Anomalous Effects in
Thermoluminescence
Arkadiusz Mandowski
Jacek Orzechowski
Ewa Mandowska
Institute of Physics
Jan Długosz University
Częstochowa, Poland
RAD 2012, Niš
Principles of luminescence dosimetry
 Purpose:
Determination of dose of ionizing radiation using
optical (luminescence) techniques
 Methods:
 Thermoluminescence (TL)
[thermal stimulation – heating]
 Optically Stimulated Luminescence (OSL)
[optical stimulation]
Principles of luminescence dosimetry
preparing a detector
(signal reset)
irradiation
storage
luminescence
readout (TL / OSL)
Relaxation processes during
thermoluminescence
Excitation  perturbation of a solid from
equilibrium; energy storage;
Metastable state  very slow relaxation
processes with respect to to given time scale
(from minutes to centuries), practically
undetectable
Heating  fast relaxation, easy to detect,
TL  luminescence
other properties for other TSR processes
TL kinetic theories
TL theoretical models
excited states
S1
A
S2
traps
deep traps
RC
Examples of anomalous
TL behaviour
• TL dose-rate effect
• first order shape of most TL glow peaks
• the occurrence of very high frequency
factors
• dose-dependent peak parameters (peak
positions, activation energies and frequency factors)
• anomalous heating-rate effect (total number of
emitted photons increases with heating rate)
Examples of anomalous
TL behaviour
• TL dose-rate effect
• first order shape of most TL glow peaks
• the occurrence of very high frequency
factors
• dose-dependent peak parameters (peak
positions, activation energies and frequency factors)
• anomalous heating-rate effect (total number of
emitted photons increases with heating rate)
Classification of TL/OSL models
 With respect to charge carriers type
•
•
one-carrier kinetics (e.g. active electrons)
two-carrier kinetics (active electrons and holes)
 With respect to energy distribution
•
•
•
OTOR (one trap one recombination centre)
discrete distribution or traps and RCs
continuous energy distribution of traps and RCs
e-STM
 With respect to spatial distribution
•
•
•
geminate pairs T-RC
trap clusters
random distribution of traps and RCs
 With respect to type of interaction
•
•
localized transitions
delocalized transitions (band-like)
LT
The simple trap model (STM)
(extended)
æ- Ei ö
÷
- n&i = ni ni expçç
- nc Ai ( N i - ni ), i=1..p,
÷
çè kT ÷
ø
- h&
s = Bs hs nc ,
q
J TSC
s=1..q,
p
å
hs =
å
s= 1
dh
º - h&
dt
µ nc
J TL µ -
conduction
band
ni + nc + M ,
nc
i= 1
Ai
shallow
traps
Bj
 


































deep
traps
recombination
centres





M
traps
hj




 







Ei
Ni, ni active



 






 




Di


valence
band
hv
The model of localized
transitions (LT)
æ- E ö
÷
- n&= nn exp çç
- Ane ,
÷
÷
è kT ø
- h&= Bne ,
conduction
band
nc
ne
h = n + ne ,
Ai
Bj



















active
traps
ni
hj












Ei
Di
recombination
centres



valence
band
hv
Various topologies of delocalization
Clustering 
STM
LT
Displacement of charge carriers 
The model of semi-localized transitions (SLT)
Clustering 
LT
SLT
Displacement of charge carriers 
STM
The model of semi-localized
transitions (SLT)
conduction band
trap excited
level
trap
recombination
centre
valence band
The model of semi-localized
transitions (SLT)
nc
V
K
ne
C
D
A
n
B
h
hv
The model of semilocalized
transitions (SLT)
nc
V
K
V
K
ne
C
A
D
V
K
ne
C
D
n
ne
A
C
A
D
n
B
n
B
h
B
h
T-RC units
h
hv
T-RC
H
0
0
H
0
1
T-RC
H
1
0
0
1
E
T-RC
E
1
0
0
0
E
Mandowski A 2005
J. Phys. D: Appl. Phys. 38, 17
TLD-100 (LiF:Mg,Ti)
E10 , E01
H10 , H 01
H
0
0
Horowitz et al. 2003 J. Phys. D: Appl. Phys. 36 446
Picture by courtesy of prof. Horowitz and prof. Oster
E00
SLT system – kinetics... ?
SLT = STM + LT ?
SLT = Semi-localized Transitions
STM = Simple Trap Model
LT = Localized Transitions
NO !
The model of semilocalized
transitions (SLT)
H10
TL kinetics for K=0
C¯
E10
H& = - (D + Cnc )H + AH
H& = DH10 - (A + B + V + Cnc )H 01
H&00 = VH 01 - Cnc H 00
E&0 = Cn H 0 - DE 0 + AE1
0
1
1
0
1
0
1
c
1
1
1
0
0
E&01 = Cnc H 01 + DE10 - (A + V )E01
E&0 = BH 1 + Cn H 0 + VE1
0
0
c
0
D
¾
¾®
¬ ¾¾
A
0
0
0
C¯
D
¾
¾®
¬ ¾¾
A
E01
¾ V¾®
]
B
¾ V¾®
H 00
C¯
E00
LB = BH 01
LC = Cnc ( H10 + H 01 + H 00 )
n&c = - Cnc ( H10 + H 01 + H ) + V ( H 01 + E01 )
Mandowski A 2005 J. Phys. D: Appl. Phys. 38, 17
H 01
The riddle of very high
frequency factors
Unphysical values !
=1020 s-1
E=2.05 eV
(allowed 108    1014 s-1)
LiF:Mg,Ti
=1021 s-1
E=2.29 eV
LiF:Mg,Cu,P
Anomalous peaks are very narrow !
Bilski P, (2002) Radiat.Prot.Dosim. 100, 199-206
The riddle of very high frequency factors
explained by SLT energy configurations
- activation energies for various configurations may be different!
n
m
H - states with charged recombination centres
D(t ), V (t ) ® D1 (t ), V1 (t )
E
n
m
- states with empty recombination centres
D(t ), V (t ) ® D2 (t ), V2 (t )
D E º E2 - E1
activation energy gain
between charged and
non-charged T-RC unit
1.0
TL [a.u.]
0.8
0.6
0.4
a
c
0.2
b
0.0
E = -0.1 eV
EV = 0.5 eV
r=0
TL [a.u.]
0.8
a
0.6
c
0.4
Efit=1.65 eV; fit=2.01020 s-1
0.2
b
0.0
TL [a.u.]
E = -0.2 eV
EV = 0.5 eV
r=0
a
0.8
0.6
c
0.4
Efit=1.87 eV; fit=3.01024 s-1
0.2
b
0.0
E = -0.3 eV
EV = 0.5 eV
r=0
a
0.8
TL [a.u.]
Cascade detrapping
E=0.9 eV; EV=0.5 eV; = V=1010 s-1
E = 0 eV
EV = 0.5 eV
r=0
c
0.6
0.4
Efit=1.90 eV; fit=1.91026 s-1
0.2
0.0
320
340
360
380
400
Temperature [K]
420
440
460
Cascade detrapping – how does it work?
Initally (at low temperatures) most of charge carrier transitions goes within localized
pairs
A carrier (electron) thermally released to the conduction band recombines to an
adjacent hole-electron pair
The remaining „lonely” electron having decreased activation energy is rapidly excited
to the conduction band
The free carrier moves to an an adjacent hole-electron pair and the process repeats one
again
E
E
The heating-rate effect (normal)
We measure TL intensity for various heating rates:
10
8
TL/ [a.u.]
TL/ [a.u.]
without
quenching

8
10
6
4
4
2
0
0
400
500

6
2
300
300
600
tk
Tk
J T 
t0
T0

n   J  t  dt  

 W

C
,
W
,
T

1

C
exp


where:


 kT




400
500
Temperature [K]
Temperature [K]
The number of emitted photons:
with
quenching
Tk
J TL T 
T0

dT  
  C ,W , T  dT
1
is the quenching function
600
The heating-rate effect
in YPO4:Ce3+,Sm3+ (anomalous)
A.J.J. Bos et al., Radiat. Meas. (2010)
Explanation of the anomalous
heating-rate effect by SLT model
Dorenbos, P., 2003b. J. Phys.: Condens. Matter 15, 8417–8434.
Explanation of the anomalous
heating-rate effect by SLT model
Experimental data in YPO4:Ce3+, Sm3+
SLT modelling
Mandowski A, Bos A J J (2011), Radiation Measurements (doi:10.1016/j.radmeas.2011.05.018)
Dose-rate effect by SLT model
1.240
S C
1.185
1.235
1.180
1.230
1.175
1.225
1.170
 C_max
1.165
Relative area under  C peak [a.u.]
Relative peak maximum of  C [a.u.]
1.190
1.220
-15
-10
-5
0
5
10
15
log(G/G0)
Illustration of the dose rate effect. The TL output - two localizedLB(1
LB 2
and
) and one
delocalized peak ( LC ), calculated after three stages: excitation, fast relaxation and heating.
Conclusions
 The model of semi-localized transitions model (SLT) offers simple
explanation of some anomalous effects in thermoluminescence,
including
- anomalous heating rate effect
- very high effective frequency factors (cascade detrapping mechanism)
as well as
- dose rate efect
- first order shape of TL peaks, etc.
 Other experimental data indicate the necessity of taking into
account larger clusters of traps and RCs.
Anomalous Effects in Thermoluminescence
Arkadiusz Mandowski, Jacek Orzechowski, Ewa Mandowska
Thank you!