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optically stimulated luminescence glow curves
Radiation Measurements 79 (2015) 7e12
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
An algorithm for the integrated deconvolution of radioluminescence and thermally/optically stimulated luminescence glow curves K.S. Chung a, *, C.Y. Park a, J.I. Lee b, J.L. Kim b a b
The Research Institute of Natural Science and Department of Physics, Gyeongsang National University, Jinju 660-701, South Korea Health Physics Team, Korea Atomic Energy Research Institute, P.O. Box 105, Yuseong, Daejeon 305-600, South Korea
h i g h l i g h t s RL, TL and OSL glow curve deconvolution employing interacting model. Simulation both irradiation and TL/OSL readout stages for various dose level. Application in the identification OSL kinetics of Al2O3:C.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 February 2015 Received in revised form 9 April 2015 Accepted 11 May 2015 Available online 20 May 2015
Radioluminecscence (RL), the light emitted from a material immediately upon ionizing radiation, has been used to detect the dose rate. On the other hand, thermoluminescence (TL) and optically stimulated luminescence (OSL) by the stimulation with the heat and light after irradiation have been used to find out the cumulated radiation dose. Because it was considered as effective to handle these three phenomena in integration to estimate the energy band structure of the material precisely, an algorithm for calculating the glow rapidly and consistently was developed in this study when three types of stimulations including irradiation are applied concurrently or sequentially. The deconvolution using this algorithm can decide the properties contained in the material more precisely because the glows from different stimulations are related frequently to the different aspects of the properties. The computer program to realize the deconvolution by means of these schemes was also developed and it was applied to the glow curves of RL and OSL from Al2O3:C to evaluate the efficiency of the developed algorithm. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Radioluminescence (RL) Thermoluminescence (TL) Optically stimulated luminescence (OSL) Glow curve deconvolution
1. Introduction Radioluminescence (RL), thermoluminescence (TL) and optically stimulated luminescence (OSL) are the luminescence commonly related to the energy level of materials (Chen and Pagonis, 2011). These are the emission of light from a crystalline material such as insulator or semiconductor by recombination of the electrons and holes created by the irradiation immediately (RL), with heat stimulation (TL) or with light stimulation (OSL). The energy structure of the crystal can be found by analyzing the glow curves corresponding to specific stimulations. Provided that the electrons and holes are stably captured within the trap positioned at the forbidden band of the crystal, the absorbed dose on the material can be estimated by means of TL and OSL. Accordingly, these
* Corresponding author. E-mail address: [email protected] (K.S. Chung). http://dx.doi.org/10.1016/j.radmeas.2015.05.006 1350-4487/© 2015 Elsevier Ltd. All rights reserved.
phenomena are being broadly used in dosimetry as well as in dating of archaeological samples (McKeever, 1985; Botter-Jensen, 2003). However, RL is used to measure ionizing radiation in real time by detecting the light emerged from a material when it is irradiated. Even though the mechanisms of RL, TL and OSL are identically related to the energy band structure, they have been studied independently in most cases. Because the traps are created by the presence of impurities or crystal defects in crystal, it is necessary to find the trend of differing the energy level structure depending on the complication of impurities injected into the material or the manufacturing process in order to develop an efficient dosimetric material. For these purposes, the glow curve deconvolution analyzing the trap information from the glow curve has been used. Many algorithms and computer programs for the glow curve deconvolution have been developed for dosimetric purposes (Chen and Pagonis, 2011). But most of these algorithms are based on the assumption that each trap
8
K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
independently composes one glow curve. This assumption is based on a simplified model of one trap and one recombination center (OTOR) which make a glow peak. The superposition of these peaks makes the whole glow curve consisting of many overlapping peaks. It is general to interpret a certain glow curve by making further assumptions (Halperin and Braner, 1960). But this model does not reflect the physical reality because the interaction possibility of the electrons or holes moving between traps via the conduction band or the valence band is excluded (Sakurai, 2001). Therefore, we developed the appropriate numerical analysis method to solve the flow equations reflecting all possible flows of electrons and holes through the conduction band and through the valence band. By applying this method, the glow curves of TL and OSL was analyzed efficiently (Chung et al., 2011, 2012, 2013, 2014). However, the glow curves are not analyzed easily which require several types of trap because there are many parameters in each trap, and the flow equations of the electrons and holes are closely related each other. It is due to the fact that particular parameters are situated to affect the glow less or two or more parameters affect to the glow in combination under the measuring conditions. A set of the glow curves measured by wide range of radiation dose and various profiles of stimulation shall be analyzed on the same specimen integrally in order to avoid such ambiguities. Nevertheless, this method is limited in use because the repeated measuring on the same specimen may change the physical properties such as the accumulation of the electrons in deep trap and etc. The algorithm analyzing glow curves emitted from the concurrent or sequential application of ionizing radiation, thermal stimulation and light stimulation was developed in this study. The computer program realizing and investigating this algorithm was developed as well. The cases of continuous measuring of RL and OSL, i.e. after applying the irradiation for certain duration and the light stimulation after a short relaxation time on the specimen, could be taken as an example. It was expected that each parameter can be calculated more precisely when two glow curves were analyzed integrally because many parameters on the trap contributed to RL and OSL differently in this case.
2. Model and numerical analysis Electron-hole pairs are created when the electrons in the valence band are excited by the irradiation on the crystal with the energy level model shown in Fig. 1. The level under the conduction band caused by the imperfection of crystal acts for the electron trap because it is initially empty and can accept the electrons. On the other hand, the level just above the valence band acts for the hole
trap because it is initially filled with electron and can accept the holes. The electrons and holes captured with these traps could keep the position stably when there is no other stimulation. The set of coupled differential equations governing the process during the excitation and stimulation by heat or light is
dni ¼ pi ni þ Ani ðNi ni Þnc Api ni mv ; dt
(1)
dmj ¼ pj mj þ Aqj Mj mj mv Amj mj nc ; dt
(2)
X X X dnc ¼Xþ pi ni Ani ðNi ni Þnc Amj mj nc ; dt i i j
(3)
X X X dmv ¼Xþ pj mj Aqj Mj mj mv Api ni mv : dt j j i
(4)
Here, ni, nc, mj and mv are the occupancies for the i-th electron trap, for the conduction band, the j-th hole trap and for the valence band respectively and all of them are functions of time. The coefficients (Ni,Ani,Api) related to the i-th electron trap are the concentration, the trapping probability from conduction band and the recombination probability for capturing holes from the valence band, respectively. Actually the finally mentioned recombination process is the transition of electrons from this trap to the holes in the valence band and light could be emitted from there as shown for a horizontal arrow in Fig. 1. (Mj,Aqj,Amj) related to the j-th hole trap are similar to the parameters of the electron trap. The final recombination process is also the transition of electrons in the conduction band to the holes in the hole trap and light could be emitted also. X denotes the transition probability of electrons from the valence band to the conduction band and it is proportional to the dose rate of excitation. It is understood as the production of electronehole pairs. pi (pj) is the transition probability rate of electrons (holes) stimulated out of the i-th electron traps (j-th hole trap) per unit time. This rate is related to the temperature T(t) and the photon flux F(t) and it is described by the following:
pi;j ¼ si;j exp Ei;j kT þ si;j F:
(5)
Here, Ei, si and si are the activation energy, preexponential factor and photoionization cross section of the i-th electron trap respectively. (The subscript j notes for the hole trap). X or p is the factor creating or exciting the electron and hole, and eventually induced the flow of charge. Table 1 displays how these factors are related to three processes of irradiation, relaxation and stimulation. The luminescence from the irradiation process is RL and the lights from the stimulation process are TL and OSL. The emitted RL/TL/OSL light, shown as the horizontal arrows in Fig. 1, is related to the rate of recombination of free electrons with holes, which is formulated by
I¼
X i
Api ni mv hi þ
X
Amj mj nc hj :
(6)
j
Here, hi as luminescence efficiency associated with the thermalTable 1 The existence of X and p in each irradiation, relaxation and stimulation stage.
Fig. 1. Schematic energyelevel diagram with various kind of electron trap and hole trap. Transitions of electron and hole occur both during excitation (X) and during stimulation by heat (T) or light (F).
Stage
Irradiation
Relaxation
Stimulation
X pi
Xs0 pi ¼ 0
X¼0 pi ¼ 0
X¼0 pi s 0
K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
quenching phenomenon is related with the properties of the i-th trap, Ki and Wi, as follows (Yukihara and McKeever, 2011).
hi ðTÞ ¼
1 1 þ Ki expð Wi =kTÞ
(7)
Provided that Ap s 0 in electron trap or Am s 0 in the hole trap, this trap is called as recombination center (RC) because it plays the role of recombining the electrons and holes. In the case of nonradiative RC, i.e. non-emitting light from the RC, Ki is regarded as ∞ so as to be hi ¼ 0. The entire procedures expressed in the above were perfectly symmetric for the electrons and holes. It was expected that there might be the same luminescence properties when the electrons were replaced with the holes and vice versa. Because the roles of the electron and hole cannot be classified actually from only RL/TL/ OSL, the other method, for example, the thermally stimulated exoelectron (TSEE) could additionally be used for clear classifying. Many dosimetric material were normally considered to have many types of electron traps and one or a few hole traps. Usually the electrons in the electron trap are not allowed to transit to the valence band directly (Ap ¼ 0) and the hole trap involves to the light emission in the role of the recombination center (Am s 0). The flow equations of Eqs. (1)e(4) are the non-linear simultaneous equations in combination of the conduction band and valence band to the number of electron and hole trap. The electric charge conservation is met because these equations keep the constant value of P P the total charge carrier, j mj þ mv i ni nc , naturally. The glow curve deconvolution is the work of calculating all properties of the traps from the measured I(t). But this process is typically difficult with the normal numerical analysis, because a small relative error in equations would cause a large error and the solutions are easily diverged within a few time steps. Considerable time is required for calculation in spite of using a special algorithm for avoiding such divergence. Moreover, it is more difficult to start from the estimation of the number of traps in case the trap to be introduced would not be well defined. We developed the method, named as quasi-static approximation (QSA), to solve the simultaneous equations for TL and OSL (Chung et al., 2011). It was easily checked that this approximation method could be applied to Eqs. (1)e(4) which additionally contain X by the irradiation. In the other words, all equations (ni, nc, mj, mv) have the time dependent variation which is negatively proportional to the own current concentration as follows.
df ¼ a bf dt
(8)
Here, f can be any concentration of (ni, nc, mj, mv) with positive values of a and b which are dependent on the other concentration except own concentration. In the QSA method, as and bs are considered as maintaining the almost constant values of a0 and b0 in short time. When the above equation is solved with this approximation, it becomes
f ðt0 þ DtÞzf0 eb0 Dt þ
a0 1 eb0 Dt : b0
(9)
This form of f does neither diverge nor oscillate in the subsequent calculating process as a0 and b0 are positive, and the stiffness of the original equation can be avoided. The usefulness of this method had been verified in the numerical analysis for the artificially generated glow curves with diversified physical properties. The properties of the given material could be restored higher than 99.99% accuracy by assuming the material with many electron traps and hole traps, creating the glow curves without approximating and analyzing the glow curves with QSA.
9
3. Algorithm for integrated analysis Light is promptly emitted by ionizing radiation on a dosimetric material (RL). RL from this process in most case is neglected because it is not measured in traditional TL and OSL. But such glow could give the information to decide the recombination probability Ani (Aqj) more clearly because pi (pj) is not involved in RL. Consequently, the physical parameters on the trap can be decided more accurately than the cases analyzed with only TL/OSL when TL/OSL including RL is analyzed at once. By means of this, the glow was measured consistently while the same measuring conditions were maintained by dividing into irradiation stage, relaxation stage and stimulation stage for this algorithm and such measurement finally composed one data set. The algorithm was made to analyze a few data sets at once even though different type radiation profile, thermal stimulation and light stimulation were applied to the same specimen. Let radiation dose, temperature and light applied on the specimen be Xk, Tk and Fk respectively. And let the corresponding glow be Ik. Here, the subscript k means the data measured at the time tk. Regard that the most proper numbers of the electron trap and hole trap to this specimen had been estimated from the glow curve using the stimulation with various profiles like Tm Tstop procedure (McKeever, 1985). The quantity of the simultaneous equations of Eqs. (1)e(4) is P þ Q þ 2 when the quantities of introduced electron trap and hole trap are P and Q respectively. Ap or Am will be 0 when each trap does not act for RC, and h ¼ 0 in case of no radiation even though it is RC. For electron trap, there are 8 properties of the material N, E, s, s, An, Ap, K and W when the properties of a trap are introduced without omission. Here, the initial electron concentration, n0 is added. The undefined parameters are 9(P þ Q) related to the trap because it is same in the hole trap. The initial concentration of the holes in valence band, mv0 and the initial concentration of the electrons in the conduction band, nc0 are added to the undefined parameters. In addition, the proportional coefficients are added for these measurements when the situation to be forced for the measuring device to measure not the absolute value but the relative one for three data except Tk out of 4 series of measurements for Ik, Xk, Tk and Fk. Besides those, all undefined coefficients are to be 9(P þ Q) þ 7 in maximum when background and blackbody radiation are added. Because of the difficulty of deconvolution for all the undefined coefficients with one glow curve, it is possible to put some undefined coefficients as fixed as mentions previously through physical consideration or to use the set of the glow curves measured in varied conditions. The series of glow, I(tk), from the stimulation by Xk, Tk and Fk will be calculated when a particular value is given to all undefined coefficients. The index for the fitting of the curve, figure of merit (FOM) is shown for
FOM ¼ 100
X jIðtk Þ Ik j=A
(10)
k
Here, Ik is measured glow and A is the area of entire glow curve. The FOM as defined in Eq. (10) is dimensionless, and the better it is, the smaller it is. It is regarded as good result when it is less than 3% usually. Here, the simplex method was adopted for the algorithm finding the coefficients making the smallest FOM (Gerald and Wheatley, 1994). The approximate scheme in making the program for this procedure is similar with that of Chung et al. (2012). The computer program written in C# by Microsoft Visual Studio.NET has the graphic user interface (GUI) as shown in Fig. 2. It is operated in Microsoft Windows system. It shows the composition with the measured glow curve (left) and the informations of traps and the
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K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
Fig. 2. The screen for executing the integrated analysis program for RL/TL/OSL.
measuring device (right). The meaning of each part on the screen is illustrated with speech balloon. Firstly, the measured glow data are marked with in the graph on the left. The glow curve is RL in the beginning and OSL after a short relaxation time. The RL for the irradiation in constant dose rate is shown almost as flat, and the glow is stopped immediately when the irradiation is terminated. The OSL displays the typical property of CW-OSL of Al2O3:C which is exemplified here. The data in the table on the right, namely the numerically analyzed glow curves by putting the values related to the properties of the trap and measuring device is shown in the bold line by overlapping with the measured glow data. The exemplified screen is the case for the good analysis comparatively. It is displayed that the measurements marked with and the theoretical data in solid line are quietly well coincided. The graph shows the change in the concentration of the electrons and holes on each trap as well. It is not shown here, but the introduction of the trap for the given measurements and adjusting the approximation of the data for each trap manually can be made through the separate dialog window. Especially, this program can analyze a few sets of the glow curves measured in the same specimen and with the same device at once as it was mentioned in the above.
4. The application result to Al2O3:C The efficiency of the algorithm developed in this study was verified with Al2O3:C (Landauer Inc.) which has been used widely for the OSL material. It was revealed that this material is involved into three types of the electron trap in OSL under room temperature and the response of optical stimulation in each trap has been known well. The experimental devices to measure the RL and OSL consistently are shown in Fig. 3. The radiation stimulation is facing down from the top and the X-ray (SOFTTEX K2, Japan, 60 kV, 5 mA) was used for the radioactive source. The optical stimulation was made from the LED facing upwards to the specimen obliquely when the X-ray radiation was terminated after a short period of relaxation. The glow curve was measured by keeping the same conditions in room temperature. There were three electron trap which are sensitive to the optical stimulation, one deep electron trap and one hole trap to be analyzed in Al2O3:C. The hole trap plays the role of RC, and it was possible to put h ¼ 1 because the W ¼ 1.1 eV and K ¼ 1011 had been known for its thermal quenching constants (Kitis, 2002). The electron on the deep trap could be regarded as not affected by the
Fig. 3. The configuration of the devices measuring the RL and OSL in sequence.
light stimulation or irradiation and had been saturated as it was analyzed to maintain constant value through the entire process. This glow curve satisfied the condition of N [ n(t) and M [ m(t) for the electron trap and hole trap respectively, and two undefined coefficients are combined into one like AnN and AqM. The number of the undefined coefficients for a pair of glow curves was reduced to 17 in consideration of a few points as mentioned. It was reported that one hole trap was glowing and the other one was nonradiative for two holes traps as RC played the central role of the recombining withAl2O3:C model (Zahedifar et al., 2012). But the reason of introducing the additional nonradiative RC was not found in this study. The analyzed results are shown in Fig. 4. Table 2 displays the properties of traps within Al2O3:C involving with luminescence. n0 (m0) is the concentration of the electron (hole) captured by the trap before the irradiation of radiation and nOSL is the concentration of the electron in the beginning of the OSL measurement after termination of RL. The result of FOM defined in Eq. (10) was 1.66% from analyzing the irradiation of X-ray for 30 and 60 s with same dose at the same time. It can be said as quietly exact in consideration of the concurrent analysis. Here, it shall be understood as a relative data because the unit of these data was not determined as the volume of the specimen and the acceptance of the measuring device were not considered.
K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
11
Fig. 4. Analyzed results through RL and OSL glow curve exposing Al2O3:C to the X-ray for 30 s (left graph) and 60 s (right graph). Time variations of electron and hole concentration in each trap are plotted in log scale (right axis). Hole concentration of valence band (mv) is not appeared here because its value is almostly 0 all the while.
Table 2 Results of devonvoluted parameters of two RL þ OSL glow curves of Al2O3:C irradiated with 30 s and 60 s X ray. Trap Electron#1 Electron#2 Electron#3 Deep Hole (RC)#1
n0 (m0) 0 0 0 3.02 109 3.02 109
s
NAn(MAq) 12
2.85 10 7.28 1013 1.01 1011 ~0 ~0
8.00 2.64 2.67 e 2.05
In conclusion, it was revealed that the electrons on the deep trap were captured in considerable amount in this specimen, in addition, the holes in same amount were initially captured on the hole trap. Also, there were three electron traps with differentiated photoionization cross section and they were related to three glows of fast (#3), mediate (#1) and slow (#2). The electrons were condensed in order of #1, #2 and #3 on respective trap at the start of OSL measuring. It could be understood as distributed in ratio of NAn, the probability of moving from the conduction band to the trap. In addition, the electron concentrations were considered as proportional to the time for the irradiation approximately. It was found that the #3 trap was emptied firstly when the optical stimulation was started and #1 and #2 were emptied sequentially. It was confirmed that considerable amount of the electrons emptied from #1 in the beginning filled #2 temporarily. 5. Conclusion and discussion The physical properties related to the luminescence could be estimated precisely when the RL and TL/OSL were measured consistently and analyzed integrally. It was found from the result applied to the glow curves of artificially generated and Al2O3:C. The value of the FOM defined in Eq. (10) was less than 0.01% for the case of artificially generated, even though the detailed results were not
Ap (Am) 3
10 103 103 1027
~0 ~0 ~0 ~0 4.67106
nOSL (30 s) 2.60 8.73 8.25 3.02 3.02
6
10 105 105 109 109
nOSL (60 s) 5.01 1.96 1.57 3.02 3.02
106 106 106 109 109
shown here. The FOM of Al2O3:C was confirmed as 1.66% as shown in the above. The result of such preciseness was considered because this analysis adopted more realistic model which reflects the traffic of electrons between the traps. Many properties were estimated properly in complement of integral analysis because the level of involving by the properties of RL and OSL was different. As it was shown in the schematic diagram of the experiment devices, the equipment for measuring RL and TL/OSL in the same condition was necessary to measure RL and TL/OSL for these analyses. The exclusive equipment specialized for the measurement could be helpful. It was easily used for the analysis because the program of integral analysis could be operated in GUI environment for its convenience to the user. The simplex method was adopted to estimate many properties, a few hours was consumed in analyzing a set of glow curves with usual personal computer. It took a long time in estimating the radiation dose immediately, but it could be regarded as reasonable when the unknown parameters were about 15~30. Provided that data range had been compressed owing to the considerably known properties of the material, the analysis time will be reduced. When the properties of material are known completely and so the electronehole production rate X, namely dose rate, is the only unknown parameter, it could be used to the real dosimetry because the glow curves could be analyzed within
12
K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
reasonable time. The application result of this program to Al2O3:C showed that the conventional model considering as having three electron traps and one hole trap was plausible. The existence of the deep trap not involving to the OSL at all was evident here. Expected that the OSL characteristics could be differed with the level of annealing, because it could be changed with annealing in high temperature in spite that the electrons captured by this trap could not come out rarely in ordinary situation. Consequently, it is required for measuring and analyzing RL and OSL by keeping the specimen temperature differently or after annealing in varied temperatures are necessary. For this matter, the exclusive equipment to experiment the thermal stimulation, optical stimulation and irradiation on the specimen in parallel will be useful as mentioned previously.
Acknowledgments This research was supported by the National Intermediate and Long Term Project of Nuclear Energy Development of the Ministry of Education, Science and Technology and by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology, Republic of Korea (Grant No. 2012R1A1A2006974).
References Chen, R., Pagonis, V., 2011. Thermally and Optically Stimulated Luminescence: a Simulation Approach. John Wiley & Sons Ltd, West Sussex. Chung, K.S., Choe, H.S., Lee, J.I., Kim, J.L., 2011. An algorithm for the deconvolution of the optically stimulated luminescence glow curves involving the mutual interactions among the electron traps. Radiat. Meas. 46, 1598e1601. Chung, K.S., Lee, J.I., Kim, J.L., 2012. A computer program for the deconvolution of the thermoluminescence glow curves by employing the interactive trap model. Radiat. Meas. 47, 766e769. Chung, K.S., Park, C.Y., Lee, J.I., Kim, J.L., 2013. Thermoluminescence glow curve deconvolution of LiF: Mg,Cu,Si with more realistic kinetic models. Radiat. Meas. 59, 151e154. Chung, K.S., Park, C.Y., Lee, J.I., Kim, J.L., 2014. An algorithm for unified analysis on the thermoluminescence glow curve. Radiat. Meas. 71, 193e196. Gerald, C.F., Wheatley, P.O., 1994. Applied Numerical Analysis. Addison Wesley, New York. Halperin, A., Braner, A.A., 1960. Evaluation of thermal activation energies from glow curves. Phys. Rev. 117, 408e415. Kitis, G., 2002. Confirmation of the influence of thermal quenching on the initial rise method in a-Al2O3:C. Phys. Status Solidi A 191, 621e627. McKeever, S.W.S., 1985. Thermoluminescence of Solids. Cambridge University Press, Cambridge. Sakurai, T., 2001. Fatal defect in computerized glow curve deconvolution of thermoluminescence. J. Phys. D. Appl. Phys. 34, L105eL107. Yukihara, E.G., McKeever, S.W.S., 2011. Optically Stimulated Luminescence: Fundamentals and Applications. John Wiley & Sons. Zahedifar, M., Eshraghi, L., Sadeghi, E., 2012. Thermoluminescence kinetics analysis of a-Al2O3:C at different dose levels and populations of trapping states and a model for its dose response. Radiat. Meas. 47, 957e964.
Contents lists available at ScienceDirect
Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas
An algorithm for the integrated deconvolution of radioluminescence and thermally/optically stimulated luminescence glow curves K.S. Chung a, *, C.Y. Park a, J.I. Lee b, J.L. Kim b a b
The Research Institute of Natural Science and Department of Physics, Gyeongsang National University, Jinju 660-701, South Korea Health Physics Team, Korea Atomic Energy Research Institute, P.O. Box 105, Yuseong, Daejeon 305-600, South Korea
h i g h l i g h t s RL, TL and OSL glow curve deconvolution employing interacting model. Simulation both irradiation and TL/OSL readout stages for various dose level. Application in the identification OSL kinetics of Al2O3:C.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 February 2015 Received in revised form 9 April 2015 Accepted 11 May 2015 Available online 20 May 2015
Radioluminecscence (RL), the light emitted from a material immediately upon ionizing radiation, has been used to detect the dose rate. On the other hand, thermoluminescence (TL) and optically stimulated luminescence (OSL) by the stimulation with the heat and light after irradiation have been used to find out the cumulated radiation dose. Because it was considered as effective to handle these three phenomena in integration to estimate the energy band structure of the material precisely, an algorithm for calculating the glow rapidly and consistently was developed in this study when three types of stimulations including irradiation are applied concurrently or sequentially. The deconvolution using this algorithm can decide the properties contained in the material more precisely because the glows from different stimulations are related frequently to the different aspects of the properties. The computer program to realize the deconvolution by means of these schemes was also developed and it was applied to the glow curves of RL and OSL from Al2O3:C to evaluate the efficiency of the developed algorithm. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Radioluminescence (RL) Thermoluminescence (TL) Optically stimulated luminescence (OSL) Glow curve deconvolution
1. Introduction Radioluminescence (RL), thermoluminescence (TL) and optically stimulated luminescence (OSL) are the luminescence commonly related to the energy level of materials (Chen and Pagonis, 2011). These are the emission of light from a crystalline material such as insulator or semiconductor by recombination of the electrons and holes created by the irradiation immediately (RL), with heat stimulation (TL) or with light stimulation (OSL). The energy structure of the crystal can be found by analyzing the glow curves corresponding to specific stimulations. Provided that the electrons and holes are stably captured within the trap positioned at the forbidden band of the crystal, the absorbed dose on the material can be estimated by means of TL and OSL. Accordingly, these
* Corresponding author. E-mail address: [email protected] (K.S. Chung). http://dx.doi.org/10.1016/j.radmeas.2015.05.006 1350-4487/© 2015 Elsevier Ltd. All rights reserved.
phenomena are being broadly used in dosimetry as well as in dating of archaeological samples (McKeever, 1985; Botter-Jensen, 2003). However, RL is used to measure ionizing radiation in real time by detecting the light emerged from a material when it is irradiated. Even though the mechanisms of RL, TL and OSL are identically related to the energy band structure, they have been studied independently in most cases. Because the traps are created by the presence of impurities or crystal defects in crystal, it is necessary to find the trend of differing the energy level structure depending on the complication of impurities injected into the material or the manufacturing process in order to develop an efficient dosimetric material. For these purposes, the glow curve deconvolution analyzing the trap information from the glow curve has been used. Many algorithms and computer programs for the glow curve deconvolution have been developed for dosimetric purposes (Chen and Pagonis, 2011). But most of these algorithms are based on the assumption that each trap
8
K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
independently composes one glow curve. This assumption is based on a simplified model of one trap and one recombination center (OTOR) which make a glow peak. The superposition of these peaks makes the whole glow curve consisting of many overlapping peaks. It is general to interpret a certain glow curve by making further assumptions (Halperin and Braner, 1960). But this model does not reflect the physical reality because the interaction possibility of the electrons or holes moving between traps via the conduction band or the valence band is excluded (Sakurai, 2001). Therefore, we developed the appropriate numerical analysis method to solve the flow equations reflecting all possible flows of electrons and holes through the conduction band and through the valence band. By applying this method, the glow curves of TL and OSL was analyzed efficiently (Chung et al., 2011, 2012, 2013, 2014). However, the glow curves are not analyzed easily which require several types of trap because there are many parameters in each trap, and the flow equations of the electrons and holes are closely related each other. It is due to the fact that particular parameters are situated to affect the glow less or two or more parameters affect to the glow in combination under the measuring conditions. A set of the glow curves measured by wide range of radiation dose and various profiles of stimulation shall be analyzed on the same specimen integrally in order to avoid such ambiguities. Nevertheless, this method is limited in use because the repeated measuring on the same specimen may change the physical properties such as the accumulation of the electrons in deep trap and etc. The algorithm analyzing glow curves emitted from the concurrent or sequential application of ionizing radiation, thermal stimulation and light stimulation was developed in this study. The computer program realizing and investigating this algorithm was developed as well. The cases of continuous measuring of RL and OSL, i.e. after applying the irradiation for certain duration and the light stimulation after a short relaxation time on the specimen, could be taken as an example. It was expected that each parameter can be calculated more precisely when two glow curves were analyzed integrally because many parameters on the trap contributed to RL and OSL differently in this case.
2. Model and numerical analysis Electron-hole pairs are created when the electrons in the valence band are excited by the irradiation on the crystal with the energy level model shown in Fig. 1. The level under the conduction band caused by the imperfection of crystal acts for the electron trap because it is initially empty and can accept the electrons. On the other hand, the level just above the valence band acts for the hole
trap because it is initially filled with electron and can accept the holes. The electrons and holes captured with these traps could keep the position stably when there is no other stimulation. The set of coupled differential equations governing the process during the excitation and stimulation by heat or light is
dni ¼ pi ni þ Ani ðNi ni Þnc Api ni mv ; dt
(1)
dmj ¼ pj mj þ Aqj Mj mj mv Amj mj nc ; dt
(2)
X X X dnc ¼Xþ pi ni Ani ðNi ni Þnc Amj mj nc ; dt i i j
(3)
X X X dmv ¼Xþ pj mj Aqj Mj mj mv Api ni mv : dt j j i
(4)
Here, ni, nc, mj and mv are the occupancies for the i-th electron trap, for the conduction band, the j-th hole trap and for the valence band respectively and all of them are functions of time. The coefficients (Ni,Ani,Api) related to the i-th electron trap are the concentration, the trapping probability from conduction band and the recombination probability for capturing holes from the valence band, respectively. Actually the finally mentioned recombination process is the transition of electrons from this trap to the holes in the valence band and light could be emitted from there as shown for a horizontal arrow in Fig. 1. (Mj,Aqj,Amj) related to the j-th hole trap are similar to the parameters of the electron trap. The final recombination process is also the transition of electrons in the conduction band to the holes in the hole trap and light could be emitted also. X denotes the transition probability of electrons from the valence band to the conduction band and it is proportional to the dose rate of excitation. It is understood as the production of electronehole pairs. pi (pj) is the transition probability rate of electrons (holes) stimulated out of the i-th electron traps (j-th hole trap) per unit time. This rate is related to the temperature T(t) and the photon flux F(t) and it is described by the following:
pi;j ¼ si;j exp Ei;j kT þ si;j F:
(5)
Here, Ei, si and si are the activation energy, preexponential factor and photoionization cross section of the i-th electron trap respectively. (The subscript j notes for the hole trap). X or p is the factor creating or exciting the electron and hole, and eventually induced the flow of charge. Table 1 displays how these factors are related to three processes of irradiation, relaxation and stimulation. The luminescence from the irradiation process is RL and the lights from the stimulation process are TL and OSL. The emitted RL/TL/OSL light, shown as the horizontal arrows in Fig. 1, is related to the rate of recombination of free electrons with holes, which is formulated by
I¼
X i
Api ni mv hi þ
X
Amj mj nc hj :
(6)
j
Here, hi as luminescence efficiency associated with the thermalTable 1 The existence of X and p in each irradiation, relaxation and stimulation stage.
Fig. 1. Schematic energyelevel diagram with various kind of electron trap and hole trap. Transitions of electron and hole occur both during excitation (X) and during stimulation by heat (T) or light (F).
Stage
Irradiation
Relaxation
Stimulation
X pi
Xs0 pi ¼ 0
X¼0 pi ¼ 0
X¼0 pi s 0
K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
quenching phenomenon is related with the properties of the i-th trap, Ki and Wi, as follows (Yukihara and McKeever, 2011).
hi ðTÞ ¼
1 1 þ Ki expð Wi =kTÞ
(7)
Provided that Ap s 0 in electron trap or Am s 0 in the hole trap, this trap is called as recombination center (RC) because it plays the role of recombining the electrons and holes. In the case of nonradiative RC, i.e. non-emitting light from the RC, Ki is regarded as ∞ so as to be hi ¼ 0. The entire procedures expressed in the above were perfectly symmetric for the electrons and holes. It was expected that there might be the same luminescence properties when the electrons were replaced with the holes and vice versa. Because the roles of the electron and hole cannot be classified actually from only RL/TL/ OSL, the other method, for example, the thermally stimulated exoelectron (TSEE) could additionally be used for clear classifying. Many dosimetric material were normally considered to have many types of electron traps and one or a few hole traps. Usually the electrons in the electron trap are not allowed to transit to the valence band directly (Ap ¼ 0) and the hole trap involves to the light emission in the role of the recombination center (Am s 0). The flow equations of Eqs. (1)e(4) are the non-linear simultaneous equations in combination of the conduction band and valence band to the number of electron and hole trap. The electric charge conservation is met because these equations keep the constant value of P P the total charge carrier, j mj þ mv i ni nc , naturally. The glow curve deconvolution is the work of calculating all properties of the traps from the measured I(t). But this process is typically difficult with the normal numerical analysis, because a small relative error in equations would cause a large error and the solutions are easily diverged within a few time steps. Considerable time is required for calculation in spite of using a special algorithm for avoiding such divergence. Moreover, it is more difficult to start from the estimation of the number of traps in case the trap to be introduced would not be well defined. We developed the method, named as quasi-static approximation (QSA), to solve the simultaneous equations for TL and OSL (Chung et al., 2011). It was easily checked that this approximation method could be applied to Eqs. (1)e(4) which additionally contain X by the irradiation. In the other words, all equations (ni, nc, mj, mv) have the time dependent variation which is negatively proportional to the own current concentration as follows.
df ¼ a bf dt
(8)
Here, f can be any concentration of (ni, nc, mj, mv) with positive values of a and b which are dependent on the other concentration except own concentration. In the QSA method, as and bs are considered as maintaining the almost constant values of a0 and b0 in short time. When the above equation is solved with this approximation, it becomes
f ðt0 þ DtÞzf0 eb0 Dt þ
a0 1 eb0 Dt : b0
(9)
This form of f does neither diverge nor oscillate in the subsequent calculating process as a0 and b0 are positive, and the stiffness of the original equation can be avoided. The usefulness of this method had been verified in the numerical analysis for the artificially generated glow curves with diversified physical properties. The properties of the given material could be restored higher than 99.99% accuracy by assuming the material with many electron traps and hole traps, creating the glow curves without approximating and analyzing the glow curves with QSA.
9
3. Algorithm for integrated analysis Light is promptly emitted by ionizing radiation on a dosimetric material (RL). RL from this process in most case is neglected because it is not measured in traditional TL and OSL. But such glow could give the information to decide the recombination probability Ani (Aqj) more clearly because pi (pj) is not involved in RL. Consequently, the physical parameters on the trap can be decided more accurately than the cases analyzed with only TL/OSL when TL/OSL including RL is analyzed at once. By means of this, the glow was measured consistently while the same measuring conditions were maintained by dividing into irradiation stage, relaxation stage and stimulation stage for this algorithm and such measurement finally composed one data set. The algorithm was made to analyze a few data sets at once even though different type radiation profile, thermal stimulation and light stimulation were applied to the same specimen. Let radiation dose, temperature and light applied on the specimen be Xk, Tk and Fk respectively. And let the corresponding glow be Ik. Here, the subscript k means the data measured at the time tk. Regard that the most proper numbers of the electron trap and hole trap to this specimen had been estimated from the glow curve using the stimulation with various profiles like Tm Tstop procedure (McKeever, 1985). The quantity of the simultaneous equations of Eqs. (1)e(4) is P þ Q þ 2 when the quantities of introduced electron trap and hole trap are P and Q respectively. Ap or Am will be 0 when each trap does not act for RC, and h ¼ 0 in case of no radiation even though it is RC. For electron trap, there are 8 properties of the material N, E, s, s, An, Ap, K and W when the properties of a trap are introduced without omission. Here, the initial electron concentration, n0 is added. The undefined parameters are 9(P þ Q) related to the trap because it is same in the hole trap. The initial concentration of the holes in valence band, mv0 and the initial concentration of the electrons in the conduction band, nc0 are added to the undefined parameters. In addition, the proportional coefficients are added for these measurements when the situation to be forced for the measuring device to measure not the absolute value but the relative one for three data except Tk out of 4 series of measurements for Ik, Xk, Tk and Fk. Besides those, all undefined coefficients are to be 9(P þ Q) þ 7 in maximum when background and blackbody radiation are added. Because of the difficulty of deconvolution for all the undefined coefficients with one glow curve, it is possible to put some undefined coefficients as fixed as mentions previously through physical consideration or to use the set of the glow curves measured in varied conditions. The series of glow, I(tk), from the stimulation by Xk, Tk and Fk will be calculated when a particular value is given to all undefined coefficients. The index for the fitting of the curve, figure of merit (FOM) is shown for
FOM ¼ 100
X jIðtk Þ Ik j=A
(10)
k
Here, Ik is measured glow and A is the area of entire glow curve. The FOM as defined in Eq. (10) is dimensionless, and the better it is, the smaller it is. It is regarded as good result when it is less than 3% usually. Here, the simplex method was adopted for the algorithm finding the coefficients making the smallest FOM (Gerald and Wheatley, 1994). The approximate scheme in making the program for this procedure is similar with that of Chung et al. (2012). The computer program written in C# by Microsoft Visual Studio.NET has the graphic user interface (GUI) as shown in Fig. 2. It is operated in Microsoft Windows system. It shows the composition with the measured glow curve (left) and the informations of traps and the
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K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
Fig. 2. The screen for executing the integrated analysis program for RL/TL/OSL.
measuring device (right). The meaning of each part on the screen is illustrated with speech balloon. Firstly, the measured glow data are marked with in the graph on the left. The glow curve is RL in the beginning and OSL after a short relaxation time. The RL for the irradiation in constant dose rate is shown almost as flat, and the glow is stopped immediately when the irradiation is terminated. The OSL displays the typical property of CW-OSL of Al2O3:C which is exemplified here. The data in the table on the right, namely the numerically analyzed glow curves by putting the values related to the properties of the trap and measuring device is shown in the bold line by overlapping with the measured glow data. The exemplified screen is the case for the good analysis comparatively. It is displayed that the measurements marked with and the theoretical data in solid line are quietly well coincided. The graph shows the change in the concentration of the electrons and holes on each trap as well. It is not shown here, but the introduction of the trap for the given measurements and adjusting the approximation of the data for each trap manually can be made through the separate dialog window. Especially, this program can analyze a few sets of the glow curves measured in the same specimen and with the same device at once as it was mentioned in the above.
4. The application result to Al2O3:C The efficiency of the algorithm developed in this study was verified with Al2O3:C (Landauer Inc.) which has been used widely for the OSL material. It was revealed that this material is involved into three types of the electron trap in OSL under room temperature and the response of optical stimulation in each trap has been known well. The experimental devices to measure the RL and OSL consistently are shown in Fig. 3. The radiation stimulation is facing down from the top and the X-ray (SOFTTEX K2, Japan, 60 kV, 5 mA) was used for the radioactive source. The optical stimulation was made from the LED facing upwards to the specimen obliquely when the X-ray radiation was terminated after a short period of relaxation. The glow curve was measured by keeping the same conditions in room temperature. There were three electron trap which are sensitive to the optical stimulation, one deep electron trap and one hole trap to be analyzed in Al2O3:C. The hole trap plays the role of RC, and it was possible to put h ¼ 1 because the W ¼ 1.1 eV and K ¼ 1011 had been known for its thermal quenching constants (Kitis, 2002). The electron on the deep trap could be regarded as not affected by the
Fig. 3. The configuration of the devices measuring the RL and OSL in sequence.
light stimulation or irradiation and had been saturated as it was analyzed to maintain constant value through the entire process. This glow curve satisfied the condition of N [ n(t) and M [ m(t) for the electron trap and hole trap respectively, and two undefined coefficients are combined into one like AnN and AqM. The number of the undefined coefficients for a pair of glow curves was reduced to 17 in consideration of a few points as mentioned. It was reported that one hole trap was glowing and the other one was nonradiative for two holes traps as RC played the central role of the recombining withAl2O3:C model (Zahedifar et al., 2012). But the reason of introducing the additional nonradiative RC was not found in this study. The analyzed results are shown in Fig. 4. Table 2 displays the properties of traps within Al2O3:C involving with luminescence. n0 (m0) is the concentration of the electron (hole) captured by the trap before the irradiation of radiation and nOSL is the concentration of the electron in the beginning of the OSL measurement after termination of RL. The result of FOM defined in Eq. (10) was 1.66% from analyzing the irradiation of X-ray for 30 and 60 s with same dose at the same time. It can be said as quietly exact in consideration of the concurrent analysis. Here, it shall be understood as a relative data because the unit of these data was not determined as the volume of the specimen and the acceptance of the measuring device were not considered.
K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
11
Fig. 4. Analyzed results through RL and OSL glow curve exposing Al2O3:C to the X-ray for 30 s (left graph) and 60 s (right graph). Time variations of electron and hole concentration in each trap are plotted in log scale (right axis). Hole concentration of valence band (mv) is not appeared here because its value is almostly 0 all the while.
Table 2 Results of devonvoluted parameters of two RL þ OSL glow curves of Al2O3:C irradiated with 30 s and 60 s X ray. Trap Electron#1 Electron#2 Electron#3 Deep Hole (RC)#1
n0 (m0) 0 0 0 3.02 109 3.02 109
s
NAn(MAq) 12
2.85 10 7.28 1013 1.01 1011 ~0 ~0
8.00 2.64 2.67 e 2.05
In conclusion, it was revealed that the electrons on the deep trap were captured in considerable amount in this specimen, in addition, the holes in same amount were initially captured on the hole trap. Also, there were three electron traps with differentiated photoionization cross section and they were related to three glows of fast (#3), mediate (#1) and slow (#2). The electrons were condensed in order of #1, #2 and #3 on respective trap at the start of OSL measuring. It could be understood as distributed in ratio of NAn, the probability of moving from the conduction band to the trap. In addition, the electron concentrations were considered as proportional to the time for the irradiation approximately. It was found that the #3 trap was emptied firstly when the optical stimulation was started and #1 and #2 were emptied sequentially. It was confirmed that considerable amount of the electrons emptied from #1 in the beginning filled #2 temporarily. 5. Conclusion and discussion The physical properties related to the luminescence could be estimated precisely when the RL and TL/OSL were measured consistently and analyzed integrally. It was found from the result applied to the glow curves of artificially generated and Al2O3:C. The value of the FOM defined in Eq. (10) was less than 0.01% for the case of artificially generated, even though the detailed results were not
Ap (Am) 3
10 103 103 1027
~0 ~0 ~0 ~0 4.67106
nOSL (30 s) 2.60 8.73 8.25 3.02 3.02
6
10 105 105 109 109
nOSL (60 s) 5.01 1.96 1.57 3.02 3.02
106 106 106 109 109
shown here. The FOM of Al2O3:C was confirmed as 1.66% as shown in the above. The result of such preciseness was considered because this analysis adopted more realistic model which reflects the traffic of electrons between the traps. Many properties were estimated properly in complement of integral analysis because the level of involving by the properties of RL and OSL was different. As it was shown in the schematic diagram of the experiment devices, the equipment for measuring RL and TL/OSL in the same condition was necessary to measure RL and TL/OSL for these analyses. The exclusive equipment specialized for the measurement could be helpful. It was easily used for the analysis because the program of integral analysis could be operated in GUI environment for its convenience to the user. The simplex method was adopted to estimate many properties, a few hours was consumed in analyzing a set of glow curves with usual personal computer. It took a long time in estimating the radiation dose immediately, but it could be regarded as reasonable when the unknown parameters were about 15~30. Provided that data range had been compressed owing to the considerably known properties of the material, the analysis time will be reduced. When the properties of material are known completely and so the electronehole production rate X, namely dose rate, is the only unknown parameter, it could be used to the real dosimetry because the glow curves could be analyzed within
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K.S. Chung et al. / Radiation Measurements 79 (2015) 7e12
reasonable time. The application result of this program to Al2O3:C showed that the conventional model considering as having three electron traps and one hole trap was plausible. The existence of the deep trap not involving to the OSL at all was evident here. Expected that the OSL characteristics could be differed with the level of annealing, because it could be changed with annealing in high temperature in spite that the electrons captured by this trap could not come out rarely in ordinary situation. Consequently, it is required for measuring and analyzing RL and OSL by keeping the specimen temperature differently or after annealing in varied temperatures are necessary. For this matter, the exclusive equipment to experiment the thermal stimulation, optical stimulation and irradiation on the specimen in parallel will be useful as mentioned previously.
Acknowledgments This research was supported by the National Intermediate and Long Term Project of Nuclear Energy Development of the Ministry of Education, Science and Technology and by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology, Republic of Korea (Grant No. 2012R1A1A2006974).
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