ELECTRICAL CONDUCTIVITY STUDIES ON ANTHRACENE...
Transcript of ELECTRICAL CONDUCTIVITY STUDIES ON ANTHRACENE...
Chapter-4
ELECTRICAL CONDUCTIVITY STUDIES ON ANTHRACENE CARBAZOLE AND OLIGOANILINE THIN FILMS
4.1 Introduction
Studies on the current-voltage-temperature characteristics of polymer
films are very important in understanding the conduction mechanism.
Various mechanisms such as tunneling, Schottky emission, field and thermal
ionization of traps and impurities and avalanche multiplication have been
proposed to explain the electrical transport in thin insulating films. However,
there is no universally accepted theory in the literature that explains the
conductivity of polymers since they are in general a uniform mixture of
polycrystalline and amorphous regions. Many workers engaged in polymer
research have proposed electronic, ionic and protonic conduction for various
polymers. The mechanisms generally discussed for various polymer films are
tunneling, Schottky and Poole-Frenkel emissions and space charge limited
conduction (SCLC) [1, 2]. A detailed description of these various conduction
mechanisms are described in Chapter 3. This chapter deals the studies on d.c.
conductivity in high and low temperature conditions and also a.c.
conductivity.
4.2 Theory
4.2.1 D.C. Conductivity
An ideal crystal has a three-dimensional architecture characterized by
the infinite repetition of identical structure units in space. Its structure can be
described in terms of a lattice characterized by long-range order and strongly
86 Chapter IV
coupled atoms. For silicon or germanium this strong coupling results in the
formation of long-range delocalized energy bands separated by a forbidden
energy gap. In organic crystals, the molecules are held together by weak van
der Waals or London forces. This weak coupling result in a narrow width for
the valence and conduction bands and the band structure can be easily
disrupted by introducing disorder in the system. Although organic molecular
crystals exhibit band conduction, excitations and interactions localized on
individual molecules play a dominant role. By contrast, conjugated polymers
do not have a well-ordered structural configuration as crystals. The
conjugation of the polymer backbone is disrupted by chemical or structural
defects, such as kinks or twists. The band structure model of a periodic lattice
implies sharp edges both for the valence and conduction bands due to the
well defined uniform potential wells of the atoms in crystal lattice resulting
in a uniform density of states N(E) in the band. Anderson [3] envisaged some
fluctuations of the potential well distribution in the crystal lattice due to
perturbation caused by the disorders in the lattice. The configurational
disorder in amorphous materials results from the spatial fluctuation in
potential which will lead to the formation of localized states. As a result there
will be a variation in the density of states from a critical to low value, which
can be treated as localized states. Mott [4] suggested an extended density of
states with a long-range order in phase and these would lead to the formation
of tails in the forbidden gap. The sharp edges of valence and conduction
bands of a crystal will be replaced by their gradual transition to long tails of
localized states extended into the forbidden gap. The extensions outside the
two band edges are known as extended regions. The tail formation is a
consequence of the perturbation of the lattice instead of tight bonding model
for a periodic lattice.
Electrical Conductivity Studies… 87
According to Cohen et al. [5] the tails due to localized states
originating from the conduction and valence bands can some times merge
together depending on the band gap and overlap when the concentration of
disorder is very high. Mott and Davis [6] envisaged that instead of the
overlapping of tails arising from localized states, there will be a defect band
arising near the middle of forbidden energy gap due to the presence of
unsatisfied or dangling bonds leading to some local states at the so-called
pseudo Fermi level regions.
According to Davis and Mott conduction in a semiconducting material
is due to three processes and the total conductivity can be expressed as
Total=Intrinsic+Excitation+Hopping (4.1)
The intrinsic conductivity is related to the generation of carriers
which when thermally excited from Fermi level (EF) to the conduction band
or valence band for electrons and holes respectively. The expression for
conductivity is given as
kT/)EE(exp Fc0Intrinsic , (4.2a) for electrons or
kT/)EE(exp VF0Intrinsic (4.2b) for holes, where 0 is
a constant.
The above equations are generally expressed as,
kTaEIntrinsic /)(exp0 (4.2c) the quantity Ea is the
thermal activation energy for charge carriers and k is Boltzmann’s constant
and T is absolute temperature.
The excitation conductivity is related to the generation of carriers
when electrons excited to the localized states, thus adding to the current.
Conductivity in this case can be expressed as
88 Chapter IV
)/kTΔWE(Eexpσσ 1FA1Excitation (4.3a) for electrons or
)/kTΔWE(Eexpσσ 1BF0Excitation (4.3b) for holes, where
1ΔW is the activation energy for hopping, EA is the localized state nearer to
conduction band and EB is the localized state nearer to conduction band.
Hopping conduction is related to the generation of additional carriers
when charge carriers hopping between neighbours in the localized states. In
the case of a real crystal there are defects found in the periodic potential,
such as due to positional disorder (“wrong position”) or substitutional
disorder (a different chemical species), leads to localization of wave
functions of the electrons. Thus the electron states are localized and are
transported in an electric field by moving across potential barriers separating
the individual localized states. However at finite temperature the electron can
be activated and may hop from one localized position to another causing
‘hopping conduction’ [7]
At a localized site the wave function of the electron can be considered
to decrease exponentially as (-r), where is a constant and r is the distance
from the localized center. Hence the probability of overlapping with another
localized wave function at a distance r is proportional to exp (-2r). By
thermal activation the electron can occupy the higher energy state and this
probability is associated with the difference in energy (E) between these two
states. The conductivity due to hopping is expected to be proportional to the
product of these two probabilities.
exp
B
ΔE-2αr-
k T
(4.4a)
At low temperatures the average energy E may be estimated from the
density of states g(E)rd. The total density of states contained in the volume in
Electrical Conductivity Studies… 89
a d-dimensional space with a characteristic length r is g(E) . An average
energy difference E near the Fermi energy is given by
dr)E(gE
(4.4b)
Since E is now expressed as a function of r, one can find a particular value
of r that corresponds to a maximum of. The optimal condition is
0Tkr)E(g
r2dr
d
Bd
(4.4c)
Hence, the conductivity at low temperature vary with temperature as
1d/10
T
Texp (4.4d)
where To is a constant. This formula, due to Mott represents variable range
hopping (VRH) conduction. The temperature dependence varies with
dimension.
For three dimensions d=3 and
4/1
00
T
Texpσσ (4.4e)
The derivation of Mott’s law for the d.c. conductivity is based upon
the assumption that the density of states near the Fermi level is constant.
Pollok [8] and Ambegaokar et al. [9] have pointed out that actually electron
–electron Coulomb interaction should reduce the density of states near the
Fermi level. The Coulomb gap plays an important role in the low
temperature d.c. conductivity. The influence of gap can be neglected when
T>Tc and if T< Tc the states with in the gap are important. The conductivity
in such cases can be described as
90 Chapter IV
1/2
00
T
Texpσσ (4.4f)
The same result is also valid for two- dimensional case. Where T0 is
the characteristic temperature and it is related to the average hopping energy
and average hopping distance under the following equations,
1/ 2
02
kW T T (4.4g)
1
20
4
TRave
T
(4.4h)
where k is the Boltzmann’s constant and is the wave function decay length
(localization length).
4.2.2 A.C. Conductivity
The dielectric phenomena arises form the interaction of
electromagnetic fields with different charged species such as electrons,
protons or ions. The oppositely charged species in a solid will be bound by
electrostatic forces to form the neutral species but separated by a distance to
constitute a dipole with some moments. Interactions of micro level electric
field with these dipoles manifest in the form of some macroscopic behaviour
of the dielectric material such as permittivity, dielectric constant,
capacitance, dipolar relaxation and the resonance. The distribution of dipoles
to align under a field is opposed by the damping forces of the solid, frictional
resistance of the medium and thermal fluctuations.
In a time varying field, polarization of dielectric takes place and the
polarization will lag the applied field by an angle ‘’. Thus dielectric
constant is a complex quantity and can be expressed in terms of real (| )
imaginary parts (|| ) as
Electrical Conductivity Studies… 91
||| j (4.5a)
The polarization may not follow the field variation. Thus displacement due to
polarization may persist even when the field is stopped. This gives rise to a
decay time to attain equilibrium and the phenomenon is called Debye’s
relaxation [10].
jj
1
0||| (4.5b)
Now equating real and imaginary parts leads to
22
0|
1
and
22
00
0||
(4.5c)
The above equations are called Debye’s equations. As tends to zero ||
tends to zero but || approaches to a value s which is the static dielectric
constant. When tends to infinity i.e. the frequency is very high say in the
optical region () approaches a constant value which is also known as
dielectric constant at optical frequencies. Thus the real part has two limits
static and optical frequencies.
The frequency dependent conductivity is usually explained by
assuming a multi component system of conductivity has been envisaged by
Webb and Bordie [11] leading to the relation,
relacdctot (4.6a) where
)kT/Eexp( a0dc (4.6b)
)kT/)T,(Eexp(A nac (4.6c)
nKrel , where0
, A and K are constants.
In an ideal parallel plate capacitor no energy losses should occur and
the current should lead the applied voltage exactly 900. In reality the total
92 Chapter IV
current transversing the capacitor produces an inclination against the
applied voltage and is referred as power factor angle (usually <900). The
main reason behind this behaviour is the existence of internal capacitative
element that leads to a dissipation of power. In any dielectric material there
will be some power loss because of the work done to overcome the frictional
damping forces encountered by the dipoles during their rotation. The
imaginary part || is related to the conductivity of the dielectric. The loss
factor is generally expressed as
||
|
tan
(4.7)
In terms of capacitative Cs and resistive R components tan can be expressed as
sRC
1tan
(4.8)
4.3 Experimental details
Spectroscopically pure Anthracene, Carbazole and Oligoaniline in
the powder form are procured from Aldirch (USA). Thoroughly cleaned
micro glass slides are used as substrates. The substrates are cleaned using the
procedure described in the section 2.6 of chapter 2. Evaporation of the
material is carried out using Hind Hivac vacuum (Model 12 4A) coating
plant at a base pressure of 10-5
Torr. Molybdenum boat of dimension
2.91.20.5cm is used for the evaporation. During evaporation the substrates
are kept at a distance of 12cm from the source. Annealing is carried out in a
specially designed furnace equipped with digital temperature controller cum
recorder. A detailed description of furnace and the controllers used in the
present study is given in chapter 2 section 10. Annealing is performed before
the deposition of top electrode. Thicknesses of the films are counter checked
using Tolansky’s multiple beam interference technique [12].
Electrical Conductivity Studies… 93
Electrical measurements are performed using Keithley electrometer
(model No.617). The samples are mounted on the sample holder of the
conductivity cell. Electrical contacts are made using copper strands of
diameter 0.6mm and are fixed to the specimen with silver paste. The samples
are heated using a resistive heating filament attached to the sample holder of
the conductivity cell and the temperature in the conductivity cell is measured
using a calibrated chromel-alumel thermocouple. Current to substrate heater
is controlled by a variable voltage transformer. Conductivity measurements
are also made in the temperature range 303 – 127K by cooling the samples
using liquid nitrogen. For conductivity studies longitudinal structure is
preferred. A detailed description of longitudinal thin film structure used in
the present study is given in section 2.9 of Chapter 2.
In order to study the a.c. conductivity we use sandwich structure. A
detailed description of sandwich structure used in the present study is given
in section 2.9. The capacitance, dielectric constant and loss tangent are
directly measured using Hioki3532 LCR Hi-tester in the range 100Hz-
5MHz. Since these semiconductors are photosensitive in nature all the
electrical measurements are performed in darkness. To avoid any possible
contamination all the measurements are carried out in a vacuum of 10-3
Torr.
4.4 Results and Discussion
4.4.1 D.C. conductivity studies at high temperature
Figures 4.1, 4.2 and 4.3 show the variation of d.c. conductivity with
1000/T for as-deposited and annealed Anthracene, Carbazole and
Oligoaniline thin films of thickness 2000Ǻ measured above the room
temperature region. The annealing is done at 750C for 30min, 60min, 90min
and 120min. Form the observed characteristics, it is found that the measured
d.c. conductivity increases with increase in temperature. The dependence of
94 Chapter IV
conductivity on the temperature follows the relation (4.2C). From the slope
of these graphs the activation energies are determined. The determined
activation energies as a function of annealing period are summarized in the
Table 4.1 for Anthracene and Carbazole thin films. The activation energy
determined in this work for as-deposited Anthracene thin film is comparable
with the value 0.55eV reported by Jeena and Xavier [8] from their single
crystal studies. The activation energy determined for as-deposited
Oligoaniline is 0.12eV. The activation energy for Oligoaniline remains
constant with annealing. From the table it is clear that the activation energy
increases with annealing for Anthracene and Carbazole thin films.
It is common practice that in an organic semiconductor, a single
thermally-activated conduction is often explained by using the concept of
charged-defect models. The activation energies determined in this work are
very low and this implies the conduction is an extrinsic process. In a p-type
sample, a possible conduction process gives rise to the high temperature
thermally-activated conductivity of the type described by the equation 4.2b
can be related to excitation of charge carriers (holes) from the Fermi level EF
into the extended states below the valence-band mobility edge EV with the
activation energy Ea=EF-EV. Another conduction mechanism that would be
responsible for the electronic transport in p-type semiconductor is that due to
the excitation of holes from the Fermi level to the energy level EB, the end of
the localized states in the band tail above the valence band, with the
activation energy Ea = (EF - EB) +W1, where W1 is the hopping energy
between the localized states [14].
It may be pointed out that, the activation energy Ea alone does not
provide enough indication to whether the conduction takes place in the
extended states below the mobility edge or by hopping in the localized states.
Electrical Conductivity Studies… 95
This is because of the fact that the band-energy structure describing
amorphous materials like organic semiconductors is not known a priori to
give a conclusive evidence for the type of conduction mechanism in these
semiconductors. Thus it is concluded that both these conduction mechanisms
can occur simultaneously, where the band-type conduction occurs at high
temperatures where as the conduction via localized states dominates at low
temperatures [15]. The latter transport process is often known as the variable-
range hopping conduction mechanism due to tunneling between far-distant
defect centers. This hopping conduction often occurs at sufficiently low
temperatures. Detailed discussions of low temperature d.c. conduction in
these films are made in the following sections.
Table 4.1 Variation of activation energy with annealing for Anthracene and
Carbazole thin films
Annealing period
min
Ea (for Anthracene)
eV
Ea (for Carbazole)
eV
As-deposited 0.510.05 0.300.05
30 0.490.05 0.290.05
60 0.490.05 0.270.05
90 0.480.05 0.240.05
120 0.450.05 0.210.05
96 Chapter IV
2.9 3.0 3.1 3.2 3.3
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
As deposited
30min
60min
90min
120min
ln(s
)
1000/T(K-1)
Figure 4.1 Variation of ln(σ) with 1000/T for as-deposited and annealed
Anthracene thin films
2.9 3.0 3.1 3.2 3.3
-6.5
-6.0
-5.5
-5.0
-4.5
As deposited
30min
60min
90min
120min
ln(s
)
1000/T(K-1)
Figure 4.2 Variation of ln(σ) with 1000/T for as-deposited and annealed
Carbazole thin films
2.9 3.0 3.1 3.2 3.3
-7.00
-6.75
-6.50
-6.25
As deposited
30min
60min
90min
120min
ln(s
)
1000/T(K-1)
Figure 4.3 Variation of ln(σ) with 1000/T for as-deposited and annealed
Oligoaniline thin films
Electrical Conductivity Studies… 97
4.4.2 D.C. conductivity studies in the low temperature region
Figure 4.4 shows the plot of ln() versus 100/T1/2
for as-
deposited and air annealed Anthracene thin film of thickness 2000Å
measured in the low temperature region. The annealing is done at
750C for 30min, 60min, 90min and 120min. The slope of the straight
line region gives T0. The average hopping energy and hopping
distances are determined from the relations 4.4g and 4.4h. The
determined values for as-deposited and annealed samples are listed in
Table 4.2. Figure 4.5 shows the plot of ln() versus 100/T1/2
for as-
deposited and air annealed Carbazole thin film of thickness 2000Å
and Figure 4.6 shows similar plot for Oligoaniline thin film of
thickness 2000Å. All the samples are annealed at 750C for 30min,
60min, 90min and 120min. The hopping parameters obtained for as-
deposited and annealed films of Carbazole are listed in Table 4.3 and
the parameters for Oligoaniline films are collected in Table 4.4. From
the tables it is clear that the average hopping energy and hopping
distances are increased due to annealing. Many authors [16, 17]
suggest that during the process of annealing the nearly amorphous
film crystallizes. Annealing produces a more crystalline film and the
hopping sites are filled with charge carriers. This reduces the energy
sites available for hopping and carriers require higher energy for
hopping between adjacent available sites.
The conduction mechanism in these semiconductors can be
explained as follows. In these semiconductors the interactions
between neighbouring molecules give rise to new states which are
delocalized over the entire molecule. The first step of conduction is
the excitation of π-electrons from the uppermost filled π-orbital to
98 Chapter IV
lowest empty-molecular orbital. In the hopping model the charge
carriers are hop from one localized state to the next. When it falls on
a defect state it is virtually trapped in this state due to the potential
well created by the atomic polarization. Thus the activation energy in
the hopping process is to excite charge carriers from one localized
state to next.
The formation of grain boundaries can also affect the
conductivity in the following way. The charged states at the grain
boundary create depleted regions and potential barriers , which
provide a resistance for the passage of carriers from one grain to the
neighbouring ones. The grain-boundary barrier models have been
successfully used to explain the electrical properties of many
polycrystalline materials. The grain boundaries may be assumed to
have the same structure as that of intrinsic trapping defect states and
they are formed in the film due to defects formed during film
preparation. In such cases the resistivity is due to the deplete space
charge regions and grain-boundary potential barriers that impede
thermionic emission of charge carriers into the grains. The increase in
conductivity upon annealing is thus due to the low energy of potential
barrier heights, and can be enhanced by the improvement in the
grain’s growth. The small variation in activation energy observed in
this study can be attributed to the reduction in extrinsic trapping
states and thus increases the conductivity.
Electrical Conductivity Studies… 99
6 7 8 9
-11
-10
-9
-8
-7
-6
As deposited
30min
60min
90min
120min
ln(s
)
100/(T)1/2
(K)-1/2
Figure 4.4 Variation of ln(σ) with 100/(T)
1/2 for as-deposited and annealed
Anthracene thin films
6 7 8 9
-7
-6
-5 As deposited
30min
60min
90min
120mIn
ln(s
)
100/(T)1/2
(K)-1/2
Figure 4.5 Variation of ln(σ) with 100/(T)1/2
for as-deposited and annealed
Carbazole thin films
6 7 8 9
-9
-8
-7
-6
-5 As deposited
30min
60min
90min
120min
ln(s
)
100/T1/2
(K)-1/2
Figure 4.6 Variation of ln(σ) with 100/(T)1/2
for as-deposited and annealed
Oligoaniline thin films
100 Chapter IV
Table 4.2 Variation of hopping parameters as a function of annealing period
for Anthracene film of thickness 2000Å
Hopping parameters Annealing periods
As-deposited 30min 60min 90min 120min
T0(K) 3299 8869 11342 13294 19182
Hopping energy meV 41 67 76 82 99
Hopping distance nm 0.78 1.28 1.45 1.57 1.89
Table 4.3 Variation of hopping parameters as a function of annealing period
for Carbazole film of thickness 2000Å
Hopping parameters Annealing periods
As-deposited 30min 60min 90min 120min
T0(K) 6416 8217 9122 10000 10506
Hopping energy (meV) 57 65 68 71 73
Hopping distance(nm) 11 12.34 13 13.61 13.95
Table 4.4 Variation of hopping parameters as a function of annealing period for
Oligoaniline film of thickness 2000Å
Hopping parameters Annealing periods
As-deposited 30min 60min 90min 120min
T0 K 3080 3387 3600 4033 4465
Hopping energy meV 16.39 17.68 18.98 18.38 20.27
Hopping distance nm 0.48 0.50 0.52 0.55 0.58
4.4.3 A.C. Conductivity studies
4.4.3a Capacitance- frequency characteristics
The variation of capacitance with frequency measured in the frequency
range 100Hz – 3.16 MHz for Anthracene films of thickness 5500Å annealed at
750C for different periods of time are shown in Figure 4.7. Figures 4.8 and 4.9
show the variation of capacitance with the frequency for Carbazole and
Oligoaniline thin films of thickness 5500Ǻ annealed for different periods of
time. The capacitance decreases with increase in frequency for all samples. This
effect is believed due to the screening of the electric field across the film by
Electrical Conductivity Studies… 101
charge redistribution [21, 22]. At low frequencies, the charges on defects are
more readily redistributed, such that defects closer to the positive side of the
applied field become negatively charged while the defects closer to the negative
side of the field become positively charged. As the frequency is increased, in all
cases the capacitance decreases to the same limit, as the charges on the defects
no longer have time to rearrange in response to the applied voltage.
The decrease in capacitance with increase in frequency can also
explained in terms of equivalent circuit model of Goswami and Goswami [23]
which comprises a frequency and temperature independent capacitive element
C′ with a discreet temperature dependent resistive element R due to the
conducting film parallel with C′ both elements in series with a resistance r due to
connecting leads. According to this model measured series capacitance is given
asCR
1CC
22 (4.9a)
The resistive element is temperature dependent. Form the above expression it is
clear that the measured capacitance should decrease with increase in frequency,
and attains a constant value CC at very high frequencies.
The capacitance of annealed samples is higher than the capacitance of
as-deposited samples. The effect is attributed to the reduction of trapping centers
due to annealing. Due to annealing the structural disorders which can act as
trapping centers are reduced. This in turn increases the conductivity of the film.
From the above mentioned equation it is clear that the reduction in resistance
leads to an increase in the capacitance. The capacitance increases with annealing
in the lower frequency region and their variation is very low in higher frequency
region. This is due to the fact that the contribution of second term in the right
hand side of the equation decreases in the higher frequency region.
102 Chapter IV
2 3 4 5 6 7
15
20
25
30
35
40
45
50
55
As deosited
30min
60min
90min
120min
Ca
pa
cita
nce
(pF
)
log(f) Figure 4.7 Frequency dependence of capacitance for Anthracene thin
films annealed for different periods of time
2 3 4 5 6 7
2
3
4
5
6
7
8
9
As deposited
30min
60min
90min
120min
Cap
acitace
(pF
)
log(f)
Figure 4.8 Frequency dependence of capacitance for Carbazole thin
films annealed for different periods of time
2 3 4 5 6 7
2
3
4
5
6
7 As deposited
30min
60min
90min
120min
Cap
acitan
ce
(pF
)
log(f)
Figure 4.9 Frequency dependence of capacitance for Oligoaniline thin films
annealed for different periods of time
Electrical Conductivity Studies… 103
4.4.3b Conductivity-frequency characteristics
Figures 4.10, 4.11 and 4.12 show the variation of conductivity with
frequency for Anthracene, Carbazole and Oligoaniline thin films annealed for
different periods of time. From the figures it is clear that the conductivity
increases linearly with the frequency in a double logarithmic scale. The
conductivity of annealed samples is greater than that of as-deposited samples.
The conductivity generally follows the relation σ ωs where ω is the angular
frequency and s is an index which is temperature dependent. The factor s is
directly determined from the slope of the graphs. The value of s is 0.67 for as-
deposited Anthracene thin film and 0.74 for all annealed Anthracene thin
films. The value of s determined in this work is close to the values reported by
Roberts et al [24]. In the case of as- deposited Carbazole thin film, the slope is
0.68 and for Oligoaniline slope is 0.78.
The experimental results are interpreted in terms of a model initially
proposed by Pollak [25] and modified by Elliot [26]. This model involves a
thermally assisted hopping conduction mechanism between localized states. It
was observed that the a.c. conductivity in all the samples increases with
increase in frequency. Generally a decrease of conductivity with increase in
frequency is associated with band type conduction, while increase indicates
hopping type conduction [27, 28]. The frequency dependence of conductivity
can generally expressed using the following relation,
σa.c. = σtotal – σd.c. = Aωs (4.10)
104 Chapter IV
2 3 4 5 6 7
-8
-7
-6
-5
-4
As deposited
30min
60min
90min
120min
log(s
)
log(f)
Figure 4.10 Variation of conductivity with frequency for as-deposited
and annealed Anthracene thin film
2 3 4 5 6 7
-8
-7
-6
-5
-4
As deposited
30min
60min
90min
120min
log
(s)
log(f)
Figure 4.11 Variation of conductivity with frequency for as-deposited
and annealed Carbazole thin film
2 3 4 5 6 7
-8
-7
-6
-5
As deposited
30min
60min
90min
120min
log(s
)
log(f)
Figure 4.12 Variation of conductivity with frequency for as-deposited
and annealed Oligoaniline thin film
Electrical Conductivity Studies… 105
where ω is the angular frequency A is a complex parameter that is weakly
temperature dependent and the value of s depends on whether the effect
considered is an intrinsic (lattice) effect or an extrinsic process like thermal
generation or injection of charge carriers. Values close to unity are measured
when the process involved is dipolar and the values in the range 0.5-0.9 are
normally associated with the higher losses due to charge carrier transport [29,
30]. This effect is generally due to screened hopping of charge carriers where the
charges or dipoles responsible for polarization exhibit many body interactions.
4.4.3c Dielectric constant-frequency characteristics
The frequency dependence of dielectric constant for as-deposited
and annealed Anthracene thin films is shown in Figure 4.13. The dielectric
constant shows a strong dispersion character in the low frequency region.
The dielectric constant falls to low values with increase in frequency. A
relatively high dielectric constant at low frequency and a fast decrease with
the frequency are characteristics of organic semiconductors and are
consistent with other reports [24]. The initial high value of dielectric
constant is due to the faster polarization mechanisms (electronic, atomic)
occurring in the material.
The observed reduction in dielectric constant with increase in
frequency may be due to the tendency of induced dipoles to orient
themselves in the direction of the applied field. When the frequency is
increased, the dipoles are no longer able to rotate sufficiently or rapidly so
that their oscillations begin to lag behind the field by explaining the
observed decrease in the dielectric constant with increasing frequency [31].
In organic molecules, dipoles cannot orient themselves in a rapidly varying
electric field and charge carriers are released slowly from relatively deep
traps in the amorphous state [32]
106 Chapter IV
2 3 4 5 6 7
1.0
1.5
2.0
2.5
3.0
3.5
As deposited
30min
60min
90min
120min
e'
log(f)
Figure 4.13 Variation of dielectric constant as a function of frequency for
Anthracene thin films annealed for different periods of time
2 3 4 5 6 7
1
2
3
4
5 As deposited
30min
60min
90min
120min
e'
log(f)
Figure 4.14 Variation of dielectric constant as a function of frequency for
Carbazole thin films annealed for different periods of time
2 3 4 5 6 7
1
2
3
4
As deposited
30min
60min
90min
120min
e'
log(f)
Figure 4.15 Variation of dielectric constant as a function of frequency for
Oligoaniline thin films annealed for different periods of time
Electrical Conductivity Studies… 107
0 20 40 60 80 100 120
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Oligoaniline
Carbazole
Anthracene
die
lectr
ic c
on
sta
nt
Annealing period(min)
Figure 4.16 Variation of dielectric constant as a function of annealing
period for different films
The dielectric constant determined for as-deposited
Anthracene thin film is 2.24 at 100Hz and for an annealing period of
120min, the dielectric constant increases to 3.30. Similar
experimental results are reported elsewhere [33]. Figures 4.14 and
4.15 show the variations of dielectric constant with the frequency for
as-deposited and annealed Carbazole and Oligoaniline thin films
respectively. The variation of dielectric constant with the annealing
period measured at a constant frequency 100Hz for these films is
shown in the Figure 4.16. From the figure it is clear that the dielectric
constant increases with annealing period.
4.4.4d Dielectric loss-frequency characteristics
The dielectric loss factor or loss tangent (tan), for the as-
deposited and annealed Anthracene thin films are shown below
(Figure 4.17). From the figure it is clear that the highest value of loss
factor is at low frequency. This is because the migration of charge
carriers in semiconductor is the main source of dielectric loss at low
frequency and decreases with increase in frequency. Accordingly, the
108 Chapter IV
dielectric loss at low and moderate frequencies characterized by high
values due to the contribution of conduction losses in addition to the
electron polarization loss. The dielectric relaxation phenomena are
associated with the frequency dependence of orientational
polarization and hence with polar dielectrics. In static or slowly
varying fields the permanent dipoles align themselves along the field
acting upon them and thus contribute fully to the polarization of the
dielectric.
Figures 4.18 and 4.19 show the variation of tan as a function
of frequency for as-deposited and annealed thin films of Carbazole
and Oligoaniline respectively. In the case of all samples tan has a
maximum value in the lower applied field and decreases with increase
in frequency. Furthermore the tan increases with annealing in all
these samples. Measuring the tan actually discriminates between real
and imaginary parts of the complex dielectric constant. For 450, the
pure capacitance character is the dominant while the dissipative part
is dominating for >450. Since the values of measured in these
samples are relatively high, the dissipative factor dominates in these
materials.
Electrical Conductivity Studies… 109
2 3 4 5 6 7
0.0
0.2
0.4
0.6
As deposited
30min
60min
90min
120min
tan(
)
log(f) Figure 4.17 Variation of tan as a function of frequency for as-deposited
and annealed Anthracene thin films
2 3 4 5 6 7
0.2
0.4
As deposited
30min
60min
90min
120min
tan(
)
log(f) Figure 4.18 Variation of tan as a function of frequency for as- deposited
and annealed Carbazole thin films
2 3 4 5 6 7
0.0
0.2
0.4
0.6 As deposited
30min
60min
90min
120min
tan(
)
log(f) Figure 4.19 Variation of tan as a function of frequency for as- deposited
and annealed Oligoaniline thin films
110 Chapter IV
The dielectric loss arises from two mechanisms: the resistive loss
and relaxation loss of the dipole. In resistive loss mechanism the energy is
consumed by the mobile carriers with in the film. The contribution from
mobile carriers reduces in the high frequency region since they are
immobile in high frequency range. Shen et al. [34] experimentally proved
that annealing increases the density of mobile carriers and the carriers are
accumulated in the interface region between the film and the electrode. In
the case of the materials under present studies the annealing results in a
reduction of trap density and thus an increase in the free carriers. This
effect leads to the observed dielectric relaxation in these materials.
It is found that tan decreases with increase in frequency in the case
of Anthracene and Oligoaniline thin films. But in the case of Carbazole thin
films tan decreases first and show a minimum and then increases. Similar
type of variation is observed for many organic semiconductors like -
Nickel phthalocyanine [35] and cobalt phthalocyanine [28]. This effect can
also be explained with the model of Goswami and Goswami[23].
According to this model loss tangent is given by,
rCRC
R
r1
tan
(4.9b) where
r is the series resistance due to leads (usually frequency and temperature
independent), is angular frequency (=2πf) and C is the frequency
independent inherent capacitative element. From the above equation it is
clear that the tan shows an inverse dependence on frequency and attains a
low value at a particular frequency denoted as min. The minimum
frequency is given as rRC
1min . There after the increase in tan is due
Electrical Conductivity Studies… 111
to the supremacy of second term in the right hand side of the equation. In
the higher frequency region the above equation reduces to Crtan .
The min is different for different semiconductors depending on the
resistance and capacitance. Another fact which can be explained with the
above equation is the variation in tan with annealing. As annealing
increases the resistance decreases and the tan increase with annealing and
the variation is comparatively small in higher frequency range since the
dominancy of second term in the equation (4.9b).
4.5 Conclusion
Thin films of Anthracene, Carbazole and Oligoaniline are prepared
and the electrical conductivities in the lower and higher temperature ranges
are studied. In the lower temperature region conduction mechanism is
variable range hopping in a coulomb gap. The annealing increases the
conductivity of the films due to the reduction of delocalized states which
can act as trap centers. The frequency dependent conduction in these films
gives valuable information about the dielectric relaxation. The capacitance
exhibits initial high value which drops to a constant value with the increase
in frequency due to polarization of carriers. In general, the dependence of
capacitance on frequency in these samples could be accounted for using the
equivalent circuit model of Goswami and Goswami [23]. The capacitance
and conductivity increases with annealing due to the reduction of trap
centers. The conductivity follows a power dependence on frequency. The
measurement of power factor yields the information that the conduction
mechanism is hopping type. The variations in capacitance and resistance of
the films are in consistent with the equivalent circuit model. The dielectric
constant and the loss tangent have also high values in the low frequency
112 Chapter IV
regions and drops to constant values with increase in frequency. These
parameters also increase with the changes in conductivity induced by
annealing. Thus in conclusion, electrical properties of these semiconductors
are strongly influenced by annealing and the influence of annealing on the
optical properties due to the variations in surface morphology is studied in
the next chapter.
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