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

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 theoretically; specifically, the time or temperature values (tm, Tm) of their maximum intensity (Im).

Available online 7 March 2022

1350-4487/© 2022 Elsevier Ltd All rights reserved

Electron trap filling and emptying through simulations: Studying the shift

of the maximum intensity position in Thermoluminescence and Linearly

Modulated Optically Stimulated Luminescence curves

aCondensed Matter Physics Laboratory, Physics Department, University of Thessaly, GR-35100, Lamia, Greece

bInstitute of Nanoscience and Nanotechnology, NCSR “Demokritos”, GR-15310, Ag Paraskevi, (Athens), Greece

cNuclear 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

Keywords:

Linearly modulated optically stimulated

luminescence

One trap one recombination center model

Thermoluminescence

Simulation

Python

A B S T R A C T

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 (t m , T m ) of their maximum intensity (I m) 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 T m

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 t m , T m shifting in trap emptying processes, is proven, according to

sim-ulations, to follow a similar behavior to the t m , T m shift as a function of heating or optical stimulation rate

Regarding trap filling, t m and T m 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

works since the 1970s (Becker, 1973; Chen and Kirsh, 1981; B¨ohm and

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 LM-

OSL, the maximum intensity (I m) and the stimulation position

corre-sponding to maximum intensity (T m or t m) 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: etsoutsoum@uth.gr, e.tsoutsoumanos@inn.demokritos.gr (E Tsoutsoumanos)

Contents lists available at ScienceDirect Radiation Measurements journal homepage: www.elsevier.com/locate/radmeas

https://doi.org/10.1016/j.radmeas.2022.106735

Received 27 November 2021; Received in revised form 28 February 2022; Accepted 2 March 2022

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 T m 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 T m 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 T m 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

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

band in OTOR are:

dn / dt = A n ⋅(N − n)⋅n c − n⋅p(t) (2.1)

dn c / dt = n⋅p(t) − A n ⋅(N − n)⋅n c − A m ⋅m⋅n c (2.3)

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, n c (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, A n

(cm3 ⋅ s− 1) is the capture probability of the electron traps and A m (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 /k b⋅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, k b 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 LM-

OSL 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 time P(t) (Bulur, 1996; Bulur and G¨oksu, 1999; Pagonis, 2021; Kon-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, T m, 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 t m 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

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− E

Here s (s− 1) is the frequency factor, E (eV) is the activation energy, and

the T iso is a selected temperature position for decaying For the case of

LM-OSL t iso corresponds to the time duration in which decaying T iso

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 G¨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):

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 D i

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

Protocol II: trap filling by increasing the dose

Step 1: Delivering of a Dose D i

Step 2: Readout for a specific heating/optical stimulation rate

Step 3: Repeat of Steps 1 and 2 for a higher D i

Step 4: Recording its highest dose signal as N, and integrated signal

as n0

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 t iso 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

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 (tcw i) 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 tcw i

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 T iso Thus, t iso is not the isothermal decay tem-perature; instead, the duration of the isothermal decay

In the particular case of OTOR, the ratio R ​ (R = A n / A m)has replaced

the kinetic parameter b Shifting of either T m or t m is anticipated mainly

for the case of second order kinetics, in which the values of A n and A m were selected so that R = 1

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 T iso in which the

isothermal TL takes place, while in Protocol IV it is tcw i; 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

3 Results and discussion

The luminescence curves resulting from the simulation processes are

Table 1

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

OTOR processes

Symbol

(Units) Value Alterability

1 N (cm− 3 ) 1 ⋅ 10 10 Constant throughout

2 A n (cm 3 ⋅

s − 1 ) 1 ⋅ 10

9 Constant throughout

3 A m (cm 3 ⋅

s − 1 ) 1 ⋅ 10

9 Constant throughout

4 s (s− 1 ) 1 ⋅ 10 12 Constant throughout

5 E (eV) 1 Constant throughout

6 k b (eV/K) 8.617 ⋅

10 − 5 Constant throughout

7 λ(photons

s − 1 ) 0.5 Constant throughout

8 β(K/s) 1 Constant throughout, except Protocol I;

(0.25–20)

9 α(eV/s) 1 Constant throughout, except Protocol I;

(0.25–20)

10 D i

(electrons) 1 ⋅ 10

10 Constant throughout, except Protocol II; (5 ⋅

10 5 –1 ⋅ 10 10 )

11 T iso (K) – Only in Protocol III, where ranges (350–385) in

TL and remains constant in LM-OSL (352)

12 t iso (s) – Only in Protocol III, where ranges (5–175)

13 tcw i (s) – Only in Protocol IV, where ranges (10–50,000)

shown in Fig 1 The shift of T m in TL is shown in plots a, c, e and g

whereas the shift of t m in LM-OSL is shown in plots b, d, f and h

Moreover, the shift of T m or t m 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 T m and t m 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

3.1 Shifting results in trap filling

An interesting behavior of these shifts is presented in Fig 1c and d,

where T m & t m are presented as a function of trap filling Initially for both

cases a small dose of electrons D i=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 T m 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 (D i =N = 1⋅ 1010), the I m

occurred at 368.2 K, meaning that for an initial low dose until the state

of saturation (Table 2), the T m shifted 131.3 K lower (ΔT = − 131.3 K)

For the lowest dose of LM-OSL, the t m was at 1363.4 s As the dose

increased to the state of saturation the shift of t m was much greater, in

contrast with TL, as t m occurred at 18 s Specifically the duration where

the peak reaches its I m 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 T m and t m 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 T m & t m 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 T m & t m 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)

3.2 Shifting results in trap emptying

There is a shift of T m and t m as functions of trap emptying via thermal

bleaching (Fig 1e and f) and via optical bleaching (Fig 1g and h) in

Protocols III and IV respectively In all processes, before the emptying stages were initiated, the system was stimulated by the maximum dose (D i=1 ⋅1010)and n0 / N was equal to unity due to saturation

In Protocol III, Fig 1e, after defining the T m in saturation state, all the

parameters remained constant except for the T iso, which varies from 350

up to 385 K, in which the I m 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 T m varied from 389.5 K to 401.2 K (Δ T = 11.7 K) For the LM-OSL simulation (Fig 1f), the T iso, and by

extension λ, is stable while the t iso value was set to vary from 5 to 175 s

(up to I m ) Finally, similarly to TL, t m varied from 180.2 s to 619.2 s (Δt =

439 s), meaning that t iso reaches the t m of the saturation state

In Protocol IV, Fig 1g & h, all the parameters remained constant

except the tcw i value (CW-OSL stimulation duration) which varied from

5 to 50,000 s In TL, as the CW-OSL duration sequentially increased T m 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, t m

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 LM-

OSL readout remained constant at 3000 s

Regarding all the cases of trap emptying, I m decreased, while T m and

t m 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 T m and t m 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)

3.3 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 T m and t m

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

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

5⋅ 10 5 499 0.00005 1363 0.00005 0 389 1.000 0 180 1.000 0 389 1.000 180 1.000 1⋅ 10 6 487 0.0001 1363 0.0001 350 390 0.935 5 204 0.379 10 389 0.971 180 0.498 5⋅ 10 6 461 0.0005 621 0.0005 355 390 0.901 15 246 0.254 50 391 0.862 190 0.442 1⋅ 10 7 450 0.001 441 0.001 360 391 0.847 25 288 0.191 100 392 0.763 200 0.388 5⋅ 10 7 429 0.005 198 0.005 365 392 0.775 50 360 0.116 500 401 0.388 290 0.195 1⋅ 10 8 420 0.01 198 0.01 370 394 0.694 75 426 0.083 1000 407 0.239 360 0.120 5⋅ 10 8 393 0.05 63 0.05 375 396 0.599 100 481 0.064 5000 426 0.058 731 0.028 1⋅ 10 9 373 0.1 45 0.1 380 398 0.498 125 529 0.052 10,000 435 0.029 1012 0.014 5⋅ 10 9 368 0.5 45 0.5 385 401 0.398 150 577 0.043 30,000 451 0.009 1743 0.004

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

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 T m , t m 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 = A n / A m =

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 T m , t m as function of

both β and a, are not practical at all

Also, the representation of T m and t m shifting in respect to different

values of the parameter R is of high importance; these are reproduced by

varying ratios of the values A n and A m 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 t m 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 (T m & t m) versus the heating or

stimulation rate At the same time, curve (b) depicts the change in T m &

t m versus the dose, as measured by Protocol II in the framework of the

trap filling procedure Curve (c) represents the change in T m & t m versus

the trap occupancy as a result of using Protocol III in trap emptying with

thermal bleaching, while curve (d) represents the shift of T m & t m 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 pre-

existing 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 (T m ) and time (t m) 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 T m and t m shift to higher values as the heating/optical stimulation rate increases Also, Protocol II

shows that T m and t m shift to lower temperature and time values as the

dose increases Based on Protocol III, T m and t m shift to higher temper-ature and time values as Step 4 (Thermal emptying) reaches the

recor-ded maximum positions T m and t m of saturation of Step 1 The last

Protocol shows that T m and t m shift to higher values as in Step 4 (Optical

emptying) the readout time spans tcw i 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 t m 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 T m and t m 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 T m and t m 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 t m 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)

interests or personal relationships that could have appeared to influence

the work reported in this paper

References

Becker, K., 1973 Solid State Dosimetry CRC Press, Cleveland Ohio, 0878190465

9780878190461

B¨ohm, M., Scharmann, A., 1981 Applied Thermoluminescence Dosimetry Adam Hilger

Ltd, Bristol, ISBN 0852745443

Bøtter-Jensen, L., McKeever, S.W.S., Wintle, A.G., 2003 Optically Stimulated

Luminescence Dosimetry Elsevier Science B.V, ISBN 9780080538075

Bulur, E., 1996 An alternative technique for optically stimulated luminescence (OSL)

experiment Radiat Meas 26 (5), 701–709

Bulur, E., G¨oksu, H.Y., 1999 Infrared (IR) stimulated luminescence from feldspars with

linearly increasing excitation light intensity Radiat Meas 30 (4), 505–512

Chen, R., Kirsh, Y., 1981 Analysis of Thermally Stimulated Relaxation Processes

Pergamon Press, ISBN 9781483285511

Chen, R., McKeever, S.W.S., 1997 Theory of Thermoluminescence and Related

Phenomena World Scientific

Chen, R., Pagonis, V., 2011 Thermally and Optically Stimulated Luminescence: A

Simulation Approach Wiley, ISBN 978-1-119-99576-0

Chithambo, M.L., Niyonzima, P., 2014 On isothermal heating as a method of separating

closely collocated thermoluminescence peaks for kinetic analysis J Lumin 155,

70–78

Dallas, G.I., Afouxenidis, D., Stefanaki, E.C., Tsagas, N.F., Polymeris, G.S., Tsirliganis, N

C., Kitis, G., 2008a Reconstruction of the thermally quenched glow-curve of Al2O3:

C Phys Status Solidi 205 (7), 1672–1679

Dallas, G.I., Polymeris, G.S., Stefanaki, E.C., Afouxenidis, D., Tsirliganis, N.C., Kitis, G.,

2008b Sample dependent correlation between TL and LM-OSL in Radiat Meas 43

(2–6), 335–340

Furetta, C., 2003 Handbook of Thermoluminescence World Scientific https://doi.org/ 10.1142/5167

Furetta, C., Marcazz´o, J., Santiago, M., Caselli, E., 2007 Isothermal decay method for analysis of thermoluminescence: a new approach Radiat Eff Defect Solid 162 (6), 385–391

Garlick, G.F.J., Gibson, A.F., 1948 The electron trap mechanism of luminescence in sulphide and silicate phosphors Proc Phys Soc 60 (6), 574–590

Hoogenstraaten, W., 1958 Electron traps in ZnS phosphors Philips Res Rep 13, 515–693

Kitis, G., Pagonis, V., 2007 Peak shape methods for general order thermoluminescence glow-peaks: a reappraisal Nucl Instrum Methods Phys Res Sect B Beam Interact Mater Atoms 262 (2), 313–322

Kitis, G., Vlachos, N.D., 2013 General semi-analytical expressions for TL, OSL and other luminescence stimulation modes derived from the OTOR model using the Lambert W-function Radiat Meas 48, 47–54

Kitis, G., Furetta, C., Pagonis, V., 2009 Mixed-order kinetics model for optically stimulated luminescence Mod Phys Lett B 23 (27), 3191–3207

Kitis, G., Mouza, E., Polymeris, G.S., 2020 The shift of the thermoluminescence peak maximum temperature versus heating rate, trap filling and trap emptying: predictions, experimental verification and comparison Phys B Condens Matter

411754

Kitis, G., Polymeris, G.S., Pagonis, V., 2019 Stimulated luminescence emission: From phenomenological models to master analytical equations Appl Radiat Isot 153,

108799

Kiyak, N.G., Polymeris, G.S., Kitis, G., 2008 LM-OSL thermal activation curves of quartz: Relevance to the thermal activation of the 110 ◦ C TL glow-peak Radiat Meas 43 (2–6), 263–268

Konstantinidis, P., Kioumourtzoglou, S., Polymeris, G.S., Kitis, G., 2021 Stimulated luminescence; Analysis of complex signals and fitting of dose response curves using analytical expressions based on the Lambert W function implemented in a commercial spreadsheet Appl Radiat Isot 176, 109870

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)

Martini, M., Meinardi, F., 1997 Thermally stimulated luminescence: new perspectives in

the study of defects in solids La Rivista Del Nuovo Cimento 20 (8), 1–71

May, C.E., Partridge, J.A., 1964 Thermoluminescent Kinetics of Alpha-Irradiated Alkali

Halides J Chem Phys 40 (5), 1401–1409 https://doi.org/10.1063/1.1725324

McKeever, S.W.S., 1985 Thermoluminescence in Solids Cambridge Solid State Science

Theories Cambridge University Press, 9780511564994 0511564996

Pagonis, V., 2021 Luminescence: Data Analysis and Modeling Using R Springer

Pagonis, V., Kitis, G., Furetta, C., 2006 Numerical and Practical Exercises in

Thermoluminescence, 2006 Springer, New York, NY, USA, ISBN 0-387-26063-3

Pagonis, V., Kreutzer, S., Duncan, A.R., Rajovic, E., Laag, C., Schmidt, C., 2019 On the

stochastic uncertainties of thermally and optically stimulated luminescence signals:

a Monte Carlo approach J Lumin 116945

Petrov, S.A., Bailiff, I.K., 1997 Determination of trap depths associated with TL peaks in synthetic quartz (350–550 K) Radiat Meas 27 (2), 185–191

Polymeris, G.S., Afouxenidis, D., Tsirliganis, N.C., Kitis, G., 2009 The TL and room temperature OSL properties of the glow peak at 110 ◦ C in natural milky quartz: a case study Radiat Meas 44 (1), 23–31

Polymeris, G.S., Kitis, G., Tsirliganis, N.C., 2006 Correlation between TL and OSL properties of CaF2:N Nucl Instrum Methods Phys Res Sect B Beam Interact Mater Atoms 251 (1), 133–142

Polymeris, G., Kiyak, N., Kitis, G., 2008 Component resolved IR bleaching study of the blue LM-OSL signal of various quartz samples Geochronometria 32 (-1), 79–85

Randall, J.T., Wilkins, M.H.F., 1945 Phosphorescence and electron traps II The interpretation of long-period phosphorescence Proc Math Phys Eng Sci 184 (999), 390–407