a.c. conductivity and capacitance measurements have been performed on polycrystalline thin films of copper phthalocyanine (CuPc) in the frequency range 102.
334
Thin Solid b)'hns, 223 (1993) 334 340
A.c. electrical properties of thermally evaporated thin films of copper phthalocyanine R. D. Gould and A. K. Hassan Thin Films Laboratory, Department q[" Physics, Keeh" University, Keele, Stqff~s'. ST5 5BG (UK)
(Received July 9, 1992; accepted September 21, 1992)
Abstract The a.c. electrical properties of copper phthalocyanine (CuPc) thin films have been studied in the frequency range 10 2 -2 × 1 0 4 Hz and in the temperature range 173 360 K. The a.c. conductivity a(~0) was found to vary as o)' with the index s ~< 1, indicating a dominant hopping process at low temperatures and high frequencies. At higher temperatures and lower frequencies, free carrier conduction with mean activation energy of 0.3 eV was observed. Capacitance and loss tangent decreased with frequency and increased with temperature. Such characteristics were found to be in good qualitative agreement with the existing model of Goswami and Goswami. Both the conductance and capacitance were lowered over the entire frequency spectrum after heat treatment at 370 K. This reduction was ascribed to the desorption of oxygen by the heat treatment, as previously observed in d.c. conduction measurements.
1. Introduction While the d.c. conductivity in phthalocyanine compounds has received intensive investigation in the form of both single crystals [I] and thin films [2 4] there have been only a few studies on their a.c. conduction properties [5-8]. It is well understood that d.c. measurements provide information concerning conduction processes in m e t a l - i n s u l a t o r metal ( M I M ) and metal s e m i c o n d u c t o r - m e t a l (MSM) structures, and identification of electrode-limited and/or bulk-limited processes may be made [9]. Such identification is made by varying several parameters including the type of metal electrodes, strength of the applied electric field, and sample temperature. Conversely, a.c. conductivity measurements provide information about the interior of the insulator or semiconductor which is a region of relatively low conductivity even when the conduction process is electrode-limited [10, 11]. A.C. conductivity having a frequency dependence cr(~o) of the form a(o~)oc ~o~', where co is the angular frequency and s ~< 1, has been observed in m a n y noncrystalline materials [12]. This behaviour was ascribed to the inhomogeneity within the solid caused by the absence of long-range crystalline order. Carrier transport via a hopping process was identified with this type of dielectric response [ 13, 14]. Abkowitz et al. [ 15] have observed a similar sublinear frequency-dependent conductivity for both crystalline and amorphous As2S3, and have associated this behaviour with the displacement of charge in localized electronic states, resulting from defects, impurities or internal micro-interfaces.
0040-6090/93/$6.00
Polycrystalline nickel phthalocyanine [16] (NiPc) as well as crystalline anthracene [15] organic compounds have also been shown to exhibit a similar type of frequency-dependent conductivity. In a detailed discussion, Jonscher [11] has proposed that such a dependence represents a universal law, applicable to a very wide range of dielectric materials, regardless of their chemical and physical structure and the type of dominant charge carrier. In recent work James et al. [8] have made room temperature measurements of conductance, capacitance and loss tangent as functions of frequency in sublimed molybdenum phthalocyanine thin films. The measurements also showed behaviour consistent with a hopping conduction process. In the present work a.c. conductivity and capacitance measurements have been performed on polycrystalline thin films of copper phthalocyanine (CuPc) in the frequency range 102 2 x 104 Hz, over a temperature range of 170 360 K.
2. Experimental details Copper phthalocyanine powder was obtained from Fluka A G and purified twice using entrainer sublimation. The entrainer gas used was oxygen-free nitrogen at a flow rate of 0.2 0.3 1 min ~. Elementary analysis revealed the following proportions of the elements by weight: carbon, 66.99% (calculated 66.72%); nitrogen, 19.57% (calculated 19.45%); hydrogen, 2.63% (calculated 2.80%). Thin films of thickness 0.4 ~tm were deposited at pressures of approximately 10 3 Pa onto Corning 7059 microscope slides held at room tempera-
i: 1993
ElsevierSequoia. All rights reserved
R. D. Gould, A. K. Hassan / A.c. electrical properties o f thin films
ture. Gold electrodes of thickness 100 nm were evaporated to form both b o t t o m and top ohmic contacts to the phthalocyanine films. A sequential masking system was used so that A u - C u P c - A u sandwich structures of active area 4.5 x 1 0 - 6 m 2 were formed without breaking the vacuum. The phthalocyanine layers were evaporated from tantalum boats at a rate of 0 . 5 n m s -l, while the gold electrodes were evaporated from molybdenum boats at a rate of 1 nm s -]. All film thicknesses and evaporation rates were continuously monitored using a quartz crystal monitoring system, and accurate thickness measurements were derived after deposition using a Planer Surfometer SF200 stylus instrument. Some samples were heat treated in vacuum at approximately 370 K before measurements were taken. It is well known that vacuum evaporated films of CuPc deposited onto substrates at room temperature give rise to the a-form structure. The present authors [17] have also observed that such films are preferentially oriented in the [001] direction. Such films may transform to the fl-form when heated for prolonged periods at temperatures above 200 °C [17]; in the present case the temperature at which heat treatment was performed was kept well below this value so that the film structure remained -form. After deposition, electrical contacts were made to the samples using silver paste. This process was carried out in air at atmospheric pressure, to which the samples were exposed for approximately 30 min. All electrical measurements were taken inside a subsidiary vacuum system at a pressure of approximately 10 3 Pa. Liquid nitrogen was introduced into a copper block to which samples were attached, and the temperature was varied in the range 1 7 0 - 3 6 0 K by controlled cooling and heating. Substrate temperatures were monitored using a c h r o m e l - a l u m e l thermocouple junction and a Fluke 52 K/J digital thermometer. Conductance and capacitance of the samples were measured in the frequency range 102-2 × 1 0 4 Hz using a Hewlett-Packard 4276A L C Z meter equipped with a four-terminal test fixture to minimize the experimental error.
3. Results and discussion 3.1. Variation o f a.c. conductivity with f r e q u e n c y and temperature
Figure 1 shows the frequency ( f ) dependence of the a.c. conductivity and conductance of a CuPc thin film at different temperatures in the range 173-353 K. The conductivity shows a strong frequency dependence at low temperatures, with frequency-variant slope. Such a dependence m a y be described by the relation [12]
~(¢o) =
Ao9 s
(1)
335
I0-s
i0-~ 53~
IO-G
_ 10-5 273 I*
u') 10.7 - ~ / B ~ m ~ ' ~ . . ~ _ b
~
10-8
10"9 102
531WI0"sv~ ~173M
10-7
1 I 103 10~" f (Hz)
10-8 105
Fig. 1. Dependence of a.c. conductivity and conductance on frequency at different temperatures.
where A is a complex proportionality constant, co is the angular frequency and the index s is less than unity. This index is not constant, taking small values at low frequencies and high temperatures, and increasing with increasing frequency. At high temperatures the conductivity becomes almost frequency independent over the entire frequency range. Table 1 lists the mean values of the index s in various ranges of frequency and for different temperatures. A similar frequency dependence of the a.c. conductivity in CuPc and magnesium phthalocyanine (MgPc) thin films has been observed by Vidadi et al. [6] where the index s reached a m a x i m u m value of 1.75 at frequencies greater than 1 0 4 Hz. James et al. [8] have observed an index of approximately 0.9 in molybdenum phthalocyanine films at room temperature. On the contrary Blagodarov et al. [18] have noticed a weak frequency dependence of the a.c. conductivity of metal phthalocyanine thin films that disappeared when a constant voltage was applied across the films. They ascribe such an effect to the domination of a band conduction mechanism in this case. Results by Abdel-Malik et al. [16] on pellets of NiPc have shown that a(~o) remains constant at high temperatures throughout most of the frequency range except for a high-frequency region where a(~o) is proportional to co~. At lower temperatures frequency dependence was observed at lower frequencies and the value of s was just below unity. Figure 2 shows the variation in a.c. conductivity of a CuPc film with temperature at three different frequency values. These curves show that at temperatures below approximately 240 K the conductivity is strongly frequency dependent and is associated with very low activation energies. Such behaviour has previously been ascribed to conduction by hopping of charge carriers between localized states in various inorganic materials such as SiO-CeO2 [19] as well as magnesium and
336
R. D. Gould, A. K. Hassan / A.c. eh, ctrical properties o f thin .films
TABLE 1. Derived values of the index s as a function of temperature and frequency range Frequency (Hz)
173 K
243 K
253 K
263 K
273 K
293 K
353 K
100 300 2x 104
0.268 0.413 0.639 0.778
0.202 0.331 0.535 0.591
0.119 0.182 0.354 0.418
0.079 0.120 0.249 0.327
0.076 0.082 0.170 0.238
0.063 0.063 0.099 0.143
0.045 0.071 0.094 0.091
300 2 x 103 103 104 2 × 104
10-5 I
i
1'0~_
i
i
I
I
i
Oo:
! TE~ I0-6 I 10-7 I'b /
kHz 6 kl~lz
I
_ oo.z
m
ul
20
0-4
0-20
50
lIT (x 10-3 K "1) Fig. 2. Dependence of a.c. conductivity on inverse temperature at different frequencies.
copper phthalocyanines [6] and iron phthalocyanine [20]. At temperatures above 240 K, the conductivity becomes progressively frequency independent but increases more rapidly with temperature. This variation in the conductivity may be caused by charge transport through extended energy bands as was suggested by Vidadi et al. [6]. The activation energy of 0.30 eV obtained from these curves may be associated with impurities such as oxygen molecules that behave as acceptor levels situated above the valence band edge [21]. Variation of the index s with temperature is illustrated in Fig. 3 for four different frequency ranges. Increasing values of s with decreasing temperature have been observed by A1-Dhhan and Hogarth [19] for amorphous oxide films. Moreover the value of s was higher when measured at a higher frequency, a feature shared with the current results. Their low temperature results were consistent with calculations based on a model proposed by Elliott [13] to explain the a.c. conductivity of amorphous materials, particularly the chalcogenide glasses. This model considers the conductivity to be mainly caused by hopping of charge carriers between localized sites separated by barriers of height Wm. The expression for a.c. conductivity according to this model is given by g2N2,t:[~8e2 ~6~s
~7(co) =
I
24
ISled
ro/~
(2)
I
200
250 300 T (K)
IL - -
350
400
Fig. 3. Dependence of the index s on temperature for different frequency ranges of 100-300 Hz (A), 300 Hz 2 kHz (B), 2 10 kHz (C) and 10 20 kHz (D). The theoretical dependence of s on temperature calculated from eqn. (3) is also illustrated (T). Agreement becomes better as the temperature is lowered and the frequency increased.
where N is the density of localized states, e. is the permittivity, r0 the effective relaxation time (approximately 10-'3 s), e the electronic charge and the index s is given by 1 - / 3 at low temperatures, where fl is small and temperature dependent. /3 tends to zero as the temperature decreases and is inversely proportional to the magnitude of the energy Wm according to the relation /3 =
6k T l/Vm
(3)
where k is Boltzmann's constant. The energy I41,, has been identified with the optical energy gap of the material [l 3]. In the case of the phthalocyanines Chadderton [22] has reported an optical band gap for CuPc thin films of 1.58 eV that is reasonably consistent with a thermal activation value for similar films of approximately 1.7 eV [23], although Fielding and Mackay [24] have suggested that agreement between quantities derived from electrical and optical measurements are fortuitous, there being no direct link between electrical conduction and excited molecular states. However considering a value of Wm= 1.6 eV and substituting into eqn. (3) yields a value of s ~ 0.94 at T = 173 K. The
R. D. Gould, A. K. Hassan / A.c. electrical properties of thin films
value of s calculated as a function of T from eqn. (3) is also shown in Fig. 3. From the figure it is clear that at high temperatures and low frequencies there is little correlation between the calculated and measured values of s. This is not unexpected as free band conduction, with activation energy 0.30 eV, occurs under these circumstances as described above. However, it is interesting to note that at low temperatures and high frequencies the measured values of s approach the calculated values, and for even lower temperatures and/or higher frequencies better agreement might be expected. Although the model of Elliott is not likely to be directly applicable to organic films, there is clearly a similar qualitative dependence of G on f and T, indicating a similar hopping process in the low temperature-high frequency region. The dependence of s on T shown in Fig. 3 is non-linear, and does not therefore imply a simple a ocf CAT+m dependence (A and B are constants), as has previously been described in mixed oxide films [ 19]. The hopping process in organic films is likely to be of greater complexity than in oxides, resulting in the sigmoidal dependence of s on T shown in Fig. 3. The general dependence of s on frequency as given in Table 1 appears to follow the trend summarized by Jonscher [25] in the context of amorphous semiconductors. In particular the index s ~< 1 at lower frequencies as observed in the present work. At higher frequencies the trend is for s to increase to a value of 2. Clearly in the intermediate frequency range a gradual increase in the value of s between these two values would be expected. It should be noted that at the frequencies used in the current work the value of s never exceeded unity; however Vidadi et al. [6] did observe a value as high as 1.75 in MgPc at their highest frequency. The explanation for the increase in s with frequency observed in the current work is probably related to a steady transition from an extended hopping regime to one dominated by two-centre hopping at higher frequencies, as discussed by Jonscher. Increases in s with frequency at lower temperatures are considerably more significant than those at higher temperatures. At lower temperatures conduction is expected to be almost entirely by hopping, while at higher temperatures free band conduction is dominant. It would thus appear that the increase in s with frequency, particularly at lower temperatures, is related to a progressive transition between different hopping regimes. 3.2. Variation of capacitance and loss tangent with frequency and temperature The capacitance of CuPc thin films was measured as a function of frequency in the range 102-2 × 104 H z , at different temperatures, as shown in Fig. 4. The capacitance is shown to be frequency dependent at relatively high temperatures and low frequencies. R o o m tempera-
I'01
337
~
l
0"8
u
0'/* m.
73 K"¢
. . . . . . .
0' 9 302
I
I
103
I0 t'
105
f (Hz) Fig. 4. Dependence of capacitance on frequency at different temperatures. 1.0
I
I
~
/101
0.8 50(
0.6 rv (J
0"4~ -
-
20
_
0.2 I
150
200
I
I
250 300 T (K)
I
350
400
Fig. 5. D e p e n d e n c e of capacitance on temperature at different frequencies.
ture capacitance in molybdenum phthalocyanine films shows a similar decrease with increasing frequency [8]. These results are also shown in Fig. 5 where the capacitance is plotted as a function of temperature at constant frequency. It can be seen in this figure that the capacitance is strongly frequency dependent at higher temperatures, and that all the curves saturate to a constant value at temperatures below 250 K. Similar results have been obtained for polycrystalline Dy203 [26] and CdTe [27] as well as amorphous SiO-SnO2 [28] inorganic thin films. In pellets of cobalt phthalocyanine (CoPc) a similar increase in capacitance with temperature occurred that then decreased above 170 °C; this effect was interpreted in terms of nomadic polarization that was thought to arise from an increase in the number of free carriers with increasing temperature [7]. Vidadi et al. [ 5] have previously shown that the capacitance of a photocapacitor having a metal-free phthalocyanine (H2Pc) thin film as the photosemiconductor, exhibited a rapid increase at lower frequencies when the illuminating light intensity was increased. The higher-
R. Oi Goltld~ A. KI Ilassan / A.c. electrical properties oj thin .films
338
frequency capacitance was constant and independent of light intensity. These results were interpreted in terms of a two-layer capacitor structure, where at lower frequencies the effective permittivity, and hence the capacitance were dependent on the conductivity of the H2Pc layer, which was enhanced by photo-carrier generation. Using a similar argument the increase of low-frequency capacitance with increasing temperature may be ascribed to enhanced conductivity via thermal excitation of charge carriers. Of particular interest is the work of Vidadi et a/. [29] who measured series capacitance in A1 CuPc AI samples as a function of frequency and temperature. Aluminium electrodes are well known to provide blocking contacts (Schottky barriers) to CuPc. Their results were adequately explained in terms of the model of Simmons et al. [10] which models the structure in terms of a temperature-dependent resistance shunted by a fixed capacitance and in series with two capacitances corresponding to the two Schottky barriers. This model also predicts a maximum in tan 6 at a particular frequency (corresponding to a minimum in the quality factor Q) which was also observed, thus giving additional confirmation of the applicability of the model. A m a x i m u m in tan ~5 was also observed at 190 kHz by James et al. [8] for molybdenum phthalocyanine films. This was interpreted in terms of a room temperature relaxation time of 798 13s. A Debye relaxation time of 878 gs was also estimated, together with an average relaxation time of 942 gs using the Cole Cole model. In the present case, although the capacitance decreases with increasing frequency, there is also a decrease in tan 6 with frequency, and no indication of a m a x i m u m as shown in Fig. 6. Furthermore an increase in tan 6 with temperature occurs, particularly for values above r o o m temperature, as shown in Fig. 7. Such
102
101
I
I
I
~500 /
--
10° -.,,:,
10"1
10-2 150
I 200
I I 250 300 T (K)
400
behaviour is inconsistent with the model of Simmons et al. [10], but may be explained at least qualitatively in terms of a model originally proposed by Goswami and Goswami [30] for ZnS films. In this model the capacitor system is assumed to comprise a frequency-dependent capacitive element C' in parallel with a discrete temperature-dependent resistive element R, both in series with a constant low value resistance r. (Note that in the original formulation of the model the symbol C is used for the frequency-independent parallel capacitance instead of C'. In the present work the former symbol is reserved for the measured capacitance value.) Such a model is expected to be more appropriate in the present case, as gold electrodes are well known to provide ohmic contacts to CuPc [31] in contrast to Schottky barriers as provided by aluminium [32]. According to this model, the measured series capacitance Cs is given by 1
(4)
and the loss tangent by I
(,
I
tan 6 - - •RC'
101
~10 °
10 -1
10-2 102
I 350
Fig. 7. Dependence of loss tangent on temperature at different frequencies.
C~ = C ' + ( o 2 R 2 C , 102
H_Z
I 103
I 10~
105
f (Hz) Fig. 6. Dependence of loss tangent on frequency at different temperatures.
+ corC'
(5)
where e) is the angular frequency. In c o m m o n with the model of Simmons et al. [10] the temperature dependence of the characteristics is determined through the variation of the interior resistance R via a thermal activation process described by R = R o e x p ( A E / k T ) , where R0 is a constant, AE an activation energy and T the absolute temperature. Although this type of expression is quite plausible, it is necessary to assume merely that R decreases with temperature to describe qualitatively the results of Figs. 4 - 7 inclusive. Equation (4) predicts that measured capacitance C~ should decrease with increasing frequency, that at high
R. D. Gould, A. K. Hassan /A.c. electrical properties of thin .films
frequency Cs should fall to a constant value C' for all temperatures, and that for any given frequency Cs will increase with temperature because of the decreasing value of R. All of these effects are clearly evident from Figs. 4 and 5. In the expression for tan 6 of eqn. (5), at low frequency the co ~ term is dominant while at high frequency the term in co is dominant. The expression thus predicts a decrease in tan 6 at low frequency followed by a loss minimum a t O g m i n ~ l / C ' ( r R ) 1/2 (Goswami and Goswami [30]) and an increase in tan at high frequency. In Fig. 6 a clear decrease in tan with increasing frequency is observed as predicted for low frequencies; moreover, tan 6 increases with temperature as expected. A minimum in tan 6 is not apparent over the frequency range investigated, but the curves are consistent with the appearance of minima at higher frequencies, all of them showing concave curvature when plotted using a linear tan 6 scale. As mentioned by Goswami and Goswami [30], a minimum should occur at lower frequency for lower temperatures. The very rapid increase in tan ~ with temperature above 300 K which is shown in Fig. 7 is also consistent with eqn. (5) as the co-~ term becomes dominant because of the decreasing value of R with temperature. 3.3. Effects o f heat treatment on the conductance and capacitance Some samples were heat treated for approximately 2 h at about 370 K before the conductance and capacitance were measured at room temperature. The effects on both the conductance and capacitance are illustrated in Fig. 8. Curves G1 and G2 show that the conductance of CuPc films measured as a function of signal frequency has decreased by almost an order ot~ magnitude compared to that of the fresh CuPc samples. This effect 0"4 ~
I
I
lo-S
lO-° C1
C2
0'~0 2~
I 103
I 10~
10 -7 I0 s
f (Hz)
Fig. 8. Dependence of capacitance and conductance on frequency for a fresh sample and for a sample heat treated at 370 K for 2 h. For the fresh sample both the capacitance (C1) and the conductance (GI) are significantly higher than corresponding quantities for the heat-treated sample (C2 and G2 respectively). These effects are consistent with the desorption of oxygen during the heat treatment.
339
may be ascribed to the release of adsorbed oxygen molecules from the CuPc layer. Oxygen is well known to act as an acceptor impurity level in CuPc films, and its removal is consistent with a reduction in both the d.c. conductivity observed previously [33] and with the present results. Curve C2 of Fig. 8 shows the frequency variation of capacitance of a heat-treated CuPc thin film as compared to a similar fresh sample (curve C1). The capacitance of the heat-treated layer is reduced at low frequency, and the decrease with frequency is less pronounced than in a fresh sample. These results are also consistent with the desorption of oxygen discussed above, which leads to a reduction in the conductance of the CuPc and thus an increase in R in the model of Goswami and Goswami. F r o m eqn. (4) it may be seen that not only should the capacitance be lowered with respect to that measured in a fresh film, but also the reduction in current with increasing frequency should be less because of the increased value of R. The decreases induced in both conductivity and capacitance by the heat treatment were not reversible providing the samples remained under vacuum and the temperature at which the heat treatment took place (370 K) was not exceeded. As mentioned in Section 2 the samples did not undergo an ~-/3 phase transition at this temperature. Although measurements of conductivity and capacitance were not repeated after subsequent exposure to air or oxygen it is well known that the d.c. conductivity increases under these circumstances because of oxygen absorption [33]. We would therefore expect the a.c. parameters to similarly increase, giving a measure of reversibility under pressure-cycling conditions in an oxygen-containing ambient.
4. Summary and conclusions It has been observed that a.c. conductivity in CuPc films follows a a(~o) vc ~" dependence where s ~< 1. Such behaviour appears to indicate that hopping is the predominant conduction process over the frequency range studied as observed by James et al. [8] for molybdenum phthalocyanine films. At low temperatures and high frequencies the observed values of s approach those predicted by the model of Elliott [ 13], originally derived to explain the a.c. behaviour of amorphous materials. For high temperatures and low frequencies free-carrier conduction with mean activation energy of approximately 0.3 eV was observed. Capacitance was found to decrease with increasing frequency, and also to increase with temperature. Loss tangent tan ~i decreased with increasing frequency and increased with temperature, with a tendency for a minim u m to appear in the tan 6 frequency dependence at
340
R. D. Gould, A. K. Hassan /A.e. electrical properties o f thin films
low temperatures. Such behaviour has been shown to be in qualitative agreement with the model of Goswami and Goswami [30], originally proposed for ZnS films without Schottky barriers. Although there is not an exact functional correlation between the predictions of this model and our measurements, the qualitative agreement is considerably better than with that of the model of Simmons [10] which gives adequate agreement with the results of Vidadi et al. [29] on CuPc films with aluminium Schottky barrier contacts. Clearly, although the model of Goswami and Goswami predicts the general features shown in our work, even better agreement would require refinements to the model to include perhaps the effects of the intergranular capacitance in the CuPc films or the effects of temperature on the series resistance r. The effects of heat treatment are to lower both the conductance and capacitance values over the whole frequency spectrum, while also reducing the relative fall in capacitance with frequency. Heat treatment is known to desorb oxygen acceptors from the phthalocyanines [33, 34] thus reducing the d.c. conductivity, and the same process is thought to lead to an increase in the interior resistance R in the present case. Under these circumstances the model of Goswami and Goswami predicts the observed behaviour. It has been shown that the use of ohmic contacts to CuPc thin films results in significantly different a.c. behaviour from that observed using blocking contacts [29]. Results are in good qualitative agreement with the predictions of the model of Goswami and Goswami [30]. Further work is aimed at extending the measurements to higher frequencies and extending the range of temperatures employed in an attempt to observe welldefined minima in tan 6 as predicted by this model. It is also hoped to investigate dielectric losses at very low frequencies where loss peaks have been observed in other organic materials.
References I c . H a m a n n , Phys. Status Solidi, 20(1967) 481. 2 A. Sussman, J. Appl. Phys., 38 (1967) 2738.
3 R. D. Gould, Thin Solid Films, 125 (1985) 63. 4 R. D. Gould, J. Phys. D: Appl. Phys., 19 (1986) 1785. 5 Yu. A. Vidadi, L. D. Rozenshtein and E. A. Chistyakov, Soy. Phys.-Semiconductors, 1 (1968) 1049. 6 Yu. A. Vidadi, L. D. Rozenshtein and E. A. Chistyakov, Soy. Phys.-Solid State, 11 (1969) 173. 7 H. S. Nalwa and P. Vasudevan, J. Mat. Sei. Lett., 2 (19833 22. 8 S. A. James, A. K. Ray and S. Silver, Phys. Status Solidi A, 129 (1992) 435. 9 J. G. Simmons, Br. J. Appl. Phys., 18 (1967) 269. 10 J. G. Simmons, G. S. Nadkarni and M. C. Lancaster, J. Appl. Phys., 41 (1970) 538. 11 A. K. Jonscher, ;thin Solid Films, 36 (1976) 1. 12 N. F. Mort and E. A. Davis, Eleetroni~ Processes in Non-~rystalline Materials, Clarendon Press, Oxford, 1971. 13 S. R. Elliott, Phil. Mag., 36 (19773 1291. 14 B. K. Chaudhury, K. K. Som and A. Ghosh, Jap. J. Appl. Phys., 29 (1990) 120. 15 M. Abkowitz, D. F. Blossey and A. I. Lakatos, Phys. Rev. B, 12 ( 19753 3400. 16 T. G. Abdel-Malik, R. M. Abdel-Latif, M. E1-Shabasy and M. Abdel-Hamid, Ind. J. Phys., 62A (1988) 17. 17 A. K. Hassan and R. D. Gould, Phys. Status Solidi A, 132 (1992) 91. 18 A. N. Blagodarov, E. L. Lutsenko and L. D. Rozenshtein, Soy. Phys.-Solid State, I I (1970) 2747. 19 T. T. AI-Dhhan and C. A. Hogarth, Int. J. Eh, ctron., 63 (1987) 707. 20 J. Le Moigne and R. Even, J. Chem. Phys., 83 (19853 6472. 21 S. E. Harrison and K. H. Ludewig, J. Chem. Phys., 45 (19663 343. 22 L. T. Chadderton, J. Phys. Chem. Solids, 24 (1963) 751. 23 A. K. Hassan, Ph.D. Thesis, Keele University, U K 1991. 24 P. E. Fielding and A. G. Mackay, Australian J. Chem., 17(19643 750. 25 A. K. Jonscher, J. Vae. Sci. Technol., 8(1971) 135. 26 A. Goswami and R. R. Varma, Thin Solid Films, 28 (1975) 157. 27 V. S. Dharmadhikari, Int. J. Electron., 54 (1983) 787. 28 A. S. Md. S. R a h m a n , M. H. Islam and C. A. Hogarth, Int. J. Electron., 62 (1987) 685. 29 Yu. A. Vidadi, K. Sh. Kocharli, B. Sh. Barkhalov and S. A. Sadreddinov, Phys. Status Solidi A, 34 ( 19763 K77. 30 A. Goswami and A. P. Goswami, Thin Solid Films, 16 (1973) 175. 31 B. Boudjema, G. Guillaud, M. Gamoudi, M. Maitrot, J.-J. Andre, M. Martin and J. Simon, J. Appl. Phys., 56 (19843 2323. 32 A. K. Hassan and R. D. Gould, lnt J. Electron., 69 (19903 11. 33 A. K. Hassan and R. D. Gould, J. Phys: Condens. Matter, 1 (1989) 6679. 34 A. Twarowski, J. (71era. Phys., 77 (1982) 4698.
