Electrical Strength and Electron Trapping Energy in a Dielectric from Experimental Data
Abstract Generated abstract
This paper examines the relation between the electric strength of dielectrics and the binding energy of their most weakly trapped electrons. Using experimental data for alkali halide crystals, color centers, sulfur, MgO, and related materials, the authors compare breakdown field strengths with optical absorption energies associated with electron transitions into the conduction band. They argue that electric strength increases with the energy required to liberate weakly bound electrons, giving an empirical linear relation for crystals with F center absorption and noting that this trend is opposite to that expected from Fröhlich’s theory. The discussion further suggests that lattice weakening by impurities or ions of large radius and high polarizability reduces electron binding and thereby lowers dielectric strength.
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ELECTRIC STRENGTH AND ELECTRON TRAPPING ENERGY IN A DIELECTRIC BASED ON EXPERIMENTAL DATA
A. A. VOROB'EV and E. K. ZAVADOVSKAYA
The electrical destruction of a dielectric is preceded by its loss of electric strength, which occurs as a result of an increase in electronic conductivity. The more weakly the electrons are trapped, the lower the electric-field strength at which they will be released.
Thus, it is of interest to compare the value of the electric strength of a dielectric with the value of the trapping energy of the most weakly bound electrons.
A comparison of the electric strength of crystals of salts of the alkali-halide series with the value of the energy corresponding to the edge of the general intrinsic absorption showed that an increasing dependence is observed here. Dielectrics with high electric strength are characterized by a larger value of the binding energy of electrons in the lattice. The position of the edge of the intrinsic absorption band for crystals of alkali-halide salts depends almost not at all on the metal, but changes when the halide is replaced.
A comparison of the electric strength of crystals with the value of the electron affinity energy to the halide showed that, with an increase in the electron-affinity energy to the halide, the electric strength of the dielectric increases.
In real crystals of alkali-halide crystals, the scheme of energy levels is more complex than for crystals with an undisturbed structure. Theoretical conditions for the occurrence of energy levels in crystals were studied by Soviet scientists Tamm, Sokolov, Vul'kenshtein, Bonch-Bruevich, and others.
Tartakovskii’s studies of the internal photoelectric effect in dielectrics made it possible to construct a scheme of energy levels for electrons in real crystals. In addition to the two principal energy bands—the conduction band and the ground band—for real crystals, additional energy levels have also been determined experimentally, corresponding to inhomogeneities and to so-called color centers ($F$ centers). The difference between these and the other levels is small and amounts to fractions of an electron-volt.
The transition of electrons from the ground band to the conduction band corresponds to the edge of the intrinsic absorption of the crystal in the ultraviolet part of the spectrum. The absorption of light in the visible part of the spectrum, observed in colored crystals of alkali-halide salts, corresponds to a transition from the $F$ band into the conduction band. The transition of electrons into the conduction band upon absorption of light is accompanied by the appearance of conductivity.
This phenomenon, well studied by Soviet scientists Ioffe, Lukir-
by Tartakovskii, Nasledov, and others, has been called the photoconductivity of dielectrics under the internal photoelectric effect.
In ionic crystals the most weakly bound electrons are those located at levels corresponding to inhomogeneities and color centers.
Figure 1 gives the dependence of the magnitude of the electric strength on the quantum energy corresponding to the maximum of the \(F\)-absorption band.
From these data it is seen that between the magnitude of the electric strength and the energy required to liberate the most weakly bound lattice electrons there is a simple dependence. Analytically this dependence can be represented by the equation of a straight line in the form:
\[ E_{\mathrm{pr}}=\Delta W_F-1.2, \tag{1} \]
where \(E_{\mathrm{pr}}\) is in \(\mathrm{MV/cm}\),
\[ \Delta W_F \]
is in electron volts.
According to Fröhlich’s theory of electrical breakdown, the magnitude of the electric strength should decrease with increasing energy required for the liberation of electrons. The experimental data lead to the conclusion that the opposite dependence exists.
Fig. 1. Electric strength and the energy \(\Delta W_F\), corresponding to the maximum of the \(F\)-absorption band.
In accordance with the regularity presented in Fig. 1, the low electric strength of semiconductors is also to be found. In semiconductors the width of the forbidden energy gap for electrons is small and amounts to fractions of an electron volt.
In this case the transition of electrons into the conduction band occurs under the action of visible light and even infrared radiation. The transition of electrons is also possible when the temperature is raised. The small value of the energy required for liberation and for transfer of electrons into the conduction band also determines the low electric strength of semiconductors.
Let us also point out that, for metal oxides having high electric strength, the first absorption maximum corresponds to 10–15 electron volts.
Tartakovskii and Rekalova established, for single crystals of sulfur, the presence of an energy level at a distance of 0.45 electron volt from the main band. The low value of the binding energy of electrons in sulfur corresponds to the high polarizability of the sulfur ion, which is ten times greater than the polarizability of the fluorine ion and three times greater than the polarizability of oxygen ions.
If it is assumed that the electric strength is determined only by the binding energy of the most weakly bound electrons, then for sulfur single crystals, from formula (1), we obtain \(E_{\mathrm{pr}}=1.5\ \mathrm{MV/cm}\).
This corresponds to the values of the electric strength of sulfur single crystals \((1.5\text{–}1.8\ \mathrm{MV/cm})\), obtained by one of us. In MgO single crystals the edge of intrinsic absorption lies near 6 electron volts. In colored MgO single crystals, having excess oxygen, the maxi-
the absorption-band maximum corresponds to \(4.34\,ev\), while in the presence of excess Mg three absorption maxima are observed, corresponding to \(4.95\), \(3.6\), and \(2.35\,ev\).
The electric strength of colored MgO crystals, respectively, according to formula (1), proves to be equal to: \(2.14\,mv/cm\) and \(3.74\,mv/cm\).
The considerable decrease in the electric strength of the MgO crystal lattice in the case of excess oxygen is probably associated with the large size of the radius of the doubly charged negative oxygen ion \((1.40\,\text{Å})\) in comparison with the radius of the doubly charged positive magnesium ion \((0.65\,\text{Å})\). The presence of the oxygen ion deforms the lattice of the MgO crystal more strongly than the presence of the smaller magnesium ion. The polarizability of the oxygen ion \(O^{--}\) is \(3.8\cdot 10^{-24}\), while that of the magnesium ion \(Mg^{++}\) is \(0.12\cdot 10^{-24}\,cm^3\).
Correspondingly, from the greater polarizability of the oxygen ion one should also expect a greater decrease in the electric strength of MgO single crystals with excess oxygen.
These comparisons show that weakening of the crystal lattice, its “loosening” by the introduction of impurities with large ionic radii, lowers the electric strength. At the same time this circumstance indicates that weakening of the bonds of electrons in the crystal lattice is accompanied by a decrease in its electric strength.
REFERENCES
- Tartakovskii P. S. Internal Photoeffect in Dielectrics. GTTI, 1940.
- Vol’kenshtein F. F. Electrical Conductivity of Semiconductors. OGIZ, Gostekhizdat, 1947.
- Tartakovskii P. S. and Rekalova G. ZhETF, 10, 1025–1030, 1930.
H. Frölich Proc. Roy. Soc. A. 160, 230–241, 1937.