Wahab
a
, H. A. Shehata

Physics Department, Faculty of Education, Ain Shams University, Cairo, Egypt
a
National Center for Radiation Research and Technology, Cairo, Egypt

Se
70
Te
30
and

Se
70
Te
20
Cd
10
films of different thicknesses were prepared by thermal
evaporation technique. X-ray diffraction patterns analysis showed that the films were in
the amorphous state. The ac conductivity and dielectric properties of the obtained films in
the frequency range (10
2
-10
5
Hz) has been investigated. The ac conductivity is found to be
proportional to s
where s<1. The temperature dependence of both the ac conductivity and
the parameter s is reasonably interpreted by the correlated barrier hopping CBH model.
The maximum barrier height W
M
,for each composition calculated from dielectric
measurements according to Guintini equation, agrees with that proposed by the theory of
hopping of charge carriers over potential barrier as suggested by Elliott in case of
chalcogenide glasses.

(Received August 18, 2007; accepted August 30, 2007)

Keywords: Ge-Te thin films; Dielectric properties; Cd addition; XRD; Conductivity

1. Introduction

Research on electrical and dielectric properties of amorphous chalcogenide materials has
accelerated in recent years. This is because electronic applications have continuously provided the
impetus pushing the development of new materials in a fascinating and rich variety of applications
[1-3]. The common feature of this class of glasses is the presence of localized states in the mobility
gap due to the absence of long-range order as well as various inherent defects [4-6]. The hopping
conduction can be easily distinguished from that of the band conduction by measuring the
frequency dependence of conductivity [7], which as expected, is due to conduction in localized
states. Measurements of frequency dependent electrical conductivity of amorphous chalcogenides
are, therefore powerful tool for obtaining information about these states. This led to adapt and to
elaborate models allowing the electronic properties of these materials to be described [8-12].
The present study deals with some experimental observations of the temperature and
frequency dependence of ac conductivity and dielectric properties of Se
70
Te
30-x
Cd
x
(x= 0, 10) films
of different thicknesses to understand the conduction mechanism in these materials.

2. Experimental techniques

Glassy alloys of Se
70
Te
30-x
Cd
x
(x= 0, 10) were prepared by a quenching technique as
mentioned before [13]. Thin films with different thicknesses of the investigated glasses (211-491
nm) were deposited under vacuum of 10
-5
Torr, by thermal evaporation technique using
molybdenum boats at constant rate on dry-clean glass substrates, using a coating unit (Edward 306
A). The substrate temperature was held at that of the room during deposition. The film thickness
was measured by Tolanskys interferometric method. X-ray diffraction patterns obtained for the
films reveal the amorphous nature of the structure of the films.

72
For ac measurements, films were sandwiched between two Al electrodes. A programmable
automatic RLC bridge (PM 6304 Philips) was used to measure the sample impedance Z, the
capacitance C
X
and the loss tangent tan
directly. All investigated samples are represented on the
screen of the bridge by a resistance R connected in parallel with a capacitance C
X
. The total
conductivity was calculated from the equation: t
(
) =d /Z A, where d is the thickness of the film
and A is the cross sectional area. The dielectric constant was calculated from the equation:

1
=dC
X
/A

o
, where o
is the permittivity of free space. The dielectric loss 2
was calculated from
the equation: 2
= 1
tan
, where (=90), is the phase angle. Films are annealed in air at 373 K
for 2 h. The measurements were carried out through the temperature range (298-383 K) and
frequency range (10
2
-10
5
Hz). The temperature measurements were recorded by means of digital
multimeter (Protec 81) provided by a chromel-alumel thermocouple adjacent to the sample.

3. Results and discussion

3.1 Frequency and temperature dependencies of ac conductivity

A common feature to all amorphous semiconductors is that ac electrical conductivity ac
(
) increases with increasing frequency according to the equation[14].

ac
(
)
= tot
(
)
- dc
= C s
(1)



where
is the angular frequency ( = 2f),
tot
(
) is the measured total electrical conductivity, dc
is the dc electrical conductivity, s is the frequency exponent (s<1) and C is constant dependent
on temperature. It is found that the s
dependence of ac conductivity ac
(
) is a general
characteristic for chalcogenide glasses up to a frequency of 10
6
Hz. Fig. 1 a,b shows a
representative example for the relation between ln ac
(
) and ln for Se
70
Te
30
and Se
70
Te
20
Cd
10

films of thicknesses 211 nm and 444 nm respectively at different temperatures. It is clear from the
figure that ac
(
) increases linearly with increasing frequency according to equation (1). The same
behavior was obtained for all investigated films. Values of the frequency exponent s were
calculated for all the investigated samples of different thicknesses from the slopes of the linear
lines of ln ac
(
) = f () through the studied frequency and temperature ranges. It is observed that
the frequency is found to have a pronounced effect on conductivity at relatively lower
temperatures. The temperature dependence of the mean value of s for the investigated films is
shown in Fig. 2. It is seen that
s
decreases as the temperature increases, independent on film
thickness in the investigated range.
In most chalcogenide glasses the obtained values of s ranged from 0.7 to 1 at room
temperature, and have a tendency to decrease with increasing temperature[15]. Therefore, the
correlated barrier hopping model CBH [11] has been extensively applied to most chalcogenide
semiconductors. The frequency exponent s is found to decrease with increasing temperature, as

(
)
[
]


ln

kT


W
6kT
-
1


S

o
M +
=
(2)
This means that the obtained experimental results agree with the correlated barrier
hopping model CBH.
According to the Austin-Mott formula[16], based on CBH model, ac conductivity ac
(
)
can be explained in terms of the hopping of electrons between pairs of localized states at the Fermi
level. ac
(
) is related to the density of states N(E
f
) at the Fermi level by:
ac
(
) = (/3) [N(E
f
)]
2
K T e
2
-5

[ln ( /]
4
(3)

where
is the exponential decay parameter of the localized states wave function, and is the
phonon frequency. By assuming
=10
12
Hz and -1
=10� [17], the density of states is calculated

73
and is given in Table (1) for the Se
70
Te
30
and Se
70
Te
20
Cd
10
at frequency 1kHz. The value of N(E
f
)
is found to decrease with Cd addition.

d=211nm
-15
-14
-13
-12
-11
-10
6
7
8
9
10
11
12
ln ln ac
,( ac

-1
.m
-1
)
343K
323K
318K
298K

(a)
d=444nm
-17
-16
-15
-14
-13
-12
-11
-10
6
7
8
9
10
11
12
ln ln ac
,( ac

-1
.m
-1
)
333K
323K
313K
290K


(b)

Fig. 1. Frequency dependence of the electrical conductivity ( ac
) for: a- Se
70
Te
30
film of thickness
211 nm. b- Se
70
Te
20
Cd
10
film of thickness 444 nm.


0.65
0.7
0.75
0.8
0.85
0.9
0.95
290
300
310
320
330
340
350
T,K
S
Se70Te30
Se70Te20Cd10

Fig. 2. Temperature dependence of the frequency exponent s for Se
70
Te
30
and Se
70
Te
20
Cd
10
films.

Temperature dependence of the ac conductivity ac
(
) at different frequencies was studied
for the investigated films. Fig. 3a,b shows a plot of ln ac
(
) against 1000/T for the investigated
film compositions of thicknesses 295 nm and 492 nm respectively as a representative example. It
is clear from this figure that ln ac
(
) increases linearly with the reciprocal of absolute
temperature. This suggested that the ac conductivity is a thermally activated process from different
localized states in the gap or its tails. The activation energy of conduction,
E (
) is calculated at

74
different frequencies from the slopes of the straight lines, obtained for all investigated thicknesses
using the well known equation
=
o
exp (-
E (
)) / kT). The obtained values of E (
) are
independent on film thickness in the investigation range. The frequency dependence of the
activation energy for the investigated films is shown in Fig. 4 for all film thicknesses of both
compositions. It clear that
E (
) decreases with increase of frequency. It is also noticed that
E (
) at any frequency is much lower than the dc activation energy obtained before (0.41 eV in
case of Se
70
Te
30
and 0.5 eV in case of Se
70
Te
20
Cd
10
films)[13] over the same range of temperature.
This seems to be obvious since the charge carriers in the dc conduction choose the easiest paths
which include some large jumps, while this is not so important in the ac conduction[18]. It can
also be seen that
E (
) tends to decrease with increasing frequency as found for other
amorphous materials[19-21]. The increase of the applied field frequency enhances the electronic
jumps between the localized states, consequently the activation energy
E (
) decreases with
increasing frequency. The smaller values of the ac activation energy compared with th