases above \(T_k\), the thermal vibrations of the ions sharply increase, which leads to a decrease in the discharge-formation velocity. The maximum velocity \(v\) corresponds to the critical temperature \(T_k\) of the ionic crystal. With decreasing crystal-lattice energy, the maximum of the discharge-formation velocity shifts toward higher temperatures.

References

1. Strigel R., Elektrische Stossfestigkeit, Berlin, 1939.
2. Inuishi Y. and Suita T., J. Phys. Soc. Japan, 9, 431, 1954.
3. Seitz F., Phys. Rev., 76, 1376, 1949.
4. Whitehead S., Dielectric Breakdown of Solids, Oxford, 1951.
5. Val’ter A. F. and Inge L. D., DAN SSSR, 2, 65, 1934.
6. Vorob’ev G. A., Izv. TPI, 91, 79, 1956.
7. Crowe R. W., J. Appl. Phys., 27, 155, 1956.
8. Edited by L. I. Sirotinskii, High-Voltage Engineering, pt. 1, GEI, 1951.
9. Simpson J. H., ERA Report L/T178, 1947.
10. Val’ter A. F. and Inge L. D., Physics of Dielectrics, GTTI, 1932.
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12. Hippel A. and Alger R. S., Phys. Rev., 76, 127, 1949.
13. Kuchin V. D., Report at the All-Union Conference on the Physical Properties of Solid and Liquid Dielectrics, Dnepropetrovsk, 1956.
14. Vorob’ev G. A. and Kuchin V. D., Izv. TPI (in the present issue).
15. Inuishi Y. and Suita T., J. Inst. El. Eng. Japan, 74, 150, 1954.
16. Sonchik K. K., Report at the All-Union Conference on the Physical Properties of Solid and Liquid Dielectrics, Dnepropetrovsk, 1956.