Biomedical Engineering Reference
In-Depth Information
To analyze the effect of temperature on conductivity of the samples, Arrhenious curves
( logσ vs 10
3
/T) for different polarizing fields (0.75kV/cm, 1.50kV/cm, 2.25kV/
cm,3.00kV/cm, and 3.75kV/cm) were plotted (Fig. 9) using the Arrhenius Eq. (11);
−
E
kT
⎛
⎞
σσ
=
0
exp
⎠
(11)
⎜
⎟
⎝
where
σ
is conductivity,
σ
o
the pre-exponential factor,
E
a
the activation energy, k is
Boltzmann's constant, and T is temperature in Kelvin. Conductivity was obtained from the
Eq. (12);
Id
VA
σ=
(12)
where
I
is measured current,
V
is measured Voltage,
d
is the thickness of the samples (≈4.0
×10
-4
cm), and
A
is the electrode active area ( circular electrode of diameter 0.56cm was
used). Initial increase in conductivity at low temperature is due to the injection of charge
carriers directly from the electrodes. The increase in conductivity at selectively low field is
due to the increase in the magnitude of the mean free path of the photon (Sangawar et al.,
2006). At high temperatures, the increase in conductivity may be attributed to softening of
the polymer which causes the injected charge carrier to move more easily into the volume of
the polymer giving rise to a large current. Increased conductivity at higher temperatures
could also be due to thermionic emission across the barrier potential.
Temperature (K)
Experimental β × 10
-23
(Jm
1/2
V
1/2
) values
Forward bias
Reverse bias
320
5.65 ± 0.12
3.17± 0.12
350
6.31 ± 0.14
3.56± 0.12
370
3.44± 0.04
0.93± 0.02
Table 1. Values of β obtained from experimental data
1/2
Variable range hopping mechanism predicts linear dependence of
σ versus
T
-1/4
with negative slope (Fig.9, inset b). The Mott parameters-
T
d
,
γ and
N(E
F
)-
are determined
from equations 6 to 10 using the slope and intercept values of the plots in inset (b ) of Fig. 9
and assuming a phonon frequency ( (
ln(
)
p
υ of 10
13
s
-1
. Other Mott parameters, the hopping
distance
R
and average hopping energy
W
are determined from Eq. (9) and Eq. (10)
respectively. Mott parameters from this calculation are listed in Table 2. Table 3 shows the
variations of the Mott parameters with temperature in our samples. It is evident from Table
3 that γ
R >
1 and
W > kT,
which agrees with Mott's condition for variable range hopping. It
can therefore be concluded that the main conduction mechanism in NFSC is the variable
range hopping.
)
