RADIATION GENERATION OF VACANCIES IN ALKALI-HALIDE CRYSTALS DOPED WITH STRONTIUM

V. M. Lisitsyn, I. Ya. Melik-Gaikazyan

(Presented by the scientific seminar of the Laboratory of Dielectrics and Semiconductors)

Several works [2–7] have been devoted to the study of the influence of alkaline-earth impurities on the process of accumulation of \(F\)-centers. The increase in the first stage of accumulation of \(F\)-centers in doped crystals was first explained by Seitz [1] as an improvement in the conditions for localization of holes, that is, as a decrease in the probability of recombination of electrons of \(F\)-centers and holes. Koeffin and Ridley [2] proposed another mechanism for the influence of an impurity on coloration. They assumed that impurity ions, replacing regular lattice sites, act as vacancy traps during growth of a crystal from the melt. In the case of NaCl, the complex \(\mathrm{Ca}^{++}\Box + 2+\Box\) can be obtained. Thus, the impurity makes it possible to preserve an additional number of vacancies in the crystal. This mechanism is consistent with the work of Rabin [3], where it is shown that, for the same concentration of \(F\)-centers, the expansion of crystals containing an impurity is smaller, but it contradicts the data obtained by L. V. Grigoryuk [4], who showed that the enhancement of \(F\)-center generation in doped crystals grown from solution is no less than in melt-grown ones.

The appearance of new models of hole centers of the molecular-ion type, sufficiently substantiated by EPR, enabled Hayes and Nichols [5] to propose a new mechanism of coloration. According to the work of Crawford and Nelson [6], in the presence of a cation vacancy in a crystal a defect may be created, consisting of a molecular halide ion \(x_2^-\), occupying the place of a halide and a cation and oriented along the \((100)\) axis. In this case a free anion vacancy is formed, which, after capturing an electron, can become an \(F\)-center. Since a divalent impurity introduces a cation vacancy with it, it may be assumed that such centers can be created in large numbers in doped crystals. Hayes and Nichols succeeded in proving this experimentally by comparing the optical and EPR spectra of crystals.

Schneider [7], discussing the mechanisms of coloration of doped crystals, comes to the following conclusion. It is known that alkali-halide crystals have a substructure at intersections of dislocations, containing an atmosphere of impurity and vacancies. At the rapid stage of coloration, hole centers associated with the impurity are formed here, possibly by the Hayes–Nichols mechanism; these then decay, forming the complex \(\mathrm{Me}^{++}|\Box|\) and a \(V_2\)-center, that is, the impurity serves as a catalyst for the process of formation of color centers.

From our point of view, the action of the complex \(\mathrm{Me}^{++}|\Box|\) as a catalyst of the process of generation of anion vacancies should have a substantial influence also on the second stage of generation of \(F\)-centers, since the satu-

the catalyst action cannot arise from the mismatch between large concentrations of \(F\)-centers at the second stage of accumulation and the relatively small impurity content. Under such a mechanism the impurity does not intensify the process of overall radiation generation, but, as it were, transfers defects of the cation sublattice into defects of the anion sublattice. Experiments carried out by Fröhlich [8] showed an increase in the rate of generation of \(F\)-centers in doped crystals at the second stage of accumulation under X-ray irradiation. However, without taking into account the radiation annealing of the crystals, it is impossible to draw an unambiguous conclusion about the influence of the impurity on the generation of anion vacancies [10], since it is possible that the effect is due to an increase in radiation stability. In fact, Arinshtein [9] showed that the radiation decoloration of a KCl—Sr crystal is less than that of KCl. Thus, the increase in \(a^*\) may be due to an increase in the radiation stability of \(F\)-centers.

How, then, are the rate of vacancy generation, the rate of accumulation of \(F\)-centers, and radiation annealing related? Analyzing the accumulation of color centers under irradiation, Mitchell et al. [11] came to the conclusion that the accumulation of \(F\)-centers can be described by an equation of the form:

\[ n_f = n_0^* \left(1 - e^{-b^* t}\right) + \left(n_1 - \frac{a^*}{c^*}\right)\left(1 - e^{-c^* t}\right) + a^* t, \]

where \(n_f\) is the concentration of \(F\)-centers,
\(t\) is the irradiation time,
\(n_0^*\) is the concentration of anion vacancies that were present in the crystal before irradiation and were uniformly distributed in the crystal,
\(b^*\) is the rate of electron capture by these vacancies,
\(n_1\) is the concentration of anion vacancies that were present before irradiation and were distributed in the crystal with high local density,
\(c^*\) is the rate of electron capture by vacancies distributed with high local density and by newly created vacancies,
\(a^*\) is the rate of generation of \(F\)-centers in vacancies created by radiation.

The asterisks indicate that the specified parameters also include the radiation decay of color centers.

The rate of generation of \(F\)-centers is determined from the slope of the linear portion of the accumulation of \(F\)-centers, occurring due to vacancies created by radiation, and depends on the rate of vacancy generation \(a\), on the rate of electron capture by vacancies \(c\), and on radiation annealing, characterized by the constant \(\beta\).

\[ a_k^* = \frac{ac}{c + \beta}. \]

From the study of the accumulation curves of \(F\)-centers in crystals containing different amounts of impurity, one can determine the relationship between these quantities, i.e., find out whether the introduction of the impurity affects vacancy generation.

Experimental method

For the study, KCl and KBr crystals were taken, grown from the melt with additions of Sr impurity. The study of the kinetics of accumulation of \(F\)-centers requires high irradiation intensities of the crystals. Such intensities can be obtained with the selected radiation source—a cyclotron accelerating protons to an energy of 6.5 MeV in vacuum.

Protons penetrate into the crystal to a depth of up to 400 μ, i.e., they produce a volume coloration effect. We have shown that small additions of impurity to the crystal do not affect the penetration depth of the protons. By passing the proton beam incident on the crystal through a foil of a certain thickness, as proposed by Weisbord [12], it is possible to reduce the proton energy and, consequently, the proton penetration depth and the depth of the colored layer in the crystal. This is necessary in studying the accumulation of color centers at high concentrations. Irradiation of the crystals was carried out in a special holder, which made it possible to irradiate the crystals in the dark at constant temperature. The measurements and irradiation of the crystals were performed at room temperature. The absorbed dose was measured by measuring the proton current with a dc amplifier. The dose was calculated from the formula

\[ D = 3.2 \times 10^{12}\,\frac{I \cdot t \cdot U}{q \cdot S}, \]

where \(I\) is the proton current,
\(t\) is the irradiation time,
\(U\) is the proton energy,
\(q\) is the proton charge,
\(S\) is the area of the measuring electrode.

The absorption spectra were measured on an SF-4 spectrophotometer. The impurity concentration in each investigated sample was determined by a complexometric method using an FEK-56 colorimeter-nephelometer.

From the obtained accumulation curves of the \(F\)-centers, the parameters of the Mitchell–Fröhlich equation were calculated by the iteration method. In our calculations the discrepancy between the experimental and calculated curves did not exceed 4.8%.

Results

A study of the accumulation curves of \(F\)-centers showed that the rate of generation of \(F\)-centers changes in crystals with the introduction of impurity. This is evident from the experimental results presented in Figs. 1 and 2 and in column 1 of Table 2. As was indicated earlier, the rate of generation of \(F\)-centers may increase owing to an increase in the rate of generation of vacancies \(a\), or owing to a decrease in \(\beta\), the constant of radiation bleaching,

\[ a^{*} = \frac{ac}{c + \beta}. \]

The quantity \(\beta\) has the same order of magnitude as the quantity \(c\), i.e., this quantity cannot be neglected.

It is impossible to judge the change in the rate of vacancy generation in the crystal upon introduction of an impurity from the value of \(a^{*}\), since the value of \(\beta\) is unknown. The relative change in the rate of vacancy generation can be determined in the following way. The quantity \(c + \beta\) is equal to the quantity \(c^{x}\), the parameter of the Mitchell–Fröhlich equation characterizing the rate of electron capture by newly created vacancies, i.e.,

\[ ac = a^{x}c^{x}. \]

The quantity \(c\) is the rate of electron capture by a vacancy. This quantity is proportional to the capture cross section \(\Phi\) and to the number of electrons in the conduction band \(n_e\)

\[ c = \Phi \cdot n_e \]

The capture cross section is a quantity constant for a given crystal. The number of electrons in the conduction band is determined by the differential relation

\[ \frac{dn_e}{dt}=kI-n_e\left(B_e n_e+\sum_{j=1}^{j} B_j n_j\right), \]

where \(I\) is the irradiation intensity,
\(k\) is the proportionality coefficient,
\(n_e\) is the number of electrons or the number of holes,
\(B_e\) is the coefficient of the rate of their recombination,
\(n_j\) is the number of defects of type \(j\), and \(B_j\) is the coefficient of the rate of electron capture by these defects.

Let us consider the influence of small additions of impurities of the Sr, Ca type on the rate of change in the number of electrons in the conduction band.

1. Capture of electrons by a divalent impurity leads to the formation of \(Z\)-type centers according to the models of Seitz and Pick [1]. However, thermodynamic calculations by Lidiard [13] show that the formation of \(Z_1\)- and \(Z_2\)-centers occurs when an ion of a divalent metal or a complex “metal ion—cation vacancy” combines with an \(F\)-center (possible models: \(Z_1\) according to Pick and \(Z_2\) according to Seitz). In this case no capture of electrons from the conduction band occurs. Centers \(Z_3\) and \(Z_4\) are unstable at room temperature.

Fig. 1. Accumulation of \(F\)-centers in crystals
\((1)\) — KBr and \((2)\) — KBr + 0.018 M% SrBr\(_2\).

1. It is known that an impurity located at the boundaries of grain blocks, etc., is a good trap for electrons. In some cases this explains the presence of a maximum in the dependence of the density of \(F\)-centers on the concentration of the impurity introduced into the crystal under isodose irradiation [15]. At high concentrations the impurity does not dissolve completely in the lattice; part of it remains at the boundaries of blocks and grains and, by capturing electrons, decreases the probability of creating \(F\)-centers. This has been shown in NaCl—Pb and NaCl—Mn crystals. The introduction of Ca into NaCl and Sr into KCl, as shown by Grigoryuk and Ignat’eva, only slightly decreases the density of \(F\)-centers at high content—

Fig. 2. Accumulation of \(F\)-centers in crystals
\((1)\) — KCl and \((2)\) — KCl + 0.024 M% SrCl\(_2\).

concentration of impurity exceeding the solubility limit of these impurities in the crystal. Our experiments have shown that the maximum in such dependences for KCl—Sr, KBr—Sr irradiated with protons is absent [16]. These discrepancies are probably associated with the use, in our case, of high irradiation intensities, i.e., with the contribution of the generation of \(F\)-centers from radiation-created vacancies to their accumulation in the first stage. Thus, the presence of impurity at block boundaries has only a slight effect on electron capture.

Table 1

Parameters of the kinetic equation for the accumulation of \(F\)-centers, obtained from calculation of the experimental accumulation curves

1. Calculations show that at the irradiation intensities used by us, approximately \(10^{17}\) electrons per \(\mathrm{cm}^3\) per sec are generated. The concentration of the impurity introduced into the crystal ranges from \(10^{17}\) to \(10^{18}\) ions per \(\mathrm{cm}^3\). With such a ratio it is quite probable that all im-

Table 2

Change in the vacancy-generation rate in crystals upon introduction of Sr impurity

purity traps will be saturated with electrons during the first stage of accumulation of \(F\)-centers, i.e., the presence of impurities will affect only the value of \(B\)—the rate of electron capture by vacancies that existed in the crystal before irradiation—and will not affect the value \(c\). From these three propositions one may conclude that \(c\) does not depend substantially on the Sr impurity content in the crystal, and therefore the relative change in the rate of vacancy generation in crystals with the introduction of impurity can be determined as follows. Having obtained, as a result of calculating the \(F\)-center accumulation curves by the iteration method in a “pure”

and in the doped crystal, the values of the parameters \(a^*\) and \(c^*\) give the ratio:

\[ \frac{a_1 c_1}{a_2 c_1}=\frac{a_1^* c_1^*}{a_2^* c_2^*}. \]

Assuming \(c_1=c_2\), we obtain

\[ \frac{a_1}{a_2}=\frac{a_1^* c_1^*}{a_2^* c_2^*}. \]

The results of the calculations are given in Tables 1 and 2 for KBr crystals and KBr \(+0.023\) M% \(\mathrm{SrBr}_2\) at two different irradiation intensities.

Thus, one can draw the unambiguous conclusion that the introduction of Sr impurity into the crystal increases the rate of generation of anion vacancies in the crystal.

REFERENCES

1. F. Seitz, Rev. Mod. Phys. 26, 7, 1954.
2. J. E. Caffin, B. K. Ridley, Proc. Phys. Soc. 77, 153, 1961.
3. H. Rabin, Phys. Rev. 116, 1381, 1959.
4. L. V. Grigoryuk. Dissertation, Tomsk, 1964.
5. W. Hayes, G. M. Nichols, Phys. Rev. 117, 993, 1960.
6. J. H. Crawford, J. C. Nelson, Phys. Rev. Lett. 5, 314, 1960.
7. E. E. Schneider, Disc. Faraday Soc. 31, 176, 1961.
8. F. Fröhlich, Z. Naturforschung 17a, 327, 1962.
9. I. Ya. Melik-Gaikazyan, M. N. Arinshtein. Destruction of \(F\)-centers by X-rays in pure and activated KCl crystals, Optics and Spectroscopy (in press).
10. E. Abramson, M. E. Gaspari, Phys. Rev. 129, 536, 1963.
11. P. V. Mitchell, D. A. Wiegand, R. S. Smoluchowski, Phys. Rev. 121, 484, 1961.
12. D. I. Vaisburd, I. Ya. Melik-Gaikazyan. Kinetics of accumulation of \(F\)-centers in alkali-halide crystals irradiated with protons. Izvestiya AN SSSR (in press).
13. A. B. Lidiard, J. Appl. Phys. 33, 416, 1962.
14. J. Trnka, M. Káčěrka, A. Bohun, Czech. J. Phys. 14, 1, 1964.
15. I. Ya. Melik-Gaikazyan, E. K. Zavadovskaya, M. I. Ignat’eva, FTT 6, 1243, 1964.
16. V. M. Lisitsyn. Influence of alkaline-earth impurities on the rate of accumulation of color centers in alkali-halide crystals irradiated with protons. Izvestiya AN SSSR (in press).