59
Benghazi University Press
Journal of Science and Its Applications
Vol. 1, No. 1, pp 59-65, February 2007
Low-Temperature dc Electrical Conductivity of Semiconducting
CoO-NiO-P2O5 Glasses
D. M. Tawati, M. J. Basha Adlan*, M. J. Abdullah*
Physics
Department, Faculty of Science, Benghazi University,Benghazi-Libya
*
School of physics, University of Science Malaysia, 11800 Penang, Malaysia
ABSTRACT
The dc electrical conductivity of ternary CoO-NiO-P2O5 Glasses of five
different compositions has been measured at temperatures in range of 213 –
556 K. Over a temperature range of 213 – 440 K, the conductivity is
described by both Mott’s variable range hopping (VRH) and Greaves’
intermediate range hopping models. The parameter analysis of those models
gave the density of states at the Fermi level, N(Ef) in the order of 1019 eV-1
cm-3 at 243 K, and N(Ef) increased with increasing CoO content in the glass.
VRH at this range of temperatures is attributed to large values of the
disorder energy of these glasses.
Keywords: Low-temperature conductivity; D.C conductivity; Semiconducting
glasses; Phosphate glasses.
INTRODUCTION
Oxide glasses containing transition metal (TM) ions have been studied frequently, because
of their semiconducting properties, switching behaviour and potential applications
(Mackenzie, 1964; Austin & Garbett, 1973; Murawski, Chung, & Mackenzie, 1979; Ghosh,
1988). The general condition for this semiconducting behaviour is that the TM ion should
exist in more than one oxidation state, so that conduction can take place by the transfer of
electrons from low to high valence state (Mott, 1968; Austin & Mott, 1969). The charge
transport in these glasses is usually considered in terms of small polaron hopping (SPH)
theory (Mott, 1968; Austin & Mott, 1969) based on strong electron lattice interaction.
DC conductivity of many binary and ternary transition metal oxide (TMO) glasses
(Tandon & Vaid, 1978; Murawski, et al., 1979; Dhawan & Mansingh, 1982; Hogarth &
Basha, 1983; Mansingh, Dhawan, Ghosh & Chaudhuri, 1986; Ghosh & Chakravorty, 1991;
Mori, Gotoh & Sakata, 1995; Mori, Matsuno & Sakata, 2000; Tawati & Basha, to be
published) has been extensively studied. These studies have shown that the SPH model can be
used to describe the electronic transport phenomena in these materials at high temperatures
(T) when T > θD/2, (θD is the Debye temperature), while at low temperatures (below θD/2),
where the polaron binding energy smaller than KT (K is the Boltzmann constant and T is the
absolute temperature) and static disorder energy of the system plays the dominant role in the
conduction mechanism, Mott’s T1/4 analysis for three dimensional (3D) VRH (Mott, 1969)
60
D. M. Tawati et al.
takes place. Greaves (Greaves, 1973) suggested that the VRH model maybe applied even at
high temperatures ~ 300 K and above.
Recent finding shows that the structures of some TMO glasses (Sayer, Mansingh, Reyes,
& Roseblatt, 1971; Sayer & Mansingh, 1972; Dhawan & Mansingh, 1982) have
microcrystallinty phases and can be described by Shimakawa model (Shimakawa, 1989).
Shimakawa assumed microclusters in glass network revealed that the dc and ac conduction of
these glasses could be interpreted by multiphonon tunneling of large polarons between
microclusters in the glass.
DC conductivity of different compositions of binary CoO-P2O5 and ternary CoO-NiO-P2O5
glasses at temperatures from room temperature (300 K) to 553 K and composition containing
50-mole % of CoO were reported by several workers (Sayer & Mansingh, 1972; Hogarth &
Basha, 1983). They reported that the conduction mechanism in these glasses can be explained
by small polaron hopping (SPH) model at high temperatures when T > 450 K.
The aim of the present work is to study the dc conductivity at low temperatures from RT to
213 K.
EXPERIMENTAL
Appropriate weights of analytical reagent grades of CoO (99.99%), NiO (99.99%) and
P2O5 (99.99%) were carefully mixed in an alumina crucible and placed in a furnace
maintained at 300 ºC for 1h. This initial heating served to minimize material volatilization.
The crucible was then transferred to melting furnace maintained at 1250 ºC and left for about
2h with frequent stirring. The homogenized melts were quickly cast on to a steel-plate mould
(pre-heated to 400 ºC). This procedure served to minimize cracking of the glass due to thermal
stress. The glasses formed were transferred to an annealing furnace at 400 ºC for 1h and then
allowed to cool slowly. The glasses obtained were dark and opaque in appearance. The
amorphous nature of the glass was checked visually and by x-ray analysis.
Disk-shaped samples of diameter (~ 2.5 cm) and thickness (~ 2.3 mm) were cut and
polished with very fine quality lapping papers. For performing dc conductivity measurements,
both opposite surfaces of the samples were coated manually with a thin layer of silver. For
each sample, the I-V characteristic was measured to verify the ohmic properties of the
contacts. For voltages between 100 and 900V, the current was found to depend linearly on the
applied voltage for all samples, and no dc polarization due to ionic currents was observed for
all these glasses.
DC conductivity measurements were carried out in the temperature range 213 – 556K using
two-probe measurement technique. The applied voltage between the surfaces of the sample
was measured by a Keithley 246 high voltage supply. The current was measured using Mv852 A DC Micro-Volt-Ammeter and the temperature was recorded by a thermocouple
embedded in the specimen holder (for temperatures in the range 300K – 556K). For lowtemperature measurements, the sample cell was inserted in a liquid nitrogen cryostat, and the
temperature was recorded by Lake Shore DRC-93CA controller (the temperatures in the range
213 – 300 K). All measurements were made with the samples under vacuum in the order of
Low-Temperature dc Electrical Conductivity of Semiconducting
61
10-5 torr for high temperature measurements (300 K – 556 K) and in the order of 10-7 torr for
low temperature measurements (213 K – 300 K). The values of dc conductivity on the same
glass samples in different runs agreed within 3%, and samples of the same composition from
different batches gave agreement within 4% for room-temperature conductivity. The time
independence of the resistance observed after application of the dc voltage suggests that the
electronic transport is dominant in these glass compositions.
RUSLTS AND DISCUSSION
The x-ray diffraction (XRD) pattern of these quenched samples indicated homogeneous
glassy character without showing any trace of crystallinity. The present glass was n-type
semiconductors based on thermoelectric power measurements done previously (Tawati &
Basha, 2004).
Fig. 1 shows the variation of logarithmic conductivity Log(σdc) as a function of reciprocal
temperature (1000/T) for different glass compositions in the temperature range 213 – 556 K.
It is observed that the plot is linear above ~ 440 K for all studied glasses of different
compositions, while below 440 K, the polts deviated from the log (σ ) – T-1 relationship and
changes in the slope in this region were observed for all glass compositions. Such a case was
found for binary glasses in the systems of CoO-P2O5 (Hogarth & Basha, 1983; Tawati &
Basha, to be published) and other different TMO glasses (Greaves, 1973; Mansingh,
Dhawan, Tandon, & Vaid, 1978; Dhawan & Mansingh, 1982; Ghosh & Chaudhuri, 1986) at
different temperatures. This phenomenon is attributed to the conduction mode changing from
SPH to VRH with decrease in temperatures (Dhawan & Mansingh, 1982; Ghosh &
Chaudhuri, 1986). We then assumed in the
20%CoO-25%NiO
-8
25%CoO-20%NiO
30%CoO-15%NiO
-9
35%CoO-10%NiO
-1
Log σ (Scm )
-10
40%CoO-05%NiO
-11
-12
-13
-14
-15
-16
1.6
2
2.4
2.8
3.2
3.6
4
4.4
4.8
-1
1000/T (K )
Fig. 1. Conductivity as a function of inverse temperature for
a series of ternary CoO-NiO-P2O5 glasses.
D. M. Tawati et al.
62
present case that changes in the slopes were caused by a transition from low SPH to VRH. For
these glasses, we, therefore, attempted to apply Mott’s VRH model, which is based on a
single optical approach in the region below ~ 440 K. The conduction mechanism of this
model is described as follows (Mott, 1969):
σ = B exp( -A/ T1/4 ),
(1a)
A = 2.06[α3 / kN(Ef ) ]1/4
B = [e2 / 2(8π)1/2 ] ν0 [ N(Ef )/ αkT ]1/2,
(1b)
(1c)
where
where α is the decay of the localized state wave function, N(Ef ) is the density of states at the
fermi-level, k is the Boltzmann constant, e is the electron charge and ν0 is the optical phonon
frequency obtained from the Debye temperature, which is expressed by
kΘD = h ν0,
(2)
where h is the Plank’s constant. ΘD of the present glasses was found to be ~ 880 K, which was
similar to the value obtained from previous works of the same glasses (Hogarth & Basha,
1983; Tawati & Basha, to be published), and was nearly the same as the values of the other
authors for different glasses (Field, 1969; Mori et al, 2000). The value of ν0 was calculated
using eq. (2), which was equal to ~1.83x1013 Hz.
The constants A and B which were obtained from the slopes of the ln(σ) vs. T-1/4 as in Fig.
2,
-18
-1
Ln[σ(S cm )]
20%CoO-25%NiO
25%CoO-20%NiO
-22
30%CoO-15%NiO
35%CoO-10%NiO
40%CoO-05%NiO
-26
Series7
-30
-34
-38
0.18
0.2
0.22
0.24
-1/4
T
(K
0.26
0.28
-1/4
)
Fig. 2. Plot of ln (σ) versus T-1/4 for five compositions of ternary
CoO-NiO-P2O5 glasses.
are shown in Table 1. The values of α and N(Ef ) were estimated using eqs. 1b & 1c, are
tabulated in table 1 are reasonable for localized states and indicate strong localization in the
Low-Temperature dc Electrical Conductivity of Semiconducting
63
glass compositions (Mott & Davis, 1979). The mean hopping distance in VRH, RVRH ,
and the hopping site energy W0 can be calculated using the values of α and
Table 1. Mott parameters of ternary CoO-NiO-P2O5 glasses for variable-range hopping
conduction and dc conductivity at 243 K.
Glass composition
(mol %)
CoO
NiO
P2O5
20
25
30
35
40
25
20
15
10
05
55
55
55
55
55
A
(K1/4)
132.69
131.45
130.32
127.04
129.55
B
α
(Scm-1) (nm-1)
1.437
2.74
1.586
2.96
1.970
3.62
2.293
4.00
2.674
4.85
N(Ef)
(eV-1cm-3)
1.39 x 1019
1.82 x 1019
3.44 x 1019
5.14 x 1019
8.46 x 1019
RVRH
(nm)
4.60
4.22
3.42
3.02
2.54
WD
(eV)
0.176
0.175
0.173
0.169
0.172
σDC
(Scm-1)
3.811 x 10-15
5.781 x 10-15
9.354 x 10-15
2.489 x 10-14
1.340 x 10-14
N(Ef ) by the following equations :
RVRH = [9 / 8πN(Ef)αkT]1/4,
(3)
3
W0 = 3 / [4πR VRH N(Ef )]
(4)
At lower temperatures (generally T < 100 K) (Dhawan & Mansingh, 1982; Ghosh &
Chaudhuri, 1986), in the present case (T < 440 K), the polaron binding energy becomes lower
than the disorder energy, WD, where WD dominates the low-temperature VRH conduction.
Thus W0 = WD at low temperatures (Mott, 1969; Dhawan & Mansingh, 1982). Accordingly,
WD can be estimated using eq. (4). The Mott parameters (α, RVRH and WD) were calculated at
T = 243 K as shown in Table 1. From this table, N(Ef ) increases by increase in CoO content
in the glass. This increase is attributed to the increase in cobalt ion density. Values of N(Ef )
were found to be in the order of 1019, which was comparable to N(Ef ) results of TMO glasses
obtained previously (Mansingh et al, 1978; Dhawan & Mansingh, 1982; Ghosh & Chaudhuri,
1986; Mori et al, 1995; Tawati & Basha, to be published) and this satisfied VRH model.
For the occurrence of VRH conduction, the requirements is α RVRH >> 1 and WD >> KT.
Evaluation of the data in Table (1) at T = 243 K gave the results αRVRH = 12.08 – 12.60 and
WD = 0.169 – 0.176 ev, (kT = 0.021 ev). From these values, the above criteria were confirmed
to be satisfied, and this leads to the conclusion that conduction is attributed to VRH at
temperature from 213 to 444K.
We shall now discuss the validity of VRH model below ~ 440 K as proposed by Greaves
(Greaves, 1973) which suggested that the VRH dominates even at intermediate temperature
(below θD/2). The expression of dc conductivity for this model can be written as:
σ T1/2 = A exp(-B / T1/4 ),
(5)
where A & B are constants with the constant B is the slope of ln(σ T1/2) vs. T-1/4 as given in
Fig. 3 and can be calculated by the following equation :
B = 2.1 [α3 / kN(Ef)]1/4
(6)
The values of the parameters A and B obtained form Fig. 3 are given in Table (2). N(Ef)
values which are estimated from eq. (6) by using α values from table (1), are also given in
Table (2). The values of α and N(Ef) are found to be reasonable for localized states (Mott &
Davis, 1979) and comparable to that of the usual semiconducting oxide glasses. So both
D. M. Tawati et al.
64
Mott and Greaves VRH models are found to be appropriate to explain the low temperature
(below ΘD/2, where ΘD /2 < 440 K) behaviour.
20%C o O-25%NiO
25%C o O-20%NiO
30%C o O-15%NiO
35%C o O-10%NiO
40%C o O-05%NiO
Ln[σ T1/2 (S cm-1 K1/2)]
-16
-20
-24
-28
-32
-36
0.18
0.2
0.22
0.24
0.26
0.28
T-1/4 (K-1/4)
Fig. 3. Plot of ln(σT1/2) versus T-1/4 for five compositions
of ternary CoO-NiO-P2O5 glasses.
Table 2. Parameters for Greaves’ variable-range
hopping conduction.
Glass composition (mol %)
CoO
20
25
30
35
40
NiO
25
20
15
10
05
B
P2O5
55
55
55
55
55
A
(K1/4)
141.00
139.78
138.63
135.36
137.85
N(Ef)
(Scm-1K1/2)
183.92
203.55
251.99
294.12
341.93
(eV-1cm-3)
1.17 x 1019
1.53 x 1019
2.90 x 1019
4.30 x 1019
7.13 x 1019
CONCLUSION
The DC conductivity of ternary CoO-NiO-P2O5 has been determined in the temperature
range 213 – 300. To clarify the conduction mechanism, the temperatures range from RT–530
K were investigated, and the results were found to be similar to the previous work (Hogarth &
Basha, 1983). Analysis of the observed dc data shows that at temperatures from 213 – 440 K,
the VRH models proposed by Mott and Greave are valid. The phenomenon of deviation from
linearity below 440 K of ln(σ) – T-1 is attributed to the change in conduction mode from SPH
to VRH with the decrease in temperatures. The validity of VRH at this range of temperatures
is attributed to large values of the disorder energy of these glasses.
Low-Temperature dc Electrical Conductivity of Semiconducting
65
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