RADIATION-INDUCED CHANGE IN THE ELECTRICAL CONDUCTIVITY OF FORSTERITE CERAMICS

Yu. I. Galanov, I. S. Shishkin

(Presented by the scientific seminar of the Laboratory of Radiation Physics, Research Institute of Nuclear Physics, TPI)

When dielectrics are irradiated with electrons, nonuniform generation of radiation defects over the thickness of the specimen is observed [1]; in addition, a negative charge accumulates in the specimen. The strength of the electric field that arises in this process may reach the value of the dielectric strength of the material, which leads to spontaneous electrical breakdown of dielectrics [2]. When specimens with a nonuniform distribution of radiation defects are heated in a short-circuited circuit, discharge currents are observed [3–11], which we shall hereafter call radiation-stimulated thermocurrents (RSTC). If the magnitude of the RSTC is of the same order as the conduction currents of the dielectric, then they must be taken into account when measuring the electrical conductivity of the given material after irradiation.

RSTC can be measured simultaneously with conduction currents. Then the electrical conductivity is determined as

\[ \sigma = \frac{j - j_{\mathrm{rst}}}{E_0}, \tag{1} \]

where \(j\) is the density of the measured current;
\(j_{\mathrm{rst}}\) is the RSTC density;
\(E_0\) is the strength of the applied electric field.

The present work is devoted to studying the change in the electrical conductivity of LF-2 forsterite ceramics, with allowance for RSTC, after electron irradiation. An electrostatic generator ESG-2.5 of TPI was used as the radiation source. The electron energy was \(1.2\ \mathrm{MeV}\), and the flux density was \(3.13 \cdot 10^{12}\) electrons/\(\mathrm{cm}^2\cdot\mathrm{s}\). For the study, specimens in the form of disks 25 mm in diameter and 1.7 mm thick were used. The conduction currents and RSTC were measured in a vacuum of \(5 \cdot 10^{-3}\) mm Hg with an SP-1M electrometric amplifier in the temperature range \(20\text{–}400^\circ\mathrm{C}\), at a heating rate of 2 deg/min. The strength of the applied electric field was 400 V/cm.

Figure 1 presents the temperature dependence of the RSTC when the specimen is irradiated from the side of the high-voltage electrode. Irradiation from the side of the measuring electrode gives an RSTC dependence that is mirror-symmetric with respect to the temperature axis. The RSTC density reaches a value of \(10^{-11}\ \mathrm{A}/\mathrm{cm}^2\), which exceeds the conduction-current density of the unirradiated dielectric, which in this temperature interval is of the order of \(10^{-12}\ \mathrm{A}/\mathrm{cm}^2\).

Figure 2 presents the dependence of the logarithm of the conduction currents on reciprocal temperature for LF-2 ceramics. Curve 1 corresponds to the conduction currents of the unirradiated ceramic. Curves 2 and 3 are the conduction currents of the ceramic irradiated with an exposure dose of \(2.5 \cdot 10^{15}\) electrons/cm\(^2\), with 2 for the specimen irradiated from the side of the measuring electrode, and 3 for the specimen irradiated from the side of the high-voltage electrode. Curve 4 is the conduction current after subtracting the RCT.

Fig. 1. Dependence of RCT on temperature for LF-2 ceramics after electron irradiation with an exposure dose of \(2.25 \cdot 10^{15}\) electrons/cm\(^2\). Irradiation from the side of the high-voltage electrode.

It is seen from Fig. 2 that the RCT strongly distorts the results of measurements of conduction currents. At the same time, the temperature positions of the maxima of the RCT and of the conduction currents coincide; consequently, in calculating the electrical conductivity one may use expression (1).

Figure 3 shows the dependences \(\lg \sigma = f(1/T)\), allowing for expression (1), for LF-2 ceramic specimens irradiated with various exposure doses. For the unirradiated material one can distinguish five straight-line sections with activation energies of \(0.45\) eV, \(0.6\) eV, \(1.2\) eV, \(1.7\) eV, respectively (Fig. 3, curve 1). Curves 2–4 correspond to specimens irradiated with doses \((0.25—135)\cdot 10^{15}\) electrons/cm\(^2\). Here one can distinguish three straight-line sections with activation energies of \(0.45\) eV, \(0.05\) eV, and \(0.45\) eV, respectively.

Figure 4 shows the dependence of electrical conductivity on irradiation dose for each of the three sections. The character of the dependences is the same: a sharp initial increase in electrical conductivity, followed by a slow increase up to a dose of \(1.4 \cdot 10^{17}\) electrons/cm\(^2\). The slope of the initial sections of the curves decreases with increasing temperature. The relative change in electrical conductivity also decreases. RCTs can provide valuable information about radiation defects.

Fig. 2. Temperature dependence of conduction currents in LF-2 ceramics: 1 — before irradiation; 2, 3, 4 — after irradiation with an exposure dose of \(2.25 \cdot 10^{15}\) electrons/cm\(^2\); 2 — irradiation from the side of the measuring electrode; 3 — irradiation from the side of the high-voltage electrode; 4 — result of taking the RCT into account according to formula (1).

In measuring the RCT, the short-circuit conditions of the specimen are satisfied:

\[ \int_{0}^{l} E(x)\,dx = 0 \tag{2} \]

where \(l\) is the thickness of the specimen;

\(E(x)\) is the field in the dielectric induced by irradiation; we assume that it is uniform, i.e., that the thickness of the sample is much smaller than its diameter.

The expression for the RIC can be obtained from the total current, which we write in the following form:

\[ j=\sigma(x)E(x)+\frac{\varepsilon}{4\pi}\frac{\partial E}{\partial t} -gD\frac{\partial n(x)}{\partial x} +\frac{\partial}{\partial t}P(x), \tag{3} \]

where \(\sigma=\sigma_0+\Delta\sigma(x)\) is the electrical conductivity at the point \(x\) of the sample, consisting of the electrical conductivity of the unirradiated material and the additional electrical conductivity due to radiation damage;
\(\varepsilon\) is the dielectric permittivity of the material;
\(g, D, n\) are, respectively, the charge, the diffusion coefficient, and the concentration of charge carriers contributing to the additional electrical conductivity;
\(P(x)\) is the induced polarization.

Fig. 3. Temperature dependence of the electrical conductivity of irradiated LF-2 ceramics: 1—before irradiation; 2—irradiation with a dose of \(2.25\cdot10^{15}\) electron/cm\(^2\); 3—irradiation with a dose of \(9\cdot10^{15}\) electron/cm\(^2\); 4—irradiation with a dose of \(135\cdot10^{15}\) electron/cm\(^2\).

Fig. 4. Dose dependence of the electrical conductivity of LF-2 ceramics for three temperature regions.

Since the total current does not depend on the coordinate, expression (3) can be written as

\[ j=\frac{1}{l}\int_{0}^{l}E(x)\sigma(x)\,dx +\frac{\varepsilon}{4\pi}\int_{0}^{l}E(x)\,dx -gD\frac{n(l)-n_0}{l} + \frac{\partial}{\partial t} \left[ \frac{1}{l}\int_{0}^{l}P(x)\,dx \right]. \tag{4a} \]

By virtue of condition (2), we finally obtain

\[ j=\frac{1}{l}\int_{0}^{l}\Delta\sigma(x)E(x)\,dx -gD\frac{n(l)-n_0}{l} + \frac{\partial}{\partial t} \left[ \frac{1}{l}\int_{0}^{l}P(x)\,dx \right]. \tag{4б} \]

The first term in (4б) is the drift component of the RIC. To obtain it in explicit form, additional assumptions must be made about the geometry of the electric fields in the dielectric and about the distribution of radiation defects, which depend on the irradiation conditions.

The second term in (4б) is the concentration component of the RIC. It does not depend on the distribution of charge carriers through the thickness, but only on the ratios of their concentrations at the ends of the sample and on their thermal generation.

The polarization decay current is the third component of the RST. When the conditions (2) are met at the moment of irradiation, only those polarization mechanisms for which the polarizability is a function of the distribution of radiation-induced defects over the specimen thickness will contribute to the depolarization component of the RST. The RST can be written in the form

\[ j(T)=\sum_i q_i\left(n,\frac{d}{l},T\right)\exp\left(-\frac{W_i}{\kappa T}\right) \exp\left\{-\int_{T_0}^{T}\frac{dT}{\beta \tau_i(T)}\right\}, \tag{5} \]

where \(q_i\left(n,\frac{d}{l},T\right)\) is the weight of each RST component, depending on the ratio of the electron range to the specimen thickness. The dependence on temperature \((T)\) is weaker than exponential.

\(W_i\) is the activation energy of the corresponding process;

\(\kappa\) is Boltzmann’s constant;

\(T_0\) is the temperature corresponding to the start of heating;

\[ \beta=\frac{dT}{dt} \]

is the heating rate;

\(\tau_i(T)\) is the relaxation time of the corresponding process.

The contribution of each RST component \((q_i)\) tends to zero for \(\frac{d}{l}\gg 1\). The activation energy of the process can be found from the initial portion of the curve, when the difference \((T-T_0)\) is small.

Thus, for the low-temperature RST peak (Fig. 1), the activation energy is 0.45 eV, which coincides with the activation energy of electrical conductivity.

The radiation-stimulated currents (5) are, in the general case, a superposition of several processes with different activation energies; therefore their time evolution may not coincide. In addition, in the irradiated material there may be several types of charge carriers participating in electrical transport. All this will lead to the appearance of several peaks in the temperature course of the RST.

By choosing suitable irradiation conditions (specimen thickness, boundary conditions), one can separate the RST components and study them individually.

Conclusions

1. In studying the influence of electron irradiation on the electrical conductivity of dielectrics, if the electron range in the material is commensurate with the specimen dimensions, the influence of internal electrical inhomogeneities in the specimen should be taken into account; their annealing manifests itself as discharge currents in short-circuited circuits (radiation-stimulated thermocurrents). Therefore the electrical conductivity should be calculated with allowance for the RST according to expression (1).

2. The electrical conductivity of forsterite ceramics increases after irradiation with electrons. Moreover, as the temperature increases, the radiation-induced change in electrical conductivity decreases.

3. The RST method may be a valuable supplement to existing methods for studying radiation defects in ceramic materials.

References

1. B. A. Kononov, O. B. Evdokimov. Izv. TPI, Tomsk Polytechnic Institute Press, Tomsk, 1965, 139, 68–70.
2. B. Gross. Phys. Rev., 107, 2, 368 (1957).
3. Proctor T. M., Phys. Rev., 116, 6, 1436 (1959).
4. Preston V., Murphy and Sergio Costa Ribeiro. J. Appl. Phys., 34, p. 2061–2063 (1963).
5. Knechtel J., Lharmann. Zeitschrift für Physik, 19, 5 (1965).
6. F. Hardtke. J. Chem. Phys., 42, 300 (1965).
7. F. Hardtke. Phys. Rev. Letters, 9, 339 (1962).
8. Preston V., Murphy, B. Gross. J. Appl. Phys., 35, 1 (1964).
9. B. Gross. J. Appl. Phys., 36, 5 (1965).
10. J. Furuta, J. H. Okamoto, E. H. Hiraoko. J. Appl. Phys., 37, 4 (1966).
11. T. I. Berdov, M. G. Grisyuk, Kh. B. Kogan, T. F. Madrichenko. Elektronika, 4, 1959.