mmmm

1. Full Length Article
Thermally modulated optically stimulated luminescence (TM–OSL)
as a tool of trap parameter analysis
Alicja Chruścińska n
, N. Kijek
Institute 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 2015
Accepted 10 January 2016
Available online 5 February 2016
Keywords:
Optically stimulated luminescence
Thermally modulated stimulation
Optical trap depth
a b s t r a c t
The methods of optically stimulated luminescence (OSL) measurements used until recently, used optical
stimulation 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 traps
is 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 traps
can 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 cannot
find a wide application. Inducing the appropriate changes of the probabilities of the optical release of
electrons from traps by increasing the sample temperature during the optical stimulation with a constant
stimulation band do not face such obstacles. Such a stimulation can be realised by means of the standard
OSL readers after a slight modification and offers the possibility for direct estimation of optical trap
depth. The simulations of the OSL process during linear heating show that the experimental parameters
such as the heating rate, the stimulation light intensity and the stimulation energy strongly affect the
shape of the OSL curve and can be the very useful tools for the OSL process regulation. By this kind of
stimulation one can reach very deep traps that are not detectable by thermoluminescence measurements
below 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 optically
stimulated luminescence (OSL) measurements is the optical cross-
section (OCS) σ (cm2
). However, it is not defined unambiguously. It
depends on the optical trap depth E and the parameters deter-
mining the strength of electron–phonon coupling as well as on the
stimulation energy (the energy of photons used for optical sti-
mulation) and temperature. In the simplest model that assumes a
single configuration–coordinate for the transition of electrons
from traps to the conduction band and equal force constants for
the trap and the conduction band, these parameters are the
Huang-Rhys factor S and the phonon energy specific for the trap
centre hω/2π. The dependence of OCS on the stimulation energy
hν and the temperature T (x is a bound variable having the
dimension of energy) has the following form [1,2]:
σ hνð Þ ¼
κ
ν
ffiffiffiffi
π
p
Z 1
0
x
1
2exp Àκ2
xÀ hνÀEð Þ
 à 2
È É
dx ð1Þ
κ ¼ 2S ℏωð Þ2
coth ℏω=2kT
À Áh i
À1
2 ð2Þ
the calculations of the improper integral can be simplified by
narrowing the integration range to a few electron volts. This does
not change the value of σ(hν) noticeably [1].
Up to now, the methods of OSL measurement, when used for
trap investigations, have relied on recording luminescence decay
during the optical stimulation with a constant energy hν and a
constant (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 the
optical release of electrons from traps (ϕ¼f σ ) that have different
optical cross-sections σ1 and σ2 is constant: f σ1/f σ2 ¼const,
because σ1 and σ2 remain constant at constant temperature and
constant stimulation energy. This means that it is hard to separate
the signal originating from different traps. In particular, the initial
optical emptying of shallower traps before investigating the dee-
per ones does not bring good results [5], contrary to the TL analysis
where the initial thermal emptying of the shallow traps is a usual
treatment when a signal from deep traps is going to be tested. In
the TL measurements, the ratio of probabilities of the thermal
release of electrons from different traps changes in such a way that
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/jlumin
Journal of Luminescence
http://dx.doi.org/10.1016/j.jlumin.2016.01.012
0022-2313/& 2016 Elsevier B.V. All rights reserved.
n
Corresponding author. Tel.: +48 566113316.
E-mail address: alicja@fizyka.umk.pl (A. Chruścińska).
Journal of Luminescence 174 (2016) 42–48

2. it is possible to empty the shallow traps effectively without
depopulating the deeper traps (for example by the multiple
heating of the sample in a narrow temperature range significantly
below the range of thermal emptying the deeper traps in the
fractional glow technique). As it was shown recently, the similar
advantageous changes of the probability ratio during the OSL
experiments, and in consequence more information about the trap
than only the OCS value, can be obtained by inducing the changes
of OCSs by increasing the stimulation energy (Variable Energy of
Stimulation - OSL, VES-OSL) [6,7]. This method requires a strong
tuneable light source that supplies the stable flux of photons
during the stimulation energy changes and, presumably, because
of this the VES-OSL cannot be widely used. Such limitations,
however, do not concern the possibility of inducing the OCS
changes by increasing the temperature. The thermally modulated
OSL (TM–OSL) measurement can be realised by means of the
standard OSL readers after a slight modification.
The method of experiment that is going to be presented here is
related to a measurement called thermo-optical luminescence
(TOL) [8–12], however, the difference between the proposed
regime of stimulation and the TOL should be noted. In the TOL
experiment the OSL signal is stimulated by short (e.g. 0.1 s) pulses
every few degrees (e.g.10 °C) during the linear heating (a few
degrees per second) in order to test the OSL intensity at higher
temperatures. In this way the thermal assistance effects can be
investigated. In the TM–OSL method proposed here a continuous
stimulation is used in order to cause the OCS changes during the
stimulation and generate the OSL curve shape that can help to
obtain more information about the trap, e.g. the optical depth of
trap and the electron–phonon coupling parameters, in the fra-
mework of the simplest OSL models. Although it was earlier
shown how the OCS depends on temperature [2,13], this work,
beside its main aim, gives a deeper insight into the character of
this 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 simulations
have been realised for a basic OSL model that assumes the tran-
sition through the conduction band and includes one trap and one
luminescence centre and, next, for a model including two kinds of
traps and one luminescence centre. The second case has been
chosen in order to test the resolution of such a method, i.e. its
ability to separate the OSL signal from different traps. The two-
traps model also allows investigation of the effects related to the
competition of different channels of the electron relaxation from
the conduction band and their influence on the reliability of trap
parameters estimated by a proposed method of the experimental
curve analysis. The quality of the recovery of the parameters used
in OSL modelling by the curve analysis method is a simple test of
the 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 the
shape 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 during
heating have been realised by the simulations. The following
differential equations system have been solved for modelling all
the above-mentioned processes in the case of one trap-one
luminescence centre model:
dn
dt
¼ Àφ Σ Tð ÞnÀsexp ÀET =kT
À Á
nþA NÀnð Þ nc ; ð3Þ
dm
dt
¼ Am MÀmð Þ mv Àβ m nc; ð4Þ
dnc
dt
¼ Rþφ Σ Tð Þnþsexp ÀET =kT
À Á
nÀA NÀnð Þ nc Àβ m nc; ð5Þ
dmv
dt
¼ RÀAm MÀmð Þ mv; ð6Þ
mþmv ¼ nþnc; ð7Þ
Additionally, only for an easy demonstration of the resolution
potential of the investigated stimulation method a widened model
for two traps was used:
dni
dt
¼ Àφ Σi Tð Þni Àsiexp ÀETi=kT
À Á
ni þAi Ni Ànið Þ nc ; i ¼ 1; 2 ;
ð8Þ
dm
dt
¼ Am MÀmð Þ mv Àβ m nc; ð9Þ
dnc
dt
¼ Rþ
X2
i ¼ 1
φ Σi Tð Þ ni ÀAi Ni Ànið Þ nc
Â
þsiexp ÀETi=kT
À Á
ni
Ã
Àβ m nc; ð10Þ
dmv
dt
¼ RÀAm MÀmð Þ mv; ð11Þ
mþmv ¼
X2
i ¼ 1
ni þnc; ð12Þ
where N (cmÀ3
) and n (cmÀ3
) or Ni (cmÀ3
) and ni (cmÀ3
) i¼1, 2,
are the concentrations of trapping states and trapped electrons in
the traps, respectively; M (cmÀ3
) and m (cmÀ3
) are the con-
centration of recombination centres and the concentration of
holes trapped in these centres; nc (cmÀ3
) and mv (cmÀ3
) are the
concentrations 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
(sÀ1
) or si (sÀ1
) i¼1, 2, are the frequency factors of traps, A
(cm3
sÀ1
) or Ai (cm3
sÀ1
), i¼1, 2, are the probabilities of electron
trapping in the traps, Am (cm3
sÀ1
) is the probability of hole
trapping in the recombination centre, β (cm3
sÀ1
) is the prob-
ability of a free electron recombination with a hole trapped in the
luminescence centre; R is the intensity of the excitation irradiation
producing pairs of free electrons and holes (it is taken as
5x109
cmÀ3
sÀ1
during excitation process and 0 for other pro-
cesses), ϕ – the photon flux used for the optical stimulation
(cmÀ2
sÀ1
, ϕ¼0 during the excitation and relaxation). The OSL
intensity during the stimulation is given by: I(t) ¼ Àdm/dt. The
value Σ or Σi (cm2
) is the so called effective OCS (EOCS) that allows
the shape of the spectral band of optical stimulation to be taken
into account in the kinetics equations. The EOCS is a kind of
weighted average of the OCS value over the range of the stimu-
lation band where the weight is determined by the shape of the
stimulation band and it is expressed by the following formula [14]:
Σ ¼
Z hν2
hν1
Φ hνð Þσ hνð Þdhν=
Z hν2
hν1
Φ hνð Þdhν; ð13Þ
where hν1 and hν2 are the stimulation band limits, Φ(hν) (eVÀ1
) is
the shape of the spectral band and σ is expressed by Eqs. (1) and
(2). In this study the function Φ has been approximated by a
Gaussian function with the half-width of about 30 nm. All calcu-
lations have been performed using the differential equation solver
A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–48 43

3. – ode23 s, which is specially designed for stiff equation sets in the
MATLAB environment.
The parameter that in one trap – one luminescence centre
model is the one mainly responsible for the kinetics order of the
OSL process is the probability of electron trapping A. In the case of
two-traps model, in order to minimise the complications caused
by the effects of trap coupling the values of A1 and A2 have been
chosen in such a way that each trap, treated separately, could fulfil
the assumption of first order kinetics. Therefore the whole analysis
concerns the cases for which the first order kinetics of the OSL
process is expected and the sum of first order OSL curves can be
fitted to the experimental curves.
In simulations of the OSL measurement during the linear
heating: T¼T0þwt (here w is the heating rate), the probability of
optical excitation of electrons from a trap to the conduction band
ϕσ(T) increases during the stimulation and, as a consequence, the
same applies to the EOCS, which changes its value during the
stimulation according to the formula:
Σ Tð Þ ¼
Z hν2
hν1
Φ hνð Þσ T; hνð Þdhν=
Z hν2
hν1
Φ hνð Þdhν ð14Þ
In the case of such stimulation the first-order kinetics curve for
a single trap is a peak-shaped curve that is similar to the Randall-
Wilkins TL curve. Its form can be derived, analogously like the TL
first-order TL curve [3], when the quasi-equilibrium assumption
dn
dt
;
dm
dt
4 4
dnc
dt
% 0 ð15Þ
and the first order assumption
A NÀnð Þ o oβ m ð16Þ
are taken into account for a one trap - one luminescence centre
model. When, because of Eq. (16), one omits the term A(NÀn)nc,
Eq. (3) can be analytically solved and, taking into account that
T¼T0 þwt, an expression for n(T) can be obtained:
n Tð Þ ¼ n0 exp½À 1=α
À Á
Z T
T0
φ Σ T0
À Á
þsexpðÀET =kT0
Þ
 Ã
dT0
Š: ð17Þ
Using the same assumptions (Eqs. (15) and (16)) one can obtain
from Eq. (5) (R¼0 for optical stimulation process):
nc ¼
φ Σ Tð Þþsexp ÀET =kT
À Á
β m
n: ð18Þ
and, finally, taking into account Eq. (17) and bearing in mind that
I¼β m n c one can write:
I Tð Þ ¼ n0 φ Σ Tð ÞþsexpðÀET =kTÞ
 Ã
exp½À 1=α
À Á
Z T
T0
φ Σ T0
À ÁÂ
þsexpðÀET =kT0
Þ
Ã
dT0
Š: ð19Þ
In the temperature range where the thermal release of elec-
trons from the trap can be ignored this formula for the first-order
TM–OSL curve becomes less complicated:
I Tð Þ ¼ φΣ Tð Þn Tð Þ ¼ n0φΣ Tð Þexp½À φ=α
À Á
Z T
T0
Σ T0
À Á
dT0
Š: ð20Þ
In this study the sum of the first-order kinetics TM–OSL curves
computed for the trap parameters assumed in the model has been
compared 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 stimulation
energy, the stimulation photon flux and the heating rate. These
parameters 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 specific
trap in the temperature range used in the experiment. This can be
observed in Figs.1. and 2 which present the simulation results for
selected values of the experimental parameters.
Fig.1 demonstrates, for the fixed photon flux and heating rate,
how intensively the stimulation energy influences the position of
the 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 figure
whereas the stimulation band is shifted by 20 nm into higher
wavelengths from one part of the figure to another. The pure TL
curves (dashed lines) are presented next to the TM–OSL curves in
Fig. 1a. The values 2.40 and 2.45 eV were chosen for illustrating the
difference between maxima of the TM–OSL peaks for the traps
having relatively close optical depths. The difference in the peak
position in this case is about 130 K (see Fig.1b) while the difference
between the position of the TL peaks for the same traps is about
20 K (see Fig.1a). Symptomatic is, however, that the both TM–OSL
peaks (for 2.4 and 2.45 eV) observed quite clearly for a stimulation
band with the maximum at 600 nm (Fig. 1b) are dominated by the
TL signal originating from these traps for a band with the max-
imum at 620 nm (Fig. 1a) and barely fall into the temperature
range 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 present
how narrow is the range of optical depth values for which the TM–
OSL signal can be measured below the temperatures of thermal
Fig. 1. The TM–OSL curves obtained for the one-trap model for four different
optical depths of traps: 2.2, 2.4, 2.45 and 2.6 eV. On the separate parts of the figure
results 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 the
temperature ranges where the effective thermal trap depopulation appears in the
case of the traps for 2.4, 2.45. 2.6 eV, the TL curves (obtained with the same heating
rate) are shown as dashed lines in part (a). The following model parameters are
fixed during the simulation for all parts of the figure: N ¼1012
cmÀ3
, M
¼1013
cmÀ3
, A ¼10À10
cm3
sÀ1
, Am¼ 4 Â 10À11
cm3
sÀ1
, β ¼10À8
cm3
sÀ1
, S¼ 20,
hω/2π ¼0.02 eV, s ¼1013
sÀ1
, ϕ¼1017
cmÀ2
sÀ1
, w¼1 KsÀ1
, the excitation time
was 105
s.
A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–4844

4. depopulation of traps. For all three cases of the stimulation band
the signal related to the trap of 2.2 eV decays quickly just above
300 K, whereas the signal from the deeper trap of 2.6 eV, for the
lower stimulation energies (Fig. 1a and b), is simply the pure TL
signal. For the band with the maximum at 580 nm, the OSL from
the 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 in
its high temperature part (Fig. 1c). This indicates the importance of
the proper selection of experimental parameters in order to obtain
the TM–OSL peak from a trap of a defined depth in the tempera-
ture range used in the experiment. For a fixed stimulation band
two other parameters may be considered: the heating rate and the
photon flux.
The dependence of the TM–OSL curve on these parameters is
shown in Fig. 2 for the same optical depths that were used in Fig. 1
and for the spectral band with the maximum at 620 nm. Fig. 2a
and b together with Fig. 1a illustrate the effect of heating rate on
the TM–OSL peak shape and position. For each case of the heating
rate the TL peaks related to considered traps are also shown. As
can be seen, halving the heating rate used in the simulations
presented in Fig. 1a (1 K sÀ1
) shifts the TM–OSL maximum for the
2.4 eV trap into lower temperatures by about 60 K (from 557 K in
Fig. 1a to 495 K in Fig. 2a). The same change of heating rate in the
case of TL signal for the same trap causes the temperature shift of
about 20 K. For the heating rate of 0.2 K sÀ1
the maximum for the
2.4 eV trap is shifted by the next 60 K (to about 423 K, Fig. 2b) and
one can observe also a clear (not disturbed by the TL signal) TM–
OSL maximum for the trap 2.45 eV. Significant modification of the
TM–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
to
2x1017
cmÀ2
sÀ1
shifts the peak maximum for the 2.4 eV trap by
about 60 °C towards lower temperatures.
The experimental conditions can be varied in order to get a
clear TM–OSL peak for a given trap in the temperature range used
in measurements. As can be seen in Fig. 1, the most efficient factor
here is the stimulation energy. The higher the stimulation energy
the deeper the traps reached by the method and, for the defined
trap depth, the lower the temperature of the TM–OSL peak max-
imum. The same direction of changes of the TM–OSL curve results
from increasing the photon flux and from decreasing the heating
rate but simultaneously such changes lead to narrowing the TM–
OSL peak. The last effect is shown more clearly in Fig. 3, where the
TM–OSL peaks are presented for three different heating rates. The
curves are obtained again for the 2.4 eV trap, but for significantly
lower stimulation energy (λmax ¼670 nm) and for higher photon
flux. These plots demonstrate that it is advantageous to measure
the OSL using stimulation energy which is much lower than the
optical depth of trap (670 nm corresponds to 1.85 eV in energy
scale). For such stimulation energies the character of OCS changes
with temperature is more dynamic, which leads to slimmer TM–
OSL peaks. Simultaneously, however, for the lower stimulation
energies, the OCSs are also low, so the values of photon flux have
to be high enough (here 1019
cmÀ2
sÀ1
) in order to obtain a peak
in the desired temperature range.
The TM–OSL method gives a unique possibility to investigate
very deep traps for which the TL peaks appear above 800 K. This
temperature range is rarely used for TL measurements because of
the high incandescence of heater and the poor capabilities for
determining the sample temperature. As it can be seen in Fig. 4,
applying an adequate stimulation energy and sufficiently big
photon flux as well as very low heating rate allows for the
detection of TM–OSL peak below 500 K for a trap having the
optical depth of 3.0 eV and being the source of the TL peak high
above 800 K.
It is interesting to see how the parameters determining the
strength of electron–phonon coupling S and hω/2π influence the
TM–OSL curve. Fig. 5 proves that they strongly affect the TM–OSL
peak position. This figure in part (a) presents the TM–OSL curves
for the trap with the optical depth of 2.4 eV and the hω/2π equal
20 meV for three different S values: 40, 20 and 10. The TL peaks for
such defined traps have the maxima adequately at about 570, 700
Fig. 2. TM–OSL curves obtained for the one-trap model with the same centre
parameters that were used for the simulations presented in Fig. 1a (stimulation
band maximum at 620 nm, heating rate w¼1 KsÀ1
and photon flux:
ϕ¼1017
cmÀ2
sÀ1
) obtained for different heating rate: w¼0.5 KsÀ1
(a) and
w¼0.2 KsÀ1
(b) or photon flux: ϕ¼2x1017
cmÀ2
sÀ1
(c). In parts a and b of the
figure the TL peaks related to traps 2.4, 2.45. 2.6 eV are added for adequate value of
the heating rate (dashed lines).
Fig. 3. Illustration of the effect of narrowing the TM–OSL peak by decreasing the
heating rate. Simulations for the optical trap depth equal 2.4 eV and the rest of
centre parameters used for simulations presented in Fig. 1. The wavelength of the
maximum of stimulation band is 670 nm and the photon flux 1019
cmÀ2
sÀ1
. The
TL curves (dashed lines) are given for indicating the temperature range of the active
thermo-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

5. (see Fig. 1a) and 780 K. In the first case the high value of S causes
such significant increase of the OCS that the OSL signal can be
observed as a fast decay at the beginning of heating. The lowest S
value results in so slow optical depopulation of trap that the
TM–OSL curve is dominated by the TL. Similarly intensive changes
are induced by the variation of hω/2π The higher the hω/2π value
the lower the temperature of peak maximum. The TM–OSL curves
for 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. These
effects are a simple consequence of the OCS increase with the
parameters determining the strength of electron–phonon coupling
(see, e.g. [2], Fig. 1).
A good visualisation of the resolution of the optical stimulation
method are the results of simulations carried out for the model
including two kinds of traps. Here they are demonstrated for the
traps having equal parameters except the optical depth. The ratio of
the radiative recombination probability β to the probabilities of
electron trapping in the traps Ami was of 103
in order to test the case
close to the first-order kinetics. The outcomes are presented in
Fig. 6 for different photon flux values. Fig. 6a was prepared for the
traps whose TL is observed below 800 K (2.4 and 2.5 eV). Here, two
clear TM–OSL peaks in the temperature range below 700 K can be
measured for the stimulation light intensity ϕ¼1018
cmÀ2
sÀ1
. The
maxima of the peaks originating from the traps whose optical
depths differ by 0.1 eV are shifted with respect to one another by
about 215 K (Tmax for the low temperature peak À 385 K, Tmax for
the high temperature peak – 600 K). It is worth noting that the
maxima 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 the
position and shape of the TM–OSL peaks on the photon flux) for
deep traps whose TL can be detected over 800 K. In this case the
best TM–OSL results for the heating rate of 1 K sÀ1
can be observed
for the stimulation band at 520 nm and the light intensity
ϕ¼1019
cmÀ2
sÀ1
. The results for the two-trap model confirm the
Fig. 4. The TM–OSL curves for traps having the optical depth of 3.0 eV (all other
centre 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
cmÀ2
sÀ1
and.
TL signal related to the trap (peak maximum above 800 K) is marked by dashed
black 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 of
model parameters the same as these used in the case presented in Fig. 1 and two
additional values of S (a) and hω/2π (b) which are given in figures. The stimulation
band maximum is at 670 nm, the photon flux 1019
cmÀ2
sÀ1
(as in Fig. 3) and the
heating rate 1 K sÀ1
.
Fig. 6. Dependence of the TM–OSL curve on the photon flux ϕ - simulation results
for model consisting of two kinds of traps and one recombination centre: (a) - trap
depths 2.4 and 2.5 eV, maximum of stimulation band at 620 nm; (b) - trap depths
2.9 and 3.0 eV, maximum of stimulation band at 520 nm. Heating rate in all cases
was 1 K sÀ1
. The centre parameters: Ni ¼1012
cmÀ3
, M¼1013
cmÀ3
, A i
¼10À11
cm3
sÀ1
, Am ¼4 Â 10À11
cm3
sÀ1
, β¼ 10À8
cm3
sÀ1
, Si ¼20, hω i
/2π¼0.02 eV, s i ¼1013
sÀ1
, i ¼ 1, 2, excitation time105
s.
A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–4846

6. good resolution of the method and show a chance of applying it for
an effective initial cleaning of the shallower traps while keeping
constant the occupation of deeper traps.
As it has been mentioned above the first-order kinetics curve of
TM–OSL is described by Eq. (19). Fig. 7 demonstrates the quality of
such approximation in the case of simulation results for the one
trap – one luminescence centre model for two values of the
trapping probability A. The first-order curve was calculated for the
parameters E, S, hω/2π, s, w and ϕ used in the simulations. As it
can be observed, when the trapping probability is 100 times
smaller than the recombination probability (curve for
A¼10À10
cm3
sÀ1
, β¼10À8
cm3
sÀ1
) the first-order curve repro-
duces the shape of the TM–OSL correctly until the trap occupation
becomes very low. For a smaller difference between the trapping
probability and the recombination probability, as can be inferred,
the first-order curve agrees with the simulated curve only in its
initial part. The procedure of fitting the first-order curve to the
TM–OSL curve obtained from experiments is more complicated
than fitting the sum of exponential curves to the CW–OSL curve
but the profit is the estimation of parameters uniquely deter-
mining the trap, in particular the optical depth of trap. In order to
reduce the number of fitting parameters it is advisable to use
measurements of the experimental conditions (stimulation
energy, stimulation photon flux and heating rate) in combinations
such that the TM–OSL curve is obtained in the temperature range
where the thermal stimulation is negligible and the Eq. (15) can be
applied in calculations. Further reduction of the number of para-
meters can be achieved when instead of finding S and hω/2π one
confines oneself to the parameter κ defined by Eq. (2) [7].
It is interesting to see as an illustration of the above theoretical
consideration an example of some very early experiments carried
out for a quartz sample. Fig. 8 presents the TM–OSL curve, the
background 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). The
experiment was carried out using the Risø TL/OSL System TL-DA-
12 and a special illuminator connected to the Risø System by
means of a light guide [6]. The comparison of the TM–OSL curve
with the TL curve obtained after the same initial treatment shows
clearly the light-resistance of the traps that are responsible for
the peaks about 220 °C and 295 °C (for heating rate 0.1 K/s). The
small difference between the TL and TM–OSL curves in the range
200–350 °C appears as a complex TM–OSL signal below 170 °C.
The effect of thermal quenching present in quartz exposes itself
expressly. The area under the TM–OSL curve between RT and
170 °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 range
above 200 °C are important because of the application of quartz in
the luminescence dating [15] and the retrospective dosimetry [16].
The TM–OSL curve confirms the complex nature of the OSL signal
related to these traps. Simultaneously, the shape of this curve
shows that there is a chance for a better separation of the indi-
vidual OSL components than is possible in the CW–OSL or LM–OSL
methods. Results of the TM–OSL experiments for quartz will be
presented in detail elsewhere.
4. Conclusions
Increasing the temperature during the optical stimulation
enables such a modulation of the probability of electron excitation
from traps to the conduction band that the ratio of these prob-
abilities for different traps changes during the stimulation in a
specific and advantageous manner. This provides an opportunity
to separate the individual OSL components more efficiently than in
the CW–OSL or LM–OSL methods. The possibility of controlling the
TM–OSL process and simultaneously the TM–OSL peak position
not only by the stimulation energy but also by the heating rate and
by the photon flux is a big advantage of this method. Another one
is the possibility of direct determination of the optical trap depth
and the parameters determining the strength of the electron–
phonon coupling. Estimation of these parameters allows a direct
correlation of the traps active in the OSL and TL processes. Further
investigations in this subject should include considering the
complications caused by the presence of shallower traps or the
photo-transfer from deeper traps during stimulation as well as
introducing a formula describing the OCS dependency on the sti-
mulation energy and the temperature which takes into account
more advanced models of the electron–phonon coupling.
Acknowledgements
This work has been financed by the Grant of the Polish National
Centre for Research and Development No. PBS1/A9/4/2012.
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 10À10
(black dashed line) and 10À9
cm3
sÀ1
(black solid line). All
other 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 quartz
extracted 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 in
order to quench the TL peaks below this temperature. The TM–OSL curve (black
dash 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 Â
1016
cmÀ2
sÀ1
. The same measurement was then repeated for recording the
background curve (black dot line). The difference between the both curves is also
presented (black solid line) as well as the TL curve obtained with the heating rate
0.1 K/s after the same irradiation and preheat (grey solid line).
A. Chruścińska, N. Kijek / Journal of Luminescence 174 (2016) 42–48 47

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