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TRAPPING OF MOBILE INTERSTITIALS DURING IRRADIATION OF ALKALI HALIDES
E. Sonder
To cite this version:
E. Sonder. TRAPPING OF MOBILE INTERSTITIALS DURING IRRADIATION OF ALKALI HALIDES. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-483-C9-487.
�10.1051/jphyscol:1973979�. �jpa-00215455�
TRAPPING OF MOBILE INTERSTITIALS DURING IRRADIATION OF ALKALI HALIDES (*)
E. S O N D E R
Solid State Division, Oak Ridge National Laboratory (**) O a k Ridge, Tennessee, 37830, USPA
RbsumB. - Dans de nombreux halogenures alcalins i l existe un assez large domaine de tempt- rature dans lequel les interstitiels anioniques crees par irradiation sont tres mobiles alors que les lacunes concomitantes ne le sont pas. Dans ces conditions, i l est possible de deduire des equations simples pour la vitesse de formation de lacunes stables (centres F) et la vitesse de disparition de bilacunes (centres F2) introduites au prealable. La comparaison des resultats prCdits par ces equa- tions aux resultats experimentaux dans KC1 a donne des valeurs du taux de production des centres F primaires dans le domaine de temperature 80-250 K qui ont conduit aux conclusions suivantes :
a) L'accroissement precedemment observC dans la vitesse de production des centres F provoque par une impurete a 80 K est dO a un accroissernent du piegeage interstitiel. 1 ~ ) L'augmentation avec la temperature de la vitesse de production des centres F entre 120 et 240 K est due a un accrois- sement intrinseque du taux de formation priniaire des centres F. c) La vale~lr absolue du taux de formation primaire des centres F a 240 K est superieure 0,Ol eV-1 ce qui n'est possible que si la production de defauts d'irradiation est due a un mecanisme d'ionisation unique.
Abstract. - F o r many alkali halides there exists a rather large temperature range in which radiation produced anion interstitials are quite mobile whereas tlie acconlpanying vacancies are not. For these conditions, it is possible to derive simple rate equations for the production rate of stable vacancies (F-centers) and the disappearance rate of previously introduced divacancies (F1-centers). Comparison of the predictions of these equations with experimental results for KC1 has yielded values for the primary F-center production efficiency for the temperature range 80- 250 K from which a number of conclusions have been drawn : n) The previously observed increase in F-center production rate due to impurity at 80 K is due to increased interstitial trapping. b) The increase with temperature of tlie F-center production rate between 120 and 240 K is due to an intrinsic increase in the priniary F-center production efficiency. c) The absolute value of the pri- mary F-center production efficiency at 240 K is greater than .01 eV-1 which is possible only if radiation defect production proceeds by a single ionization mechanism.
The goal of o u r group a t O R N L for a number of years has been t o understand the processes that occur when an alkali halide is subjected t o ionizing radiation. I shall describe today one small part of this effort. A number of groups have been working in this field, and it has been the large variety of expe- riments performed by these various groups that has made progress possible. Thus, the present state of understanding should be credited a s much to other -
workers [ l ] as to us at Oak Ridge. I n particular, there are two major conclusions drawn from previous work which I take as a starting point :
1) Ionizing radiation in alkali halide crystals produces primarily Frenkel defects in the anion sublattice. This fact was first suspected as a result of the analysis of the spin resonance of the H-center [2]
and was later confirmed by mechanical measure- ments [3] and by precisc X-ray lattice constant measurements [4].
(*) A more detailcd description of some of this work is p~lblished in Plrj*r. Rev. B 5 (1972) 3259.
(**) Research sponsored by the US Atomic Energy Comrnis- sion under contract with Union Carhide Corporai~on
2) Interstitials are 111uch more mobile than are vacancies. This information came chiefly from a variety of annealing experiments [ 5 ] . Figure 1 is a sunimary of the temperatures a t which interstitial and vacancy centers become mobile. This figure illustrates that there is n large range of temperatures for which only one member of tlie Frenkel pair, the interstitial, is mobile. Let us limit outselves to that temperature range.
Consider what happens when a n alkali halide is irradiated : Energy is absorbed from the electron o r photon beam a t the rate
i.
This energy, causing pri- marily electronic excitation, results in the formation of ionic displacen~ent by a mechanism such as that proposed by Pooley [6] and by Hersch [7]. Let us define the efficiency of this series of steps as the primary production efficiency, r, that isIf either mernbcr of [lie defect pair is mobile, there will be reconihlrl:~tion, and only those pairs for which recombin;iticw tloes no[ take place will be observed
3 2
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973979
C9-484 E. SONDER
tions and trapping probabilities vary with irradiation- dose. Those symbols under the sum have been the source of much of the difficulty in trying to understand quantitatively radiation defect production.
There is a method of solving this problem. Consider one particular type of interstitial trap : Let its concen- tration be NA and let us assume that every time one of these centers traps a n interstitial, it ceases t o exist.
The same reasoning, which was used above for F-center production, can be used t o formulate a rate equation for the destruction of these traps :
I I
I
0 400 2 OC 300
T E M P E R A T U R E (OK)
FIG. 1. -Temperature at which defects in alkali halides become mobile. The lines connecting the point symbols have no signi- ficance aside from connecting all the points, respectively, for interstitial ions (far left), interstitial atoms or H-centers (left border of shaded region), and negative ion vacancies or FB+
centers (right border of shaded region). The different point symbols are indicative of the different halide compounds. The shaded region indicates the large teniperature cange within which interstitial ions and atoms are mobile but vacancies
are not.
Note that there is 110 sum term in the numerator.
If, moreover, the F-center concentration and recombi- nation probability is much greater than that of the traps, then the equation for the destruction rate of these traps can be approximated and integrated as follows :
-
dNA PAN,--
d t - ELY----,
PF N F
N A = N A ( r = O ) exp -
[
a --$ 1
(4b)when a measurement is made at a later time. Above we limited this treatment to the case in which inters- t i t i a l ~ are mobile but vacancies are not. A newly produced, mobile interstitial may d o one of two things : It may recombine with an F center, o r it may be trapped by some species of trapping center.
The probability that it not recombine is simply the ratio of trapping probability a t all trapping sites t o the sum of trapping and recombination proba- bilities, or
pi Ni
In this expression pi is the trapping probability at a site of type i which exists in concentration Ni. The subscript F refers to F centers. It is now possible t o write a n equation for the F-center concentration in terms of the energy absorbed, the primary production efficiency of Frenkel pairs, and the concentrations and trapping probabilities of interstitials traps and F centers :
The difficulty in applying this rate equation to expe- rimental data of F center concentration as a function of absorbed dose is tliat one doesn't know the various species of interstitial traps o r how their concentra-
In order to apply eq. (4b) t o experimental data, it is necessary to find a trap center whose concentration is easily measured
-
one which can be introduced prior to tlie experiment in which the parameters of eq. (4) are to be measured. Moreover, throughout that experiment y,N,
must be greater than pi N i .i
A number of investigators have observed that the F2-center (two adjacent negative ion vacancies containing two electrons) can be produced only in tlie vicinity of room temperature and disappears upon low temperature irradiation. This defect is a n excellent candidate for our trap center, A . It absorbs 11ght in an easily measured absorption band so that N,, is easily determined. It has the same charge state w ~ t h respect to thc lattice as tlic F-center and there- fore, it should have a recombination probability of the same order of magn~tude as tliat of tlie F-center.
Moreover, in a KC1 sample irradiated so that
-
F-centers are produced, tlicrc will be approximately l o L 7 F,-centers ; thus on tlie onc hand, tlie F,-centers are a significant, tf not the ~iiost s~gnificant interstitial traps and, on the other h'~nd, their concentration is less than that of the F-center, thereby establishing the validity of tlie approximation of eq. (4).
The experiments we have performed consisted of first pre-irradiating samples of KC1 (pure o r lead- doped) near room temperature until they contained a few times 10'' F-centers/ctiihalid a few titiles l o t 7 F,-centers/cni" The samples were then cooled and irradiated at various telnperatures between 80 K and 250 K. These il-r'tdiations were interrupted
repeatedly t o measure the F- and F,-center concen- trations.
Figure 2 shows how NA decays with dose. It is clear from the data in the figure that the decay rate
FIG. 2.
-
Radiation-induced decrease of F-aggregate centers plotted vs dose for two initial F-center concentrations. The same data are plotted vs the ratio of (dose/F-center concen-tration) in the inset.
depends upon the initial F-center concentration and that the curves deviate slightly from a pure exponential dose dependence. If, however, Log N , is plotted vs ( E t / N F ) , then, as shown in the inset, the slopes are constant a n d independent of F-center concentration.
Eq. (4b) shows that this is what one should expect from the model proposed and the assumptions made.
The slope gives a value for u ( ~ , / / J ~ ) : all other symbols appearing in the equation are measured quantities.
Figure 3 shows decay curves for three samples doped with differing amounts of P b + + . There is n o great difference in the slope For the three samples.
Compare this with F-center production curves shown in figure 4. For thesc, lead doping causes a 5-fold increase in the F-centcr production rate. According to our model, the d n t ~ i illustrated in figures 3 ~ t n d 4 can be represented by eq. (4) and (3), respectively.
If these equations ar-e compared. i t is clear that the only difference between dN,/dr and - dN,,/dt is in the numerator of the recombination probability expression. The obvious intel-pl-ctation is that one of the terms under the sum of eq. (3) is p,,,, ,I1,,,,.
The fact tliat there is no effect ol' impurity on - dN,/dt shows not only that tlie numerator of rlic recombination prob~~bility (p,, A',) ill ccl. (4) is unre- lated to the lead concentration. but more impo13an1,
FIG. 3. - Aggregate-center-decay curves for KC1 san~ples containing different amounts of impurity. The numbers on the curves refer to lead impurity in ppm. The data were obtained
by irradiating the samples with 2 MeV electrons at 80 K.
FIG. 4. - F-center production curves for KC1 samples contain- ing different amounts of lead impurity. The data were obtained
by irradiating at 80 K.
tliat the primary production efficiency, Y, is inde- pendent of impurity.
Figure 5 shows how the slopes of curves such as those of figure 3 vary with temperature. Also shown is the temperature dependence of the F-center PI-o- duction rate. The most obvious conclusion to be drawn from tlie almost identical curve shapes is that tlic temperature dependence illustrated is related to tlic same flictor in both cq. ( 2 ) and ( 3 ) . Thus. recalling
~ h c assuniption leading from eq. (3) to cq. (4). tlie
~cmpcraturc dependence of the data illus(r:~ted in this figure cannot be attributccl to tlic recombin:~tion prob:tbilir), cxprcssion. X:~ther. it nus st bc d ~ ~ e to the fi~ctor -/ E which appears in both cq. ( 3 ) and ( 3 ) .
C9-486 E. SONDER
TEMPERATURE ( O K )
500 250 167 125 (00 80
2 , I I I I 1 I I I
FIG. 5. - Rates of F-aggregate-center decay and F-center growth in KC1 containing 100 ppm PbC+ plotted vs reciprocal
temperature.
It would be very difficult indeed to account for more than an order of magnitude change in the ratio pA/pF (eq. (4)). However, the production efficiency, u, could very well increase with temperature, if, as one would expect, most of the Frenkel pairs are initially produced close enough to attract each other.
Consider the potential energy of a Frenkel pair as a function of separation distance. Such a curve has a shape similar to that shown in figure 6. An interstitial
FIG. 6 . - Proposed form of the potential between a vacancy and an interstitial in an alkali halide crystal.
in a well, as illustrated, can recombine thermally with the vacancy if it surmounts the energy barrier, E, ; it can wander further from the vacancy if i t surmounts the larger barrier, E,. The ratio of pro- babilities of separation to recombination is (o,/o,) exp
-
(E, - E,)/IiT, where w, and w , are entropyfactors for which the chief contribution comes from the number of possible ways an interstitial can move away from (or towards) the vacancy. At relatively low temperatures the difference E,
-
E, is large enough to cause recombination to predominate.At high temperatures, however, (E, - E,)/kT is smaller and the entropy factor predominates and hence separation is favored. Since there are a number of metastable energy wells and a variety of paths, and since, moreover, we do not know the distribution of separation distances with whicl~ the Frenkel pairs are produced, it is not possible to arrive at a relation between E,
-
E, and the activation energy deduced from the data of figure 5. However, the slope of the more or less linear portion of the curve of figure 5 corresponds to 0.07 eV, which is of the order of magnitude to be expected for the interaction energy between the members of a Frenkel pair.Finally, let us extract some numbers from these data. As mentioned previously, the slopes of curves such as those of figure 2 yield values for a(p,/p,).
The ratio of p's can be approximated by the ratio of the geometric cross sections of F, and F centers, whicl~ is between
3
and 2. This means that the value for cc (see Fig. 5) rises to above 0.01 Frenkel pair per eV of absorbed energy near 250 K. In other expe- riments, performed with purer samples, the reversal at 1000/T = 4.5, evident in the curves of figure 5, did not occur until higher temperatures were reached, and the efficiency climbed to 0.02 defects per eV.That is, it was possible to form a defect in the primary process with as little as 50 eV of absorbed energy.
A number of calculations [lo] have been made of the efficiency of defect production due to multiple ionization of a halide ion, either directly from the ionizing radiation or by an Auger process. The probability of such multiple ionization is of necessity lower than that for single ionization. Such a defect production mechanism requires a minimum of a few hundred eV of absorbed energy to produce a defect. Thus, the very high production efficiency deduced from these experinlents is contrary to that expected, if double ionization is the principal mecha- nism for producing defects in alkali halides.
In summary we have been able to draw three conclusions from measurement of interstitial trapping by F-aggregate centers :
1) The impurity dependence of F-center production at liquid nitrogen temperature is due to trapping of interstitials by these impurities.
2) The rapid rise of the defect production efficiency with temperature is not related to interstitial trapping, but appears to be due to the variation of interaction potential with separation distance for interstitials and vacancies.
3) The defect production efficiency is sufficiently high to be inconsistent with multiple ionization mechanisms for defect production.
References
[I] For a summary and literature, see for example, SONDER, E. [5] See for example, tables VI and VII of [I] and the references and SIBLEY, W. A., Chapter 4 of Point Defects in Solids, given in that table.
ed' by J' H' Crawford' Jr' and L' M' 'Iifkin [6] POOLEY, D. and RUNCIMAN, W. A., Solid State Commrrn.
Press) 1972.
[2] KANZIG, W., J. Phys. & Chem. Solids 17 (1960) 88. 4 (1966) 351.
KANZIG, W. and WOODRUFF, T. O., Phys. Rev. 109 (1958) [TI HERSCH, H. N., P ~ I Y ~ . Rev. 148 (1966) 928.
220. [8] SCHNATTERLY, S. and COMPTON, W. D., Phys. Rev. 135
[3] NADEAU, J. S., J. Appl. Phys. 33 (1962) 3480; J. Appl. (1 966) A 227.
.
,Phys. 34 (1963) 2248 ; J. Appl. P l l y ~ . 35 (1 964) 1248.
SIBLEY, W. A. and SONDER, E., J. Appl. P11y.c. 34 (1963) 2366. [91 DURAND, P.l Y. and LAMBERT, M.l Ph~'s. & Chenl.
141 BALZER, R., PEISL. H. and WAIDLLICH, W., PIIJ~s. Stat. Solich 30 (1969) 1353.
sol: 15(1966) 495 ; Phys. Star. Sol. 28 (1968) 207 ; [lo] VARLEY, J. H. O., J. Plrys. & Chenl. Solids 23 (1962) 985 ;
Z . Phys. 204 (1967) 405. ITOH, N., PIIJJS. Stat. Sol. 30 (1968) 199.
DISCUSSION
F. LUTY. - In connection with the energy amount suspect that there may be an essential similarity needed for the elementary interstitial formation between the production of F-centers intrinsically process (z 50 eV) which you mentioned, one should and from substitutional hydrogen ions.
point to. the old ~ a r t i e i s s e n - p i c k experiments on X-ray coloration of KC1 and KBr at R T doped with various amount of U-centers. This is an example of a model (( first-stage coloration )) experiment with a well characterized impurity, in which one produces F- centers and hydrogen interstitials. For low U-center doping the initial F-center production rate increases with the U-center concentration ; above 2 x 1017 U- centers/cm3, however, it' becomes completely cons- tant with a value, which corresponds to 30-35 eV per produced F-center interstitial pair. Thus in retro- spect this was possibly the first measurement of this energy quantity.
E. SONDER.
-
I t is only now, after realizing how efficient intrinsic Frenkel Pair production is, that weN. ITOH. - I think that the temperature depen- dence of ci Y O U obtained can be explained using the temperature dependence of the range of the repla- cement sequence. The activation energy for the latter would be sn~aller (0.025 eV in KBr) than you obtained.
L. W. HOBBS. - Is the depth of the potential wells you have suggested a n intrinsic property of the perfect lattice or due to the impurity content of the crystal ?
H. A G U L L ~ - L ~ P E Z . - DO Y O U think that your method for measuring F-center creation efficiencies is to be prefered on that using the initial slope of the F-growth curve ? In this case you would not need any additional assumption on interstitial capture rates by F- and M-centers.
