Charge trapping mechanisms and microdosimetric processes in lithium fluoride

0146-5724/90 $3.00+0.00 Copyright © 1990PergamonPress plc

Radiat. Phys. Chem. Vol. 36, No. 1, pp. 35~t6, 1990 Int. J. Radiat. Appl. lnstrum., Part C

Printed in Great Britain. All rights reserved

CHARGE TRAPPING MECHANISMS A N D MICRODOSIMETRIC PROCESSES IN LITHIUM FLUORIDE S. W. S. McKEEVER1 and Y. S. HOROWlTZ2 ~Department of Physics, Oklahoma State University, Stillwater, OK 74078-0444, U.S.A. and 2Department of Physics, Ben-Gurion University, P.O.B. 653, 84105 Beer Sheva, Israel

present a review of the charge trapping and recombination mechanisms in LiF thermoluminescence(TL) dosimeters and discuss several dosimetric properties of this material in the light of these processes. The complex TL glow-curvefrom LiF doped with Mg, Ti and OH impurities consists of several individual peaks which emit in the region of 420-460 nm, depending on the glow peak temperature. The kinetics of the process appear to be first-order. From an accumulation of experimental data from a variety of sources (dielectric loss, ionic thermocurrents, ionic conductivity, photoluminescence, X-ray-induced luminescence, optical absorption, electron spin resonance, and others) it is inferred that the TL emission near 200°C is the result of electron-hole recombination at defect complexes consisting of Mg trimers and TiOH, centers. The spatial localization of the Mg defects and the Ti defects is seen to be of fundamental importance in describing certain aspects of the dose response function of this material and the stability of the TL signal. Coupled with this, however, the microscopic processes of energy deposition, in which regions of high ionization density are formed inside the irradiated sample, are seen to provide the essential framework around which it is possible to establish a model to describe all the major features of the dose response function in LiF:Mg,Ti,OH for a variety of irradiation types. Abstract--We

DESCRIPTION OF THE TL EMISSION FROM LITHIUM FLUORIDE

INTRODUCTION

The use of lithium fluoride as a thermoluminescence dosimeter (TLD) has prompted an enormous amount of research activity into the processes of charge trapping and detrapping in this material over the past three decades. An understanding of the fundamental processes by which energy is first stored in the material (after the sample has been exposed to a field of ionizing radiation) and is then released in the form of visible light during warming of the sample, has been slowly emerging from a wide variety of experimental investigations. Several reviews have been published on the data obtained from the earlier work (Jain, 1982; McKeever, 1985; Stoebe and Morgan, 1984; Stoebe and Watanabe, 1975) but more recent data has allowed greater insights to emerge regarding the identity of the primary defects involved in the production of TL. Along with this has come an increased understanding of the mechanisms by which charge (both ionic and electronic) is localized at these defects and is then delocalized, allowing recombination and energy release to take place. It is the intent of this paper to review our current understanding of these charge trapping and detrapping processes, with emphasis being given to the more recent data. We then discuss how this knowledge can aid in the understanding of the primary dosimetry properties of LiF TLDs, particularly with regard to their fading properties and the dose response functions that one obtains following exposure to different types of radiation field.

Glow -curves

Thermoluminescence is possibly the most sensitive experimental probe that one can employ to search for charge localization in insulating materials (Townsend and Kelly, 1973). This sensitivity is what one exploits in radiation dosimetry, but at the same time it gives rise to most of the major problems that afflict the method. One of these is the complexity of the glowcurve obtained with most popular TLDs. Perhaps the worst among them is LiF co-doped with Mg, Ti and OH impurities. This form of LiF has been produced by Harshaw/Filtrol as TLD-100, TLD-600 and TLD700 (depending on the relative isotopic abundances of 6Li and 7Li). A large number of individual peaks, of varying size, are observed in the glow-curve of this material, with the precise characteristics depending upon such factors as pre- and post-irradiation annealing procedures, the dose and type of radiation used, the spectral wavelengths over which the TL is being recorded and the exact manufacturer's batch from which the samples were obtained. Possibly the most complete analysis of the glowcurve (from TLD-100) was performed by Fairchild e t al. (1978a,b). A total of 13 TL peaks were resolved, depending on the dose used. It is popular to number the low-temperature peaks (i.e. <200°C) 1-5 and since these are well known and recognized we will refer to them under these numbers in this paper. 35

36

S.W.S. McKEEVERand Y. S. HOROWITZ

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An example of the changes in the glow-curve structure that can occur following heat treatment is shown in Fig. 1 in which we illustrate the glow-curve only in the region of peaks 1-5. These peaks are prominent after a pre-irradiation anneal of 400°C for 1 h followed by a fast quench to room temperature. However, peaks 4 and 5 are seen to dominate after an 80°C anneal for 24 h. If precipitation of Mg impurities is induced, the glow-curve changes shape dramatically. Most of the experimental efforts over the past few decades have focussed on an attempt to understand these effects. A thorough description of the major properties of the glow-curves from TLD-100 is offered by Horowitz (1984a, Vol. l, p. 89) but our primary concern here is to describe the trapping and detrapping processes which give rise to the signals observed in Fig. 1.

Temperoture (°C) Fig. 1. Glow-curves for TLD-100 after (A) a pre-irradiation anneal at 400°C for 1 h followed by a fast quench to room temperature; (B) a pre-irradiation anneal at 400°C for 1 h followed by an anneal at 80°C for 24 h; (C) a pre-irradiation anneal at 400°C for l h followed by an anneal at 190°C for I0 h. After McKeever (1985).

Figure 2 shows an isometric plot of T L temperature-wavelength for a 7-irradiated sample of TLD-100. The main emission peaks at ca 420 nm but a closer examination reveals it to be made up of several components, peaking at 2.71,290 and 3.01 eV (Fairchild et al., 1978a). The individual TL peaks emit at the following wavelengths: 460 (peak 2); 435 (peak 3): 425 (peak 4); and 420nm (peak 5) (Townsend et al., 1983). Samples containing only Ti

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Fig. 2. Isometric plot of TL intensity vs wavelength vs temperature for TLD-100. After Townsend et al. (1983).

Charge trapping mechanisms I0

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ABSORPTION SPECTRUM EXCITATION

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Fig. 3. T L e m i s s i o n s p e c t r a f r o m q u e n c h e d s a m p l e s o f T L D - 1 0 0 , w i t h initial a n d final t e m p e r a t u r e s as the spect r u m is s c a n n e d b e i n g i n d i c a t e d [(a) a n d (b)], a n d p h o t o l u m i n e s c e n c e s p e c t r a f r o m q u e n c h e d T L D - 1 0 0 t a k e n a t 100 a n d 2 0 0 ° C [(c) a n d (d)]. T h e fitted G a u s s i a n c o m p o n e n t s a r e s h o w n . A f t e r D e l g a d o a n d D e l g a d o (1984).

as a dopant reveal just two TL peaks (125 and 200°C) both of which emit at about 410 nm. X-ray-induced emission from these samples reveal spectra which are similar in many ways to the TL spectra (McKeever, 1984a). The exact wavelength at which the emission reaches a maximum is dependent upon the degree to which the Mg is aggregated in large defect complexes. When Mg is in the form of Mg-Livac dipoles the emission maximum is at ca 460 nm (the same as TL peak 2) and when the sample is heat-treated so as to distribute the Mg in the form of Mg trimer complexes (a cluster of three dipoles) the emission peaks at ca 420 nm (the same as TL peak 5). Finally, as the Mg is forced to precipitate from solid solution the emission reverts to that from Mg-free samples containing only Ti (and presumably OH; McKeever, 1984a). Zimmerman and Jones (1967) and more recently, Delgado and Delgado (1984) compared the luminescence spectra induced by absorption of 200 nm light with that observed during TL emission at a variety of temperatures. The data produced by the latter authors is illustrated in Fig. 3 in which it is demonstrated that the photoluminescence (PL) emission spectra show many features which are similar to those displayed by the TL spectra. We see that the peak of the composite emission appears at ca 420 nm when the photoluminescence spectrum is measured at 210°C. This is the same as the TL spectrum for peak 5 and the three Gaussian components are present in the same relative amounts in both the PL and the TL spectra. The PL spectrum is seen to be unaltered when the temperature is changed to 100°C, but the TL that appears at 100°C (i.e. peak 2) shows a somewhat different mix of components. It seems that the main component of TL peak 2 emission (at 2.71 eV, or 460 nm) in only weakly excited in PL. In Fig. 4 we show data from Zimmerman and Jones (1967) which demonstrates that the excitation

Fig. 4. Optical absorption and excitation spectra from unirradiated LiF:Ti. The relative excitation efficiency has been normalized at 200 nm. After Zimmerman and Jones (1967). band for the PL emission is the same as the optical absorption band at 200 nm in unirradiated samples. The origin of this absorption band is discussed in a later section. Activation energy analysis

The experimental work of Fairchild et al. (1978b), Taylor and Lilley (1978), McKeever (1980) and A. J. J. Bos (Personal communication) indicate that the TL process for LiF follows first-order kinetics. All of these works calculate similar activation energies for the major TL peaks. The data from the work of Fairchild et al. (1978b) is listed in Table 1. All of the above workers, except Taylor and Lilley, performed computerized glow-curve deconvolution of the LiF glow-curve, using nonlinear, least-squares fitting routines. Taylor and Lilley (1978) used the total glow peak, the isothermal decay and the heating rate methods. Of particular interest are the calculated values of E and s for TL peak 5. The estimated values are from 6.19 x 1019 to 1.0 x 1023s - I for s, and 2.06-2.20eV for E. The s values quoted here appear to be somewhat unphysical since s is determined from the Debye lattice vibration frequency and the change in entropy that occurs during the thermally activated process. Thus s values would be expected to range from about 1012 to 10 ~4s-L The explanation of s values 8-10 Table 1. Values for the peak temperature (at a heating rate of 10.3°C/min), E and s for each peak from TLD-100 irradiated at room temperature. Data from Fairchild et al. (1978b) Peak number

Peak temperature (°C)

E (eV)

I 2 3a 3 4 5 5a 6 7 8 9 l0 II

62 94 112 137 170 190 210 235 260 285 315 345 370

1.04 1.07 0.987 1.05 1.54 2.20 1.61 1.70 1.79 1.96 2.10 2.19 2.27

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1014 10t3 10 I] 10 [I l015 1022 l0 Is l0 ~5 l015 l015 l016 l016 1016

38

S.W.S. MCKEEVERand Y. S. HOROWITZ

orders of magnitude higher than this presents one of the most formidable challenges to our understanding of the TL process in LiF.

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LATTICE DEFECTS AND DEFECT EQUILIBRIA

Magnesium related defects

The structure of LiF is that of two interpenetrating fcc lattices, one for Li + ions and one for F - i o n s . Deviations from stoichiometry in the perfect crystal lattice constitute structural defects and at thermodynamic equilibrium the LiF crystals contain lattice vacancies and interstitial ions. Schottky defects, consisting of equal numbers of Li + and F vacancies are the most numerous, and Frenkel defects (vacancy plus interstitial) only become important at high temperatures (approaching the melting point). The substitution of Mg 2+ in place of Li + in the lattice requires the presence of Li + vacancies in order to preserve charge neutrality. These extrinsic vacancies dominate at low temperatures, whereas the intrinsic Schottky vacancies dominate at higher temperatures. At still lower temperatures, association of the Mg 2+ ions with the Li + vacancies occurs. Owing to the lattice strain energy and the Coulombic attraction between the positively-charged impurity and the negatively-charged vacancy, the total free energy of the system is reduced when the impurity and vacancy associate in nearest-neighbor positions to form an impurity-vacancy Mg-Livac pair, or dipole. At even lower temperatures clustering among the Mg-Liva~ dipoles occurs to form Mg " t r i m e r s " - clusters of three dipoles. There is some controversy concerning the idea that three dipoles combine to form a trimer, owing to the unlikelihood of a threebody encounter, in a reaction of the type AI + Ai + AI = A3

(1)

where A~ and A 3 are the dipoles and trimers, respectively. However, the data of Strutt and Lilley (1981) and McKeever and Lilley (1982) are unequivocal in this regard. The initial reaction product, however, is probably an unstable dimer (Munoz et al., 1985). Heat-treating LiF samples containing Mg by annealing them at 400°C for 1 h, followed by a fast quench to room temperature will freeze-in a metastable concentration of dipoles at room temperature. On the other hand, an anneal at 80°C for 24 h will ensure that most of the Mg is in the form of trimers. The effect of clustering can be observed most clearly in a plot of ionic conductivity vs temperature. Such plots can be found in several publications on LiF:Mg (for example, Vora et al., 1974). At temperatures below 250°C (the so-called "knee" of the ionic conductivity plot) a decrease in ionic conductivity is observed. Extensive work by Liiley and colleagues (Barsis et al., 1967; Bradbury and Lilley, 1977; Lilley and Newkirk, 1967) has demon-

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Fig. 5. A temperature-transformation-time plot of Suzuki precipitate growth in TLD-|00. After Taylor and Li|ley (]982a).

strated that this marks the onset of precipitation of Mg from solid solution. Two Mg precipitate phases are possible--a stable MgF 2 phase and a metastable 6LiF:MgF2 phase, known as a Suzuki phase. Lilley and his colleagues have shown from X-ray diffraction measurements that the Suzuki phase forms easily in slowly cooled LiF at all temperatures below the solubility limit (250°C). The temperaturetransformation-time plot for Suzuki phase precipitation in TLD-100, as obtained by Taylor and Lilley (1982a) from ionic conductivity data, is shown in Fig. 5. This illustrates the fraction of Mg present as a precipitate as a function of temperature and time, and shows that even at low temperatures substantial precipitate formation can be expected if sufficient time is allowed. The effects of precipitation on the glow-curve from LiF TLD-100 are shown in Fig. 1. Titanium and hydroxyl ion centers

Titanium enters the LiF lattice substituting for Liin either the Ti 3+ or the Ti 4+ state. Charge compensation takes place in several ways. For example, there have been suggestions that oxygen impurities, in the form of 02- ions, replace the nearest-neighbor F - i o n s (Davies, 1974). The evidence for this is particularly strong from the ion implantation studies of Wintersgill et aL (1977). The latter authors observed the changes in the thermoluminescence and the X-ray-induced luminescence following the introduction of O 2- ions via implantation and interpreted the results in terms of the formation of [T4+, 302- ] defect complexes. In samples which have not been subjected to ion implantation the oxygen may arise at a decomposition product of O H - i o n s (Vora et al., 1975). Ionic conductivity and infrared absorption measurements by Vora et al. (1975) and Stoebe and DeWerd (1985) led these authors to suggest that Ti clusters with OH impurities to form TiOH, complexes, in which more than one O H - ion associates with a Ti impurity. These complexes have been shown to

Charge trapping mechanisms

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Fig. 6. Optical absorption (at - 196°C) from LiE irradiated

at room temperature. The spectra have been resolved into individual Gaussian components (broken curves). The circles are the experimental data and the full curve is the sum of the broken curves. After Landreth and McKeever (1985). be responsible for the 200 nm optical absorption band that appears in unirradiated samples of LiF:Mg,Ti,OH. When Ti-doped samples are grown in an inert atmosphere they give rise to ionic thermocurrent (ITC) signals, presumably due to the association of the TP + or Ti 3÷ ions with Li ÷ vacancies. In these samples no 200 nm absorption is observed (Capelletti et al. 1984; Watterich et al., 1984). However, when grown in air the ITC signal disappears and the TiOH, 200 nm absorption band is seen. Clearly this suggests that the O H - ions are acting as the charge compensators in the air-grown material, but at least some of the Ti impurities are compensated by Li ÷ vacancies in those samples grown in an inert atmosphere. OH impurities are also known to cluster with Mg impurities to form MgOH, complexes. This has been observed most clearly in the infrared absorption measurements of Stoebe (1967) and Stoebe and DeWerd (1985). Wachter (1982) discusses the optimum concentrations of Mg, Ti and OH impurities that are necessary to give the maximum TL sensitivity.

39

280 nm and 380 nm were caused by various forms of Z-center (Nink and Kos, 1976) but detailed studies of the behavior of these centers during irradiation and annealing led to the conclusion that none of these absorption bands were in fact related to Z-centers. Similar conclusions have also been arrived at by other researchers (Caldas et al., 1983; Watterich et al., 1984). Comparisons of the behavior of these absorption bands with that of Mg-Liv,c dipoles as monitored by dielectric loss measurements demonstrates that the band at 380 nm (3.25 eV) is directly associated with the dipoles (McKeever, 1984a). During clustering of these defects into trimers, the 380 nm band decreases in a manner which is totally consistent with a thirdorder process. During this process the 310 nm band (4.00 eV) increases in a manner which is reminiscent of the growth of trimers. This has led to the speculation that this band is caused by Mg trimers, but direct evidence is lacking. A band at 217nm (5.71eV) does have the properties necessary for Z-centers (Landreth and McKeever, 1985). It has been suggested that it is in fact caused by Z3-centers (for example, by Caldas et al., 1983). Other, unidentified, Mg-related centers give absorption bands at 280 nm (4.43 eV) and at 234 nm (5.30eV) (Landreth and McKeever, 1985). Finally we note the fact that radiation can alter the degree of clustering among the Mg defects in the LiF lattice. Muccillo and Rolfe (1974) and Rubio et al. (1982) present strong evidence from other alkali halides that radiation can induce clustering of dipoles into higber-order aggregates. At different dose levels, however, evidence has been presented to illustrate that the exact opposite can happen, namely that the aggregates can be induced to dissociate into their dipole components (Nakamura et al., 1981; Watterich and Voszka, 1979). Clearly the situation is still somewhat confused. TRAPPING AND RECOMBINATION PROCESSES AND MODELS FOR TL

Radiation-induced centers

Correlations between optical absorption and T L

Irradiation of LiF:Mg,Ti,OH produces several optical absorption bands which are not present before irradiation. The most intense of these is the F-center which produces absorption peaking at 245 nm (5.00 eV; see Fig. 6; Landreth and McKeever, 1985). The F-center is created by the non-radiative relaxation of excitons, producing both F - ion vacancies which trap electrons (the F-centers) and interstitial F - ions which trap holes (producing H-centers; Itoh, 1982). When divalent impurities are present in the lattice F-centers associate with them to form a variety of Z-centers, of which there are many (Z 0. . . . . Z 3). The identification of these centers in the LiF:Mg,Ti,OH lattice has caused much debate. Several authors claimed that the radiation-induced bands between

Many publications report correlations between various optical absorption bands and particular TL peaks and one of the clearest and most often reported is that between the absorption band at 310 nm and TL peak 5. Post-irradiation pulse-annealing of the absorption bands demonstrated a definite correlation between these two signals (McKeever, 1984a). Since, as we argued above, this absorption band is thought to be caused by Mg trimers, then the TL peak is said to be related to trimers also. Similar measurements have related the 380nm band to TL peak 2. However, this particular relationship is not so definitive. We noted above that the absorption band appears to be caused by Mg-Liv,c dipoles. However, comparisons of the decay rates of dielectric loss signals and TL by Taylor and Lilley

40

S.W.S. McKEEvErt and Y, S. HOROWITZ

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have noted already that the absorption band may be a Z3-center. Many of the other defects are changing their concentrations over the temperature ranges in which TL is being produced (Landreth and McKeever, 1985) and it is difficult to pinpoint any other definite correlations between the absorption bands and the TL peaks. However, we should note that the F-center appears to undergo step annealing over a wide range of temperatures, implying that it is somehow involved in the production of many of the TL peaks. Furthermore, Mayhugh (1970) notes the existence of an absorption band at 113 nm which he associates with V-centers. This band disappears during the production of TL in the region of peak 5.

time (rnin)

Fig. 7. Selected data from Taylor and Lilley (1982) showing the decay of TL peaks 2 and 5, along with the decay of Mg-Li~ac dipoles and the growth of Suzuki precipitates (ppt) at temperatures of (a) 80°C and (b) 170°C in TLD-100. (1982) showed that TL peak 2 was only indirectly related to the dipoles. Indeed, at one period during the decay, the TL signal could be seen to be increasing while at the same time the dipole concentration was decreasing (Fig. 7). It is to be remarked that this occurs as the amount of Mg in precipitates is growing. Taylor and Lilley (1982b) interpreted this as evidence for the close spatial correlation between Mgdefects and Ti-defects and that during precipitation Ti is rejected from the Mg Suzuki precipitates. Townsend et al. (1983) and McKeever (1984a) went further and adopted this idea to explain the emission spectra results. The experimental data can be interpreted on the basis of the Mg-defects being formed close to the Ti-defects in the lattice. Luminescence stems from the Ti-defects (probably TiOH, defects as already discussed) but the luminescence is perturbed according to the aggregation state of the Mg. Thus, unperturbed TiOH, centers give rise to emission near 410--420 nm. This is the main emission observed in the PL experiments. TiOH, defects near Mg-dipoles, however, emit nearer 460 nm, while those near Mg trimers emit near 420 nm. Once Mg precipitates from the lattice the emission reverts to that from samples containing only Ti (McKeever, 1984a). This is consistent with the original ideas of Taylor and Lilley (1982b) concerning the rejection of Ti from the precipitate phase (i.e. the Suzuki phase). The above evidence thus supports the notion that the Mg and Ti defects have a strong degree of spatial correlation in the LiF lattice. As we will see this notion has a powerful bearing on several of the dosimetric properties of this material. The only other correlation that is clearly established in LiF:Mg,Ti,OH is that between the absorption at 217 nm (5.71 eV) and a TL peak at 400°C (TL peak 10). Caldas et al. (1983) and Landreth and McKeever (1985), among others, show good evidence to associate these two signals with each other. We

T L models

Since the TiOHn centers are thought to be the luminescence sites it is inferred that the Mg defects are the trapping sites, Mayhugh (1970) believes that the Mg centers trap electrons during irradiation, support for which comes from phototransferred TL. Here bleaching of F-centers is found to refill the traps after they have been depleted during heating. One way in which the trapping of electrons might occur is for the Mg 2÷ ions to change valency to Mg+; in this way one might imagine that the Mg-Livac dipoles could trap one electron, but that the Mg trimers might trap up to three electrons. In either case one could expect that the binding energies of the defects are affected such that radiation-induced changes in the aggregation state may well be expected. In Mayhugh's model for TL the electrons are thermally released from their traps and recombine with holes at V3-centers, converting them to transient Vk-centers. These immediately release their holes which recombine with electrons at TiOH, centers, producing TL emission. The electrons have tunnelled to the TiOH, centers from nearby F-centers. The concept of spatial correlation between the Mg and the Ti defects can be incorporated into this model without much difficulty, but a serious disadvantage of the model is that it involves two mechanisms which cannot be observed--namely transient Vk-center formation and tunnelling of electrons from F-centers. What happens to the empty F-center (i.e. the F - ion vacancy) after TL production is unclear. Furthermore, it predicts the occurrence of thermally stimulated currents (TSC) during TL emission whereas none have yet been observed. The model is illustrated in Fig. 8. An alternative explanation is offered by Sagastibelza and Alvarez-Rivas (1981). These authors maintain that the TL is a result of the recombination between interstitial F atoms and vacancy centers such as F-centers or Z-centers, Thus, in this model the interstitials are trapped at the different Mg sites and are thermally released during heating. This model finds support from Taylor and Lilley (1982b). However, while no TSC is expected from this model, the F-center bleaching results are difficult to explain.

Charge trapping mechanisms (q)

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"0"..0.

F 27Ohm

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~

!/k

Fig. 8. The Mayhugh (1970) model of TL emission from TLD-100 (as modified by Cooke and Rhodes (1981) to include emission below room temperature). Process (1) illustrates the release of trapped electrons (solid circles) and their recombination with trapped holes (open circles) at Vk centers producing 270 nm emission during thermoluminescence below 160 K. Above 160 K, process (2) illustrates the recombination of electrons with //3 centers converting these to Vk centers which release holes to recombine at an activator site with electrons which have tunneled from F centers to yield 400 nm emission. The thermal release of shallow trapped holes [process (3)] also stimulates 400 nm emission.

Recent data by Lakshmanan et al. (1985) points to some possible middle ground between the above two models. By monitoring the production of TL and of F-center absorption at different irradiation temperatures these authors have shown that it is unlikely that peaks 2 and 5 are caused by interstitialvacancy recombination mechanisms, but that peak 10 very likely is. It should be recalled that this peak may be related to Z3-centers and so this mechanism is entirely feasible for this peak. The observed emission may then be the result of energy transfer to the TiOH, centers from the interstitial-vacancy recombination. Electron-hole recombination is favored by Lakshmanan et al. for the low temperature peaks. Interpretation o f the E and s values

We now consider the puzzling question of how one interprets the E and s values obtained from the kinetic analysis. In the case of peak 2 one may be satisfied with the interpretation that the E value represents the energy needed to raise the trapped electron to the conduction band--i.e, it is a trap depth. For peak 10, one could be forced to accept that the activation energy represents the energy required to free the F interstitial from its (unidentified) trap. For peak 5, however, the interpretation is not straightforward and several groups have attempted to explain the unusually high E and s values. Fairchild et al. (1978b) include in their analysis the possibility of simultaneous hole and electron release. This analysis produces an expression for the TL peak which, if analysed using conventional first-order equations,

41

will produce an activation energy of Ee + Eh and a frequency factor of SeSh. Here, Ee, Eh, s, and sh are the trap depths and frequency factors for the electron and hole traps, respectively. However, it is difficult to see how this mechanism can be introduced into the Mayhugh model. Townsend et al. (1979) suggest that the electron trap is a Mg-defect/V3 complex. A result of this model is that the normal TL equation has to be multiplied by a factor s e ~-e/kr~ and this results in an expression for TL which contains terms s 2 and 2E. This proposal may be incorporated into the above TL models without much difficulty. Finally, one may note that the temperature range for the production of peak 5 is exactly that over which the Mg trimers are unstable and break up into dipoles (McKeever, 1984b). Thus, the dissociation of the trimers may be the trigger for the TL production in this temperature range. DOSIMETRY PROPERTIES

The fundamental criterion for a radiation detector to serve as an integrating dosimeter is, of course, sufficient sensitivity and signal to noise ratio ( S / N ) to enable the dose measurements with the required precision in any particular application. On optimized systems, LiF:Mg,Ti,OH has been shown to the capable of measuring doses as low as 2 # G y with a precision of + 2 0 % (1 standard deviation, SD; Horowitz et al., 1986) which is more than sufficient for the requirements of environmental radiation protection. In addition, extremely high dose levels required, for example, in food preservation, polymer or gem modification, sterilization, etc. may be measured (Horowitz and Moscovitch, 1986). At intermediate dose levels optimized LiF TLD systems are capable of yielding 1-2% precision (l SD) although, for most commercial, non-research systems the average reported precision seems to be ca 3-5% (1 SD). It follows that LiF:Mg,Ti,OH can be used as an integrating radiation dosimeter over more than ten dose orders of magnitude and this, in itself, is an unusual achievement for any detector system. Other important figures of merit are as follows: (i) linearity of the dose response; (ii) stability (both thermal and optical) of the radiation-induced signal; (iii) dose-rate independence; (iv) a "well-behaved" response to various types of radiation, e.g. X-rays, neutrons, heavy charged particles (HCPs), etc.; (v) reusability; and (vi) universality of the TL characteristics. Ideally we should like a theory capable of predicting the behaviour and inter-relationship of the above-mentioned dosimetric parameters. Unfortunately, LiF:Mg,Ti,OH is an extraordinarily complicated system. Aside from the solid state aspects, microdosimetric phenomena play an important role in the TL dose response and the TL efficiency characteristics of various types of radiation fields of differ-

42

S.W.S. MCKEEVERand Y. S. HOROWITZ

ent ionization density. In the following we will outline the present state of our knowledge concerning some of the theroetical models and the extent of their agreement with experimental observations on LiFbased dosimeter systems.

,

+

Thermal stability

From equation (2), based on the Randall-Wilkins monomolecular kinetics model, the expected mean lifetime r of a charge carrier in a trap of depth E and escape frequency s, at a storage temperature T, is given by z = s -1 exp(E/kT).

(2)

From kinetic studies of the TL process, it is possible to estimate that for the charge carriers released at ca 200°C, lifetimes at 25°C should range from several thousand to several millions of years. However, for many materials the TL signal fades, i.e. the charge carriers are released much faster than expected from the above equation. This "anomalous" fading may be attributed to charge recombination via quantum mechanical tunnelling through the potential barrier separating the charges (Visocekas, 1979, 1981; Visocekas et al., 1976) or from localized transitions between states (Templer, 1986). The calculated fading rates using the E and s values quoted earlier for peak 5 range from ca 10 to 15% per year, in general agreement with the experimental data indicating ca 5-10% per year (Christensen et al., 1982; Horowitz, 1984a; McKeever, 1985). This agreement may, however, be totally fortuitous since, as already noted, the theoretical value of s is many orders of magnitude greater than the expected values. Recent data (Julius and de Planque, 1984) show that, at low storage temperatures, the decrease in the TL signal obtained from samples stored before irradiation is similar to the signal loss from those samples stored after irradiation. This indicates that the defect distribution is itself changing during the storage periods. Recall that precipitation can take place at all temperatures below the solubility limit (250°C). Since the TL defects may be large complexes containing both Mg and Ti, there is a strong possibility that the precipitate particles nucleate heterogeneously on the Mg/Ti complexes and, as the Mg-rich precipitates grow, Ti is rejected from the new phase and remains dissolved in the lattice. An immediate consequence of this process will be that the TL signals will be extremely sensitive to precipitation and will decrease even in the very early stages of precipitate growth. T L dose response

The TL dose response F ( D ) usually shows a linear, then supralinear, then sublinear behaviour with increasing dose. The normalized TL dose response function f ( D ) is defined thus: f ( D ) = {F(O)/D}/{F(D,)/D,},

(3)

where F(Dt) is measured at low dose Dr, somewhere

1

I0 0

I0 ~

I0 2

~)3

10 4

I0 5

Dose (Gy)

Fig. 9. Normalized TL dose response of LiF:Mg,OH following (a) 6°Co irradiation, (b) 50 kVp X-ray irradiation, (c) 20 kVp X-ray irradiation, and LiF:Mg,Cu,P following 6°Co y-ray irradiation (d). After Horowitz and Ben Shachar (1987).

in the linear region of F(D). An ideal detector would satisfy the criterion f ( D ) = 1 into the M G y dose range. Unfortunately, f ( D ) equals unity only up to a few Gy in LiF:Mg,Ti,OH and in most other materials. In the supralinear dose region the maximum value o f f ( D ) for peak 5 in TLD-100 is ca 3.5 and occurs for 6°Co v-rays (1.25 MeV) with no increase of f(D)max with increasing v-ray or electron energy. The details of the behaviour o f f ( D ) depend upon a large number of experimental and material-dependent factors (Horowitz, 1984a). However, the behaviour which has aroused great interest is the strong dependence of the supralinearity on the linear energy transfer (LET) or ionization density created by the radiation field in the TL material. The maximum supralinearity for peak 5 begins to decrease with decreasing electron energy below ca 275 keV, reaching a value of only 1.2 for 5 keV electrons (Lasky and Moran, 1977). The behaviour of typical, normalized dose response curves as a function of incident photon energy for peak 5 in LiF:Mg,Ti,OH is shown in Fig. 9. This behaviour is even more pronounced for peak 7, where for 95 keV X-rays the supralinearity has almost disappeared (Ben Shachar and Horowitz, 1988). Even more dramatic is the disappearance of peak 5 supralinearity for low energy (ca 1 MeV) HCPs or fast neutrons. On the other hand, peaks 8 and 9 show strong supralinearity induced by ~particles (Horowtiz and Moscovitch, 1986). In general, therefore, the TL dose response in LiF:Mg,Ti,OH can be described by two dominant characteristics: a decrease in the supralinearity with increasing ionization density and an increase in the supralinearity with increasing glow peak temperature. This behaviour is illustrated in Figs 10 and 1 I. The dependence of the supralinearity upon ionization density suggests that the wavefunction of the thermally-freed electron maintains a high degree of localization around the track of the incident radiation. At first sight this apears to conflict with

Charge trapping mechanisms

sorption stage and/or recombination stage mechanisms (Chen and Kirsh, 1981; Horowitz, 1984a,b; McKeever, 1985). Only two models, however, have been proposed which can explain the decreasing supralinearity with increasing ionization density as well as the linear-supralinear dose response. The first one is the absorption stage, deep trap competition model (Bowman and Chen, 1979; Chen et al., 1981; Suntharalingham and Cameron, 1969). Horowitz (1984b), however, has argued against all radiation absorption stage models on the basis of the experimentally observed non-supralinear growth of all the radiation created optical absorption bands in LiF:Mg,Ti,OH (for example, Caldas et al., 1983; Landreth and McKeever, 1985). The other, the track interaction model (TIM), was first suggested by Claffy et al. (1968), elaborated by Attix (1975) and analytically formulated for HCPs by Horowitz and Moscovitch (1984), Horowitz et al. (1982), Moscovitch and Horowitz (1986, 1988) and Rose (1963). The TIM postulates that electrons and holes are trapped near the track of the ionizing particle, and that some of them activate centers which serve as TL trapping and recombination centers. The distances between the tracks at low doses are large enough for the recombination, during glow-curve

10 9

10 a

10 7

10 6

:~ 10 5

"-

43

10 4

.J I..- 10~

10 2

1o

Io 2 Dose

1o 3

Io~

Io 5

(Gy)

Fig. 10. TL dose response curves for peaks 2-8 in LiF:Mg,Ti,OH (TLD-100) after 50 kVp X-ray irradiation, After Horowitz and Moscovitch 0986).

accepted ideas that the electron wave packet is delocalized once the electron is raised to the conduction band and therefore one might expect that it could recombine anywhere in the crystal and not just within the track. However, it should be recalled that the track represents a region of high defect density (especially in the case of HCPs) and the potential distribution in the vicinity of the track will be markedly different from the "perfect" crystal outside the track. Thus, solutions to the Schrodinger equation inside the track will predict a different energy gap than outside the track. In this sense, the freed electron will be "delocalized" but will be confined to the track volume and will have to overcome potential barriers before it can move between the tracks. Kinetic models which assume a constant energy gap throughout the crystal volume may be inappropriate for describing charge migration and recombination over regions greater than the track volume. They will, however, still be good approximations of the situation within approximately homogeneously irradiated regions of the track. For this reason the kinetic E and s analyses described above remain approximately valid. Many models have been proposed to explain TL supralinearity in LiF:Mg,Ti,OH invoking both ab-

J~ I:1

tO

1o

lo 2

lo 3

lo ~

lo ~

Dose (Gy)

Fig. 11. TL dose response curves for peaks 2-9 in LiF:Mg,Ti,OH (TLD-100) following 4MeV ~t-particle irradiation. After Moscovitch and Horowitz (1988).

44

S.W.S. McKEEVER and Y. S. HoRowlrz

heating, to occur between charge carriers and the activated luminescence centers in the same track only. The TL dose response is linear in this region. In order for inter-track migration not to occur at low dose levels, the unirradiated regions between the tracks must be inhabited by non-radiative, competing centers which can capture charge carriers without producing luminescence. At higher doses when the distances between the tracks become comparable with the average separation of the activated centers along each track, the probability that a charge carrier generated in one track will recombine with a luminescence recombination center produced along another track increases and the TL dose response rises more rapidly than linearly. As the incident y-ray energy decreases, or if the irradiation is via HCPs or neutrons, the tracks become more localized requiring even greater dose levels to initiate track interaction. Thus, the TIM naturally accommodates the ionization density dependence of TL supralinearity. Since the capture cross section for Coulombic attractive traps and recombination centers is believed to follow a T-" dependence (Rose, 1963) the effectiveness of the competing centers may decrease with increasing glow-peak temperature. Alternatively, if the mobile carriers are actually interstitial atoms, as in apparently a possibility for some of the TL peaks in LiF, then one would expect that the mobility of the charge carrier would increase with temperature anyway. From either point of view the TIM naturally accommodates the generally observed increasing supralinearity with increasing glow-peak temperature. A similar mechanism, co-existing with and possibly determining the relative importance of track interaction, may arise from the localization of the trapped electrons and holes due to spatially correlated trapping centers and recombination centers. There is indeed strong evidence that in LiF:Mg,Ti,OH the Mg and Ti dopants are incorporated into a large defect complex responsible for both TL trapping and luminescence recombination. A high degree of localization could imply that electron-hole pairs are trapped simultaneously (perhaps via exciton diffusion) so that each released charge carrier would have a high probability of recombination with its own "locally trapped" hole and a much lower probability of recombination with the remaining population of luminescence centers. In this case the TL dose response is simply proportional to the concentration of locally paired electrons and holes, i.e. to the dose. At higher doses, the "sphere of capture" includes other luminescence centers in nearby tracks and the TL dose response begins to behave supralinearly. For y-rays and electrons the track of electronic energy deposition is unfortunately very poorly defined and of no particular symmetry. Consequently, y-ray-induced track interaction effects are difficult to simulate mathematically. Horowitz and Moscovitch (1984), Horowitz et al. (1982), and Moscovitch and Horowitz (1986, 1988), however,

have used to advantage the fact that HCP tracks define a straight line track axis around which a nearly cylindrical volume of ionization creates, on the average, a far more amenable geometry for the calculation of inter-track effects. In the TIM applied to HCPs the probability of a released charge carrier migrating from one track to its nearest neighbour, at distance r, is approximated by a two-dimensional solid angle factor multiplied by an exponential attenuation factor, exp(-ctr), representing the probability of the migrating charge carrier not being captured by the competing centers. This probability is then multiplied by the first nearest neighbour probability distribution function and integrated over all values of r from r0 to Go, where r0 is the effective radius of the HCP irradiated volume and is ca 200/~ for 4 MeV ~-particles in LiF. The resulting expression for f(n), where n is the HCP fluence, is f i n ) = 1 + 2rcn l/2r0 e ~2'4~"erfc{rcn l/2ro

+ (~/2)(ztn)-l"2}.

(4)

Equation (4) is capable of quantitatively predicting the ~-particle induced supralinearity of glow peak 8, as well as the linear behaviour of the low temperature glow peaks. The supralinearity arises from an average charge carrier migration distance of ca 5000 ,~ at the temperature of peak 8 (ca 285°C) bringing about significant nearest neighbour track interactions at a fluence of ca 108 particles cm -2. The linear behaviour of all the low temperature peaks up to n = 10 ~° particles cm 2 yields a charge carrier migration distance of ca 250 ~. This is consistent with the premise that at low sample temperatures there is negligible inter-track migration of the charge carriers. Relative T L response ( X - r a y s a n d H C P s )

The relative TL response, qo, is defined as the ratio of the TL intensity per unit absorbed dose for radiation of type i relative to radiation of type j, where the latter radiation is usually 6°Co y-rays and the comparison is carried out in the linear dose response region. It is well known that r/ ~ 1 for low energy y-rays below approx. 150 keV and for HCPs and neutrons. This deviation from unity is, conceptually at least, a relatively straightforward microdosimetric effect arising from the linear-supralinearsublinear behaviour o f f ( D ) . For low energy y-rays, r/I,``,= 1.1 (here the superscript refers to the TL peak number). This arises due to a shift in the microscopic dose distribution along a single track to higher ionization densities, so that a slightly greater part of the distribution lies in the supralinear region of ionization densities. There are many other examples linking the onset and degree of supralinearity with the extent of deviation of r/x;,from unity. For example, (i) in LiF:Cu,Mg,P, in which no supralinearity is observed and early saturation occurs (Fig. 9), the opposite effect is observed, i.e. r/x.,. = 0.8;

Charge trapping mechanisms (ii) in LiF:Ti, Mieke and Nink (1979) have reported qx~.= 1.6. This material shows enhanced supralinearity relative to LiF:Mg,Ti,OH with the onset of supralinearity at ca 0.5 Gy. For heavy charged particles (e.g. ca 1 MeV/amu :t-particles) r/5 = 0.2 in LiF:Mg,Ti,OH and this arises due to saturation effects in the densely ionized core of the ~t-particle track. Again the amenable geometry allows the microdosimetric calculation of r/,cp.~, namely I~,.

~0Rmax~0"maxf~(D )D(r, l, E)27tr dr dl

~]HCP,~~-~]6)'~,~HLCP fRmaxC.... D(r,l, E)2nr dr dl do

do

(5) Here, r/.cp.~ is calculated via the convolution of the dose deposition profile around the HCP track, D(r, l, E), with the TL dose response function, f~ (D), generated experimentally with a carefully chosen electron or ~,-ray test irradiation (Kalef-Ezra and Horowitz, 1982). In equation (5) Rmax and rmax are the maximum axial and radial distances of penetration of the ionization created by the HCP. The application of equation (5) has yielded excellent agreement with experiment for a variety of HCPs in LiF:Mg,Ti,OH and BeO. The saturation effect is illustrated dramatically for LiF:Mg,Cu,P where the rapid onset of saturation in f ( D ) leads to very low values of the relative TL response, i.e. r/~r~ 0.05 and r/,~~ 0.01 (Horowitz and Ben Shachar, 1987). We have shown that microdosimetry as well as the physics of charge trapping and detrapping processes play a fundamental role in the TL of LiF. This duality is best illustrated by the success of the TIM in describing the TL dose response of LiF:Mg,Ti,OH and its dependence on particle type, energy and glow peak temperature. We have shown, however, that the TIM should be viewed as providing the microdosimetric framework which, when coupled with other physical mechanisms, i.e. localization of traps and recombination sites, competing centers, variation in the capture cross section with temperature, can be used to describe all the dominant features of the linear/supralinear behavior of LiF:Mg,Ti,OH. In other areas of interest, for example, the relative TL response of X-rays and HCPs, microdosimetry plays a crucial role. On the other hand it has little to say concerning the TL signal stability. Here the physics of the trapping centers themselves is of major importance. As we have mentioned, it is also necessary to reconcile the dual validity of the microdosimetric interpretation and the conduction/valence band kinetic interpretation since the former requires that the charge carriers are delocalized in the region of the track and not throughout the crystal. Exact modelling of these processes is an extremely formidable problem. RPC

36/I--D

45

Acknowledgements---The work at OSU is partially supported by the U.S. Naval Research Laboratory, subcontracted via Sachs-Freeman and Associates under grant C-12671.

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