Electron trap filling and emptying through simulations: Studying the shift of the maximum intensity position in Thermoluminescence and Linearly Modulated Optically Stimulated

Radiation Measurements 153 (2022) 106735

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Radiation Measurements
journal homepage: www.elsevier.com/locate/radmeas

Electron trap filling and emptying through simulations: Studying the shift
of the maximum intensity position in Thermoluminescence and Linearly
Modulated Optically Stimulated Luminescence curves
E. Tsoutsoumanos a, b, *, P.G. Konstantinidis c, G.S. Polymeris b, T. Karakasidis a, G. Kitis c
a
b
c

Condensed Matter Physics Laboratory, Physics Department, University of Thessaly, GR-35100, Lamia, Greece
Institute of Nanoscience and Nanotechnology, NCSR “Demokritos”, GR-15310, Ag. Paraskevi, (Athens), Greece
Nuclear and Elementary Particle Physics Laboratory, Physics Department, Aristotle University of Thessaloniki, GR-54214, Thessaloniki, Greece

A R T I C L E I N F O

A B S T R A C T

Keywords:
Linearly modulated optically stimulated
luminescence
One trap one recombination center model
Thermoluminescence
Simulation
Python

In the present work, the response of peak positions in Linearly Modulated Optically Stimulated Luminescence
(LM-OSL) curves as a function of physical and technical parameters were investigated and compared theoreti­
cally; specifically, the time or temperature values (tm , Tm ) of their maximum intensity (Im ). The stimulation
modes of Thermoluminescence (TL) and LM-OSL differ slightly in terms of peak resemblance (geometrical
structure) but differ greatly as physical phenomena, so it could be ideal to study the effects responsible for
electron trap filling or trap emptying. These simulations could also extend our knowledge in Stimulated Lumi­
nescence phenomena regarding expected experimental outcomes. In the present study, four simulation experi­
ments were conducted based on the One Trap – One Recombination center (OTOR) model for the case of equal
re-trapping and recombination probabilities signifying second order kinetics. The first experiment defines the Tm
shifting for various heating and optical stimulation rates. The second depicts an electron trap filling process, in
which dose progresses from a low value until the saturation state. In the third experiment, a trap emptying
procedure was simulated via thermal bleaching (Isothermal Decay), whereas in the final one, the same trap
emptying procedure was conducted via optical bleaching (Continuous wave optically stimulated luminescence)
for different time spans. Generally the tm , Tm shifting in trap emptying processes, is proven, according to sim­
ulations, to follow a similar behavior to the tm , Tm shift as a function of heating or optical stimulation rate.
Regarding trap filling, tm and Tm shift to lower values as the dose increases.

1. Introduction
Linearly modulated optically stimulated luminescence (LM-OSL) is a
technique which can be used in luminescence research and applications.
The LM-OSL bell-shape is the fundamental component of various com­
plex experimental LM-OSL curves, and it has its own set of character­
istics. In comparison to the voluminous theoretical and experimental
literature for the comparable TL peaks, in pioneer and cornerstone
ăhm and
works since the 1970s (Becker, 1973; Chen and Kirsh, 1981; Bo
Scharmann, 1981; Chen and McKeever, 1997; Martini and Meinardi,
1997; Bøtter-Jensen et al., 2003; Furetta, 2003; Pagonis et al., 2006;
Chen and Pagonis, 2011; McKeever, 1985). LM-OSL features, in com­
parison with TL, have received less attention since 1996 (Bulur, 1996,

1999; Bøtter-Jensen et al., 2003; Polymeris et al., 2006, 2008, 2009;

Kitis and Pagonis, 2007; Dallas et al., 2008a; Kiyak et al., 2008; Kitis and
Pagonis, 2007). This is even more accurate for the case of simulation
research; despite the existing literature on TL simulations, there are few
articles reporting simulated LM-OSL results (Kitis et al., 2009, 2019;
Pagonis et al., 2019). However, the knowledge collected by the com­
munity as a result of studying the behavior of TL peaks could be effec­
tively used towards this direction.
In both cases of bell-shaped luminescence curves, namely TL and LMOSL, the maximum intensity (Im ) and the stimulation position corre­
sponding to maximum intensity (Tm or tm ) are quite important. Due to
the use of these parameters, several other geometrical structural char­
acteristics such as the glow peak’s width at the half of its maximum
intensity (ω) are also defined for Peak Shape Methods (PSM) analysis in
order to evaluate the kinetic parameter of an isolated glow peak. Finally,

* Corresponding author. Condensed Matter Physics Laboratory, Physics Department, University of Thessaly, GR-35100, Lamia, Greece.
E-mail addresses: , (E. Tsoutsoumanos).
/>Received 27 November 2021; Received in revised form 28 February 2022; Accepted 2 March 2022
Available online 7 March 2022
1350-4487/© 2022 Elsevier Ltd. All rights reserved.


E. Tsoutsoumanos et al.

Radiation Measurements 153 (2022) 106735

these properties are also responsible for the derivation of the analytical
expressions that are used for Computerized Glow Curve Deconvolution
(CGCD) of complex luminescence glow curves, provided that the su­

perposition principle is taken into consideration (Kitis and Pagonis,
2007; Kitis et al., 2009; Kitis and Vlachos, 2013; Pagonis, 2021). The
dependence of such parameters on experimental settings such as the
heating rate and the dose has been a major topic especially for TL glow
curves over the last 30 years. In the former case, the well-known
behavior has led to establishing experimental methodologies to either
calculate the activation energy via the method for various heating rates
(Hoogenstraaten, 1958) or the thermal quenching efficiency in materials
such as quartz (Petrov and Bailiff, 1997) and Al2O3:C (Dallas et al.,
2008b). For the latter case, the dependence of the delocalization of a TL
glow peak on the radiation dose, but only for second order kinetics,
stands as fundamental knowledge in the literature of TL and related
applications (Garlick and Gibson, 1948; May and Partridge, 1964; Chen
and McKeever, 1997).
Nevertheless, experimental verification of shifting of the Tm towards
lower temperatures with increasing dose has not been systematically
reported in the literature, neither for TL nor LM-OSL curves. The lack of
shifting is regarded as the ideal experimental indication for the preva­
lence for first order kinetics in all luminescence phenomena (Chen and
McKeever, 1997; McKeever, 1985). Thus, a scientific argument emerges,
regarding whether Stimulated Luminescence analysis has a premise only
for first order kinetics, which is based on the assumption that no
re-trapping occurs in the material, and thus there are no competition
phenomena between traps and centers. Also, such competition phe­
nomena have not been undoubtedly verified experimentally, but there
are cases where this supposition seems to have a strong basis. Otherwise,
in well-known and studied cases where first order kinetics applies to the
experimental data, the corresponding equations are dominant for
describing the phenomenon (lack of shifting).
In a previous paper, Kitis et al. (2020) have studied the behavior of

the Tm as a function of various experimental parameters such as (a)
heating rate, (b) dose (trap filling) and (c) trap decay (trap emptying) for
a variety of thermoluminescence dosimeters (TLDs hereafter).
Regarding this study, three issues become extremely important: (a) this
is predominantly an experimental study; (b) the TLDs were purposefully
chosen so that the TL signals generate kinetics order spanning from first
to second order; and (c) the results revealed that the change of Tm is
noticeable as a function of both heating rate and trap emptying. None­
theless, it was difficult to track such a change in relation to the radiation
dose (trap filling). The present study follows the work of Kitis et al.
(2020) but in this case the aim is two-fold, namely (a) the shifting
behavior of the delocalization temperature of the TL peak via simula­
tions using the One Trap – One Recombination center (OTOR) model to
be verified; and (b) theoretically such behavior in the case of LM-OSL
stimulation to be simulated accordingly. In the current case, since the
stimulation modalities of TL and LM-OSL are slightly different in terms
of structure, as both cases result in similar experimental observation
exhibiting a glow peak resemblance, and since they differ greatly as
physical phenomena in terms of physical mechanism producing those
peaks, studying the effects that cause electron trap filling or trap
emptying for both cases will be beneficial. Thus, for both cases, specific
trap filling as well as trap emptying procedures will be applied.

band in OTOR are:
dn / dt = An ⋅(N − n)⋅nc − n⋅p(t)

(2.1)

m = n + nc

(2.2)

dnc / dt = n⋅p(t) − An ⋅(N − n)⋅nc − Am ⋅m⋅nc

(2.3)

dm / dt = dn/dt + dnc /dt

(2.4)

I(t) = − dm/dt = Am ⋅m⋅nc

(2.5)

where N (cm− 3) is the total concentration of electron traps inside the
crystal, n (cm− 3) is the concentration of the filled electron traps in the
crystal, nc (cm− 3) is the concentration of the free carriers in the con­
duction band, m (cm− 3) is the concentration of filled recombination
centers of the crystal and represents the charge neutrality condition, An
(cm3 ⋅ s− 1) is the capture probability of the electron traps and Am (cm3 ⋅
s− 1) is the capture probability of the recombination center, I(t) repre­
sents the luminescence intensity (a.u.).
The term p(t) represents the rate of thermal or optical excitation of
trapped electrons, expressed by p(t)TL = s⋅exp[ − E /kb ⋅T(t)] and
p(t)LM− OSL = (λ /P)⋅t. Since both expressions 2.1 and 2.3 include the
term p(t), which describes the stimulation process, there is a unique,
single main equation for peak shaped TL and LM-OSL curves; referred to
as ‘master equation’ (Kitis et al., 2013, 2019).
For TL, E (eV) is the activation energy of the trap, s (s− 1) is the fre­
quency factor, kb is the Boltzmann constant and T(t) = T0 + β⋅t repre­

sents the heating function, in which T0 = 273 Κ, β is the constant
heating rate for linearly ramping the temperature, while t (s) is time.
For LM-OSL, λ (s− 1) is the decay constant, P(t) = 1/a⋅I is the total
illumination time and represents the time dependence during the LMOSL signal recording. The stimulation rate a (1/s) is expressed as a
function of the changing rate in light stimulus, where a⋅I is the decaying
time-constant of luminescence or more specifically the probability of
trapped electrons’ escape at a light intensity I (a.u.) of stimulation. Each
time I (a.u.) expresses the initial intensity value that forms the possible
OSL component (e.g. the OSL fast component) if the stimulus was con­
stant at that point, in this case it resembles the form of Continuous Wave
Optically Stimulated Luminescence (CW-OSL) signal (Bulur, 1996). The
summation of those components, form the final LM-OSL bell shape
curve, where the I (a.u.) linearly ramped up for a specific illumination
ăksu, 1999; Pagonis, 2021; Konư
time P(t) (Bulur, 1996; Bulur and Go
stantinidis et al., 2021).
In all cases, all simulation protocols were conducted in Python, with
the OTOR model equations being numerically integrated, by importing
“odeint” (ordinary differential equation integration), as a part of Scipy,
for solving initial-value issues in ordinary differential equations. Data
visualization was achieved with the help of Matplotlib that creates
interactive plots and graphs.
2.2. Simulation protocols
The four theoretical processes focus on the investigation of
maximum intensity position shifting due to various alterations via
computer simulations, based on the work of Kitis et al. (2020). After a
specific (steady) dose, the first procedure (Protocol І) defines the
maximum intensity position, Tm , shifting for multiple heating rate
values for the case of TL. For the case of LM-OSL, the same protocol
studies the shift of the tm versus the varying stimulation rate. Protocol ІІ

depicts the electron trap filling process, which progresses from a low
dose until a maximum possible dose according to Table 1. In Protocol III,
a signal resetting process was simulated using the Isothermal Decay (ID)
method, whereas in Protocol IV, the same signal resetting process was
carried out through a simulated CW-OSL measurement.
In Stimulated Luminescence, the ID method is a well-known
approach for measuring the trap’s activation energy. It mostly entails

2. Method of analysis
2.1. The differential equations governing the OTOR model
In both cases of TL and LM-OSL, their theoretical processes can be
described efficiently by the One Trap – One Recombination center
(OTOR) model (Randall and Wilkins, 1945; Garlick and Gibson, 1948).
A thorough explanation of this model is given by Chen and Pagonis
(2011). The differential equations that govern the electron flow between
the unique trapping level, the recombination center, and the conduction
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Radiation Measurements 153 (2022) 106735

Step 1: Delivering of a Dose Di
Step 2: Readout for a specific heating/optical stimulation rate
Step 3: Repeat of Steps 1 and 2 for a higher Di
Step 4: Recording its highest dose signal as N, and integrated signal
as n0

Table 1

Symbols, Units and Values of parameters that are used for the Simulations of
OTOR processes.

1
2
3
4
5
6
7

Symbol
(Units)

Value

Alterability

N (cm− 3)
An (cm3 ⋅
s− 1)
Am (cm3 ⋅
s− 1)
s (s− 1)
E (eV)
kb (eV/K)

1 ⋅ 1010
1 ⋅ 109

Constant throughout
Constant throughout

1 ⋅ 109

Constant throughout

12

1 ⋅ 10
1
8.617 ⋅
10− 5
0.5

8

λ(photons
s− 1)
β(K/s)

9

α(eV/s)

1

10

1 ⋅ 1010

11

Di
(electrons)
Tiso (K)

12
13

tiso (s)
tcwi (s)

–
–

1

–

Protocol III: trap emptying through thermal bleaching
(isothermal decay)
Step 1: Delivering of maximum dose, integrating and recording its
signal as N
Step 2: Thermal bleaching through Isothermal decay at a T iso for TL
and tiso for LM-OSL
Step 3: Readout at rate one point per step in order to obtain the re­
sidual signal
Step 4: Recording of its characteristics, such as integrated signal, n0 ,
and peak maximum position

Step 5: Repeat of steps 1 to 4 for a new higher T iso

Constant throughout
Constant throughout
Constant throughout
Constant throughout
Constant throughout, except Protocol I;
(0.25–20)
Constant throughout, except Protocol I;
(0.25–20)
Constant throughout, except Protocol II; (5 ⋅
105–1 ⋅ 1010)
Only in Protocol III, where ranges (350–385) in
TL and remains constant in LM-OSL (352)
Only in Protocol III, where ranges (5–175)
Only in Protocol IV, where ranges (10–50,000)

Protocol IV: trap emptying through optical bleaching (contin­
uous wave optically stimulated luminescence)
Step 1: Delivering of maximum dose, integrating and recording its
signal as N
Step 2: Optical bleaching through Continuous wave optically stim­
ulated luminescence for different readouts spans (tcwi )
Step 3: Readout at rate one point per step in order to obtain the re­
sidual signal
Step 4: Recording of its characteristics, such as integrated signal, n0 ,
and peak maximum position
Step 5: Repeat of Steps 1 to 4 for a new higher readout span value tcwi

determining the decreasing intensity of light (phosphorescence) emitted

by a previously irradiated material while held at a constant temperature
higher than the irradiation temperature. After that, the form of the decay
curve is used to determine the values of several parameters that char­
acterize the trap engaged in the luminous process (Furetta et al., 2007).
In case of TL, when an irradiated sample is kept at a high temperature
(T), the isothermal TL signal decays with a temperature-dependent
thermal deteriorate constant (λ). The decay constant, in protocol III, is
determined by equation (2.6) (Chithambo and Niyonzima, 2014):
−

λ = s⋅e

It is quite important to note that, according to the selected stimula­
tion parameters, the isothermal decay for the case of the LM-OSL curve
takes place at 352 K. This temperature can be calculated using equation
(2.6) by solving versus Tiso . Thus, tiso is not the isothermal decay tem­
perature; instead, the duration of the isothermal decay.
In the particular case of OTOR, the ratio R ​ (R = An /Am ) has replaced
the kinetic parameter b. Shifting of either Tm or tm is anticipated mainly
for the case of second order kinetics, in which the values of An and Am
were selected so that R = 1.

(2.6)

E
k⋅Tiso

Here s (s− 1) is the frequency factor, E (eV) is the activation energy, and
the Tiso is a selected temperature position for decaying. For the case of
LM-OSL tiso corresponds to the time duration in which decaying Tiso

applied.
The CW-OSL is the most conventional method for measuring opti­
cally stimulated luminescence by recording the prompt light emission
during a constant light-intensity stimulation. In this case the OSL signal
decays with time (Bulur and Gă
oksu, 1999).
Pagonis et al. (2019) used Monte Carlo methods in OTOR in order to
simulate Stimulated Luminescence phenomena. In their work they
numerically integrated the differential equations using the term p(t),
which represents the rate of thermal or optical excitation of trapped
electrons, as described by equation (2.7):
p(t)CW−

OSL

= σ⋅I(t)

2.3. Selection of the appropriate simulation parameters
As the main effect that was simulated is either the trap filling or the
trap emptying, it is quite convenient to use the trap occupancy as the
simulation parameter. Using the parameters of Table 1, the occupancy
and thus the radiation dose are expressed by the ratio n0 ∕N, representing
the filling degree of either the trap responsible for a TL glow peak or an
LM-OSL component. Here the term N represents the total concentration
of electron traps inside the crystal and n0 is the integrated signal after
filling or emptying. For Protocol II, the dose increases in various steps;
thus, the ratio n0 ∕N is increasing up to the maximum saturation n0 ∕N =
1. On the other hand, in Protocols III and IV, as trap emptying takes
place from an initial saturated state, the value of this ratio decreases.
Specifically, in Protocol III the varying value is Tiso in which the

isothermal TL takes place, while in Protocol IV it is tcwi ; the duration of
CW-OSL that is measured before either TL or LM-OSL. Nevertheless, as
both isothermal decay and bleaching result in decreasing the trap oc­
cupancy, the value of n0 ∕N is also presented in Table 2. The simulation
parameters in each protocol are presented as bold and italics at the same
time.

(2.7)

where σ (cm2), represents the optical cross section and I(t) the lumi­
nescence intensity (a.u.) (Equation (2.5)). Since λ = σ⋅ I(t), the value of
the λ parameter was determined to be 0.5 s− 1 as a preset value in order
to avoid excessive calculations that could postpone the simulation re­
sults in terms of duration. (Konstantinidis et al., 2021).
The protocols were conformed accordingly for TL and LM-OSL and
are the following:
Protocol I: increase of heating/stimulation rate (β/a)
Step 1: Delivering of a Dose Di
Step 2: Readout for specific β for TL and specific a for LM-OSL
Step 3: Repeat of Steps 1 and 2 for new β or a

3. Results and discussion

Protocol II: trap filling by increasing the dose

The luminescence curves resulting from the simulation processes are
3


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Radiation Measurements 153 (2022) 106735

Table 2
Dose, maximum peak position, isothermal decay temperature and time, CW-OSL duration and trap occupancy in Protocols II, III and IV for TL and LM-OSL.
Protocol II
Di , electrons

5⋅ 105
1⋅ 106
5⋅ 106
1⋅ 107
5⋅ 107
1⋅ 108
5⋅ 108
1⋅ 109
5⋅ 109
1⋅ 1010

Protocol III
TL

LM-OSL

Protocol IV

TL

LM-OSL

tcwi , s

Tm , K

n0 /N

tm , s

n0 /N

Tiso , K

Tm , K

n0 /N

tiso , s

tm , s

n0 /N

499
487
461
450
429
420
393
373

368
368

0.00005
0.0001
0.0005
0.001
0.005
0.01
0.05
0.1
0.5
1

1363
1363
621
441
198
198
63
45
45
18

0.00005
0.0001
0.0005
0.001
0.005

0.01
0.05
0.1
0.5
1

0
350
355
360
365
370
375
380
385
–

389
390
390
391
392
394
396
398
401
–

1.000
0.935

0.901
0.847
0.775
0.694
0.599
0.498
0.398
–

0
5
15
25
50
75
100
125
150
175

180
204
246
288
360
426
481
529
577
619

1.000
0.379
0.254
0.191
0.116
0.083
0.064
0.052
0.043
0.037

shown in Fig. 1. The shift of Tm in TL is shown in plots a, c, e and g
whereas the shift of tm in LM-OSL is shown in plots b, d, f and h.
Moreover, the shift of Tm or tm versus the trap occupancy are presented
in plots c, e, g and d, f, h respectively; plots c and d correspond to trap
filling, while the rest to trap emptying. Finally, plots a and b indicate the
shift of Tm and tm respectively as a function of parameters that describe
the stimulation moduli. It is evident that for higher heating and optical
stimulation rates, the intensity (TL and OSL) decreases, and the glow
curves shift towards higher temperature and time values respectively.
Simulation describes very effectively the shift of the maximum position
as both β and α increase.

0
10
50
100
500
1000

5000
10,000
30,000
50,000

TL

LM-OSL

Tm , K

n0 /N

tm , s

n0 /N

389
389
391
392
401
407
426
435
451
458

1.000
0.971

0.862
0.763
0.388
0.239
0.058
0.029
0.009
0.005

180
180
190
200
290
360
731
1012
1743
2244

1.000
0.498
0.442
0.388
0.195
0.120
0.028
0.014
0.004
0.002

Protocols III and IV respectively. In all processes, before the emptying
stages were initiated, the system was stimulated by the maximum dose
(Di = 1 ⋅1010 ) and n0 /N was equal to unity due to saturation.
In Protocol III, Fig. 1e, after defining the Tm in saturation state, all the
parameters remained constant except for the Tiso , which varies from 350
up to 385 K, in which the Im is observed (Table 2). Before every readout,
an ID step with a duration of 30 s interpolated, in steps of 5 K, followed
by a residual measurement with Tm varied from 389.5 K to 401.2 K
(ΔT = 11.7 K). For the LM-OSL simulation (Fig. 1f), the Tiso , and by
extension λ, is stable while the tiso value was set to vary from 5 to 175 s
(up to Im). Finally, similarly to TL, tm varied from 180.2 s to 619.2 s (Δt =
439 s), meaning that tiso reaches the tm of the saturation state.
In Protocol IV, Fig. 1g & h, all the parameters remained constant
except the tcwi value (CW-OSL stimulation duration) which varied from
5 to 50,000 s. In TL, as the CW-OSL duration sequentially increased Tm
increased from 389.5 K to 458.8 K, meaning a shift of 69.3 K (ΔT =
69.3 K)). In LM-OSL, as the CW-OSL duration sequentially increased, tm
increased from 180.2 s to 2244.5 s. In this case, the shift was increased
by 2064.3 s (Δt = 2064.3 s), while the total stimulation time of the LMOSL readout remained constant at 3000 s.
Regarding all the cases of trap emptying, Im decreased, while Tm and
tm shifted to higher values. It should be underlined that, regardless of the
phenomena that occur during the trap filling, at the end of the irradia­
tion there will be a certain number of traps filled with n0 electrons, and
no leaping motions will occur after that point, in that case the system
falls into a pseudo-equilibrium state. Thus, it can be assumed that n0
corresponds to the unbleached luminescence integral of N number of
traps (n0 = N). During thermal or optical bleaching, a part of those
trapped electrons (n01 ) will escape, leaving several traps (N1 ) empty in
the crystal lattice. Upon further electron stimulation (thermal or optical)

a higher number of empty traps (N − N1 ) will increase the probability of
re-trapping, which is responsible for the Tm and tm shift towards higher
values. The overall results of trap emptying protocols (Protocol III and
IV) agree with the trap emptying theory described above and can also be
seen in Table 2, which includes the maximum peak position and trap
occupancy changes as the simulation parameters vary in each step (Kitis
et al., 2020).

3.1. Shifting results in trap filling
An interesting behavior of these shifts is presented in Fig. 1c and d,
where Tm & tm are presented as a function of trap filling. Initially for both
cases a small dose of electrons Di = 5⋅105 was delivered to the system
representing a tiny fraction of the maximum trap occupancy (n0 / N =
0.00005). In the case of TL, the Tm was at 499.5 K and as the dose
proportionally increased to the point where the number of electrons
were equal to the number of available traps (Di = N = 1⋅ 1010 ), the Im
occurred at 368.2 K, meaning that for an initial low dose until the state
of saturation (Table 2), the Tm shifted 131.3 K lower (ΔT = − 131.3 K).
For the lowest dose of LM-OSL, the tm was at 1363.4 s. As the dose
increased to the state of saturation the shift of tm was much greater, in
contrast with TL, as tm occurred at 18 s. Specifically the duration where
the peak reaches its Im was decreased by 1345.4 s. It should also be
mentioned that the total duration of simulation process remained con­
stant in all cases at 3000s.
Regarding the case of trap filling, the Tm and tm decrease as the dose
sequentially rises is caused by the fact, that at low doses, where n0 ≪ N,
the chance of retrapping almost entirely depends on the number of
accessible traps in the crystal lattice. This implies that the released
trapped electrons are leaping between the conduction band and the
available empty traps, leaving an insufficient number of electrons for

recombination. As a result, electrons do not spend enough time in the
conduction band to find a recombination pathway, which probability
can increase with the number of electrons in the conduction band. This
phenomenon is responsible for the cause of Tm & tm to appear at higher
values. However, as the dose increases to the state of saturation (n0 → N),
the re-trapping reduces and recombination probability increases causing
a shift to lower Tm & tm values. The simulation results of trap filling
protocol (Protocol II) can be seen in Table 2 and are in agreement with
the trap filling theory described above (Kitis et al., 2020).

3.3. The appropriate representation
As it was already mentioned in Section 2.3, the trap occupancy is
expressed through the ratio n0 /N representing the filling degree and is
plotted versus the heating (β) and stimulation (α) rate. However, ac­
cording to Kitis et al. (2020) the trap occupancy derived using the
analytical equation of general order kinetics model (GOK) and the total
pre-exponential factor is also affected in the same way, but in the
opposite direction. Specifically, when α and β rise, both Tm and tm in­
crease, while n0 /N decreases. Due to this polarity, plotting the presen­
tation as a function of trap occupancy and stimulation rate on the same

3.2. Shifting results in trap emptying
There is a shift of Tm and tm as functions of trap emptying via thermal
bleaching (Fig. 1e and f) and via optical bleaching (Fig. 1g and h) in
4


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Radiation Measurements 153 (2022) 106735

Fig. 1. Graphical representation of simulation protocols I - IV for TL (a, c, e and g) and LM-OSL (b, d, f, h). All simulation parameters were kept constant except for
the heating rate (a), stimulation rate (b), dose (c & d), Tiso / tiso (e & f) and tcw (g & h). For the exact value of each parameter in each protocol, the readers could
refer to Table 1.

5


E. Tsoutsoumanos et al.

Radiation Measurements 153 (2022) 106735

x-axis is difficult and impractical. So, by using the inverse expression of
trap occupancy, N/n0 , one can avoid this polarity in terms of presenta­
tion and also acquire ascending plots for better comprehension of the
results. It is important to note that the attributed dose in saturation stage
is equal to unity and it is expressed as N/n0 = 1.
In Fig. 2, the parameters Tm , tm are given as a function of either
corresponding rate β or α, as well as ordinary and inverse trap occupancy
(n0 /N, N/n0 ) respectively, in order to emphasize the aforementioned
polarity and the plots represent findings from theoretical glow peaks
produced using Eq (2.1) - (2.5) for second order kinetics (R = An / Am =
1).
In Figs. 2 and 3, the heating/stimulation parameters were regarded
as mathematical variables rather than physical, allowing to take on a
wide range of values. Іt should be noted that, according to instrumental
limitations of commercial luminescence readers in experimental pro­
cedures the heating rate applied is practically restricted within values
ranging between 0.1 and 20 ◦ C/s. Also, for higher rates, readers exhibit
phenomena of fluctuations in signal recording due to instrumental

concerns, something that in simulations is prevented due to their
mathematical nature.
In the left plots of Figs. 2 and 3, when the x-axis is converted to
logarithmic, the figures’ two branches regarding the behavior of peak
maximum position become mirrored resulting to those presented at the
right plots (Figs. 2 and 3 – right plots). This leads to the conclusion that
the common representation depicting the shift of Tm , tm as function of
both β and a, are not practical at all.
Also, the representation of Tm and tm shifting in respect to different
values of the parameter R is of high importance; these are reproduced by
varying ratios of the values An and Am in order to get values ranging
between 1 (second order kinetics) and 10− 2 (roughly first order ki­
netics). It is interesting that for a given stimulation rate, the peak
maximum position shifting depends on the kinetic parameter and
consequently the re-trapping ratio. Shifting in TL and LM-OSL is more
intense in the case when re-trapping and recombination are both
probable. Nevertheless, for the LM-OSL, infinitesimal shift takes place
for the value of tm for the case of negligible re-trapping.
Fig. 4 shows the theoretical results concerning the cases of all pro­
tocols, in which curve (a), according to Protocol I, represents the shift of
maximum temperature and time value (Tm & tm ) versus the heating or
stimulation rate. At the same time, curve (b) depicts the change in Tm &
tm versus the dose, as measured by Protocol II in the framework of the
trap filling procedure. Curve (c) represents the change in Tm & tm versus
the trap occupancy as a result of using Protocol III in trap emptying with
thermal bleaching, while curve (d) represents the shift of Tm & tm versus
the trap occupancy based on Protocol IV, trap emptying with optical

bleaching.
In all protocol processes regarding both TL and LM-OSL, the

assumption that the phenomenological models lead to a single glow
peak are predicated on the premise that the electron traps (N) are preexisting in the material and are simply filled during irradiation.
Furthermore, it is implied that there are no traps created during the
irradiation.
4. Conclusions
In the present study, the maximum temperature (Tm ) and time (tm ) of
each glow curve for the case of TL and LM-OSL peaks were investigated
and compared theoretically; specifically, as functions of heating/stim­
ulation rate, of dose, thermal bleaching, and optical bleaching.
In the first Protocol, it was observed that Tm and tm shift to higher
values as the heating/optical stimulation rate increases. Also, Protocol II
shows that Tm and tm shift to lower temperature and time values as the
dose increases. Based on Protocol III, Tm and tm shift to higher temper­
ature and time values as Step 4 (Thermal emptying) reaches the recor­
ded maximum positions Tm and tm of saturation of Step 1. The last
Protocol shows that Tm and tm shift to higher values as in Step 4 (Optical
emptying) the readout time spans tcwi extend to higher time values.
As the LM-OSL signal is used as a basic tool for the understanding the
OSL recombination mechanisms, identification of individual OSL com­
ponents in experimental cases becomes quite important in processes of
signal characterization. LM-OSL components shifted at higher tm values
could possibly enable deconvolution analysis with better resolution,
when it comes to materials with luminescence described by the second
order kinetics. However, this change is not a favorable aspect from a
dosimetric standpoint, as it is accompanied with a significant reduction
in luminous intensity.
Additionally, it should be mentioned that the shift of Tm and tm as a
function of trap emptying (Protocols III and IV) in TL and LM-OSL is
proven, according to simulations, to follow similar behavior as the shift
of Tm and tm in Protocol I, as they shift for higher heating and optical

stimulation rates to higher values.
Concluding, when performing signal analysis due to better resolu­
tion, selecting the LM-OSL experimental conditions to favor the shifting
of tm to higher values is strongly advised; although in those cases this
aspect is not consider favorable due to light intensity reduction, it would
be appealing for future dosimetric applications.
Declaration of competing interest
The authors declare that they have no known competing financial

Fig. 2. Tm versus the heating rate β (left plot) and versus the stimulation rate α (right plot), both expressed through trap occupancy (n0/N ) and inversed trap
occupancy (N/n0).
6


E. Tsoutsoumanos et al.

Radiation Measurements 153 (2022) 106735

Fig. 3. Tm versus the heating rate β (left plot) and versus the stimulation rate α (right plot), both expressed through trap occupancy ( n0/N) and inversed trap
occupancy (N/n0) and the x-axis on a logarithmic scale.

Fig. 4. Peak maximum position Tmversus the heating rate β, insert plot presents at detail Protocol III (left plot) and tm versus the stimulation rate α (right plot),
alongside the inversed trap occupancy (N/n0).

interests or personal relationships that could have appeared to influence
the work reported in this paper.

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