Surface Discharge on Ceramic Dielectrics with High Dielectric Permittivity
Abstract Generated abstract
This paper experimentally investigates surface discharge on ceramic dielectrics, including titanates and capacitor ceramics with dielectric permittivities from about 7 to 1500, under uniform and nonuniform electric fields. It examines how discharge voltage depends on electrode spacing, specimen geometry, humidity, pressure, frequency, field configuration, and dielectric permittivity, comparing the results with air breakdown and with Paschen-type behavior. The study finds that in uniform fields surface-discharge voltage is equal to or below air-breakdown voltage, while in nonuniform fields it may exceed air breakdown under certain humidity conditions, and that high permittivity and normal field components tend to reduce discharge voltage. It also shows that humidity effects are strong at direct voltage and 50 Hz but disappear at about 136 kHz and above, while increasing frequency lowers discharge voltage most markedly for high-permittivity ceramics.
Full Text
SURFACE DISCHARGE ON CERAMIC DIELECTRICS WITH HIGH PERMITTIVITY
A. N. Gubkin
Introduction
Surface discharge (flashover, surface breakdown) of solid dielectrics is the final stage of a discharge along the surface of a dielectric, characterized by the appearance of a spark between electrodes, which turns into an arc when the current source has sufficient power. In contrast to the breakdown of air, the regularities of which have been well studied, surface discharge has still not been investigated sufficiently fully. The presence of a dielectric has a substantial effect both on the dependence of the air-breakdown voltage on a number of factors (pressure, humidity, field frequency, etc.) and on the breakdown process itself; thus, for example, when a dielectric is introduced the initial field configuration changes, volume charges may be deposited on the surface of the dielectric, and capacitive currents along the surface of a dielectric placed in an alternating field influence the discharge process. For these reasons, surface discharge may be regarded as a physical phenomenon distinct from ordinary air breakdown.
Surface discharge has been studied by a number of authors on various materials. In works [1—8] it was shown that the surface-discharge voltage of solid dielectrics (glass, porcelain, turbonite, paraffin, ebonite, bakelite, presspahn, celluloid, etc.), generally speaking, is lower than the corresponding air-breakdown voltage. It was also shown that Paschen’s law is in some cases applicable to surface discharge as well. In Ritz’s work [9] the question of the dependence of the discharge voltage on humidity was investigated, and in the work of Walter and Inge [10] the cause of the reduction in surface-discharge voltage at high air humidity was clarified.
Empirical formulas describing the phenomenon of surface discharge are presented in work [11].
Existing attempts [12, 13] to give a theoretical justification for certain regularities of surface discharge are mainly formal in character or are limited to describing individual aspects of the phenomenon.
Despite the comparatively large number of works, however, there is still very little information on the regularities of surface discharge of dielectrics widely used at the present time, namely ceramic dielectrics.
The aim of the present work was to fill this gap in part. The work investigated the influence of a number of factors on the discharge process of ceramic dielectrics, titanates of group 2 of the Mendeleev system, and certain capacitor ceramic materials with very different values of permittivity (from 7 to 1500).
Surface Discharge in a Uniform Field
The regularities of surface discharge manifest themselves especially clearly in a uniform electric field. A dielectric in the form of a cylinder is placed between the electrodes so that its end faces fit tightly against them, while the generators of the cylinder are parallel to the field lines. In this case, provided there is good contact between the surfaces of the specimen and the electrodes, the uniformity of the field is not disturbed.
Fig. 1
Dependence of the surface-discharge voltage in a uniform field on the thickness of specimens with silvered end faces.
× — breakdown of air
● — MgTiO₃ ○ — CaTiO₃
▲ — SVT △ — BaTiO₃
a) at direct voltage \((f\)—relative humidity 39%).
b) at a frequency of 50 cps \((f = 37\%)\)
Specimens for investigation in a uniform field were made from the following titanates: MgTiO$_3$ ($\varepsilon = 12 \div 14$), CaTiO$_3$ ($\varepsilon \approx 150$), SBT (strontium—bismuth—titanate) ($\varepsilon \approx 750$), and BaTiO$_3$ ($\varepsilon = 1200 \div 1500$). The diameter of the specimens was 10 mm; the height varied within the range of 15 mm. Electrodes were applied to the ends of the specimens by firing on silver.
Fig. 2. Dependence of the surface-discharge voltage on the thickness of specimens with unsilvered ends in a uniform field at a frequency of 50 cps ($f = 33\%$).
$\times$ — breakdown of air, $\bullet$ — MgTiO$_3$, ○ — CaTiO$_3$, ▲ — SBT, △ — BaTiO$_3$
The results of investigating the dependence of the surface-discharge voltage on specimen thickness are presented in Fig. 1. (Here and below, amplitude values of voltage are given.) For comparison, Fig. 2 shows the same dependences, but for the case of specimens with unsilvered ends. From the data presented it follows that, at a relative humidity of 37–39%, the surface-discharge voltage coincides with the air-breakdown voltage for dielectrics with dielectric permittivity not exceeding 150, and does not coincide for dielectrics with $\varepsilon = 1000$. The latter circumstance is apparently associated with an insufficiently correct shape of the ceramic cylinders, which, for dielectrics with a very large $\varepsilon$, may noticeably disturb the uniformity of the field and thereby reduce the discharge voltage. Indeed, in the case of an obviously poor contact (Fig. 3), the surface-discharge voltage has a smaller value, which is characteristic of all materials.
Fig. 3. Dependence of the surface-discharge voltage in a uniform field on relative humidity for specimens of MgTiO$_3$ ($l = 4.1$ mm)
Figure 3 presents the dependence of the surface-discharge voltage on the relative humidity of the air for specimens of $\mathrm{MgTiO_3}$, and Fig. 4 gives the analogous dependence, for various materials, for the ratio $U_{\text{disch.}}/U_{\text{breakd.}}$—the surface-discharge voltage to the air-breakdown voltage.
Fig. 4
Dependence of the ratio $U_{\text{disch.}}/U_{\text{breakd.}}\cdot 100\%$ on relative humidity.
● — $\mathrm{MgTiO_3}$ ○ — $\mathrm{CaTiO_3}$ ▲ — CBT △ — $\mathrm{BaTiO_3}$
a) — at constant voltage in a uniform field.
b) — at a frequency of 50 cps.
As follows from the figures, the surface-discharge voltage coincides with the air-breakdown voltage in the region of comparatively low relative humidity of the air (up to 40%); in the region of 40%–50% a decrease in $U_{\text{disch.}}$ begins, sharp under constant voltage and more gradual at 50 cps. For specimens with $\varepsilon \simeq 1000$, the surface-discharge voltage is everywhere lower than $U_{\text{breakd.}}$. This is apparently explained, as was already indicated above, by imperfections in the manufacture of the specimens.
The dependence of \(U_{\text{disch.}}\) for ceramic materials on relative humidity can be explained by using the hypothesis [9], according to which, on the surface of solid dielectrics at high relative humidity and in a strong electric field, continuous layers of moisture are formed, spanning the specimen from one electrode to the other; moreover, the formation of these layers is facilitated if the dielectric surface is wetted by water (ceramics). Owing to these layers, whose conductivity is considerably greater than that of the dielectric itself, recharging of the surface takes place, i.e., an accumulation of positive charges at the cathode and negative charges at the anode. This disturbs the initial uniformity of the field and leads to the discharge actually occurring in a nonuniform field, which in turn lowers \(U_{\text{disch.}}\). The latter assumption was stated, and also experimentally verified, by Walter and Inge [10].
Thus, from the data presented it follows that, in the case of ceramic dielectrics, continuous moisture layers begin to form at a relative humidity of 40–50%.
Since the process of recharging the dielectric surface requires a certain time for its development, at high frequency it may be absent. Indeed, experiments showed that at a frequency of 136 kcps and higher no dependence of \(U_{\text{disch.}}\) on the relative humidity of the air is observed.
Investigation of the dependence of the surface-discharge voltage on pressure showed that \(U_{\text{disch.}}\) depends on pressure almost in the same way as \(U_{\text{break.}}\) of air, which is true at low relative humidity of the air, at constant voltage and at a frequency of 50 cps. In the remaining cases a sharp discrepancy is observed between them, namely: \(U_{\text{disch.}}\) increases much more slowly with increasing pressure than \(U_{\text{break.}}\).
Surface discharge in a nonuniform electric field
Surface discharge in a nonuniform field proceeds in a more complicated manner. In this case the already existing nonuniformity of the field has a substantial influence. Thus, additional processes of recharging the dielectric surface may not be of great importance.
It is expedient to divide the study of the regularities of surface discharge in a nonuniform field into two stages: surface discharge in a nonuniform field whose tangential component at the dielectric surface is much greater than the normal component, and discharge in a field with a strongly pronounced normal component of the field.
The first case of the simplest nonuniform field makes it possible to determine more clearly the influence of nonuniformity on the course of surface discharge.
The specimens for the investigation were made in the form of flat disks of ceramic dielectrics, titanates \( \mathrm{MgTiO_3} \) (\(\varepsilon = 12—14\)), \( \mathrm{CaTiO_3} \) (\(\varepsilon \simeq 150\)), SVT (\(\varepsilon \simeq 750\)), \( \mathrm{BaTiO_3} \) (\(\varepsilon = 1200—1500\)), and also in the form of tubes of capacitor ceramic materials UF—50 (\(\varepsilon \simeq 7\)), TK—20 (\(\varepsilon \simeq 25\)) and T—80 (\(\varepsilon \simeq 70\)). The electrodes were applied by firing on silver; in the case of tubular specimens they covered the entire specimen except for a narrow ring along which the discharge passed, while in the case of flat disks a strip with diverging edges was left uncovered by the electrodes, the discharge taking place across this strip. The dimensions of the specimens were as follows: the diameter of the flat specimens was 23 mm; the thickness and the distance between the electrodes (the width of the strip) varied depending on the conditions of the experiment; the diameter of the tubular specimens was 4.0 mm, the wall thickness of the tube was 0.4 mm, the length 35 mm, and the distance between the electrodes (the width of the ring) was determined by the conditions of the experiment. The discharge along the surface of such specimens
occurred in an electric field that practically has no component normal to the surface of the dielectric.
Investigation of the dependence of the surface-discharge voltage on the distance between electrodes, both for flat and for tubular specimens, showed that in the case of a nonuniform field \(U_{\text{disch.}}\) may even exceed \(U_{\text{break.}}\) of air. The latter is true for materials with \(\varepsilon \leq 150\) at comparatively large distances between the electrodes (\(\simeq 10\) mm) and a relative humidity of 50–60% and higher (direct voltage and 50 cps). This fact is apparently explained by the circumstance that, at sufficiently high relative humidity, recharging of the dielectric surface can reduce the degree of nonuniformity of the field, thereby increasing \(U_{\text{disch.}}\). As an example, a series of data is presented in Fig. 5.
Investigation of the dependence of \(U_{\text{disch.}}\) on the thickness of flat specimens at various frequencies showed that, when the thickness of the specimens is varied from 1 to 10 mm, the surface-discharge voltage does not change, although it decreases in absolute magnitude with increasing frequency. Figure 6 presents the results for one of the materials investigated. Similar data were also obtained for the other dielectrics.
Fig. 5. Dependence of the surface-discharge voltage on the distance between electrodes for flat specimens at a frequency of 50 cps (\(f = 59\%\)).
\(\times\) — breakdown of air,
\(\circ\) — \(\mathrm{CaTiO_3}\),
\(\bullet\) — \(\mathrm{MgTiO_3}\),
\(\blacktriangle\) — SVT,
\(\triangle\) — \(\mathrm{BaTiO_3}\).
Fig. 6. Dependence of the surface-discharge voltage on the thickness of flat specimens of \(\mathrm{CaTiO_3}\) (\(f = 53\%\), \(l = 3.9\) mm).
\(\circ\) — direct voltage,
\(\bullet\) — 50 cps,
\(\blacktriangle\) — 136 kcps,
\(\triangle\) — 1030 kcps.
When the humidity of the air is varied, the surface-discharge voltage changes considerably less under direct voltage than in a uniform field. This change is quite insignificant at 50 cps. In addition, in the case of a nonuniform field a maximum of \(U_{\text{disch.}}\) is observed, lying at a relative humidity of 45–55%. Figure 7 shows the indicated dependences for flat and tubular specimens of two of the materials investigated. The same picture is also observed for the other dielectrics investigated. Figure 8 shows how \(U_{\text{disch.}}\) depends on the humidity of the air relative to \(U_{\text{break.}}\), which, as is known, does not depend on humidity. It should be noted that at 50 cps \(U_{\text{disch.}}\) of dielectrics with very high \(\varepsilon\) does not reach \(U_{\text{break.}}\) at any relative humidity of the air. Similar dependences for
\[ \frac{U_{\text{disch.}}}{U_{\text{break.}}} \times 100\% \]
are also observed for tubular specimens.
The obtained dependences of \(U_{\text{disch.}}\) on relative humidity show, on the one hand, that at sufficient air humidity the process of recharging of the surface, apparently, can to some extent reduc—
reduce the degree of nonuniformity of the field. This leads to \(U_{\text{disch.}}\) increasing with increasing humidity; however, with a further increase in humidity the opposite picture is observed, i.e., the degree of nonuniformity increases and \(U_{\text{disch.}}\) decreases (maximum of \(U_{\text{disch.}}\)). On the other hand,
Fig. 7
Dependence of surface discharge on relative humidity.
○ — dc voltage ● — 50 cps ▲ — 435.5 kcps
a) — for flat specimens of \(\mathrm{MgTiO_3}\)
\((l = 3.9\ \mathrm{mm},\ d = 1.7\ \mathrm{mm})\).
b) — for tubular specimens of UF-50 \((l = 3.2\ \mathrm{mm})\).
it is evident that at 50 cps \(U_{\text{disch.}}\) depends on humidity to a lesser degree than under dc voltage. Apparently, in a nonuniform field the recharging process is more prolonged than in a uniform field, so that the dependence under consideration cannot manifest itself sufficiently clearly already at 50 cps. As is seen from Fig. 7, at low relative humidity \(U_{\text{disch.}}\) coincides with \(U_{\text{break.}}\), exceeds it somewhat at the maximum, and then becomes less than \(U_{\text{break.}}\). At high frequency (\(\sim 450\) kcps) \(U_{\text{disch.}}\), as in a uniform-
field, does not depend on the relative humidity of the air, which is true for both flat and tubular specimens.
A study of the dependence of the surface-discharge voltage on pressure for flat and tubular specimens showed that \(U_{\text{disch.}}\) increases with
Fig. 8
Dependence of the ratio
\[
\frac{U_{\text{disch.}}}{U_{\text{break.}}}\cdot 100\%
\]
on relative humidity for flat specimens
● — MgTiO\(_3\) ○ — CaTiO\(_3\) ▲ — SVT △ — BaTiO\(_3\)
a) — under direct voltage
b) — at a frequency of 50 Hz.
increasing pressure. At low relative humidity and at a value of the product \(\varepsilon \nu\) (\(\varepsilon\)—dielectric permittivity, \(\nu\)—field frequency in Hz) approximately less than \(10^{6}\)–\(10^{7}\), the dependence of \(U_{\text{disch.}}\) on pressure may differ only slightly from the corresponding dependence for \(U_{\text{break.}}\), even at pressures close to atmospheric. In the remaining cases \(U_{\text{disch.}}\) increases more slowly than \(U_{\text{break.}}\). As an example, let us consider Fig. 9, which presents the dependences of \(U_{\text{disch.}}\) for the investigated
dielectrics on pressure at a frequency of 136 kHz. From this figure, and also from the following ones (Figs. 10 and 11), it follows that as the product \(\varepsilon \nu\) increases, \(U_{\mathrm{br}}\) decreases in absolute value. Thus, \(U_{\mathrm{br}}\) does not depend on frequency for \(\mathrm{MgTiO_3}\) (\(\varepsilon = 12\), Fig. 10) and depends sharply on it for \(\mathrm{BaTiO_3}\) (\(\varepsilon \simeq 1200\), Fig. 11). In the case of tubular specimens, the regularities noted above also hold. Data showing the dependence of \(U_{\mathrm{br}}\) (in volts) of the investigated dielectrics on frequency are given in Table 1 (pressure: normal; relative humidity \(f = 30\%\); temperature: room temperature).
Table 1
| Frequency / Object of investigation | DC voltage | 50 kHz | 136 kHz | 450 kHz | 1 MHz |
|---|---|---|---|---|---|
| Flat electrodes without dielectric \(l = 3.95\) mm | 9000 | 8000 | 8000 | 8000 | 8000 |
| Flat specimens of \(\mathrm{MgTiO_3}\), \(l = 3.90\) mm, \(d = 1.6\) mm | 9500 | 7000 | 6500 | 6250 | 6000 |
| Flat specimens of \(\mathrm{CaTiO_3}\), \(l = 3.90\) mm, \(d = 2.2\) mm | 10000 | 7500 | 6750 | 6750 | 4750 |
| Flat specimens of SVT, \(l = 3.90\) mm, \(d = 2.3\) mm | 9000 | 5500 | 4000 | 4000 | 3500 |
| Flat specimens of \(\mathrm{BaTiO_3}\), \(l = 4.00\) mm, \(d = 2.0\) mm | 8000 | 4500 | 2500 | — | — |
| Tubular electrodes without dielectric, \(l = 3.40\) mm | 8000 | 7500 | 6500 | 6000 | 6000 |
| Tubular specimens of UF-50, \(l = 3.30\) mm | 8000 | 6000 | 6000 | 6000 | 6000 |
| Tubular specimens of TK-20, \(l = 3.20\) mm | 8500 | 7000 | 6500 | 6500 | 6000 |
The dependence of \(U_{\mathrm{br}}\) on frequency, which is manifested the more sharply the higher the \(\varepsilon\) of the dielectric under investigation and the higher the field frequency, is evidently due to the influence of capacitive currents along the surface of the dielectric on the process of air breakdown in the immediate vicinity of the surface.
When there is a component normal to the surface of the dielectric, the process of surface discharge in a nonuniform field proceeds in a more complicated manner. A field with a strongly pronounced normal component to the surface is produced by silvering the lower surface of flat specimens and
connection of it with one of the electrodes. In the case of tubular specimens, the inner surface of the tube was coated with silver.
The experiment showed that in this case \(U_{\text{disch.}}\) has a lower value than the corresponding \(U_{\text{disch.}}\) in a field without a normal component. Thus,
Fig. 9. Dependence of the surface-discharge voltage on pressure for flat specimens at a frequency of 136 kc/s \((l = 3.9,\ d = 20\ \text{mm},\ f = 60\%)\)
\(\times\) — breakdown of air, \(\bullet\) — \(\mathrm{MgTiO_3}\), \(\circ\) — \(\mathrm{CaTiO_3}\),
\(\blacktriangle\) — SVT, \(\triangle\) — \(\mathrm{BaTiO_3}\).
for specimens of \(\mathrm{CaTiO_3}\), at \(750\ \text{mm}\) \((f = 60\%)\), \(U_{\text{disch.}} = 6200\ \text{V}\) in the case when the normal component of the field at the surface may be neglected, and \(U_{\text{disch.}} = 4000\ \text{V}\) under the same conditions, but in the presence of a normal component. In addition, in the latter case a dependence of \(U_{\text{disch.}}\)
Fig. 10. Dependence of the surface-discharge voltage on pressure for flat specimens of \(\mathrm{MgTiO_3}\) at different frequencies \((l = 3.95\ \text{mm},\ d = 1.6\ \text{mm},\ f = 61\%)\)
\(\circ\) — dc voltage, \(\bullet\) — 50 c/s, \(\blacktriangle\) — 136 kc/s,
\(\triangle\) — 459 kc/s, \(\times\) — 939 kc/s.
on the thickness of the specimens, which had not been observed earlier; namely, \(U_{\text{disr.}}\) of the dielectrics studied decreases somewhat as the thickness of the dielectric decreases.
The decrease of \(U_{\text{disr.}}\) in the presence of a normal component of the field to the surface of the dielectric can be explained [3] by the fact that, as a result of the action of this component of the field, the propagation of the charge occurs with a certain friction, since the charges are, as it were, “pressed” to the surface of the dielectric; this causes additional thermal ionization and a decrease in \(U_{\text{disr.}}\). It is quite probable that in this case the action of the normal component of the field also reduces to the fact that charges are deposited on the surface of the dielectric near the electrode, of the same sign as this electrode [14]. Owing to this, the electrodes are, as it were, brought closer to one another, which also causes a decrease in \(U_{\text{disr.}}\) in magnitude.
Fig. 11. Same for BaTiO\(_3\) (\(l = 4.0\) mm, \(d = 2.1\) mm, \(f = 60\%\)).
○—DC voltage, ●—50 c/s, ▲—136 kc/s.
The dependence of \(U_{\text{disr.}}\) on the thickness of the dielectric, observed in the presence of a normal component of the field to the surface, is connected [13] with the fact that, for a sufficiently large value of the ratio \(l/d\) (\(l\) is the distance between the electrodes, \(d\) is the thickness of the dielectric), most of the field lines pass through the dielectric; therefore \(U_{\text{disr.}}\) increases with increasing \(d\).
Surface Discharge and Paschen’s Law
In a uniform field, in the case of low relative humidity of the air, at DC voltage or 50 c/s, Paschen’s law is obeyed quite well also for discharge along the surface of a dielectric [9]. At a relative humidity of 50–60% and higher, and also at high frequency and high dielectric permittivity of the material, Paschen’s law is obeyed only approximately in certain intervals of variation of the parameters \(p, \varepsilon, \nu\) (\(p\) is the pressure).
In the case of surface discharge in a nonuniform field, which was considered mainly in the present work (the normal component of the field to the surface of the dielectric may be neglected), Paschen’s law is fulfilled approximately for flat and tubular specimens with \(\varepsilon < 150\) at all frequencies (\(l\) varied from 1 to 10 mm, \(p\) from 75 to 750 mm Hg), and is not fulfilled for specimens with a larger value of \(\varepsilon\) (for example, for SVT and BaTiO\(_3\)).
The nonfulfillment of Paschen’s law indicates that, in surface discharge, processes may occur that do not conform to the similarity laws of gas discharge. The most probable process violating the similarity law in the case under consideration is apparently heating of the surface of the dielectric and, consequently, of the volume of gas at the surface, caused by dielectric losses. In addition, at a large value of the dielectric permittivity of the material it is necessary to strictly pri
to maintain such a change in the dimensions of the sample when changing the distance between the electrodes, although the applicability of Paschen’s law shows that this is immaterial in the case considered for dielectrics with $\varepsilon < 150$.
As was seen above, for flat and tubular samples with $\varepsilon < 150$ Paschen’s law is approximately obeyed. In this case, at $p \times l > 400$ mm Hg, proportionality is observed between $U_{\text{disch.}}$ and $p \times l$, i.e.,
\[ U_{\text{disch.}} = k(p \times l). \]
The constant $k$ can be determined from measurements of $U_{\text{disch.}}$ at different pressures. Knowing $k$, one can determine $U_{\text{disch.}}$ at any pressures and distances between the electrodes.
Table 2
| Object of study | DC voltage | 50 cps | 136 kcps | 1 Mcps |
|---|---|---|---|---|
| Flat samples | 2.4 | 3.0 | 2.0 | 2.0 |
| Tubular samples | 2.5 | 3.5 | 3.5 | 3.4 |
Table 2 presents values of the constant $k$ in $\dfrac{\text{V}}{\text{mm}\cdot\text{mm Hg}}$ for flat and tubular samples ($\varepsilon \simeq 10$) at different frequencies (room temperature, humidity 60%).
Conclusions
As a result of the work carried out, the following has been shown:
-
The surface-discharge voltage of ceramic dielectrics in a uniform field is always equal to or less than the corresponding breakdown voltage of air and, at large $\varepsilon$, is very sensitive to the degree of uniformity of the field.
-
In a nonuniform electric field the surface-discharge voltage is also lower than the corresponding breakdown voltage of air; however, in some cases, at sufficient humidity, it may exceed it.
-
In a nonuniform field with a sharply pronounced normal component to the surface of the dielectric, $U_{\text{disch.}}$ is considerably reduced.
-
The surface-discharge voltage, both in uniform and in nonuniform electric fields, depends sharply on the relative humidity of the surrounding air at DC voltage and 50 cps, and does not depend on it at a frequency of 136 kcps and higher.
-
The surface-discharge voltage decreases with increasing frequency, the more strongly the greater the dielectric permittivity of the dielectric (which is approximately valid at $\varepsilon \nu > 10^6\text{--}10^7$, where $\varepsilon$ is the dielectric permittivity and $\nu$ is the frequency in cps).
-
Paschen’s law in the case of surface discharge is fulfilled only in certain intervals of variation of pressure and distance between the electrodes, which in turn are determined by the form of the electric field,
frequency of the field, the magnitude of the dielectric permittivity of the material, and the relative humidity of the air.
The present work was carried out under the supervision of Prof. G. I. Skanavi, to whom the author expresses his deep gratitude.
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ERRATA
| Page | Line | Printed | Should read |
|---|---|---|---|
| 5 | 15 from top | Ziderman | Zingerman |
| 9 | 2 from bottom | voltage breakdown | breakdown voltage |
| 13 | 4 from top | $$\varepsilon_m \simeq 4\,\frac{h}{2\pi}$$ | $$\varepsilon \simeq 4\,\frac{h}{2\pi}\,\omega$$ |
| 24 | caption under figure | fig. | fig. 9. |
| 50 | 14 from top | $$-\frac{1}{M_{L}^{ak}}=\left\{\frac{1}{M}\right.$$ | $$-\frac{1}{M_{L}^{ak}}=\left\{\frac{1}{M_{-}}\right.$$ |
| 53 | 10 from top | $$-\frac{df^{1/2}}{d\varepsilon}$$ | $$-\frac{df^{1/2}}{d\varepsilon}$$ |
| 57 | 5 from top | $$(1-\sqrt{\,1-\frac{1}{1{,}3\,\varepsilon}\,}\,e^{\frac{q}{E}(\varepsilon-I)^2}$$ | $$(1-\sqrt{\,1-\frac{1}{1{,}3\,\varepsilon}\,})\,e^{\frac{q}{E}(\varepsilon-I)^2}$$ |
| 64 | Equation (87) | $$l_2(\varepsilon_2,\varepsilon_1)=l_1 e^{-\frac{1}{l_0}}$$ | $$l_2(\varepsilon_2,\varepsilon_1)=l_1 e^{-\frac{l_n}{l_0}}$$ |
| 65 | 18 from bottom | $$I\div 2\varepsilon_p$$ | $$I+2\varepsilon_p$$ |
| 85 | 7 from bottom | $$10^{14}\cdot\frac{\pi\,0{,}52\cdot10^{-2}}{4}\cdot10^{-}$$ | $$10^{14}\cdot\frac{\pi\,0{,}52\cdot10^{-2}}{4}\,10^{-2}$$ |
| 111 | 2 from top | manufacturability | conductivity |
| 111 | 8 and 10 from top | activation | activation |
| 120 | 5 from top | strength of chemical | strength against chemical |
| 135 | reference 6 | p. ... | p. 113 |
| 147 | 11 from bottom | $\varepsilon=1000$ | $\varepsilon\simeq1000$ |
| 148 | caption to Fig. 4 | $u_{\text{disch.}}\,u_{\text{break.}}$ | $u_{\text{disch.}}/u_{\text{break.}}$ |
| 204 | Fig. 1 | KbBr | RbBr |
| 253 | caption to Fig. 6 | $2$—$f=4\cdot10^3$ Hz; $3$—$f=10^2$ Hz | $2$—$f=4\cdot10^2$ Hz; $3$—$f=10^3$ Hz |
| 273 | 7 from top | KCJ | KCl |
| 280 | caption to Fig. 4 | $210^5$ | $2\cdot10^5$ |
| 294 | 1 from bottom | from 10 | from $10^{-4}$ at $f=2\cdot10^7$ to $6\ 10$ |
| 282 | table | table 2 | |
| 324 | 3 from top | p. 269 | p. 251 |
| 336 | 16 from bottom | [3,4] | [3] |
| 337 | 10 from top | [5] | [4] |
| 337 | 4 from bottom | [6] | [5] |
| 337 | 1 from bottom | [7] | — |
| 338 | 2 from top | [8] | [6] |
| 338 | 4 and 5 from top | [9,10] | [7,8] |
| 339 | 8 from bottom | [11,12] | [9,10] |
| 340 | 14 from top | [13] | [11] |
| 347 | 23 from bottom | [14] | [12] |
| 347 | 3,4 from bottom | [15] | — |
| 348 | 17 from bottom | [16] | [13] |
| 359 | 4 from top | $\psi_\varphi[M]x=\mathrm{Const}$ | $\psi_\varphi[M]x=\mathrm{Const}$ |
| 451 | 1 from bottom | mechanical | technical |