Microsoft Word - Journal Opto _marius.doc
Thermally Stimulated Luminescence and Current in new heterocyclic materials 
for Organic field transistors and organic light emitting diodes 
Marius Prelipceanu 1,2, Otilia Sanda Prelipceanu 1,2 , Ovidiu-Gelu Tudose 1,2, Sigurd Schrader1,2 
1University of Potsdam, Institute of Physics, Condensed Matter Physics, Am Neuen Palais 10, 
 D-14469, Germany  
2University of Applied Sciences Wildau, Department of Engineering Physics, D-15745 Wildau, 
Germany 
Corresponding author: mariusp@rz.uni-potsdam.de 
Published in Abstract Book of ICPAM07, Iasi, Romania, June 2004 
In the last years progress has been made in the field of organic electronics and in particular organic 
light emitting devices and organic field effect transistors. In this case the study of localised levels in 
technologically relevant materials like oxadiazoles and quinoxalines is of fundamental importance. 
Several scientific tools enable to study localised levels in solids and among others the thermally 
stimulated techniques give the most direct evidence of their presence. The present work is focused on 
theoretical and experimental study of localised levels in organic materials suitable for light-emitting 
devices and field effect transistors by means of thermal techniques. 
Keywords: thermally stimulated techniques, localised levels, organic materials, light-emitting    
devices (LED), field effect transistors (FET) 
1. Introduction  
The discussion about the presence of localised states and their density naturally leads to the 
question about the kind of traps we are dealing with. In a first approach we should distinguish 
between intrinsic and extrinsic defects. In the first type we should inscribe polymer end groups, grain 
boundaries, structural defects, conformational disorder up to molecular groups with large permanent 
dipole moment that could increase the level of energetic disorder [1]. For the second type we should 
mention the chemical impurities, somehow unavoidable in the synthesis of organic molecules. We 
can further distinguish the kind of traps in function of their location, interfacial or bulk, or in term of 
energy, deep traps or shallow traps. Also polarons could be seen, in a simplistic way, like defects 
caused by an electron plus an induced lattice polarisation [2] followed by a lattice distortion. Traps 
are into the samples in a great variety and in different proportion, often despite the same preparation 
procedure. For that reason sometimes their nature is difficult to investigate and the data must be 
handled with care. 
In the studies of trapped states because of the above underlined variety of defects in solids the 
most successful approach is to start introducing a single type of defect in a well-known system in a 
controlled way.  
2. Experimental Part 
 In our work we focused on low molecular compounds as well as on polymers, especially of 
two classes of materials: oxadiazoles and quinoxalines. Both organic compounds are well know as 
electron transport materials in OLEDs. PPQs (see figure 1) in general show very high solubility [3] in 
a variety of common organic solvents, and according to literature they exhibit a glass transition at 
quite high temperature (250-350 °C).  
The materials were deposited by spin coating on gold, aluminium or silicon in different speed 
or concentration for the film optimisation. The layer thickness was controlled by Dektak techniques 
and Ellypsometry. 
The thermally stimulated luminescence (TSL) and thermally stimulated current (TSC) are 
powerful instruments in order to study de-trapping and relaxation processes in organic materials. TSL 
is a contact less technique that allows to distinguish between deep and shallow trapping states. The 
proposed mathematical model for the TSL enables to study trap levels and recombination centres 
inside the band gap. The analytical solution of the rate equations allows two different de-trapping 
regimes, including or excluding subsequent re-trapping effects. The first order solution kinetic 
indicates that no re-trapping phenomena are permitted. The electron released from a localised level 
recombines with a hole in a recombination centre and its re-trapping probability, before to 
recombine, is negligible. The second order equation deals with the opposite extreme case. The 
phonon-assisted release of an electron is followed by multiple re-trapping. In this second order 
kinetic regime the probability of a released electron to get re-trapped is very high. The main factors 
governing both solutions are the energy depth of the traps calculated with respect to the conduction 
band edge and the frequency factor. This second important factor in general indicates the attempt-to-
escape frequency of electrons from the localised levels. The mathematical model takes also into 
account the occurrence of distributions of localised levels. In case of a Gaussian distribution of 
localised states a meaningful parameter is the width of the distribution. Numerical simulations, 
calculated with the proposed model, show that while a first order peak is characterised by an 
asymmetric peak shape with a steep decreasing side, the second order kinetic peaks are characterised 
by a more symmetric shape. The signal is smeared along the whole peak temperature range due to the 
re-trapping effect.  
Figure 1.  Poly-[2,2’-(1,4-phenylene)-6,6’-bis(3-phenylquinoxaline)] (PPQ IA) 
The same theoretical description holds for both techniques, TSL and TSC. However, TSC 
theory requires the presence of an extended conduction band. During a TSC experiment a driving 
voltage is applied to the sample and the de-trapped charges are extracted at the device contacts. 
However, the equations describing a TSC peak are similar to equations describing TSL. Additionally, 
it is possible to determine the density of the trapping states evaluating the area under a TSC peak.  
Simultaneous TSL and TSC measurements give useful information about the localised states 
combining the best possibilities of both thermal techniques. Unambiguous information about trap 
depth, density of states, kinetics order and frequency factor can be extract making use of the full 
possibilities of the combined measurements. 
In typical thermally stimulated process experiments a sample is heated in a controlled way and 
the current, in case of TSC, or the light emission, in case of TSL, or both simultaneously are 
monitored. The effect appears only when an optical or electrical excitation takes place prior to the 
heating. TSC, in contrast to TSL, requires the presence of good ohmic contacts.  
In the following a TSL experiment is described in more detail and the rate equations derived. 
The sample, in an equilibrium state at room temperature where all the shallow traps are empty, is 
cooled down to a low temperature. Then, it is illuminated with electromagnetic radiation of certain 
energy. The incident radiation excites the electrons from the valence band to the conduction band 
trough the gap. 
In the case of prompt fluorescence the generated electrons recombine promptly. Otherwise 
they can form an electron hole pair followed by geminate recombination or by dissociation with 
subsequent trapping. Charge carriers can get trapped in localised levels that, considering the random 
fluctuation of the potential in disordered materials, are distributed in energy. From statistical 
consideration, the distribution type should be generally Gaussian. The thermal emission from traps at 
low temperature is negligibly small. Therefore, the perturbed equilibrium created by the incident 
radiation resists for a long time and the electrons are just stored in the localised levels. 
Temperature is then raised in a controlled way, electrons acquire energy and finally escape 
from the traps by means of a phonon assisted jump and recombine with holes trough a recombination 
centre where recombination occurs with subsequent photon emission. By means of spectrally 
resolved TSL experiments it is possible to get information about recombination centres studying the 
wavelength of the emitted light as function of temperature and intensity.  
The above-described processes are illustrated in figure 2. 
The illustrated scheme for thermoluminescence is simple, but despite of its simplicity it can 
describe all fundamental features of a thermoluminescence process. Following Chen [4], the electron 
exchange between the HOMO and LUMO levels, during the trap emptying, can be described by the 
following three differential equations: 
h Ann
⋅⋅−=   (1) 
pnAnNn
c ⋅−⋅−= )(   (2) 
c AnnAnNnpn
⋅⋅−⋅−−⋅= )(  (3) 
Here nh is the concentration of holes in the recombination centres, nc is the concentration of 
electrons in the conduction band, Ar is the recombination coefficient for electrons in the conduction 
band with holes in the recombination centres, n is the concentration of electrons in traps, N is the 
function describing the concentration of electron traps at depth E below the edge of the conduction 
band, A is the transition coefficient for electrons in the conduction band becoming trapped and p is 
the same probability of thermal release of electrons from traps defined in equation (1), which 
represents in fact their release rate. Equation (2) describes the change of hole density nh in 
recombination centres versus time. The recombination rate depends both from the concentration of 
free electrons (nc) and from the concentration of holes already present in the recombination centres 
trough a probability coefficient (Ar) that depends on the cross section and the thermal velocity72 of 
electrons. An increase in these parameters results in an increase of the recombination probability. 
Equation (3) describes the exchange of electrons between conduction band and traps. The first term 
in the right hand side includes the probability A for an electron to be trapped. That probability A, like 
Ar, also depends on the thermal velocity of electrons and on the cross section of traps. The second 
term on the right hand side is the de-trapping term. It is proportional to the concentration of trapped 
Electron centre
Hole centre
Conduction band
Valence band 
Recombination centre
Figure 2. Energy diagram describing the elementary 
process of the simple model for TSL 
electrons and to the Boltzmann’s function, i.e. equation (1). The proportionality factor s, often called 
frequency factor or pre-exponential factor, should be, when interpreted in terms of attempt to escape 
of an electron from the potential well, in the order of magnitude of 1010 ÷ 1014 s-1. A saturation effect 
for carrier release from traps, caused by a limited number of available states in the conduction band, 
is neglected in this model. In each moment the number of available states in conduction band is much 
higher than the released amount of electrons from the localised states [5]. 
Equation (3) describes the variation of electron density in the conduction band and essentially 
it takes into account the charge neutrality of the whole system. The variation rate of electrons in the 
conduction band depends on electrons being released - first term on the right hand side-, electrons 
being trapped - second term - and electrons that recombine - third term. Electrons and holes in that 
model are generated at the same time - geminate couples, but they are not necessarily still bound. 
Saturation effects due to filled deeper traps or recombination centres that have already a hole on them 
are not considered.  
Complex models have the disadvantage to introduce an increased number of parameters [7]. 
Actually, several combinations of too many parameters can generate the same shape of a real glow 
curve, making impossible to find a most probable fit [8]. For that reason it is preferable to deal with a 
reasonable simple model that involves few reliable parameters. Actually, the proposed simple model 
can successfully describe the experimental glow curves, but it is necessary to take also the energetic 
distribution of localised states into account in order to describe the complex behaviour of disordered 
systems, like amorphous polymers or organic polycrystalline thin films. In such case the total number 
of traps is represented by the following equation (4). The traps do not have single activation energy, 
but they are continuously energetically distributed. 
dEENN   (4) 
 Here N(E) can be in principle any kind of distribution, but considering the statistical disorder 
in organic materials it should have a Gaussian shape. In principle also the frequency factor should 
have the same energetic distribution. In order to solve the system of differential equations (1)-(4), 
equation (5), regarding the time dependence of temperature, should be add. 
tTT ⋅+= β0   (5) 
In equation (5) β is the experimental constant heating rate. It should be note that as long as T is 
a well knows function of the time the only real variable is the time. For that reason it is very 
important, experimentally, to have a perfect control of the temperature linearity. 
3. Results and discussion 
The main peak in figure 3 has the maximum temperature at Tm = 159.7 K and the second, of the 
roughly half the intensity, at Tm = 230.7 K. The peak at Tm = 159.7 K has a symmetry factor µ = 
0.54, very near to the typical value for a second order kinetic. This fact gives a hint that in PPQ IA an 
electron, before recombination, has high probability to get re-trapped several times. Because of its 
hidden position the analysis of the minor peak of PPQ IA appearing at Tm = 230.7 K is very difficult  
[6]. 
60 80 100 120 140 160 180 200 220 240
=230.7 K
= 159.7 K
Temperature (K)
40 60 80 100 120 140 160 180 200 220 240 260
Temperature (K)
Figure 3. TSL of PPQ IA Figure 4. TSL glow curve of a PPQ IA sample (red 
line) compared with the second order numerical 
simulation of the first peak (green line) 
Figure 4 shows the numerical fitting of the main TSL peak of PPQ IA. The fit is performed by 
means of a second order equation characterised by a Gaussian distribution of traps. While the 
high temperature side perfectly fits the glow curve, the low temperature side do not follow the 
curve shape. For that reason the numerical simulation is not completely satisfactory. The 
distribution has a width σ = 0.12 eV and the distribution maximum is at Em = 0.37 eV. The 
energy maximum Em lies exactly in the middle of the integration limits E1 = 0.25 eV and E2 = 
0.49 eV, having the distribution in such case a perfect Gaussian shape. The natural frequency s of 
this peak can be estimated to be in the order of s = 1x1010 s-1, considering, as is normal, the 
recombination coefficient / trapping coefficient ratio equal to 1 and a density of traps of 1014 cm-
3. The value of Em, derived by numerical analysis, is far from the expected energy depth of a trap 
calculated with the initial rise method. However, this mismatching can be explained considering 
the particular complexity of the peak that could result from the sum of at least two distributed 
peaks. In effect the initial rise procedure reveals the activation energy of a hidden peak at low 
temperature. This is an important point to clarify because of the importance of the presence of 
shallow traps in materials suitable for plastic electronic applications. Shallow traps are, at room 
temperature, empty and they play a crucial role in the electron transport property of organic 
materials. For a different thickness we obtain glow curves from figure 5. 
40 60 80 100 120 140 160 180 200 220 240 260
Temperature (K)
Figure 5. Glow curve of PPQ IA for 1500 nm 
We made TSC measurements for Poly-3-hexyle-thiophene (P3HT) on SiO2 – treated and 
untreated in oxygen plasma. The TSC experiment consisted of: 
(1) Cooling to -180°C 
(2)  Trap filling by light (Mercury lamp) with + 4 V bias voltage  
(3)  Application of readout voltage, heating with 0.10 K/sec.  and measurement of 
detrapping current 
All measurements were carried out in vacuum  (4,5 x 10 –5 mbar). The traps were filled by 
creating carriers with band-to-band photoexcitation of the samples. The light source was a Mercury 
lamp (200 W). The thermally stimulated currents were measured by a  Keithley 617  electrometer. 
The TSC and temperature data were stored in a personal computer as described earlier. In a typical 
experiment, the samples are cooled down to T = 80 K and kept at this temperature for 15 min. Then 
they are illuminated through front electrode for a 15 minutes at a bias voltage   + 4 V. Measurements 
were started after exposure to light, and samples are then heated with a constant rate (β = 0.1 K/sec.) 
from 50 up to 240 K. We measured and compared 2 samples of P3HT on SiO2 – treated and 
untreated in oxygen plasma.  
Both experiments were performed under the same conditions.  
The concentration of the traps was estimated using (Manfredotti et. al.) the relation: 
NT =   (6) 
Here Q is the quantity of charge released during a TSC experiment and can be calculated from the 
area under the TSC peaks; A and L are the area and the thickness of the sample, respectively; e is the 
electronic charge and G is the photoconductivity gain, which equals to the number of electrons 
passing through the sample for each absorbed photon. NT was calculated by assuming G = 1. For that 
samples L = 60 nm and samples have 2,5 x 2,5 cm,    A = 6,25. 10-4 m2. The trap is characterized by 
the temperature (Tm) corresponding to the peak maximum at the thermally stimulated current.  The 
energy associated with the trap is the thermal energy at Tm given by: 
mmo KTTTfE ),,(
´βα=           (7) 
80 100 120 140 160 180 200 220 240
1.54E-010
1.55E-010
1.55E-010
1.56E-010
1.56E-010
Ea = 22.2 meV
Ea=20.1 meV
Ea = 25.8 meV
Ea=17,5 meV
=26.79x1014
=4,452x1014Nt=0.2825x10
=48.31x1014
198.56
171.08
155.05
134.43
Temperature (K)
80 100 120 140 160 180 200 220 240
1.00E-013
1.10E-013
1.20E-013
1.30E-013
1.40E-013
1.50E-013
Ea=26 meV
=1.368x1012 cm3
=0.608x1012 cm3
=0.84x1012 cm-3 Ea=21 meV
Ea=16 meV
202.914
167.161
127.709
Temperature (K)
Figure 6.  TSC for P3HT on SiO2 untreated sample Figure 7.  TSC for P3HT on SiO2 treated sample 
In this equation, α is a dimensionless model dependent constant. The variable T’ is the temperature at 
half of the maximum current value on the low temperature side of the current peak. Assuming the 
Grossweiner model, the constant α and function f are given by: 
51.1=α        (8) 
´ 1),,(
TTf mmβ      (9) 
 We observed a difference between the trap concentrations in these two samples (treated and 
untreated) of two orders of magnitude.  
4. Conclusions 
Thermal techniques are a powerful tool in the to study of localised levels in inorganic and organic 
materials. Thermally stimulated luminescence, thermally stimulated currents and thermally 
stimulated depolarisation currents allow, when applied in synergy the details shallow of traps and 
deeper levels to be investigated. They also permit to study, in synergy with dielectric spectroscopy, 
as polarisation and depolarisation effects. The analysis of the thermograms, emerging from the 
thermal techniques, can be performed starting from the differential rate equations of the de-trapping 
phenomena. Such an approach, allowed by the computing power of the modern computers, is not the 
most fruitful, while the number of free variables involved in the numerical resolution of the rate 
differential equations is too high. Sometimes completely different sets of parameters can fit the same 
thermally stimulated peak and ambiguous results are often achieved. 
5. Acknowledgements 
Many thanks for the European Commission (contract number - HPRN-CT-2002-00327 - RTN-
EUROFET) for the financial support as well as all co-workers and many friends of EUROFET 
network. 
6. References 
 [1] Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Holt, Rinehart & Winston, New York, 
1976). 
[2] McKeever, S. W. S. Thermoluminescence of Solids (eds. Cahn, R. W., Davis, E. A. & 
Ward, I. M.) (Cambridge University Press, Cambridge, 1985). 
[3] Paolo Imperia, Localised States in Organic Semiconductors and their Detection, 
University of Potsdam, 2003. 
[4] Bässler, H. Charge Transport in Disordered Organic Photoconductors, a Monte Carlo Simulation 
Study. phys. stat. sol. (b) 175, 15 (1993). 
[5] M. Prelipceanu, O.G. Tudose, S. Schrader, Thermally Stimulated Luminescence Investigations of 
New Materials For OFET’s and OLED’s, Winterschool on Organic Electronics (OEWS’04) 
Materials, Thin Films, Charge Transport & Device, Planneralm, Austria, 2004. 
[6] van Turnhout, J. in Electrets (ed. Sessler, G. M.) 81 (Springer Verlag, Berlin, 1980). 
[7] Schrader, S., Imperia, P., Koch, N., Leising, G. & Falk, B. in Organic Light-Emitting Materials 
and Devices, (ed. Kafafi, Z. H.) 209 (SPIE, San Diego, California, 1999).

  The present work is focused on theoretical and experimental study of
localised levels in organic materials suitable for light-emitting devices and
field effect transistors by means of thermal techniques. In our work we focused
on low molecular compounds as well as on polymers, especially of two classes of
materials: oxadiazoles and quinoxalines. Both organic compounds are well know
as electron transport materials in OLEDs.

Introduction  
The discussion about the presence of localised states and their density naturally leads to the 
question about the kind of traps we are dealing with. In a first approach we should distinguish 
between intrinsic and extrinsic defects. In the first type we should inscribe polymer end groups, grain 
boundaries, structural defects, conformational disorder up to molecular groups with large permanent 
dipole moment that could increase the level of energetic disorder [1]. For the second type we should 
mention the chemical impurities, somehow unavoidable in the synthesis of organic molecules. We 
can further distinguish the kind of traps in function of their location, interfacial or bulk, or in term of 
energy, deep traps or shallow traps. Also polarons could be seen, in a simplistic way, like defects 
caused by an electron plus an induced lattice polarisation [2] followed by a lattice distortion. Traps 
are into the samples in a great variety and in different proportion, often despite the same preparation 
procedure. For that reason sometimes their nature is difficult to investigate and the data must be 
handled with care. 
In the studies of trapped states because of the above underlined variety of defects in solids the 
most successful approach is to start introducing a single type of defect in a well-known system in a 
controlled way.  
2. Experimental Part 
 In our work we focused on low molecular compounds as well as on polymers, especially of 
two classes of materials: oxadiazoles and quinoxalines. Both organic compounds are well know as 
electron transport materials in OLEDs. PPQs (see figure 1) in general show very high solubility [3] in 
a variety of common organic solvents, and according to literature they exhibit a glass transition at 
quite high temperature (250-350 °C).  
The materials were deposited by spin coating on gold, aluminium or silicon in different speed 
or concentration for the film optimisation. The layer thickness was controlled by Dektak techniques 
and Ellypsometry. 
The thermally stimulated luminescence (TSL) and thermally stimulated current (TSC) are 
powerful instruments in order to study de-trapping and relaxation processes in organic materials. TSL 
is a contact less technique that allows to distinguish between deep and shallow trapping states. The 
proposed mathematical model for the TSL enables to study trap levels and recombination centres 
inside the band gap. The analytical solution of the rate equations allows two different de-trapping 
regimes, including or excluding subsequent re-trapping effects. The first order solution kinetic 
indicates that no re-trapping phenomena are permitted. The electron released from a localised level 
recombines with a hole in a recombination centre and its re-trapping probability, before to 
recombine, is negligible. The second order equation deals with the opposite extreme case. The 
phonon-assisted release of an electron is followed by multiple re-trapping. In this second order 
kinetic regime the probability of a released electron to get re-trapped is very high. The main factors 
governing both solutions are the energy depth of the traps calculated with respect to the conduction 
band edge and the frequency factor. This second important factor in general indicates the attempt-to-
escape frequency of electrons from the localised levels. The mathematical model takes also into 
account the occurrence of distributions of localised levels. In case of a Gaussian distribution of 
localised states a meaningful parameter is the width of the distribution. Numerical simulations, 
calculated with the proposed model, show that while a first order peak is characterised by an 
asymmetric peak shape with a steep decreasing side, the second order kinetic peaks are characterised 
by a more symmetric shape. The signal is smeared along the whole peak temperature range due to the 
re-trapping effect.  
Figure 1.  Poly-[2,2’-(1,4-phenylene)-6,6’-bis(3-phenylquinoxaline)] (PPQ IA) 
The same theoretical description holds for both techniques, TSL and TSC. However, TSC 
theory requires the presence of an extended conduction band. During a TSC experiment a driving 
voltage is applied to the sample and the de-trapped charges are extracted at the device contacts. 
However, the equations describing a TSC peak are similar to equations describing TSL. Additionally, 
it is possible to determine the density of the trapping states evaluating the area under a TSC peak.  
Simultaneous TSL and TSC measurements give useful information about the localised states 
combining the best possibilities of both thermal techniques. Unambiguous information about trap 
depth, density of states, kinetics order and frequency factor can be extract making use of the full 
possibilities of the combined measurements. 
In typical thermally stimulated process experiments a sample is heated in a controlled way and 
the current, in case of TSC, or the light emission, in case of TSL, or both simultaneously are 
monitored. The effect appears only when an optical or electrical excitation takes place prior to the 
heating. TSC, in contrast to TSL, requires the presence of good ohmic contacts.  
In the following a TSL experiment is described in more detail and the rate equations derived. 
The sample, in an equilibrium state at room temperature where all the shallow traps are empty, is 
cooled down to a low temperature. Then, it is illuminated with electromagnetic radiation of certain 
energy. The incident radiation excites the electrons from the valence band to the conduction band 
trough the gap. 
In the case of prompt fluorescence the generated electrons recombine promptly. Otherwise 
they can form an electron hole pair followed by geminate recombination or by dissociation with 
subsequent trapping. Charge carriers can get trapped in localised levels that, considering the random 
fluctuation of the potential in disordered materials, are distributed in energy. From statistical 
consideration, the distribution type should be generally Gaussian. The thermal emission from traps at 
low temperature is negligibly small. Therefore, the perturbed equilibrium created by the incident 
radiation resists for a long time and the electrons are just stored in the localised levels. 
Temperature is then raised in a controlled way, electrons acquire energy and finally escape 
from the traps by means of a phonon assisted jump and recombine with holes trough a recombination 
centre where recombination occurs with subsequent photon emission. By means of spectrally 
resolved TSL experiments it is possible to get information about recombination centres studying the 
wavelength of the emitted light as function of temperature and intensity.  
The above-described processes are illustrated in figure 2. 
The illustrated scheme for thermoluminescence is simple, but despite of its simplicity it can 
describe all fundamental features of a thermoluminescence process. Following Chen [4], the electron 
exchange between the HOMO and LUMO levels, during the trap emptying, can be described by the 
following three differential equations: 
h Ann
⋅⋅−=   (1) 
pnAnNn
c ⋅−⋅−= )(   (2) 
c AnnAnNnpn
⋅⋅−⋅−−⋅= )(  (3) 
Here nh is the concentration of holes in the recombination centres, nc is the concentration of 
electrons in the conduction band, Ar is the recombination coefficient for electrons in the conduction 
band with holes in the recombination centres, n is the concentration of electrons in traps, N is the 
function describing the concentration of electron traps at depth E below the edge of the conduction 
band, A is the transition coefficient for electrons in the conduction band becoming trapped and p is 
the same probability of thermal release of electrons from traps defined in equation (1), which 
represents in fact their release rate. Equation (2) describes the change of hole density nh in 
recombination centres versus time. The recombination rate depends both from the concentration of 
free electrons (nc) and from the concentration of holes already present in the recombination centres 
trough a probability coefficient (Ar) that depends on the cross section and the thermal velocity72 of 
electrons. An increase in these parameters results in an increase of the recombination probability. 
Equation (3) describes the exchange of electrons between conduction band and traps. The first term 
in the right hand side includes the probability A for an electron to be trapped. That probability A, like 
Ar, also depends on the thermal velocity of electrons and on the cross section of traps. The second 
term on the right hand side is the de-trapping term. It is proportional to the concentration of trapped 
Electron centre
Hole centre
Conduction band
Valence band 
Recombination centre
Figure 2. Energy diagram describing the elementary 
process of the simple model for TSL 
electrons and to the Boltzmann’s function, i.e. equation (1). The proportionality factor s, often called 
frequency factor or pre-exponential factor, should be, when interpreted in terms of attempt to escape 
of an electron from the potential well, in the order of magnitude of 1010 ÷ 1014 s-1. A saturation effect 
for carrier release from traps, caused by a limited number of available states in the conduction band, 
is neglected in this model. In each moment the number of available states in conduction band is much 
higher than the released amount of electrons from the localised states [5]. 
Equation (3) describes the variation of electron density in the conduction band and essentially 
it takes into account the charge neutrality of the whole system. The variation rate of electrons in the 
conduction band depends on electrons being released - first term on the right hand side-, electrons 
being trapped - second term - and electrons that recombine - third term. Electrons and holes in that 
model are generated at the same time - geminate couples, but they are not necessarily still bound. 
Saturation effects due to filled deeper traps or recombination centres that have already a hole on them 
are not considered.  
Complex models have the disadvantage to introduce an increased number of parameters [7]. 
Actually, several combinations of too many parameters can generate the same shape of a real glow 
curve, making impossible to find a most probable fit [8]. For that reason it is preferable to deal with a 
reasonable simple model that involves few reliable parameters. Actually, the proposed simple model 
can successfully describe the experimental glow curves, but it is necessary to take also the energetic 
distribution of localised states into account in order to describe the complex behaviour of disordered 
systems, like amorphous polymers or organic polycrystalline thin films. In such case the total number 
of traps is represented by the following equation (4). The traps do not have single activation energy, 
but they are continuously energetically distributed. 
dEENN   (4) 
 Here N(E) can be in principle any kind of distribution, but considering the statistical disorder 
in organic materials it should have a Gaussian shape. In principle also the frequency factor should 
have the same energetic distribution. In order to solve the system of differential equations (1)-(4), 
equation (5), regarding the time dependence of temperature, should be add. 
tTT ⋅+= β0   (5) 
In equation (5) β is the experimental constant heating rate. It should be note that as long as T is 
a well knows function of the time the only real variable is the time. For that reason it is very 
important, experimentally, to have a perfect control of the temperature linearity. 
3. Results and discussion 
The main peak in figure 3 has the maximum temperature at Tm = 159.7 K and the second, of the 
roughly half the intensity, at Tm = 230.7 K. The peak at Tm = 159.7 K has a symmetry factor µ = 
0.54, very near to the typical value for a second order kinetic. This fact gives a hint that in PPQ IA an 
electron, before recombination, has high probability to get re-trapped several times. Because of its 
hidden position the analysis of the minor peak of PPQ IA appearing at Tm = 230.7 K is very difficult  
[6]. 
60 80 100 120 140 160 180 200 220 240
=230.7 K
= 159.7 K
Temperature (K)
40 60 80 100 120 140 160 180 200 220 240 260
Temperature (K)
Figure 3. TSL of PPQ IA Figure 4. TSL glow curve of a PPQ IA sample (red 
line) compared with the second order numerical 
simulation of the first peak (green line) 
Figure 4 shows the numerical fitting of the main TSL peak of PPQ IA. The fit is performed by 
means of a second order equation characterised by a Gaussian distribution of traps. While the 
high temperature side perfectly fits the glow curve, the low temperature side do not follow the 
curve shape. For that reason the numerical simulation is not completely satisfactory. The 
distribution has a width σ = 0.12 eV and the distribution maximum is at Em = 0.37 eV. The 
energy maximum Em lies exactly in the middle of the integration limits E1 = 0.25 eV and E2 = 
0.49 eV, having the distribution in such case a perfect Gaussian shape. The natural frequency s of 
this peak can be estimated to be in the order of s = 1x1010 s-1, considering, as is normal, the 
recombination coefficient / trapping coefficient ratio equal to 1 and a density of traps of 1014 cm-
3. The value of Em, derived by numerical analysis, is far from the expected energy depth of a trap 
calculated with the initial rise method. However, this mismatching can be explained considering 
the particular complexity of the peak that could result from the sum of at least two distributed 
peaks. In effect the initial rise procedure reveals the activation energy of a hidden peak at low 
temperature. This is an important point to clarify because of the importance of the presence of 
shallow traps in materials suitable for plastic electronic applications. Shallow traps are, at room 
temperature, empty and they play a crucial role in the electron transport property of organic 
materials. For a different thickness we obtain glow curves from figure 5. 
40 60 80 100 120 140 160 180 200 220 240 260
Temperature (K)
Figure 5. Glow curve of PPQ IA for 1500 nm 
We made TSC measurements for Poly-3-hexyle-thiophene (P3HT) on SiO2 – treated and 
untreated in oxygen plasma. The TSC experiment consisted of: 
(1) Cooling to -180°C 
(2)  Trap filling by light (Mercury lamp) with + 4 V bias voltage  
(3)  Application of readout voltage, heating with 0.10 K/sec.  and measurement of 
detrapping current 
All measurements were carried out in vacuum  (4,5 x 10 –5 mbar). The traps were filled by 
creating carriers with band-to-band photoexcitation of the samples. The light source was a Mercury 
lamp (200 W). The thermally stimulated currents were measured by a  Keithley 617  electrometer. 
The TSC and temperature data were stored in a personal computer as described earlier. In a typical 
experiment, the samples are cooled down to T = 80 K and kept at this temperature for 15 min. Then 
they are illuminated through front electrode for a 15 minutes at a bias voltage   + 4 V. Measurements 
were started after exposure to light, and samples are then heated with a constant rate (β = 0.1 K/sec.) 
from 50 up to 240 K. We measured and compared 2 samples of P3HT on SiO2 – treated and 
untreated in oxygen plasma.  
Both experiments were performed under the same conditions.  
The concentration of the traps was estimated using (Manfredotti et. al.) the relation: 
NT =   (6) 
Here Q is the quantity of charge released during a TSC experiment and can be calculated from the 
area under the TSC peaks; A and L are the area and the thickness of the sample, respectively; e is the 
electronic charge and G is the photoconductivity gain, which equals to the number of electrons 
passing through the sample for each absorbed photon. NT was calculated by assuming G = 1. For that 
samples L = 60 nm and samples have 2,5 x 2,5 cm,    A = 6,25. 10-4 m2. The trap is characterized by 
the temperature (Tm) corresponding to the peak maximum at the thermally stimulated current.  The 
energy associated with the trap is the thermal energy at Tm given by: 
mmo KTTTfE ),,(
´βα=           (7) 
80 100 120 140 160 180 200 220 240
1.54E-010
1.55E-010
1.55E-010
1.56E-010
1.56E-010
Ea = 22.2 meV
Ea=20.1 meV
Ea = 25.8 meV
Ea=17,5 meV
=26.79x1014
=4,452x1014Nt=0.2825x10
=48.31x1014
198.56
171.08
155.05
134.43
Temperature (K)
80 100 120 140 160 180 200 220 240
1.00E-013
1.10E-013
1.20E-013
1.30E-013
1.40E-013
1.50E-013
Ea=26 meV
=1.368x1012 cm3
=0.608x1012 cm3
=0.84x1012 cm-3 Ea=21 meV
Ea=16 meV
202.914
167.161
127.709
Temperature (K)
Figure 6.  TSC for P3HT on SiO2 untreated sample Figure 7.  TSC for P3HT on SiO2 treated sample 
In this equation, α is a dimensionless model dependent constant. The variable T’ is the temperature at 
half of the maximum current value on the low temperature side of the current peak. Assuming the 
Grossweiner model, the constant α and function f are given by: 
51.1=α        (8) 
´ 1),,(
TTf mmβ      (9) 
 We observed a difference between the trap concentrations in these two samples (treated and 
untreated) of two orders of magnitude.  
4. Conclusions 
Thermal techniques are a powerful tool in the to study of localised levels in inorganic and organic 
materials. Thermally stimulated luminescence, thermally stimulated currents and thermally 
stimulated depolarisation currents allow, when applied in synergy the details shallow of traps and 
deeper levels to be investigated. They also permit to study, in synergy with dielectric spectroscopy, 
as polarisation and depolarisation effects. The analysis of the thermograms, emerging from the 
thermal techniques, can be performed starting from the differential rate equations of the de-trapping 
phenomena. Such an approach, allowed by the computing power of the modern computers, is not the 
most fruitful, while the number of free variables involved in the numerical resolution of the rate 
differential equations is too high. Sometimes completely different sets of parameters can fit the same 
thermally stimulated peak and ambiguous results are often achieved. 
5. Acknowledgements 
Many thanks for the European Commission (contract number - HPRN-CT-2002-00327 - RTN-
EUROFET) for the financial support as well as all co-workers and many friends of EUROFET 
network. 
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[3] Paolo Imperia, Localised States in Organic Semiconductors and their Detection, 
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[4] Bässler, H. Charge Transport in Disordered Organic Photoconductors, a Monte Carlo Simulation 
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[5] M. Prelipceanu, O.G. Tudose, S. Schrader, Thermally Stimulated Luminescence Investigations of 
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