Journal of Luminescence 174 (2016) 42–48

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Journal of Luminescence

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Full Length Article

Thermally modulated optically stimulated luminescence (TM–OSL)as a tool of trap parameter analysis

Alicja Chruścińska n, N. KijekInstitute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Torun, Poland

a r t i c l e i n f o

Article history:Received 19 June 2015Accepted 10 January 2016Available online 5 February 2016

Keywords:Optically stimulated luminescenceThermally modulated stimulationOptical trap depth

x.doi.org/10.1016/j.jlumin.2016.01.01213/& 2016 Elsevier B.V. All rights reserved.

esponding author. Tel.: +48 566113316.ail address: alicja@fizyka.umk.pl (A. Chruścińs

a b s t r a c t

The methods of optically stimulated luminescence (OSL) measurements used until recently, used opticalstimulation with a constant energy and a constant or linearly increased flux of stimulation photons.During such a stimulation the ratio of probabilities of the optical release of electrons from different trapsis constant and it is hard to separate the signals of different origins. It was shown recently that advan-tageous changes of the probability ratio during the OSL experiments, and more information about trapscan be obtained by optical stimulation with the increasing stimulation energy. This method, however,needs a strong tuneable light source that supplies a stable flux of photons and because of that it cannotfind a wide application. Inducing the appropriate changes of the probabilities of the optical release ofelectrons from traps by increasing the sample temperature during the optical stimulation with a constantstimulation band do not face such obstacles. Such a stimulation can be realised by means of the standardOSL readers after a slight modification and offers the possibility for direct estimation of optical trapdepth. The simulations of the OSL process during linear heating show that the experimental parameterssuch as the heating rate, the stimulation light intensity and the stimulation energy strongly affect theshape of the OSL curve and can be the very useful tools for the OSL process regulation. By this kind ofstimulation one can reach very deep traps that are not detectable by thermoluminescence measurementsbelow 500 °C. The resolution of the OSL signal originating from different traps is remarkable.

& 2016 Elsevier B.V. All rights reserved.

1. Introduction

The parameter that specifies the kinds of traps in opticallystimulated luminescence (OSL) measurements is the optical cross-section (OCS) σ (cm2). However, it is not defined unambiguously. Itdepends on the optical trap depth E and the parameters deter-mining the strength of electron–phonon coupling as well as on thestimulation energy (the energy of photons used for optical sti-mulation) and temperature. In the simplest model that assumes asingle configuration–coordinate for the transition of electronsfrom traps to the conduction band and equal force constants forthe trap and the conduction band, these parameters are theHuang-Rhys factor S and the phonon energy specific for the trapcentre hω/2π. The dependence of OCS on the stimulation energyhν and the temperature T (x is a bound variable having thedimension of energy) has the following form [1,2]:

σ hνð Þ ¼ κν

ffiffiffiffiπ

pZ 1

0x12exp �κ2 x� hν�Eð Þ� � 2� �

dx ð1Þ

ka).

κ ¼ 2S ℏωð Þ2 coth ℏω=2kT� �h i

� 12 ð2Þ

the calculations of the improper integral can be simplified bynarrowing the integration range to a few electron volts. This doesnot change the value of σ(hν) noticeably [1].

Up to now, the methods of OSL measurement, when used fortrap investigations, have relied on recording luminescence decayduring the optical stimulation with a constant energy hν and aconstant (Continuous Wave - OSL, CW–OSL) or linearly increased(Linearly Modulated - OSL, LM–OSL) flux of stimulation photons f[3,4]. During these measurements the ratio of probabilities of theoptical release of electrons from traps (ϕ¼ f σ ) that have differentoptical cross-sections σ1 and σ2 is constant: f σ1/f σ2¼const,because σ1 and σ2 remain constant at constant temperature andconstant stimulation energy. This means that it is hard to separatethe signal originating from different traps. In particular, the initialoptical emptying of shallower traps before investigating the dee-per ones does not bring good results [5], contrary to the TL analysiswhere the initial thermal emptying of the shallow traps is a usualtreatment when a signal from deep traps is going to be tested. Inthe TL measurements, the ratio of probabilities of the thermalrelease of electrons from different traps changes in such a way that

A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–48 43

it is possible to empty the shallow traps effectively withoutdepopulating the deeper traps (for example by the multipleheating of the sample in a narrow temperature range significantlybelow the range of thermal emptying the deeper traps in thefractional glow technique). As it was shown recently, the similaradvantageous changes of the probability ratio during the OSLexperiments, and in consequence more information about the trapthan only the OCS value, can be obtained by inducing the changesof OCSs by increasing the stimulation energy (Variable Energy ofStimulation - OSL, VES-OSL) [6,7]. This method requires a strongtuneable light source that supplies the stable flux of photonsduring the stimulation energy changes and, presumably, becauseof this the VES-OSL cannot be widely used. Such limitations,however, do not concern the possibility of inducing the OCSchanges by increasing the temperature. The thermally modulatedOSL (TM–OSL) measurement can be realised by means of thestandard OSL readers after a slight modification.

The method of experiment that is going to be presented here isrelated to a measurement called thermo-optical luminescence(TOL) [8–12], however, the difference between the proposedregime of stimulation and the TOL should be noted. In the TOLexperiment the OSL signal is stimulated by short (e.g. 0.1 s) pulsesevery few degrees (e.g.10 °C) during the linear heating (a fewdegrees per second) in order to test the OSL intensity at highertemperatures. In this way the thermal assistance effects can beinvestigated. In the TM–OSL method proposed here a continuousstimulation is used in order to cause the OCS changes during thestimulation and generate the OSL curve shape that can help toobtain more information about the trap, e.g. the optical depth oftrap and the electron–phonon coupling parameters, in the fra-mework of the simplest OSL models. Although it was earliershown how the OCS depends on temperature [2,13], this work,beside its main aim, gives a deeper insight into the character ofthis dependence and its relation with trap parameters.

The main objective of this work is to demonstrate the possi-bilities of the optical stimulation during heating. The simulationshave been realised for a basic OSL model that assumes the tran-sition through the conduction band and includes one trap and oneluminescence centre and, next, for a model including two kinds oftraps and one luminescence centre. The second case has beenchosen in order to test the resolution of such a method, i.e. itsability to separate the OSL signal from different traps. The two-traps model also allows investigation of the effects related to thecompetition of different channels of the electron relaxation fromthe conduction band and their influence on the reliability of trapparameters estimated by a proposed method of the experimentalcurve analysis. The quality of the recovery of the parameters usedin OSL modelling by the curve analysis method is a simple test ofthe practical usefulness of the proposed measurement technique.

A useful tool for the OSL data analysis when the trap para-meters are intended to be estimated is the OSL curve for first-order kinetics. Here an adequate analytical function for the pre-sented stimulation technique is given and compared with theshape of OSL curve obtained from the modelling.

2. Modelling

Three successive processes - the trap filling during irradiation,the relaxation after irradiation and the optical stimulation duringheating have been realised by the simulations. The followingdifferential equations system have been solved for modelling allthe above-mentioned processes in the case of one trap-one

luminescence centre model:

dndt

¼ �φ Σ Tð Þn�sexp �ET=kT� �

nþA N�nð Þ nc ; ð3Þ

dmdt

¼ Am M�mð Þ mv�β m nc; ð4Þ

dnc

dt¼ Rþφ Σ Tð Þnþsexp �ET=kT

� �n�A N�nð Þ nc �β m nc; ð5Þ

dmv

dt¼ R�Am M�mð Þ mv; ð6Þ

mþmv ¼ nþnc; ð7ÞAdditionally, only for an easy demonstration of the resolution

potential of the investigated stimulation method a widened modelfor two traps was used:

dni

dt¼ �φ Σ i Tð Þni�siexp �ETi=kT

� �niþAi Ni�nið Þ nc ; i¼ 1; 2 ;

ð8Þ

dmdt

¼ Am M�mð Þ mv�β m nc; ð9Þ

dnc

dt¼ Rþ

X2i ¼ 1

φ Σ i Tð Þ ni�Ai Ni�nið Þ nc�

þsiexp �ETi=kT� �

ni��β m nc; ð10Þ

dmv

dt¼ R�Am M�mð Þ mv; ð11Þ

mþmv ¼X2i ¼ 1

niþnc; ð12Þ

where N (cm�3) and n (cm�3) or Ni (cm�3) and ni (cm�3) i¼1, 2,are the concentrations of trapping states and trapped electrons inthe traps, respectively; M (cm�3) and m (cm�3) are the con-centration of recombination centres and the concentration ofholes trapped in these centres; nc (cm�3) and mv (cm�3) are theconcentrations of free electrons and holes, respectively; ET or ETi(eV) i¼1, 2, are the thermal trap depths and ET ¼ E - S(h/2π)ω, s(s�1) or si (s�1) i¼1, 2, are the frequency factors of traps, A(cm3 s�1) or Ai (cm3 s�1), i¼1, 2, are the probabilities of electrontrapping in the traps, Am (cm3 s�1) is the probability of holetrapping in the recombination centre, β (cm3 s�1) is the prob-ability of a free electron recombination with a hole trapped in theluminescence centre; R is the intensity of the excitation irradiationproducing pairs of free electrons and holes (it is taken as5x109 cm�3 s�1 during excitation process and 0 for other pro-cesses), ϕ – the photon flux used for the optical stimulation(cm�2 s�1, ϕ¼0 during the excitation and relaxation). The OSLintensity during the stimulation is given by: I(t) ¼�dm/dt. Thevalue Σ or Σi (cm2) is the so called effective OCS (EOCS) that allowsthe shape of the spectral band of optical stimulation to be takeninto account in the kinetics equations. The EOCS is a kind ofweighted average of the OCS value over the range of the stimu-lation band where the weight is determined by the shape of thestimulation band and it is expressed by the following formula [14]:

Σ ¼Z hν2

hν1Φ hνð Þσ hνð Þdhν=

Z hν2

hν1Φ hνð Þdhν; ð13Þ

where hν1 and hν2 are the stimulation band limits,Φ(hν) (eV�1) isthe shape of the spectral band and σ is expressed by Eqs. (1) and(2). In this study the function Φ has been approximated by aGaussian function with the half-width of about 30 nm. All calcu-lations have been performed using the differential equation solver

Fig. 1. The TM–OSL curves obtained for the one-trap model for four differentoptical depths of traps: 2.2, 2.4, 2.45 and 2.6 eV. On the separate parts of the figureresults for three values of the stimulation band maximum, 620 nm (a), 600 nm(b) and 580 nm (c), are presented. Additionally, for a clear demonstration of thetemperature ranges where the effective thermal trap depopulation appears in thecase of the traps for 2.4, 2.45. 2.6 eV, the TL curves (obtained with the same heatingrate) are shown as dashed lines in part (a). The following model parameters arefixed during the simulation for all parts of the figure: N ¼1012 cm�3, M¼1013 cm�3, A ¼10�10 cm3 s�1, Am¼ 4�10�11 cm3 s�1, β ¼10�8 cm3 s�1, S¼ 20,hω/2π ¼0.02 eV, s ¼1013 s�1, ϕ¼1017 cm�2 s�1, w¼1 Ks�1, the excitation timewas 105 s.

A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–4844

– ode23 s, which is specially designed for stiff equation sets in theMATLAB environment.

The parameter that in one trap – one luminescence centremodel is the one mainly responsible for the kinetics order of theOSL process is the probability of electron trapping A. In the case oftwo-traps model, in order to minimise the complications causedby the effects of trap coupling the values of A1 and A2 have beenchosen in such a way that each trap, treated separately, could fulfilthe assumption of first order kinetics. Therefore the whole analysisconcerns the cases for which the first order kinetics of the OSLprocess is expected and the sum of first order OSL curves can befitted to the experimental curves.

In simulations of the OSL measurement during the linearheating: T¼T0þwt (here w is the heating rate), the probability ofoptical excitation of electrons from a trap to the conduction bandϕσ(T) increases during the stimulation and, as a consequence, thesame applies to the EOCS, which changes its value during thestimulation according to the formula:

Σ Tð Þ ¼Z hν2

hν1Φ hνð Þσ T ;hνð Þdhν=

Z hν2

hν1Φ hνð Þdhν ð14Þ

In the case of such stimulation the first-order kinetics curve fora single trap is a peak-shaped curve that is similar to the Randall-Wilkins TL curve. Its form can be derived, analogously like the TLfirst-order TL curve [3], when the quasi-equilibrium assumption

dndt

; dm

dt

44

dnc

dt

� 0 ð15Þ

and the first order assumption

A N�nð Þ ooβ m ð16Þare taken into account for a one trap - one luminescence centremodel. When, because of Eq. (16), one omits the term A(N�n)nc,Eq. (3) can be analytically solved and, taking into account thatT¼T0þwt, an expression for n(T) can be obtained:

n Tð Þ ¼ n0 exp½� 1=α� � Z T

T0

φ Σ T 0� �þsexpð�ET=kT0Þ� �dT 0�: ð17Þ

Using the same assumptions (Eqs. (15) and (16)) one can obtainfrom Eq. (5) (R¼0 for optical stimulation process):

nc ¼φ Σ Tð Þþsexp �ET=kT

� �β m

n: ð18Þ

and, finally, taking into account Eq. (17) and bearing in mind thatI¼β m n c one can write:

I Tð Þ ¼ n0 φ Σ Tð Þþsexpð�ET=kTÞ� �

exp½� 1=α� � Z T

T0

φ Σ T 0� ��

þsexpð�ET=kT0Þ�dT 0�: ð19Þ

In the temperature range where the thermal release of elec-trons from the trap can be ignored this formula for the first-orderTM–OSL curve becomes less complicated:

I Tð Þ ¼φΣ Tð Þn Tð Þ ¼ n0φΣ Tð Þexp½� φ=α� � Z T

T0

Σ T 0� �dT 0�: ð20Þ

In this study the sum of the first-order kinetics TM–OSL curvescomputed for the trap parameters assumed in the model has beencompared with the simulated OSL curves.

3. Results and discussion

The simulation show that there are three experimental para-meters that strongly affect the process of TM–OSL: the stimulationenergy, the stimulation photon flux and the heating rate. Theseparameters can be regulated in order to obtain the better

resolution of the TM–OSL method but they also have to be prop-erly selected for measuring a clear TM–OSL signal from a specifictrap in the temperature range used in the experiment. This can beobserved in Figs.1. and 2 which present the simulation results forselected values of the experimental parameters.

Fig.1 demonstrates, for the fixed photon flux and heating rate,how intensively the stimulation energy influences the position ofthe TM–OSL peak. TM–OSL curves for four optical depth values,2.3, 2.4, 2.45 and 2.6 eV, are shown in each part of the figurewhereas the stimulation band is shifted by 20 nm into higherwavelengths from one part of the figure to another. The pure TLcurves (dashed lines) are presented next to the TM–OSL curves inFig. 1a. The values 2.40 and 2.45 eV were chosen for illustrating thedifference between maxima of the TM–OSL peaks for the trapshaving relatively close optical depths. The difference in the peakposition in this case is about 130 K (see Fig.1b) while the differencebetween the position of the TL peaks for the same traps is about20 K (see Fig.1a). Symptomatic is, however, that the both TM–OSLpeaks (for 2.4 and 2.45 eV) observed quite clearly for a stimulationband with the maximum at 600 nm (Fig. 1b) are dominated by theTL signal originating from these traps for a band with the max-imum at 620 nm (Fig. 1a) and barely fall into the temperaturerange of measurement for a slightly higher stimulation energy(Fig. 1c). Results for the additional values of optical trap depths(2.2 and 2.6 eV) are taken into account in Fig. 1 in order to presenthow narrow is the range of optical depth values for which the TM–

OSL signal can be measured below the temperatures of thermal

Fig. 2. TM–OSL curves obtained for the one-trap model with the same centreparameters that were used for the simulations presented in Fig. 1a (stimulationband maximum at 620 nm, heating rate w¼1 Ks�1 and photon flux:ϕ¼1017 cm�2 s�1) obtained for different heating rate: w¼0.5 Ks�1 (a) andw¼0.2 Ks�1 (b) or photon flux: ϕ¼2x1017 cm�2 s�1 (c). In parts a and b of thefigure the TL peaks related to traps 2.4, 2.45. 2.6 eV are added for adequate value ofthe heating rate (dashed lines).

Fig. 3. Illustration of the effect of narrowing the TM–OSL peak by decreasing theheating rate. Simulations for the optical trap depth equal 2.4 eV and the rest ofcentre parameters used for simulations presented in Fig. 1. The wavelength of themaximum of stimulation band is 670 nm and the photon flux 1019 cm�2 s�1. TheTL curves (dashed lines) are given for indicating the temperature range of the activethermo-stimulation, the TL peak intensities are not real and should not be com-pared with TM–OSL peaks intensities.

A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–48 45

depopulation of traps. For all three cases of the stimulation bandthe signal related to the trap of 2.2 eV decays quickly just above300 K, whereas the signal from the deeper trap of 2.6 eV, for thelower stimulation energies (Fig. 1a and b), is simply the pure TLsignal. For the band with the maximum at 580 nm, the OSL fromthe deepest trap can be observed as a long tail on the low tem-perature side of a broad TM–OSL peak that is dominated by TL inits high temperature part (Fig. 1c). This indicates the importance ofthe proper selection of experimental parameters in order to obtainthe TM–OSL peak from a trap of a defined depth in the tempera-ture range used in the experiment. For a fixed stimulation bandtwo other parameters may be considered: the heating rate and thephoton flux.

The dependence of the TM–OSL curve on these parameters isshown in Fig. 2 for the same optical depths that were used in Fig. 1and for the spectral band with the maximum at 620 nm. Fig. 2aand b together with Fig. 1a illustrate the effect of heating rate onthe TM–OSL peak shape and position. For each case of the heatingrate the TL peaks related to considered traps are also shown. Ascan be seen, halving the heating rate used in the simulationspresented in Fig. 1a (1 K s�1) shifts the TM–OSL maximum for the2.4 eV trap into lower temperatures by about 60 K (from 557 K inFig. 1a to 495 K in Fig. 2a). The same change of heating rate in thecase of TL signal for the same trap causes the temperature shift ofabout 20 K. For the heating rate of 0.2 K s�1 the maximum for the2.4 eV trap is shifted by the next 60 K (to about 423 K, Fig. 2b) andone can observe also a clear (not disturbed by the TL signal) TM–

OSL maximum for the trap 2.45 eV. Significant modification of theTM–OSL curve can be caused by a change of the photon flux as

well. This is demonstrated in Fig. 2c in combination with Fig. 1a.The double strengthening of the photon flux from the value 1017 to2x1017 cm�2 s�1 shifts the peak maximum for the 2.4 eV trap byabout 60 °C towards lower temperatures.

The experimental conditions can be varied in order to get aclear TM–OSL peak for a given trap in the temperature range usedin measurements. As can be seen in Fig. 1, the most efficient factorhere is the stimulation energy. The higher the stimulation energythe deeper the traps "reached" by the method and, for the definedtrap depth, the lower the temperature of the TM–OSL peak max-imum. The same direction of changes of the TM–OSL curve resultsfrom increasing the photon flux and from decreasing the heatingrate but simultaneously such changes lead to narrowing the TM–

OSL peak. The last effect is shown more clearly in Fig. 3, where theTM–OSL peaks are presented for three different heating rates. Thecurves are obtained again for the 2.4 eV trap, but for significantlylower stimulation energy (λmax¼670 nm) and for higher photonflux. These plots demonstrate that it is advantageous to measurethe OSL using stimulation energy which is much lower than theoptical depth of trap (670 nm corresponds to 1.85 eV in energyscale). For such stimulation energies the character of OCS changeswith temperature is more dynamic, which leads to slimmer TM–

OSL peaks. Simultaneously, however, for the lower stimulationenergies, the OCSs are also low, so the values of photon flux haveto be high enough (here 1019 cm�2 s�1) in order to obtain a peakin the desired temperature range.

The TM–OSL method gives a unique possibility to investigatevery deep traps for which the TL peaks appear above 800 K. Thistemperature range is rarely used for TL measurements because ofthe high incandescence of heater and the poor capabilities fordetermining the sample temperature. As it can be seen in Fig. 4,applying an adequate stimulation energy and sufficiently bigphoton flux as well as very low heating rate allows for thedetection of TM–OSL peak below 500 K for a trap having theoptical depth of 3.0 eV and being the source of the TL peak highabove 800 K.

It is interesting to see how the parameters determining thestrength of electron–phonon coupling S and hω/2π influence theTM–OSL curve. Fig. 5 proves that they strongly affect the TM–OSLpeak position. This figure in part (a) presents the TM–OSL curvesfor the trap with the optical depth of 2.4 eV and the hω/2π equal20 meV for three different S values: 40, 20 and 10. The TL peaks forsuch defined traps have the maxima adequately at about 570, 700

Fig. 4. The TM–OSL curves for traps having the optical depth of 3.0 eV (all othercentre parameters like for Fig. 1) obtained with different heating rates w. The sti-mulation band maximum is at 520 nm and the photon flux ϕ¼1018 cm�2 s�1 and.TL signal related to the trap (peak maximum above 800 K) is marked by dashedblack line.

Fig. 5. The impact of parameters S and hω/2π on the position and shape of the TM–

OSL curve. The results of simulations for the trap optical depth of 2.4 eV, the rest ofmodel parameters the same as these used in the case presented in Fig. 1 and twoadditional values of S (a) and hω/2π (b) which are given in figures. The stimulationband maximum is at 670 nm, the photon flux 1019 cm�2 s�1 (as in Fig. 3) and theheating rate 1 K s�1.

Fig. 6. Dependence of the TM–OSL curve on the photon flux ϕ - simulation resultsfor model consisting of two kinds of traps and one recombination centre: (a) - trapdepths 2.4 and 2.5 eV, maximum of stimulation band at 620 nm; (b) - trap depths2.9 and 3.0 eV, maximum of stimulation band at 520 nm. Heating rate in all caseswas 1 K s�1. The centre parameters: Ni ¼1012 cm�3, M¼1013 cm�3, A i

¼10�11 cm3 s�1, Am ¼4�10�11 cm3 s�1, β¼ 10�8 cm3 s�1, Si ¼20, hω i

/2π¼0.02 eV, s i ¼1013 s�1, i ¼ 1, 2, excitation time105 s.

A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–4846

(see Fig. 1a) and 780 K. In the first case the high value of S causessuch significant increase of the OCS that the OSL signal can beobserved as a fast decay at the beginning of heating. The lowest Svalue results in so slow optical depopulation of trap that theTM–OSL curve is dominated by the TL. Similarly intensive changesare induced by the variation of hω/2π The higher the hω/2π valuethe lower the temperature of peak maximum. The TM–OSL curvesfor the same optical depth, S being equal to 20 and three different

hω/2π values: 25, 20 and 15 meV are shown in Fig. 5b. Theseeffects are a simple consequence of the OCS increase with theparameters determining the strength of electron–phonon coupling(see, e.g. [2], Fig. 1).

A good visualisation of the resolution of the optical stimulationmethod are the results of simulations carried out for the modelincluding two kinds of traps. Here they are demonstrated for thetraps having equal parameters except the optical depth. The ratio ofthe radiative recombination probability β to the probabilities ofelectron trapping in the traps Ami was of 103 in order to test the caseclose to the first-order kinetics. The outcomes are presented inFig. 6 for different photon flux values. Fig. 6a was prepared for thetraps whose TL is observed below 800 K (2.4 and 2.5 eV). Here, twoclear TM–OSL peaks in the temperature range below 700 K can bemeasured for the stimulation light intensity ϕ¼1018 cm�2 s�1. Themaxima of the peaks originating from the traps whose opticaldepths differ by 0.1 eV are shifted with respect to one another byabout 215 K (Tmax for the low temperature peak � 385 K, Tmax forthe high temperature peak – 600 K). It is worth noting that themaxima of TL peaks for the same traps differ by no more than 30 K.Fig. 6b is an illustration of the similar effects (the dependence of theposition and shape of the TM–OSL peaks on the photon flux) fordeep traps whose TL can be detected over 800 K. In this case thebest TM–OSL results for the heating rate of 1 K s�1 can be observedfor the stimulation band at 520 nm and the light intensityϕ¼1019 cm�2 s�1. The results for the two-trap model confirm the

Fig. 7. A comparison of the first-order kinetics TM–OSL curve (light grey solid line)with the curves obtained for one-trap model (E¼2.4 eV) for two different retrap-ping probabilities 10�10 (black dashed line) and 10�9 cm3 s�1 (black solid line). Allother parameters are the same that were used for simulations presented in Fig. 1a.

Fig. 8. An example of the TM–OSL measurement result for a sample of quartzextracted from sediments and irradiated in the laboratory (dose about 140 Gy).Sample was preheated to 200 °C with the heating rate 2 K/s after irradiation inorder to quench the TL peaks below this temperature. The TM–OSL curve (blackdash line) was measured for the heating rate of 0.1 K/s, the maximum of stimula-tion band at 650 nm and with the width of 26 nm and the photon flux of about 5�1016 cm�2 s�1. The same measurement was then repeated for recording thebackground curve (black dot line). The difference between the both curves is alsopresented (black solid line) as well as the TL curve obtained with the heating rate0.1 K/s after the same irradiation and preheat (grey solid line).

A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–48 47

good resolution of the method and show a chance of applying it foran effective initial cleaning of the shallower traps while keepingconstant the occupation of deeper traps.

As it has been mentioned above the first-order kinetics curve ofTM–OSL is described by Eq. (19). Fig. 7 demonstrates the quality ofsuch approximation in the case of simulation results for the onetrap – one luminescence centre model for two values of thetrapping probability A. The first-order curve was calculated for theparameters E, S, hω/2π, s, w and ϕ used in the simulations. As itcan be observed, when the trapping probability is 100 timessmaller than the recombination probability (curve forA¼10�10 cm3 s�1, β¼10�8 cm3 s�1) the first-order curve repro-duces the shape of the TM–OSL correctly until the trap occupationbecomes very low. For a smaller difference between the trappingprobability and the recombination probability, as can be inferred,the first-order curve agrees with the simulated curve only in itsinitial part. The procedure of fitting the first-order curve to theTM–OSL curve obtained from experiments is more complicatedthan fitting the sum of exponential curves to the CW–OSL curvebut the profit is the estimation of parameters uniquely deter-mining the trap, in particular the optical depth of trap. In order toreduce the number of fitting parameters it is advisable to usemeasurements of the experimental conditions (stimulationenergy, stimulation photon flux and heating rate) in combinationssuch that the TM–OSL curve is obtained in the temperature rangewhere the thermal stimulation is negligible and the Eq. (15) can beapplied in calculations. Further reduction of the number of para-meters can be achieved when instead of finding S and hω/2π oneconfines oneself to the parameter κ defined by Eq. (2) [7].

It is interesting to see as an illustration of the above theoreticalconsideration an example of some very early experiments carriedout for a quartz sample. Fig. 8 presents the TM–OSL curve, thebackground curve measured after recording the TM–OSL curve,the result of subtraction of both curves and the TL curve (experi-mental parameters are given in details in the figure caption). Theexperiment was carried out using the Risø TL/OSL System TL-DA-12 and a special illuminator connected to the Risø System bymeans of a light guide [6]. The comparison of the TM–OSL curvewith the TL curve obtained after the same initial treatment showsclearly the "light-resistance" of the traps that are responsible forthe peaks about 220 °C and 295 °C (for heating rate 0.1 K/s). Thesmall difference between the TL and TM–OSL curves in the range200–350 °C appears as a complex TM–OSL signal below 170 °C.The effect of thermal quenching present in quartz exposes itselfexpressly. The area under the TM–OSL curve between RT and170 °C is over 11 times larger than the area under the curve being

the difference between TL and TM–OSL curves in the range 200–350 °C. The traps responsible for TL in the temperature rangeabove 200 °C are important because of the application of quartz inthe luminescence dating [15] and the retrospective dosimetry [16].The TM–OSL curve confirms the complex nature of the OSL signalrelated to these traps. Simultaneously, the shape of this curveshows that there is a chance for a better separation of the indi-vidual OSL components than is possible in the CW–OSL or LM–OSLmethods. Results of the TM–OSL experiments for quartz will bepresented in detail elsewhere.

4. Conclusions

Increasing the temperature during the optical stimulationenables such a modulation of the probability of electron excitationfrom traps to the conduction band that the ratio of these prob-abilities for different traps changes during the stimulation in aspecific and advantageous manner. This provides an opportunityto separate the individual OSL components more efficiently than inthe CW–OSL or LM–OSL methods. The possibility of controlling theTM–OSL process and simultaneously the TM–OSL peak positionnot only by the stimulation energy but also by the heating rate andby the photon flux is a big advantage of this method. Another oneis the possibility of direct determination of the optical trap depthand the parameters determining the strength of the electron–phonon coupling. Estimation of these parameters allows a directcorrelation of the traps active in the OSL and TL processes. Furtherinvestigations in this subject should include considering thecomplications caused by the presence of shallower traps or thephoto-transfer from deeper traps during stimulation as well asintroducing a formula describing the OCS dependency on the sti-mulation energy and the temperature which takes into accountmore advanced models of the electron–phonon coupling.

Acknowledgements

This work has been financed by the Grant of the Polish NationalCentre for Research and Development No. PBS1/A9/4/2012.

A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–4848

References

[1] J.M. Noras, J. Phys. C: Solid State Phys. 13 (1980) 4779.[2] A. Chruścińska, Radiat. Meas. 45 (2010) 991.[3] R. Chen, S.W.S. McKeever, Theory of Thermoluminescence and Related Phe-

nomena, World Scientific, London, 1997.[4] L. Bøtter-Jensen, S.W.S. McKeever, A.G. Wintle, Optically Stimulated Lumi-

nescence Dosimetry, Elsevier, Amsterdam, 2003.[5] N. Kijek, A. Chruścińska, Geochronometria 41 (2014) 160.[6] A. Chruścińska, Radiat. Meas. 71 (2014) 247.[7] A. Chruścińska, Radiat. Meas. 81 (2015) 205–211.

[8] G. Hütt, I. Jaek, J. Tchonka, Quat. Sci. Rev. 7 (1988) 381.[9] G.A.T. Duller, A.G. Wintle, Nucl. Tracks Radiat. Meas. 18 (1991) 379–384.[10] B.G. Markey, S.W.S. McKeever, M.S. Akselrod, L. Botter-Jensen, N. Agersnap

Larsen, L.E. Colyott, Radiat. Prot. Dosim. 65 (1996) 185–189.[11] U. Rieser, G. Hütt, M.R. Krbetschek, W. Stolz, Radiat. Meas. 27 (1997) 273–278.[12] G.A.T. Duller, Radiat. Meas. 27 (1997) 663–694.[13] A. Chruścińska, K. Przegiętka, Radiat. Meas. 45 (2010) 317–319.[14] A. Chruścińska, Radiat. Meas. 56 (2013) 18–22.[15] A.G. Wintle, Geophys. J. R. Astron. Soc. 41 (1975) 107–113.[16] I.K. Bailiff, Radiat. Meas. 24 (1995) 507–511.