Radiation-Induced Change in Electrical Conductivity in CaF₂ Crystals

V. M. Lisitsyn, V. A. Fedorov

(Presented by the scientific seminar of the laboratory of the SF NII RF)

In crystals of alkaline-earth metal fluorides, ionic conductivity is caused mainly by the diffusion of F⁻ ions over vacant lattice sites [1–3] in the temperature interval 100–600°C. Studies [4] have shown that in BaF₂ crystals in this temperature range the conductivity is determined in part by the migration of interstitial fluorine ions. The migration energies of a fluorine ion via vacancies and via interstices differ little and are, respectively, 0.5 eV and 0.79 eV.

In the structure-sensitive region of the conductivity of CaF₂ crystals, various point defects of the lattice that include anion vacancies may serve as suppliers of anion vacancies—the current carriers. Such defects may be isovalent impurities, which, when introduced during growth, bring with them interstitial F⁻ ions or anion vacancies for electrical compensation. This assertion follows from the fact that Frenkel pairs in the anion sublattice are energetically favorable in the fluorite lattice [5]. The type and concentration of compensating intrinsic defects depend on the effective charge of the impurity ion located at a lattice site or in a lattice interstice. Possible types of charge compensation in the fluorite lattice, as well as possible variants of the complexes formed that include an impurity ion and an intrinsic lattice defect, are shown in [3, 4]. The presence of the following complexes containing anion vacancies is assumed: a monovalent cation at a lattice site with an anion vacancy (Me⁺ + F⁺), and a divalent anion at a site of the anion sublattice with an anion vacancy (O²⁻ + F⁺). The ratio between the number of associated and dissociated complexes is determined by the concentration of impurity ions, the crystal temperature, and the energy of association formation [6].

Since ionic conductivity in the structure-sensitive region is determined by the perfection of the crystal lattice, and by the concentration and type of impurity, the character of the temperature dependence of conductivity can be used to judge the purity of a crystal as well as its monocrystallinity.

Irradiation of CaF₂ crystals with ionizing radiation leads predominantly to disruption of the anion sublattice [7]. Since the defectiveness of the anion sublattice determines the magnitude of ionic conductivity, studies of radiation-induced changes in conductivity can provide extensive information about damage to the crystal lattice by radiation. However, prior to the present work, studies

studies of radiation-induced changes in the conductivity of calcium fluoride were carried out only in the region of small irradiation doses, at which the concentration of defects induced in the crystal lattice is insignificant. The influence of gamma and X-ray \[8—14\], proton and neutron \[10, 13\] irradiation on the electrical properties of calcium fluoride crystals was studied. In all the works listed, except perhaps \[9, 13\], no radiation-induced change in conductivity in the structure-sensitive region was found, which was to be expected, since the concentration of defects induced at the doses studied was insignificant. The decrease in conductivity after neutron irradiation observed in \[13\] was not investigated and was not explained.

In the present work, systematic studies were carried out of the radiation-induced change in the electrical conductivity of calcium fluoride crystals of different previous histories, irradiated with electrons and protons over a broad range of doses.

For the study, calcium fluoride crystals were selected that had been grown from natural purified material at the State Optical Institute (CaF₂ I), containing 0.007% yttrium, at the Lebedev Physical Institute (CaF₂ II), and also crystals grown in the crystallization laboratory of the TPI from synthesized chemically pure salt, free from yttrium and rare-earth impurities (CaF₂ III). The procedure for measuring electrical conductivity and preparing the samples has been described by us in \[15\]. Simultaneously with the measurement of ionic conductivity, the thermoluminescence glow sum from the guard-ring side of the irradiated crystal was measured. The glow sum was measured through a quartz window by means of FEU-38 and FEU-39 photomultipliers and recorded with an EPP-0.9 3M potentiometer.

Irradiation of the crystals was carried out with protons and electrons of energies 4.5 MeV and 1.2 MeV and with flux intensities of \(3 \cdot 10^{14}\) protons · cm\(^{-2}\) s\(^{-1}\) and \(2 \cdot 10^{12}\) electrons · cm\(^{-2}\) s\(^{-1}\), respectively, on accelerators of the Nuclear Physics Research Institute at room temperature. Uniform coloration of the samples by radiation, especially in the case of proton irradiation, was achieved by selecting the crystal thickness corresponding to the particle range, and also by irradiating the crystals from two sides.

Experimental Results

The results of studying the temperature dependence of the conductivity of unirradiated crystals are presented in Fig. 1.

The temperature dependence of the conductivity \(\lg \sigma = \varphi \left( \dfrac{1}{T^\circ K} \right)\) of an unirradiated CaF₂ I single crystal has the form of two intersecting straight lines at a temperature of 105°C (curve “a,” Fig. 1). The activation energies of the processes on the linear portions of the low-temperature (30—105°C) and high-temperature (105—500°C) regions are \(0.9 \pm 0.1\) eV and \(1.35 \pm 0.13\) eV, respectively. The dependence \(\lg \sigma = \varphi \left( \dfrac{1}{T^\circ K} \right)\) for CaF₂ II crystals has the form (Fig. 1b) of a straight line in the temperature interval 50—500°C, with an activation energy equal to \(1.3 \pm 0.13\) eV. The temperature dependence of the conductivity of CaF₂ III, grown from synthesized salt, has two linear portions (Fig. 1c) with activation energies \(0.23 \pm 0.04\) eV and 1.2 eV in the intervals (30 ± to °C) and (90—500°C), respectively.

Figure 2 presents studies of the temperature dependence of CaF₂ I crystals irradiated with electrons. It is readily seen that, with a change in the irradiation dose, the character of the temperature dependence changes. The resulting set of similar conductivity dependences of cry-

crystals as a function of the irradiation dose can be classified into four groups.

I. Preliminary irradiation of a calcium fluoride crystal with doses of \(6.5 \cdot 10^6\) rad to \(3.5 \cdot 10^7\) rad leads to an increase in conductivity in the range \(30\)—\(100^\circ\mathrm{C}\) and to the appearance of a maximum in the temperature dependence (Fig. 2b). In the high-temperature region the conductivity of the crystal remains unchanged relative to the conductivity of the unirradiated crystal.

Fig. 1. Temperature dependences of the conductivity of unirradiated CaF\(_2\) crystals grown at: a) GOI—CaF\(_2\) I, b) FIAN—CaF\(_2\) II, c) TPI—CaF\(_2\) III

II. Irradiation of crystals with doses of \(3.5 \cdot 10^7\) to \(1.1 \cdot 10^8\) rad leads to an increase in conductivity in the low-temperature region (\(30 \div 130^\circ\mathrm{C}\)) and to a decrease in the high-temperature region (\(130 \div 400^\circ\mathrm{C}\)) (Fig. 2c). The maximum of the conductivity in the temperature dependence is preserved, but shifts toward higher temperatures.

III. A further increase in the dose of preliminary irradiation of the crystals to \(5.5 \cdot 10^8\) rad leads to a decrease in the radiation-induced increase in conductivity in the temperature range \(30 \div 130^\circ\mathrm{C}\) and to restoration of the initial conductivity at higher temperatures. The maximum in the dependence \(\lg\sigma = \varphi\left(\dfrac{1}{T^\circ K}\right)\) is absent (Fig. 2d).

IV. Preliminary irradiation of calcium fluoride crystals with a dose from \(5.5 \cdot 10^8\) to \(7 \cdot 10^{10}\) rad causes a significant decrease in conductivity in the high-temperature region (Fig. 2e). In the low-temperature region the conductivity increases only slightly.

The complete dose dependence of the conductivity of a CaF\(_2\) I crystal is presented in the form of isotherms for the high-temperature and low-temperature regions in Fig. 3. Similar results were obtained by us in studying the radiation-induced change in the conductivity of CaF\(_2\) I and CaF\(_2\) III crystals.

Fig. 2. Temperature dependences of the conductivity of CaF\(_2\) crystals irradiated with electrons

We carried out studies of the radiation-induced change in the conductivity of CaF\(_2\) I crystals irradiated with protons in the dose interval

$1.5 \cdot 10^{7} \div 7.5 \cdot 10^{10}$ rad. The temperature dependences of the conductivity of crystals irradiated with different doses are presented in Fig. 4. It is not difficult to note that, in the dose range $1.5 \cdot 10^{7} \div 10^{9}$ rad, a significant increase in the conductivity of CaF$_2$ I crystals is observed in the low-temperature part of the conductivity curve, and the absence of a radiation-induced change—in the high-temperature part. The radiation-induced increase in the conductivity of CaF$_2$ crystals under proton irradiation is much lower than under isodose irradiation with electrons.

Fig. 3. Dependence of the change in conductivity of CaF$_2$ I crystals on the dose of electron irradiation at constant temperature: a) temperature $80^\circ$C; b) temperature $140^\circ$C

Fig. 4. Temperature dependences of CaF$_2$ I crystals irradiated with protons

At irradiation doses of the crystals higher than $10^{9}$ rad, a gradual decrease in the conductivity of the crystals is observed in the high-temperature region ($100$—$350^\circ$C). The kinetics of the change in electrical conductivity of CaF$_2$ I crystals as a function of the proton-irradiation dose is presented in Fig. 5.

Discussion of the experimental results

The results given above from the study of the dependence of the electrical conductivity of calcium fluoride crystals on the dose of irradiation with protons and electrons made it possible to reveal two main effects.

Fig. 5. Dependence of the change in conductivity of CaF$_2$ I crystals on the dose of proton irradiation

In the low-temperature region, the conductivity increases after irradiation. In the high-temperature region, it decreases with increasing irradiation dose up to $5 \cdot 10^{8}$ rad. The following explanations of the observed effects seem reasonable to us.

The increase in conductivity in the low-temperature region in crystals irradiated with doses of $10^{6}$—$10^{8}$ rad is apparently due to,

the creation by radiation of weakly bound holes capable of thermal activity in the temperature range up to \(130^\circ\)C. This assumption, first put forward in [10], is well confirmed by our investigations. Simultaneous measurement of conductivity and thermoluminescence on the same crystal showed that the thermoluminescence peak and the maximum in the temperature dependence of the conductivity of irradiated crystals lie in the same temperature interval \((90\text{—}110^\circ\mathrm{C})\) (Fig. 6).

Apparently, the decrease in conductivity with increasing temperature in this region and the intense luminescence of the crystal are due to the same processes, for example, the release of weakly bound holes and a decrease in their concentration with increasing temperature as a result of recombination at luminescence centers. The following facts obtained by us speak in favor of the assumption that the processes have a hole character.

Fig. 6. Temperature dependences of the conductivity of CaF\(_2\) 1 crystals irradiated with electrons at a dose of \(8.5\cdot10^7\) rad: a) unirradiated crystal; b) crystal irradiated with the above dose; c) irradiated crystal, optically bleached before the conductivity measurement by light in the 680–1000 nm region for 90 min; d) TL luminescence intensity of a crystal irradiated with the above dose; e) TL luminescence intensity of a crystal irradiated and bleached by light in the 680–1000 nm region for 90 min.

1. The thermoluminescence peak in the above-mentioned temperature region coincides with the thermoelectric-emf peak. The direction of the current caused by the concentration thermoelectric emf indicates that the thermoluminescence in this temperature region is due to hole processes [16].

2. Bleaching of CaF\(_2\) 1 crystals irradiated with electrons at a dose of \(8.5\cdot10^7\) rad by light in the 680–1000 nm region for 90 min leads to a 50-fold decrease in the conductivity of these crystals (Fig. 6). At the same time, the intensity of the optical absorption spectrum bands with maxima at 225, 335, 400, and 580 nm decreases, respectively, by factors of 1.5, 1.5, 1.65, and 1.5. It is known that all four bands are due to electron centers and are associated with the presence in the crystals of

CaF$_2$ impurity ions of yttrium [17]. Probably, the destruction of electron centers when the crystal is illuminated with light in the 680–1000 nm region is due to the release of weakly bound holes; as these migrate through the crystal, their recombination at the centers is observed. At present it is difficult to represent the structure of the shallow hole traps that ensure the increase in conductivity in the low-temperature region. It is possible that such traps may be fluorine ions in interstitial positions [18] or molecular fluorine ions located near an impurity ion [19].

1. As the irradiation dose increases from $5 \cdot 10^8$ to $10^{11}$ rad, a decrease in the ratio $\sigma_{\text{irr}}/\sigma_{\text{unirr}}$ is observed at a temperature of $80 \div 110^\circ\mathrm{C}$ (see Fig. 3). The decrease in the relative increase in conductivity in the low-temperature region is probably associated with the transition of hole centers from shallow traps to deeper ones. This is confirmed by the disappearance of low-temperature thermoluminescence peaks and by the increase in the intensity of high-temperature glow as the irradiation dose increases [20, 21].

In the temperature interval $130 \div 500^\circ\mathrm{C}$ the dependence of the ratio $\sigma_{\text{irr}}/\sigma_{\text{unirr}}$ on the irradiation dose has a complex character (Fig. 3b). At comparatively small electron irradiation doses, $10^6 \div 5 \cdot 10^8$ rad, at a temperature of $140^\circ\mathrm{C}$, a minimum is observed on the curve of the dependence $\sigma_{\text{irr}}/\sigma_{\text{unirr}} = \varphi(D)$. The decrease in the conductivity of the irradiated crystal is associated with a decrease in the concentration of current carriers—anion vacancies.

It is known that the source of anion vacancies in this temperature interval is complexes of the impurity–anion vacancy type. It is possible that, when the temperature of the crystal is raised, the simplest hole centers are transformed into more complex ones that include a complex of the “impurity–anion vacancy” type, which is destroyed at a higher temperature. In order to verify this assumption, we investigated the influence of optical bleaching of CaF$_2$ I crystals preliminarily irradiated with an electron dose of $8.5 \cdot 10^8$ rad on their conductivity and on the change in the integral thermoluminescence light sum. For one group of crystals, the temperature dependence of conductivity was measured, and simultaneously the integral thermoglow curves were measured, immediately after irradiation. For the second group, similar dependences were measured after bleaching the irradiated crystals with light in the interval $680 \div 1000$ nm for 90 min.

As is seen from the experimental results presented in Fig. 6, after optical bleaching of the irradiated crystals the maximum on the conductivity curve decreases together with a decrease in the glow peaks at $96^\circ\mathrm{C}$, $135^\circ\mathrm{C}$, and $170^\circ\mathrm{C}$. However, the intensity of the glow peak at $300^\circ\mathrm{C}$ increases significantly as a result of the transformation of some hole centers into others.

A study of the spectral composition of the glow peaks at $96^\circ\mathrm{C}$, $135^\circ\mathrm{C}$, and $300^\circ\mathrm{C}$ showed that, when the intensity of the spectral lines in the first two glow peaks decreases, the intensity of analogous spectral lines increases in the glow peak at $300^\circ\mathrm{C}$.

Thus, by optically emptying shallow hole trapping levels, we increase the concentration of deeper hole levels. At the same time, as is seen from the curves of the temperature dependence of conductivity, after bleaching the conductivity in the high-temperature region of the crystal becomes significantly lower. Probably, during thermal emptying of shallow hole trapping levels, along with recombination processes causing luminescence, the formation of more complex hole centers also occurs, including in their com-

complexes of the “impurity–anion vacancy” type, which also entails a decrease in conductivity in the high-temperature region.

The decrease in conductivity in the temperature interval \(100\text{–}350^\circ\mathrm{C}\), at doses higher than \(10^9\) rad, is apparently associated with the formation of intrinsic radiation defects responsible for the absorption band with a maximum at 560 nm. It should be assumed that the observed decrease in conductivity is due to a decrease in the concentration of current carriers in the crystal. When intrinsic defects are created by radiation, neutral halide atoms appear in interstitial sites. Neutral fluorine atoms can be displaced into the anion vacancies of “impurity–anion vacancy” complexes; in this case the local charge compensation will not change. The displacement of halide atoms into anion vacancies will lead to a decrease in the number of “impurity–anion vacancy” complexes. In addition, during prolonged irradiation of a CaF\(_2\) crystal, the concentration of “impurity–anion vacancy” complexes decreases as a result of hole capture by an oxygen ion \(\mathrm{O}^{2-}\) or by a \(\mathrm{Me}^{+}\) ion [22, 23], which are components of the complexes “\(\mathrm{O}^{2-}\)—vacancy \(\mathrm{F}^{+}\)” or “\(\mathrm{Me}^{+}\)—vacancy \(\mathrm{F}^{+}\).” As a result of hole capture by an \(\mathrm{O}^{2-}\) or \(\mathrm{Me}^{+}\) ion, the anion vacancy can diffuse from the complex over a considerable distance. A migrating free anion vacancy, having a large electron-capture cross section, can localize an electron on itself, forming an electron color center. Thus, in both the first and the second cases, the capacity of the “impurity–anion vacancy” complexes must continuously decrease with increasing irradiation dose.

Consequently, the creation of intrinsic radiation defects must be accompanied by a decrease in the conductivity of calcium fluoride. Since the impurity concentration in the crystal is limited, with increasing irradiation dose the dependence curve \(\sigma_{\text{unirr}}/\sigma_{\text{irr}}\) tends toward saturation, as is observed at high irradiation doses on the order of \(10^{10}\text{–}10^{11}\) rad.

It should be noted that the efficiency of defect formation in CaF\(_2\) crystals, leading to a decrease in conductivity in the high-temperature region, as we have observed, depends to a significant degree on the prehistory of the crystal and on the type of ionizing radiation. A subsequent paper will be devoted to this question.

Thus, the action of proton and electron radiation on CaF\(_2\) crystals leads to a significant change in the electrical conductivity of the crystal.

1. At comparatively low irradiation doses of \(10^6\text{–}10^7\) rad in the temperature interval \(30\text{–}130^\circ\mathrm{C}\), the hole component of the current is dominant. In this same dose interval, a significant decrease in conductivity is observed in the temperature region \(130\text{–}250^\circ\mathrm{C}\) as a result of electron–hole processes leading to the binding of anion vacancies, which determine the conductivity in this temperature interval.

2. At irradiation doses of \(10^9\text{–}10^{11}\) rad, at which a significant concentration of intrinsic radiation defects of the lattice accumulates, far exceeding the defectiveness due to the impurities present, a significant decrease in the conductivity of CaF\(_2\) crystals is observed in the temperature interval \(100\text{–}350^\circ\mathrm{C}\). The cause of this decrease in conductivity is apparently the process of formation of complex hole centers with capture of anion vacancies that were previously part of “impurity–anion vacancy” complexes, the principal current carriers.

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