EXPERIMENTAL REGULARITIES OF ELECTRONIC PROCESSES IN IONIC CRYSTALS REQUIRING THEORETICAL GENERALIZATION

A. A. Vorob’ev

The physical properties of ionic crystals are determined by the lattice energy and by external conditions. The lattice energy of compounds increases in proportion to the product of the valences of the ions and inversely proportional to the sum of the ionic radii. Accordingly, in keeping with the periodic change in the properties of chemical elements in Mendeleev’s table, the energy of the crystal lattice of chemical compounds also changes periodically.

Fig. 1. Change in lattice energy for crystals of alkali-halide salts as a function of chemical composition.

In Fig. 1 are shown the changes in lattice energy for crystals of alkali-halide salts with composition.

The compounds are arranged in order of increasing radii of anions and cations and increasing ratio of the cation radius to the anion radius. The increase in the dimensions of the elementary cell with increasing ionic radii is accompanied by a decrease in lattice energy, occurring periodically. Replacement of the anion at a constant cation, or replacement of the cation at a constant anion, is accompanied by a monotonic change in lattice energy. The transition to halide compounds of another metal, or to compounds of metals with another halide, is accompanied by a transition to another curve.

The binding energy between neighboring ions in the crystal lattice must manifest itself in physical processes associated with displacement from the equilibrium position or with the release of electric charges. The stronger the bonds between neighboring ions, the more difficult it will be for them to be displaced;

or for particles to be freed from their equilibrium position, the greater the energy that must be expended in order to produce a physical process or phenomenon.

With an increase in lattice energy, the stability of compounds increases, the hardness of single crystals rises (Fig. 2), as does the melting temperature (Fig. 3) and the electric strength (Fig. 4); electrical conductivity decreases (Fig. 5), dielectric losses decrease, and other characteristics of crystals also change in a regular manner.

Fig. 2. Dependence of the hardness of single crystals on the energy of their lattice.

Studies have shown that the energy required for electronic processes to occur in ionic crystals depends on the magnitude of the lattice energy and, consequently, changes regularly with the chemical composition of the compound.

The increase in lattice energy for crystals of compounds of metals of the first and second groups is associated with a decrease in electronic polarizability (Fig. 6), the electronic component of the dielectric constant, and the refractive index (Figs. 7 and 8). In crystals of alkali-halide salts, with increasing lattice energy, intrinsic absorption in the ultraviolet region of the spectrum and the maximum of the absorption band shift toward shorter wavelengths. According to the measurements of A. D. Shchelokov [1], with increasing lattice energy the absorption of X-rays (Fig. 9) and the luminescence of alkali-halide salt crystals caused by them decrease.

The same regularities are also observed in specimens pressed from powders.

The absorption of X-rays is determined mainly by the number \(z\) of electrons in the atom. The absorption of X-rays in a molecule of alkali-halide compounds is determined by a certain effective number of electrons, which is associated with the lattice energy.

The crystal lattice as a whole, its energy state, and the bonds and interactions existing within it are of important and decisive significance for any electronic processes, including optical processes, in the crystal. The lattice as a system perturbing luminescence centers manifests itself in the processes of luminescence and temperature glow of crystals. In this connection it is interesting to note the presence of a vibrational structure, discovered by some researchers in luminescence spectra—

Fig. 3. Dependence of the melting temperature of ionic crystals on lattice energy.

of the luminescence of crystalline substances and indicating the existence of a direct interaction between lattice vibrations and the electronic transitions responsible for luminescence. Thus, P. S. Litvinova [2] established a similar structure in the photoluminescence spectra of zinc oxide (ZnO).

V. A. Sokolov [3] has recently found a clearly expressed vibrational structure in the spectra of thermal glow, or so-called

Fig. 4. Dependence of electrical strength on lattice energy.

Fig. 5. Dependence of the electrical conductivity ($\sigma$, $\Omega^{-1}\cdot\mathrm{cm}^{-1}$) of alkali-halide crystals at temperatures of 400 (×), 600 (○)°C on lattice energy.

“candoluminescence,” of magnesium oxide and aluminum oxide, which testifies to the presence of close interaction between lattice vibrations and optical electronic transitions in these cases as well.

Of considerable interest are the experimental and theoretical regularities of electron mobility in dielectrics and semiconductors. There exists a satisfactory theory of the temperature dependence of electron mobility in semiconductors and dielectrics, a theory that agrees well with experimental results.

The available experimental data on electron mobility in dielectrics are not numerous [4]. The experiments of V. I. Pruzhanina-Granovskaya [5] on measuring the resistance of mica in a magnetic field and of P. E. Sarzhevsky [6] on the investigation of quartz in strong electric fields are known. According to these authors, the mobility of electrons does not remain constant in high fields, and under certain conditions decreases with increasing field strength according to the laws $u \sim \frac{1}{E}$ and $u \sim \frac{1}{\sqrt{E}}$ (Fig. 10).

Fig. 6. Dependence of electronic polarizability on lattice energy at $\lambda = 5\,893\ \text{Å}$.

For dielectrics in strong fields there is a deviation from Ohm’s law. It is manifested in the constancy of the current when the field strength is varied.

N. P. Kalabukhov [7] observed a saturation current in the photoconductivity of X-irradiated NaCl. In his experiments, a constant value of the photocurrent occurred at a field strength of \(\sim 10^3\) V/cm and followed the region in which Ohm’s law is obeyed.

Fig. 7. Dependence of the electronic component of the dielectric permittivity and of the refractive index of alkali-halide salt crystals on the lattice energy.

N. P. Kalabukhov explains the saturation current by the fact that the probability of capture of electrons by atoms depends on the velocity of motion of the electrons. In the region of the saturation current, the electrons apparently attain the velocity at which the probability of their capture by atoms is greatest. In this region of field strengths the scattering of electrons increases, their number in the total flux in the direction of the field decreases, and the current density retains a constant value. N. P. Kalabukhov also observed a saturation current in the photoconductivity of colored crystals of KCl and KJ.

It should be added to N. P. Kalabukhov’s explanation of the saturation current in dielectrics that, with increasing field strength,

Fig. 8. Dependence of the refractive index of alkali-halide salt crystals on the lattice energy at \(\lambda_D = 5\,893\) Å:
— lattice structure of the NaCl type; – – – lattice structure of the CsCl type.

not only the concentration of electrons may change, but also the mobility of the electrons, and the change in electron mobility with field strength may prove to be more essential in the phenomenon of saturation current.

In elastic collisions, an electron can transfer to traps or lattice sites a part of its kinetic energy equal to \(\frac{2m}{M} W_k\). As the velocity of electron motion increases, the amount of energy transferred increases. If the electron velocity assumes a constant value over some interval of field strength, then, consequently, the mobility of the electrons must vary inversely with the field strength.

A. Hippel [8] (Fig. 11) observed saturation of the photocurrent in colored KCl crystals. The saturation current was established at a field strength of \(600\ \text{kV/cm}\). The observation was carried out up to a field strength of

Fig. 9. Dependence of the absorption of X-rays by crystals of alkali-halide salts on lattice energy. \(100\ \text{kV}\), \(1\ \text{mm}\) Al filter, \(\Delta = 3.35\ \text{mm}\) Al, \(h = 1.59\), \(\lambda_{\text{eff}} = 0.34\ \text{Å}\).

Fig. 10. Dependence of the mobility \(v\) and the number of electrons \(n\) in high fields on field strength. Temperature \(355^\circ\text{C}\).

\(900\ \text{kV/cm}\). At \(920\ \text{kV/cm}\) breakdown of the specimen occurred. The current was measured at constant illumination of the specimen and, consequently, at an unchanged concentration of electrons in the specimen.

Thus, the phenomenon of photocurrent saturation in dielectrics is a fact indicating a change in electron mobility with field strength in dielectrics.

More detailed investigations have been carried out on the mobility of electrons in semiconductors, in particular in germanium.

E. D. Ryder [9] measured the mobility of electrons in \(n\)-type germanium in the range of field strengths up to \(2 \cdot 10^4\ \text{V/cm}\). In his experiments measures were taken to reduce thermal effects to a minimum. The voltage was applied to the specimen in the form of separate pulses of duration \(10^{-7}\ \text{s}\). The experiment showed that for germanium at room temperature Ohm’s law is valid up to fields of \(6 \cdot 10^2\ \text{V/cm}\). As the field increases, constancy of the current density is observed: \(i = nueE = \text{const}\). Consequently, if the current density retains a constant value as the field strength increases, then either the mobility or the concentration of electrons in germanium must decrease with increasing field. However, in the region of field strength where the current density remains constant, the electron velocity will also have a constant value (\(v = 10^7\ \text{cm/s}\)). This circumstance indicates that the mobility of the electrons decreases with field strength.

In the region of Ohm’s law the mobility of the electrons remains constan-

value. In stronger fields, where the current density is constant, the electron mobility decreases with increasing field strength according to the condition \(u \sim \frac{1}{E}\).

A well-known experimental investigation of the mobility of electrons in germanium \(n\), carried out by E. M. Conwell and E. D. Ryder [10], is known. The measurements were made with pulsed application of voltage. In these experiments the electron concentration remained constant. E. M. Conwell and E. D. Ryder observed a change in the mobility of electrons in germanium with a change in field strength.

From their experimental data it follows that the mobility of electrons in weak fields is determined by the scattering of electrons by impurities and is proportional to the cube of the electron velocity. Therefore, in the region of fields

Fig. 11. Photocurrent as a function of field strength in KCl crystals under irradiation by the green line of a mercury lamp \((\lambda = 5461\ \text{Å})\).

Fig. 12. Change in the mobility of electrons in germanium as a function of change in field strength.

where the current begins to increase more strongly than follows from Ohm’s law, an increase in electron mobility is first observed. Then, when scattering of electrons by the lattice becomes the principal factor determining the mobility of electrons, the mobility decreases with increasing field according to the law \(u \sim \frac{1}{\sqrt{E}}\). Such a character of the change in electron mobility with field strength was observed experimentally in germanium by E. M. Conwell and E. D. Ryder.

E. D. Ryder and W. Shockley [11] observed (Fig. 12) a deviation from Ohm’s law in germanium at a field strength \(E \approx 6 \cdot 10^{2}\ \text{V/cm}\). At this value of the field strength and above, the current remained constant. The electron concentration in their experiments remained unchanged up to a field strength \(E \approx 2 \cdot 10^{4}\ \text{V/cm}\). In the region of Ohm’s law the mobility of electrons remained constant. In stronger fields, where the current has a constant value, the electron mobility changes according to the condition \(u \sim \frac{1}{E}\).

E. D. Ryder and W. Shockley give a theoretical explanation of the results obtained. They show that the field strength at which a deviation from Ohm’s law is observed is determined by collisions of electrons with lattice vibrations. If the energy losses of electrons are due to elastic vibrations, then the limiting field strength corresponds approximately to \(\frac{v_{\text{sv}}}{u_{0}} = 150\ \text{V/cm}\), where \(v_{\text{sv}}\) is the velocity of longitudinal sound waves, and \(u_{0}\) is the mobility in small fields. If energy losses caused by optical vibrations of the lattice sites predominate, then the limiting field strength will be

above. The drift velocity at the limiting field strength is determined by the condition \(\left(\frac{h\nu}{m}\right)^{1/2}\) and assumes a constant value, numerically equal to \(\sim 10^7\) cm/sec. This value of the velocity is well confirmed experimentally for germanium.

Thus, detailed studies of germanium have shown that, for semiconductors, a decrease in electron mobility with increasing field is observed experimentally, which may occur according to the law \(u \sim \frac{1}{E}\) or \(u \sim \frac{1}{\sqrt{E}}\).

The experimental and theoretical data cited on the mobility of electrons in semiconductors and dielectrics make it possible to establish two regions of dependence of electron mobility on field strength. In the first region, corresponding to Ohm’s law, the mobility of electrons retains a constant value as the field strength increases. In the second region the mobility of electrons decreases with increasing field strength. The decrease in electron mobility occurs either according to the law \(u \sim \frac{1}{E}\), or \(u \sim \frac{1}{\sqrt{E}}\). For example, for the semiconductor germanium the limiting field strength is \(E = 6 \cdot 10^2\) V/cm. For mica the electron mobility remains constant up to \(3 \cdot 10^5\) V/cm, and from \(E = 3 \cdot 10^5\) V/cm to \(10^6\) V/cm a decrease in electron mobility is observed.

The results of theoretical and experimental investigations of semiconductors generally lead to a decrease in electron mobility with field strength. An exception is formed by semiconductors with an ionic structure (according to the data of Davydov and Shmushkevich), which show that the mobility of electrons in such crystals should increase with field strength.

E. K. Zavadovskaya [12], from the condition that the value \(E\) of the electrical strength of crystals increases with lattice energy, came to the conclusion that the mobility of electrons in crystals at high electric-field strengths should decrease.

According to the investigations of V. P. Zhuze and E. K. Zavadovskaya [4 and 12], the mobility of current carriers in dielectrics and semiconductors depends on the physicochemical characteristics of the substance.

The mobility of electrons in crystals decreases with an increase in the heat of formation (V. P. Zhuze), the lattice energy, and the width of the forbidden band for electrons; with a decrease in the lattice constant (according to E. K. Zavadovskaya); and is connected with other physicochemical characteristics of the substance, for example the dielectric strength of the dielectric. The mobility of charges in crystals depends on external conditions. It decreases with temperature and with electric-field strength. Let us note that the dependence of electron mobility on field strength in insulating crystals still does not have a satisfactory theoretical explanation.

A. D. Shchelokov and N. M. Torbin [13] observed a change in the electrical conductivity of single crystals and pressed powders of alkali-halide salts under the action of X-radiation. At room temperatures, irradiation of alkali-halide salt crystals, except lithium fluoride, is accompanied by an increase in electrical conductivity by two to three orders of magnitude, as is seen in Fig. 13.

At high temperatures, above 35–180° C (depending on the salt), irradiation of crystals with X-rays is not accompanied by a noticeable change in their electrical conductivity. Irradiation of lithium fluoride crystals with X-rays at room temperature is accompanied by a decrease in their electrical conductivity, stably observed over a long period of time and upon receiving a large dose of irradiation (Fig. 14).

A decrease in electrical conductivity at a small dose of X-ray irradiation is also observed for other crystals of alkali-halide salts. A subsequent increase in the dose of X-ray irradiation is accompanied by a decrease in the duration of the negative jump in electrical conductivity (Fig. 15). Finally, at certain relatively large irradiation doses the negative jump becomes almost imperceptible, and only an increase in electrical conductivity is observed. For lithium fluoride crystals, only a decrease in electrical conductivity is observed.

It is known that in crystals of alkali-halide salts at normal temperatures the current is carried by positive ions. The change

Fig. 13. Change in electrical conductivity upon irradiation of alkali-halide salt crystals under room-temperature conditions. NaCl, \(U_{mp}=70\ \mathrm{kv}\), \(I_{mp}=10\ \mathrm{ma}\) (2) and \(20\ \mathrm{ma}\) (3),
\(E=20.9\ \mathrm{kv/cm}\).

\(1\)—without irradiation; \(2\) and \(3\)—under irradiation.

Fig. 14. Change in electrical conductivity of lithium fluoride crystals upon irradiation with X-rays under room-temperature conditions.
LiF, \(U_{mp}=102\ \mathrm{kv}\), \(I_{mp}=3\ \mathrm{ma}\),
\(E=10\ \mathrm{kv/cm}\).

\(1\)—without irradiation; \(2\)—under irradiation.

in electrical conductivity observed under X-ray irradiation may be due to changes in the mobility and concentration of positive ions, or to the appearance of current carriers of the other sign, i.e., electrons, and the subsequent change in their concentration or mobility. The available materials are still insufficient for asserting any one of these hypotheses.

The known practical interest in the action of radiation on materials requires the development of a theory of these questions.

Despite the large number of works on the breakdown of solid dielectrics, we know very little about the physics of the processes of disruption of electrical strength. Published theoretical studies as yet do not explain the known experimental regularities of breakdown of solid dielectrics and do not indicate paths for further research.

Of considerable theoretical interest is the study of the dependence of electrical strength on temperature and on the time of action.

V. D. Kuchin measured the electrical strength of NaCl, KCl, KBr, and KJ at temperatures from \(-130^\circ\mathrm{C}\) to \(+150^\circ\mathrm{C}\) under constant voltage and pulses of duration \((10^{-4}\div 10^{-8})\ \mathrm{sec}\). At temperatures below \(0^\circ\mathrm{C}\), the electrical strength of the indicated dielectrics under constant

voltages and pulses down to \(10^{-7}\) sec increases with increasing temperature at a rate of approximately \(1.75\ \text{kV}/\text{cm}\cdot\text{deg}\) (Fig. 16), which is in quantitative agreement with Fröhlich’s theory. According to Rose’s calculations, at breakdown of crystals the electron density reaches \(10^{17}\ \text{cm}^{-3}\). As Fröhlich calculated [15], already at electron densities in a dielectric of the order of \(10^{14}\ \text{cm}^{-3}\), the interaction between electrons is stronger than that between the electrons and the lattice vibrations. With increasing temperature the number of interelectronic collisions grows, and consequently the energy lost by the electrons in these collisions also grows. Thus \(E_{np}\) should increase with increasing temperature.

At temperatures above \(0^\circ\)C the lowest values of \(E_{np}\) are observed for pulses of duration \(10^{-6}\) sec, which apparently should be explained by the action of a space charge, which is formed at voltages of duration greater than \(10^{-6}\) sec. The space charge in ionic crystals under the conditions considered is predominantly ionic in nature. In fact, the delay time of discharge in a dielectric is \(10^{-8}\) sec [16, 17], whereas the time during which the space charge manifests itself is greater than \(10^{-6}\) sec. With increasing temperature the number of ions forming the space charge increases. Consequently, with rising temperature the action of the space charge will intensify, as is confirmed by the experimental data.

Fig. 15. Sequential change in the electrical conductivity of lithium fluoride crystals under irradiation by an increasing dose of X-rays. NaCl, \(t \simeq 72^\circ\)C.

*—the rays are additionally attenuated by a filter.

At \(t=10^{-8}\) sec an increase in electric strength is observed in comparison with \(E_{np}\) for pulses of duration \(10^{-6}\) sec by more than

Fig. 16. Change in the electric strength of crystals as a function of temperature.

a factor of 2, which is connected with the delay of discharge in the dielectric. The electric strength of the ionic crystals studied on \(10^{-8}\)-sec pulses does not depend on temperature, which agrees neither quantitatively nor qualitatively with any of the existing theories of breakdown of solid dielectrics. Apparently, in this case mechanical destruction of the dielectric occurs under the action of a strong electric field without any preparatory processes.

The possibility of such mechanical destruction in an electric field was pointed out earlier by E. K. Zavadovskaya [18]. It was calculated that, at a field strength close to the breakdown strength, mechanical stresses arise in a dielectric that are comparable with its mechanical strength. The existence of mechanical stresses in a dielectric placed in a strong electric field was demonstrated experimentally by Cooper and Wallace [19]. At overvoltages on the specimen 2–3 times higher than the breakdown value, the mechanical stresses in the dielectric in the presence of the field will exceed its mechanical strength. Calculations give, for the measured values of electric strength at an exposure time of \(10^{-8}\) sec, mechanical stresses in crystals of NaCl—45 kg/cm\(^2\), KCl—17 kg/cm\(^2\), KBr—11 kg/cm\(^2\), KI—6.5 kg/cm\(^2\).

According to V. D. Kuznetsov, the tensile strength of alkali-halide salt crystals varies within the following limits: for NaCl from 16 to 50 kg/cm\(^2\), for KCl from 15 to 88 kg/cm\(^2\), for KBr from 16 to 40 kg/cm\(^2\), for KI from 15 to 35 kg/cm\(^2\). Thus, during breakdown on pulses of \(10^{-8}\) sec in an electric field equal to the breakdown field, stresses arise in the dielectric that exceed its mechanical strength. Breakdown on pulses of \(10^{-8}\) sec is accompanied by a strong crushing action and brittle fracture of the specimens, which is not observed during breakdown on pulses of \(10^{-6}\) sec. The electric strength of ionic crystals on pulses of \(10^{-8}\) sec does not depend on temperature; the mechanical stresses arising in the dielectric under the action of the electric field do not depend on temperature for such short pulses. The mechanical strength of crystals under short pulses, probably, likewise does not depend on temperature, and destruction under short pulses remains brittle. For comparison of the electric strength of ionic crystals with their other physicochemical characteristics, and first of all with mechanical strength, it would be useful to study the temperature dependence of the mechanical strength of these crystals at short times of action.

In connection with the independence of the electric strength of crystals from temperature on pulses of \(10^{-8}\) sec, in the expression for the temperature dependence \(E_{pr}\) in theories of breakdown of ionic crystals it is necessary to introduce the time of application of the voltage; it is also necessary, at temperatures above 0°C, to take into account the strong action of space charge on pulses of \(10^{-6}\) sec and longer.

G. A. Vorob’ev [20] determined the time dependences of the electric strength of single crystals of NaCl, KCl, KBr, and KI and of organic glass during breakdown in a uniform field (Fig. 4). The increase in the electric strength of the single crystals studied at exposures of \(1 \cdot 10^{-7}\) sec and less is due to the delay of the discharge. To judge the rate of development of the discharge, it is important to know the statistical delay time and the formation time of the discharge. For this purpose, experiments were carried out on the breakdown of X-rayed rock salt under strong illumination. The equality of the electric strength of X-rayed rock salt and non-X-rayed rock salt at the smallest exposure, \(2 \div 3 \cdot 10^{-8}\) sec, shows that in NaCl single crystals, and also, apparently, in KCl, KBr, KI single crystals and in organic glass, the statistical delay time is practically absent. Therefore it may be assumed that, in the solid dielectrics studied, the discharge-delay time is the discharge-formation time under the given conditions of voltage rise. Knowing the discharge-formation time and the thickness of the dielectric, one can determine the mean velocity of discharge propagation.

The data obtained as a result of the calculations make it possible to draw a number of conclusions.

The mean velocity of discharge propagation in the solid dielectrics studied is of the order of \(10^6\) cm/sec. For impact ionization an electron velocity of the order of \(10^8\) cm/sec is necessary. Such a large difference in velocities can be explained by a number of circumstances. An electron in a solid

in a dielectric, as a result of interaction with the solid structure, is accelerated very slowly; therefore its average velocity will be less than \(10^8\) cm/sec. The second circumstance may be the stepwise character of impact ionization.

The average velocity of discharge propagation in the dielectrics studied increases with increasing overvoltage. As the overvoltage on the dielectric increases, the electron velocity should increase; the probability of impact ionization should also increase, and the average velocity of discharge propagation should approach the average velocity of the electron. Therefore the average electron mobility in the dielectrics studied is not less than \(1\) cm\(^2\)/sec. The same value was adopted by Seitz [21].

In going from NaCl to KJ, i.e., with a decrease in the lattice energy and with an increase in its constant, the average velocity of discharge propagation decreases. The decrease in the average velocity with increasing distance between the lattice sites indicates the predominant role of impact ionization in the breakdown process of solid dielectrics.

The increase in the electric strength of the dielectrics studied at exposures of \(10^{-5}\) sec and longer is evidently due, as many investigators believe, to the influence of space charge. It is hardly possible to accept the assumption of Inushi and Suito [22] that the space charge in solid dielectrics, which causes an increase in electric strength, is formed through the capture of electrons by sites of the solid structure. Taking into account the considerable mobility of electrons and the long time during which the influence of space charge manifests itself, it should be considered that the indicated space charge is formed in solid dielectrics as a result of ion motion.

K. K. Sonchik [23] investigated the delay of the discharge in NaCl and KJ crystals on pulses with a short front (\(2 \cdot 10^{-8}\) sec) and a flat top. The value obtained in his experiments for the average velocity of discharge propagation is also of the order of \(10^6\) cm/sec. The average velocity of discharge propagation is lower in KJ than in NaCl. In both cases (NaCl and KJ) the average velocity of discharge propagation increases with increasing overvoltage.

In studying the volt-second characteristics of rock salt, in the case of a nonuniform field a discharge delay was also found. The average velocity of discharge propagation was, in the case of negative polarity of the point, \(1.37 \cdot 10^6\) cm/sec; in the case of positive polarity of the point it was \(7.77 \cdot 10^6\) cm/sec. With negative polarity of the point and small exposures, a larger value of the breakdown voltage was obtained than with positive polarity of the point.

In breakdown in a uniform field of crystals with color centers, the electric strength decreases with decreasing exposure down to \(10^{-7}\) sec and in the transition from uncolored crystals to colored ones broken down in the dark, and to colored ones broken down under illumination. Taking into account the long time of formation in colored crystals of space charge due to the departure of electrons from \(F\)-centers [24, 25], it should be considered that the decrease in the electric strength of colored crystals is due not to space charge, but to photoelectrons and \(F\)-centers.

In the breakdown of crystals in a nonuniform field the same regularities are observed, but they are expressed considerably more weakly. The features in the regularities of breakdown of solid dielectrics for action times of the order of hundredths of a microsecond also suggest a special form of breakdown. If, for a longer action time, the breakdown of a dielectric is prepared by electronic processes, then for a short action time breakdown is a mechanical destruction of the dielectric in an electric field.

In modern theories describing the motion of an electron in a crystalline lattice, its interaction with the sites is taken into account by changing the electron energy upon absorption or emission of a quantum of vibrational energy—a phonon.

Vibrational energy enters as a linear term in the expression for the lattice energy given in solid-state theory.

The magnitude of the largest quantum of vibrational energy, determined by the quantum of residual vibrations, increases with the lattice energy.

Consequently, allowance for the vibrational energy of the lattice sites in modern theories of electron motion to some extent takes into account the properties of the crystal lattice, its chemical composition and structure. However, the vibrational energy of the lattice sites is only one of the components of the lattice energy. It may therefore be thought that such a mode of description expresses only certain particular properties of the lattice, primarily those properties that are characterized by vibrational energy.

A more complete description of the properties of crystals will be achieved if the lattice energy is introduced into the kinetic equation for electrons.

The regular connection between the energy of electronic processes and the energy of the ionic lattice is not taken into account in modern theories of electronic phenomena in crystals.

In developing a detailed theory of electronic phenomena in a particular crystal and, in particular, in formulating the kinetic equation for electrons in a crystal, in order to take account of the role of the medium it is necessary to introduce terms that take into account the connection with the lattice energy.

The experimental materials presented above show the mutual connection and often the mutual conditioning of physical processes in insulating crystals. A connection is observed between electronic and ionic processes. Considering that dielectrics often have to operate under complex conditions of simultaneous action of temperature, mechanical load, radiation, and electric and magnetic fields, it is desirable to develop a comprehensive theory of electronic processes in crystals, and not merely a theory of separate phenomena without their mutual connection.

The accumulated experimental materials await their theoretical explanation.

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