- Email: [email protected]
Dielectric studies on Cd0.4Zn0.6Te thin films
Materials Chemistry and Physics 78 (2003) 809–815
Dielectric studies on Cd0.4 Zn0.6Te thin films K. Prabakar, Sa.K. Narayandass∗ , D. Mangalaraj Department of Physics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India Received 26 June 2002; received in revised form 5 August 2002; accepted 12 August 2002
Abstract The dielectric responses of Cd0.4 Zn0.6 Te thin films, deposited by the vacuum evaporation technique, were studied as a function of frequency and temperature for different substrate temperatures of the deposited films. Combined modulus and impedance plots were used to study the response of the film, which in general contains grains, grain boundaries, and the electrode/film interface as capacitive elements. The conductivity of the deposited films decreases with increase in substrate temperature. The dielectric constant varied between 15 and 6.8 for the films deposited in the range of substrate temperatures 300–473 K. The frequency analysis of the modulus and impedance studies showed the distribution of the relaxation times due to the presence of grains and grain boundaries in the films. The values of activation energies derived from the dissipation factor and modulus were found to be 0.64 and 0.61 eV, respectively for the films deposited at room temperature, which are higher than the values calculated from conductivity (0.41 eV). The deviation in these values was attributed to the energetic conditions of the grains and grain boundaries. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Cd0.4 Zn0.6 Te thin films; Dielectric; Modulus; Impedance spectroscopy
1. Introduction Cd1−x Znx Te is a variable band gap II–VI semiconductor for which solid solutions across the entire compositional range can be prepared [1–3]. The room temperature band gap of these materials can be tuned from 1.5 eV in CdTe to 2.3 eV in ZnTe by controlling the alloy composition. In particular, Cd1−x Znx Te thin films with a band gap energy of 1.45–1.75 eV are of current interest because of their promising application as the top device of a two-cell tandem structure in high-efficiency thin-film solar cells [4]. There has been shown for many materials that dielectric relaxation phenomena in thin-film capacitors greatly affects their electrical properties [5–7]. Defects can be caused by the preparation of the thin films (grain boundaries, interfaces) and shallow/deep trap levels may exists in metal–insulator–metal capacitor films and which leads to a dielectric relaxation as a function of frequency [8]. The equivalent circuit analysis by various researchers [9,10] indicated that grain boundaries play a prominent role in the relaxation of ceramics. In the case of interface defects, it exists within the forbidden gap due to the interruption of the periodic lattice structure. Under the direct current (dc) electric field the space charge accumulation at the grain boundaries and interfaces of the ∗ Corresponding author. Tel.: +91-422-425458; fax: +91-422-422387. E-mail address: [email protected] (Sa.K. Narayandass).
dielectric/electrode reduces the barrier height at the grain boundaries and interfaces increase the leakage current and exhibit the dielectric relaxation [11]. Several techniques have been used to characterise the properties of these films and particularly the measurement of dielectric loss, conductivity and impedance as a function of frequency have proved to be valuable in providing additional information of the mechanism of charge transport that dc conductivity alone does not provide [12]. For this reason, this technique has been used extensively in condensed matter physics [13], semiconductor [14] and materials science. In addition to direct examination of the grain and/or grain boundary, complex plane analysis is commonly adopted to separate and identify the inter/intergranular impedance and also to determine the contribution of defects on the dielectric relaxation. Therefore, it is important to investigate the origin of the dielectric relaxation and its reduction. In this paper, we measured the capacitance (C), loss tangent (tan δ), impedance (Z), dielectric constant (ε), conductivity (σ ) and complex plane analysis of Cd0.4 Zn0.6 Te thin films deposited in the temperature range 300–473 K. 2. Experimental details High-purity (99.999% pure) cadmium, zinc and tellurium obtained from Balzers (Switzerland) were used in
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 3 8 8 - 7
810
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
the present investigation. The stoichiometric mixture of the cadmium, zinc and tellurium corresponding to the composition of Cd0.4 Zn0.6 Te, weighed to an accuracy of 10−5 g, was sealed in a silica ampoule under a vacuum of 3 × 10−3 Pa. The ampoule was heated to 1423 K (50 K above the melting point of CdTe and ZnTe) and then held for 36 h at the same temperature with periodic shaking and finally quenched in cold water. The resultant mass was crushed into fine powder and then evaporated from a tantalum source at a base pressure of 3 × 10−3 Pa. Al/Cd0.4 Zn0.6 Te/Al sandwich structures were fabricated at different substrate temperatures and high-temperature silver paste was used for the contact. The capacitance, impedance and tan δ were measured as a function of frequency (50 Hz–4 MHz) in the temperature range 300–445 K (Hioki 3532, Japan).
3. Results and discussion 3.1. Temperature and frequency dependence of loss tangent The frequency dependence of loss tangent (tan δ) at different temperatures for a typical film of thickness 650 nm is shown in Fig. 1. The tan δ was found to increase with frequency at different temperatures, pass through a maximum value (tan δ)max , and thereafter decreases. As the temperature is increased, the frequency at which (tan δ)max occurred shifted to higher frequencies. This type of behaviour is similar to that described by Simmons et al. [15] for films, having parallel resistance (R) and capacitance (C) of the materials in series with a parallel combination of Schottky barriers capacitances. They developed a model in which the sandwich structure is assumed to comprise a frequency-independent capacitive element in parallel with a discrete temperature-dependent resistive element R, both in series with Schottky barrier capacitance. R is related to the temperature by the equation R = R0 exp(φ R /kT) where φ R is the activation energy. From this relation, it is clear that R will decrease with increase in temperature. Hence, tan δ max shifts to the higher frequencies with increasing temperature.
Fig. 1. Variation of tan δ with frequency for a film of thickness of 650 nm deposited at room temperature.
Fig. 2. Arhennius plot of tan δ max and M max for Cd0.4 Zn0.6 Te thin films of a thickness of 650 nm.
These shifts are used to calculate the activation energy from the relation fmax = f0 exp(−φ f /kT), where fmax is the frequency at which tan δ is the maximum, k the Boltzmann’s constant and T the absolute temperature and φ f the activation energy. Fig. 2 shows the Arrhennius plot of fmax , and the activation energy calculated form the slope of the plot is 0.64 eV for a film of thickness 650 nm deposited at room temperature. As the substrate temperature increases from 300 to 473 K, the activation energy was found to decrease from 0.64 to 0.51 eV. 3.2. Temperature and frequency dependence of dielectric constant The temperature dependence of dielectric constant ε in the temperature range 300–473 K for Cd0.4 Zn0.6 Te thin films deposited at different substrate temperature is shown in Fig. 3. The dielectric constant decreased with increase in the substrate temperature. The variation of ε was small at low temperatures. A significant variation of ε was observed at higher temperatures. It is noticed that this parameter is related to the conductivity of the samples because the conductivity increases as the substrate temperature increases. As the frequency increases the dielectric constant decreases for all the films (not shown) irrespective of the substrate temperatures. In the absence of a field, the charge carriers that are
Fig. 3. Temperature dependence of the dielectric constant of Cd0.4 Zn0.6 Te thin films deposited at different substrate temperatures.
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
bounded at different localised states would have different dipole orientations. The carriers can be considered to be localised with a strong electron–phonon interaction, resulting in the formation of small polarons [16]. An electron can hop between a pair of these centres under the action of an alternating current (ac) field, and the hopping is equivalent to the reorientation of an electric dipole. This process would give rise to a frequency-dependent complex dielectric constant. Hence, the increase of the dielectric constant with decrease in the frequency can be attributed to the presence of dipoles. At room temperature, the dielectric constant varied between 15 and 6.8 at a frequency of 1 MHz for the variation of films deposited at different substrate temperatures from 300 to 473 K. 3.3. Electric modulus and impedance spectroscopy The complex impedance and electric modulus formalism for the analysis of dielectric response of materials has been discussed by various authors [17,18]. Impedance analysis provides a simple method to determine various contributions of the total conductivity of electrical materials in terms of four possible complex formalisms, viz. impedance (Z), admittance (Y∗ ), modulus (M∗ ) and permittivity (E∗ ). These parameters are interrelated as given by Z ∗ = (Y ∗ )−1 , Y ∗ = jωC0 E ∗ , E ∗ = (M ∗ )−1 and M ∗ = jωC0 Z ∗ respectively. Here, ω is the angular frequency and C0 the vacuum capacitance of the measuring thin films, i.e. C0 = ε0 (A/d), where ε0 is the permittivity of free space (8.854 × 10−12 F/m) and A and d are the area of the top electrode and thickness of the film, respectively. The complex electric modulus response with frequency is shown in Fig. 4 for a film of thickness 650 nm deposited at room temperature where a single broad peak is seen whose peak shift to higher frequencies with increasing temperatures. The maxima of the imaginary components of M∗ were shifted towards higher relaxation frequencies with the rise in temperature. This behaviour suggests that the spectral intensity of the dielectric relaxation is activated thermally in which hopping pro-
Fig. 4. Electric modulus versus frequency at different temperatures.
811
cess of charge carriers and small polarons are dominating intrinsically in the films, having grains and grain boundary effects [16]. Also, shifting of the peak frequencies in the forward direction with temperature implies that as the temperature is increased, the relaxation time decreases at high temperatures. Finally, the measuring frequency will become less than the relaxation frequency and measured impedance will equal the static impedance. The interesting point is that the electrical modulus and impedance formalism plotted produced modulus and impedance peaks, which are broader than predicted by Debye’s theory of relaxation phenomenon and are significantly asymmetric. According to ideal Debye’s theory of dielectric relaxation, the impedance (Z∗ ) and modulus (M∗ ) maxima are supposed to peak at the same frequency at a given and/or measured temperature, which was not observed in the present case. This has led to the hypothesis of distribution of relaxation times in the Cd0.4 Zn0.6 Te thin films, due to the presence of grain–grain boundary combinations. Both of these properties are interpreted as being a natural consequence of the intrinsically dispersive nature of the material concerned. According to Jonscher [19], such a type of relaxation is due to the co-operative many-body relaxation phenomenon and is dependent purely on the universal dielectric power law exponent n given by f (t) = t n . The region where peak occurs is more quantitatively defined as the condition ωτ = 1, where τ is defined as the most probable electron/hole relaxation time. The temperature dependence of the peak (µ ) relaxation frequency is shown in Fig. 2. The slope of this straight line fit gives the values of the activation energy and is found to be 0.61 eV for a film of thickness 650 nm, which is in good agreement with that calculated from the loss tan δ. In order to analyse and interpret the experimental data, it is essential to have a model equivalent circuit that provides a realistic representation of the electrical properties. In the present material such as Cd0.4 Zn0.6 Te thin films, it is clear that both inter- and intra-granular grains and grain boundary effects are present in the films, and the electrical properties are determined by a series combination of such grains and grain boundary capacitances and resistances. Each of these components may be represented by a parallel RC element, and the simplest appropriate equivalent circuit is a series array of parallel RC elements. It is not necessary to include an impedance element, representing the film/electrode interfaces in cases where the contact resistance is small, as with the present material. The circuit shown in Fig. 5 is widely used to represent bulk and grain boundary phenomena in polycrystalline materials, especially in cases, such as the present, where the grain boundary impedance is dominant in the films. With the series circuit as given in Fig. 5 it is desired to separate each of the parallel RC elements and measure their component R and C values. Fig. 6 shows the complex electric modulus plots at different temperatures for the Cd0.4 Zn0.6 Te thin films deposited at room temperature. The complex electric modulus at low temperatures below <330 K (Fig. 6a), showed the presence
812
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
Fig. 5. The equivalent circuit used to represent the electrical properties of bulk and grain boundary effects.
Fig. 6. The complex electric modulus plots at different temperatures for the Cd0.4 Zn0.6 Te thin films deposited at room temperature.
of one semicircular arcs, indicating parallel RC elements originating from the grain boundaries. However, at higher sample temperatures around and above 330 K (Fig. 6b), overlapping of two semicircular arcs were visualised and the response was attributed due to grain–grain boundaries. The first arc in the low-frequency region, passing through the origin is due to the parallel combination of grain boundary resistance (R1 ) and grain boundary capacitance (C1 ) and the second arc in the high frequency region is due to the parallel combination of bulk grain resistance (R2 ) and bulk grain capacitance (C2 ). The two semicircular arcs suggest that the distribution of various relaxation times from various grains and grain boundaries in the Cd0.4 Zn0.6 Te thin films. It is interesting to note that the size of the high-frequency arc at higher sample temperatures (>390 K) decreases (Fig. 6c) and disappears completely above 445 K (Fig. 6d); only the low-frequency arc passing through the origin is visualised. There was a small uplink deviated from the semicircle on the low-frequency side, which implied the presence of grain boundary and/or film electrode interface effects. The arc intercepts the real axis at C1 and C1 + C2 . The value of grain the boundary capacitance (due to the low-frequency arc) on the M axis was 1.7 nF at 330 K and the bulk capacitance is 12 pF and are found to be independent of temperature. Hence, the net effect would be considered to the bulk as well as the grain boundary combination. The regions are thin as indicated by their large capacitance value of few nF are deduced to be grain boundaries, while in the case of very low capacitance values of the order pF and are attributed to be due to the presence of grains [20,21]. It was found that, at lower temperatures, the semicircle was more perfect than the high-temperature ones. This confirms that at low temperatures the sample behaved more like a Debye-type element, where as the temperature is increased a departure from the ideal Debye type was noticed. The modulus plots show up the smallest capacitive elements, whereas the impedance plots show the more resistive one. For instance, if one of the capacitances is much larger than the other, its associated peak and semicircle will effectively disappear from the modulus plot. When the relaxation of different processes differs as a consequence of different capacitive components, the complex impedance is used to understand them. Fig. 7 shows the variation of the imaginary component of impedance as a function of frequency at different temperatures for the films deposited at 473 K. The imaginary component of impedance (Z ) showed peak
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
813
Fig. 7. Variation of the imaginary component of impedance as a function of frequency at different temperatures for the films deposited at 473 K.
maxima at different measured temperatures. These peak positions were shifted to higher frequencies, indicating the net relaxation time was decreasing with rise in measured temperatures. Also, it is apparent from Fig. 7 that, irrespective of the measured temperatures, all the curves at higher frequencies are merging with one another. This type of temperature and frequency dependence is well known in charge carrier systems. At higher frequencies, the bulk grain dispersion predominates due to the diminishing of the space charge effects, as their relaxation times are very high compared to the bulk grains. For the most common case of a capacitor with finite conductance, the electrical impedance can be written in the form Z∗ =
R 1 + iωτ
(1)
This equation, when plotted in a complex plane, takes the shape of a semicircle whose centre lies on the real axis. The intercept of this circle with the real axis gives the value of R, and the maxima on that curve corresponds to the situation when ωτ = 1, i.e. when the frequency of the driving voltage is just inverse of the relaxation time constant. When more than one such regions exists, differing in relaxation times, the semicircle splits up and another semicircle appears in the low-frequency scale. This is, however, a highly idealised situation where the inherent frequency dependence of the individual elements (R and C) is neglected. This is most often not the situation in the real case, and it is difficult to define a unique relaxation time (τ ). In such cases a distribution of the relaxation time is assumed, and the equation describing is modified according to the equation Z∗ =
R (1 + iωτ )1−α
(2)
where τ is an average relaxation time and α is a parameter that characterises the departure of a real semicircle from an ideal one (Cole–Davidson relation). With these particular materials, electrode-sample contacts do not have a significant impedance and can be ignored since the high frequency arc passes through the origin. Fig. 8 shows a typical com-
Fig. 8. Complex impedance response of Cd0.6 Zn0.4 Te thin films deposited at 473 K.
plex impedance response of Cd0.4 Zn0.6 Te thin films of a typical thickness of 500 nm for the film deposited at 473 K. For temperatures below 350 K, complex impedance plots showed the presence of two semicircular arcs. The first arc in the high-frequency region, passing through the origin, is due to the parallel combination of bulk resistance and bulk capacitance, and the second arc at low frequencies is due to the parallel combination of grain boundary resistance and grain boundary capacitance. It is interesting to note that the size of the high-frequency arc, corresponding to the bulk effect, decreases with increase of temperature and only one arc passing through the origin is obtained above 350 K. This arc is due to the parallel combination of grain boundary resistance and grain boundary capacitance of Cd0.4 Zn0.6 Te thin films. The second semicircular arc has not been resolved. This indicates that the resistance of the grains is very high in comparison to the grain boundary resistance. It is observed that the centre of each arc either lies on the real axis or very close to the real axis, i.e. the angle of depression is negligible. In polycrystalline materials, using the complex impedance analysis, it is possible to resolve the respective resistance values due to the grains and the grain boundaries from the intercept on the real axis. The intercept made by the semicircle at the high frequency end corresponds to the resistance offered by the grains and the intercept due to the low-frequency arc corresponds to the combined resistance of various grains and grain boundaries.
4. The ac conductivity The temperature dependence of the ac conductivity was calculated, using the relation σac = ωε0 ε 1 tan δ where ε 0 is the absolute permittivity, ω the angular frequency. Fig. 9 presents the frequency dependence of the ac conductivity deposited at different substrate temperatures of Cd0.4 Zn0.6 Te thin films. For the films deposited at substrate temperatures
814
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
Fig. 9. Frequency dependence of the conductivity of Cd0.4 Zn0.6 Te thin films deposited at room temperature.
Fig. 10. Arrhennius plot of σ for Cd0.6 Zn0.4 Te thin films deposited at different substrate temperatures for a fixed frequency of 1 MHz.
of 300 and 373 K at low frequencies, we observe an electrode contribution in which charges are not transferred across the electrode film interface. In the intermediate-frequency region the conductivity is almost frequency independent. In the higher-frequency domain the conductivity increases as the frequency increases. However, at very high frequencies (>1 MHz) the conductivity is observed to be independent of temperature, which is in good agreement as observed by various investigators [22,23] on semiconducting thin films. The conductivity values around the relaxation frequency are found to satisfy the Argall–Jonscher empirical relation [24], σ (ω) = Sωm , where S is a constant and m a function of temperature, and was found to be decreased with increase in the measuring temperature in the intermediate-frequency region. This can be explained with the temperature dependence of the parameter m, which is on the basis of the many-body interaction models. The interaction between all dipoles participating in the polarisation process is characterised by the parameter m. A unit value of m implies a pure Debye case, where the interaction between the neighbouring dipoles is almost negligible and the only conductive element is the dc resistance. This is normally the case at very low temperatures. As the temperature increases, the interaction increases, leading to a decrease in m. From Fig. 9 it is clear that for films deposited at a high substrate temperatures (473 K), the ac conductivity showed little dependence on frequency in the low frequency regime. This frequency independence is a characteristic of dc electrical conduction. Thus, the total conductivity can be expressed as σtotal = σdc + Aωm , where σ dc is the dc electrical conductivity, which is independent of frequency. It is observed that m varies between 0.54 < m < 0.88 for the films deposited at room temperature as well at higher substrate temperatures. The dispersion in conductivity at low frequencies can be explained as due to a non-adiabatic hopping of the charge carriers between the impurity sites. If hopping takes place between a random distribution of localised charge states, then m lies between 0.5 and 1.0. The lower value of m occurs for multiple hops while the higher value occurs for single hops. Hence in the present investigations, the Pollack–Geballe theory [25] holds good at higher temperatures and at high frequencies.
This theory also predicts a decrease in activation energy at high temperatures with a corresponding decrease in the frequency dependence. Our results for Cd0.4 Zn0.6 Te thin films satisfy all the major predictions of the theory of the randomly distributed hopping states. The square law dependence of the conductivity at higher frequencies has been explained by Argall and Jonscher [24], based on the two-centre hopping. A linear between the total conductivity and the inverse absolute temperature could be written as σ = σ0 exp(−Ea /kT)
(3)
Fig. 10 shows an Arrhennius plot of the conductivity for films deposited at different substrate temperatures. The activation energy is seen to decrease with increase in substrate temperature from 0.41 to 0.29 eV in the temperature range 300–473 K. These activation energy values are very low compared to the values calculated from the modulus and tan δ plots. This difference might have been due to the difference in the activation energies involved for the carrier transport mechanism in the grain and grain boundaries. The observed behaviour together with the frequency dependence of conductance suggests that the conduction mechanism in Cd0.6 Zn0.4 Te thin films may be due to the hopping of charge carriers.
5. Conclusions The complex electric modulus and impedance spectroscopic technique was used to characterise Cd0.4 Zn0.6 Te thin films. This technique provides a powerful and easy route to explain the phenomena of the conduction process within the thin films. Since impedance spectroscopy adds to the voluminous data obtained from other parametric variations, all presumptions may be considered redundant. The effect of different parts of the thin film, such as grains, grain boundaries and film electrode interfaces, can be clearly distinguished. The results could be correlated to the film microstructure related to the growth conditions and the absence of an electrode interface depletion layer. The analysis
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
proved that distributed relaxation times are present, which are originating from different grain and grain boundary combinations. The relaxation times were decreasing with the rise in the measuring temperatures, suggesting that the net relaxation phenomenon is also associated with the charge carrier transport mechanism. The activation energies calculated from the spectroscopic plot varies between 0.64 and 0.51 eV. From the conductivity measurement, it is observed that the capacitance increases towards low frequency that suggests the possibility that charge carriers are blocked at the electrodes. The variation of the conductivity as a function of temperature and frequency reveals a non-adiabatic hopping of the charge carriers between the impurity sites in the low-dispersion region. The activation energy decreases with increase in frequency and substrate temperature.
References [1] T.L. Chu, S.S. Chu, C. Ferekides, J. Britt, J. Appl. Phys. 71 (1992) 5635. [2] S.B. Qadri, J.H. Dinan, Appl. Phys. Lett. 47 (1985) 1066. [3] R.D. Feldman, R.F. Austin, A.H. Daymem, E.H. Westerwick, Appl. Phys. Lett. 49 (1986) 797. [4] S.A. Ringel, R. Sudharsanan, A. Rohatgi, W.B. Carter, J. Electron. Mater. 19 (1990) 259. [5] Y. Fukuda, A.K. Numuta, A. Nishimura, J. Appl. Phys. 33 (1994) 5255.
815
[6] M.S. Tsai, T.Y. Tseng, Mater. Chem. Phys. 57 (1998) 47. [7] C. Ang, Z. Yu, L.E. Cross, Phys. Rev. B 62 (2000) 228. [8] S. Upadhyay, O.M. Parkash, D. Kumar, J. Mater. Sci. 12 (2001) 165. [9] M.A. Alim, M.A. Seitz, R.W. Hirthe, J. Appl. Phys. 63 (1988) 2337. [10] C. Ang, J.R. Jurado, Z. Yu, M.T. Colomer, J.R. Frade, J.L. Baptissta, Phys. Rev. B 57 (1998) 11858. [11] R. Waser, T. Baiatu, K.H. Hardtl, J. Am. Ceram. Soc. 73 (1990) 3008. [12] R.M. Hill, Thin Solid Films 125 (1985) 277. [13] S. Ezhilvalavan, M.S. Tsai, T.Y. Tseng, J. Phys. D: Appl. Phys. 33 (2000) 1137. [14] A. Nasar, M. Shamsuddin, J. Mater. Sci. 35 (2000) 1465. [15] J.G. Simmons, G.S. Nadkarni, M.C. Lancaster, J. Appl. Phys. 41 (1970) 538. [16] S.S.N. Bharadwaja, S.B. Krupanidhi, Mater. Sci. Eng. B 78 (2000) 75. [17] E. Iguchi, K. Ueda, W.H. Wang, Phys. Rev. 54 (1996) 17431. [18] S. Saha, S.B. Krupanidhi, J. Appl. Phys. 87 (2000) 849. [19] A.K. Jonscher, Dielectric Relaxation of Solids, Chelsea Dielectric Press, London, 1981. [20] D.C. Singclair, A.R. West, J. Appl. Phys. 66 (1989) 3850. [21] I.M. Hodge, M.D. Ingram, A.R. West, J. Electrochem. Soc. 74 (1976) 125. [22] P. Suguna, D. Mangalaraj, S.K. Narayandass, P. Meena, Phys. Status Solidi A 155 (1996) 405. [23] P. Meena, C. Balasubramanian, S.K. Narayandass, D. Mangalaraj, Thin Solid Films 252 (1994) 67. [24] F. Argall, A.K. Jonscher, Thin Solid Films 2 (1968) 185. [25] M. Pollack, T.H. Geballe, Phys. Rev. 122 (1961) 1974.
Dielectric studies on Cd0.4 Zn0.6Te thin films K. Prabakar, Sa.K. Narayandass∗ , D. Mangalaraj Department of Physics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India Received 26 June 2002; received in revised form 5 August 2002; accepted 12 August 2002
Abstract The dielectric responses of Cd0.4 Zn0.6 Te thin films, deposited by the vacuum evaporation technique, were studied as a function of frequency and temperature for different substrate temperatures of the deposited films. Combined modulus and impedance plots were used to study the response of the film, which in general contains grains, grain boundaries, and the electrode/film interface as capacitive elements. The conductivity of the deposited films decreases with increase in substrate temperature. The dielectric constant varied between 15 and 6.8 for the films deposited in the range of substrate temperatures 300–473 K. The frequency analysis of the modulus and impedance studies showed the distribution of the relaxation times due to the presence of grains and grain boundaries in the films. The values of activation energies derived from the dissipation factor and modulus were found to be 0.64 and 0.61 eV, respectively for the films deposited at room temperature, which are higher than the values calculated from conductivity (0.41 eV). The deviation in these values was attributed to the energetic conditions of the grains and grain boundaries. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Cd0.4 Zn0.6 Te thin films; Dielectric; Modulus; Impedance spectroscopy
1. Introduction Cd1−x Znx Te is a variable band gap II–VI semiconductor for which solid solutions across the entire compositional range can be prepared [1–3]. The room temperature band gap of these materials can be tuned from 1.5 eV in CdTe to 2.3 eV in ZnTe by controlling the alloy composition. In particular, Cd1−x Znx Te thin films with a band gap energy of 1.45–1.75 eV are of current interest because of their promising application as the top device of a two-cell tandem structure in high-efficiency thin-film solar cells [4]. There has been shown for many materials that dielectric relaxation phenomena in thin-film capacitors greatly affects their electrical properties [5–7]. Defects can be caused by the preparation of the thin films (grain boundaries, interfaces) and shallow/deep trap levels may exists in metal–insulator–metal capacitor films and which leads to a dielectric relaxation as a function of frequency [8]. The equivalent circuit analysis by various researchers [9,10] indicated that grain boundaries play a prominent role in the relaxation of ceramics. In the case of interface defects, it exists within the forbidden gap due to the interruption of the periodic lattice structure. Under the direct current (dc) electric field the space charge accumulation at the grain boundaries and interfaces of the ∗ Corresponding author. Tel.: +91-422-425458; fax: +91-422-422387. E-mail address: [email protected] (Sa.K. Narayandass).
dielectric/electrode reduces the barrier height at the grain boundaries and interfaces increase the leakage current and exhibit the dielectric relaxation [11]. Several techniques have been used to characterise the properties of these films and particularly the measurement of dielectric loss, conductivity and impedance as a function of frequency have proved to be valuable in providing additional information of the mechanism of charge transport that dc conductivity alone does not provide [12]. For this reason, this technique has been used extensively in condensed matter physics [13], semiconductor [14] and materials science. In addition to direct examination of the grain and/or grain boundary, complex plane analysis is commonly adopted to separate and identify the inter/intergranular impedance and also to determine the contribution of defects on the dielectric relaxation. Therefore, it is important to investigate the origin of the dielectric relaxation and its reduction. In this paper, we measured the capacitance (C), loss tangent (tan δ), impedance (Z), dielectric constant (ε), conductivity (σ ) and complex plane analysis of Cd0.4 Zn0.6 Te thin films deposited in the temperature range 300–473 K. 2. Experimental details High-purity (99.999% pure) cadmium, zinc and tellurium obtained from Balzers (Switzerland) were used in
0254-0584/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 2 ) 0 0 3 8 8 - 7
810
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
the present investigation. The stoichiometric mixture of the cadmium, zinc and tellurium corresponding to the composition of Cd0.4 Zn0.6 Te, weighed to an accuracy of 10−5 g, was sealed in a silica ampoule under a vacuum of 3 × 10−3 Pa. The ampoule was heated to 1423 K (50 K above the melting point of CdTe and ZnTe) and then held for 36 h at the same temperature with periodic shaking and finally quenched in cold water. The resultant mass was crushed into fine powder and then evaporated from a tantalum source at a base pressure of 3 × 10−3 Pa. Al/Cd0.4 Zn0.6 Te/Al sandwich structures were fabricated at different substrate temperatures and high-temperature silver paste was used for the contact. The capacitance, impedance and tan δ were measured as a function of frequency (50 Hz–4 MHz) in the temperature range 300–445 K (Hioki 3532, Japan).
3. Results and discussion 3.1. Temperature and frequency dependence of loss tangent The frequency dependence of loss tangent (tan δ) at different temperatures for a typical film of thickness 650 nm is shown in Fig. 1. The tan δ was found to increase with frequency at different temperatures, pass through a maximum value (tan δ)max , and thereafter decreases. As the temperature is increased, the frequency at which (tan δ)max occurred shifted to higher frequencies. This type of behaviour is similar to that described by Simmons et al. [15] for films, having parallel resistance (R) and capacitance (C) of the materials in series with a parallel combination of Schottky barriers capacitances. They developed a model in which the sandwich structure is assumed to comprise a frequency-independent capacitive element in parallel with a discrete temperature-dependent resistive element R, both in series with Schottky barrier capacitance. R is related to the temperature by the equation R = R0 exp(φ R /kT) where φ R is the activation energy. From this relation, it is clear that R will decrease with increase in temperature. Hence, tan δ max shifts to the higher frequencies with increasing temperature.
Fig. 1. Variation of tan δ with frequency for a film of thickness of 650 nm deposited at room temperature.
Fig. 2. Arhennius plot of tan δ max and M max for Cd0.4 Zn0.6 Te thin films of a thickness of 650 nm.
These shifts are used to calculate the activation energy from the relation fmax = f0 exp(−φ f /kT), where fmax is the frequency at which tan δ is the maximum, k the Boltzmann’s constant and T the absolute temperature and φ f the activation energy. Fig. 2 shows the Arrhennius plot of fmax , and the activation energy calculated form the slope of the plot is 0.64 eV for a film of thickness 650 nm deposited at room temperature. As the substrate temperature increases from 300 to 473 K, the activation energy was found to decrease from 0.64 to 0.51 eV. 3.2. Temperature and frequency dependence of dielectric constant The temperature dependence of dielectric constant ε in the temperature range 300–473 K for Cd0.4 Zn0.6 Te thin films deposited at different substrate temperature is shown in Fig. 3. The dielectric constant decreased with increase in the substrate temperature. The variation of ε was small at low temperatures. A significant variation of ε was observed at higher temperatures. It is noticed that this parameter is related to the conductivity of the samples because the conductivity increases as the substrate temperature increases. As the frequency increases the dielectric constant decreases for all the films (not shown) irrespective of the substrate temperatures. In the absence of a field, the charge carriers that are
Fig. 3. Temperature dependence of the dielectric constant of Cd0.4 Zn0.6 Te thin films deposited at different substrate temperatures.
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
bounded at different localised states would have different dipole orientations. The carriers can be considered to be localised with a strong electron–phonon interaction, resulting in the formation of small polarons [16]. An electron can hop between a pair of these centres under the action of an alternating current (ac) field, and the hopping is equivalent to the reorientation of an electric dipole. This process would give rise to a frequency-dependent complex dielectric constant. Hence, the increase of the dielectric constant with decrease in the frequency can be attributed to the presence of dipoles. At room temperature, the dielectric constant varied between 15 and 6.8 at a frequency of 1 MHz for the variation of films deposited at different substrate temperatures from 300 to 473 K. 3.3. Electric modulus and impedance spectroscopy The complex impedance and electric modulus formalism for the analysis of dielectric response of materials has been discussed by various authors [17,18]. Impedance analysis provides a simple method to determine various contributions of the total conductivity of electrical materials in terms of four possible complex formalisms, viz. impedance (Z), admittance (Y∗ ), modulus (M∗ ) and permittivity (E∗ ). These parameters are interrelated as given by Z ∗ = (Y ∗ )−1 , Y ∗ = jωC0 E ∗ , E ∗ = (M ∗ )−1 and M ∗ = jωC0 Z ∗ respectively. Here, ω is the angular frequency and C0 the vacuum capacitance of the measuring thin films, i.e. C0 = ε0 (A/d), where ε0 is the permittivity of free space (8.854 × 10−12 F/m) and A and d are the area of the top electrode and thickness of the film, respectively. The complex electric modulus response with frequency is shown in Fig. 4 for a film of thickness 650 nm deposited at room temperature where a single broad peak is seen whose peak shift to higher frequencies with increasing temperatures. The maxima of the imaginary components of M∗ were shifted towards higher relaxation frequencies with the rise in temperature. This behaviour suggests that the spectral intensity of the dielectric relaxation is activated thermally in which hopping pro-
Fig. 4. Electric modulus versus frequency at different temperatures.
811
cess of charge carriers and small polarons are dominating intrinsically in the films, having grains and grain boundary effects [16]. Also, shifting of the peak frequencies in the forward direction with temperature implies that as the temperature is increased, the relaxation time decreases at high temperatures. Finally, the measuring frequency will become less than the relaxation frequency and measured impedance will equal the static impedance. The interesting point is that the electrical modulus and impedance formalism plotted produced modulus and impedance peaks, which are broader than predicted by Debye’s theory of relaxation phenomenon and are significantly asymmetric. According to ideal Debye’s theory of dielectric relaxation, the impedance (Z∗ ) and modulus (M∗ ) maxima are supposed to peak at the same frequency at a given and/or measured temperature, which was not observed in the present case. This has led to the hypothesis of distribution of relaxation times in the Cd0.4 Zn0.6 Te thin films, due to the presence of grain–grain boundary combinations. Both of these properties are interpreted as being a natural consequence of the intrinsically dispersive nature of the material concerned. According to Jonscher [19], such a type of relaxation is due to the co-operative many-body relaxation phenomenon and is dependent purely on the universal dielectric power law exponent n given by f (t) = t n . The region where peak occurs is more quantitatively defined as the condition ωτ = 1, where τ is defined as the most probable electron/hole relaxation time. The temperature dependence of the peak (µ ) relaxation frequency is shown in Fig. 2. The slope of this straight line fit gives the values of the activation energy and is found to be 0.61 eV for a film of thickness 650 nm, which is in good agreement with that calculated from the loss tan δ. In order to analyse and interpret the experimental data, it is essential to have a model equivalent circuit that provides a realistic representation of the electrical properties. In the present material such as Cd0.4 Zn0.6 Te thin films, it is clear that both inter- and intra-granular grains and grain boundary effects are present in the films, and the electrical properties are determined by a series combination of such grains and grain boundary capacitances and resistances. Each of these components may be represented by a parallel RC element, and the simplest appropriate equivalent circuit is a series array of parallel RC elements. It is not necessary to include an impedance element, representing the film/electrode interfaces in cases where the contact resistance is small, as with the present material. The circuit shown in Fig. 5 is widely used to represent bulk and grain boundary phenomena in polycrystalline materials, especially in cases, such as the present, where the grain boundary impedance is dominant in the films. With the series circuit as given in Fig. 5 it is desired to separate each of the parallel RC elements and measure their component R and C values. Fig. 6 shows the complex electric modulus plots at different temperatures for the Cd0.4 Zn0.6 Te thin films deposited at room temperature. The complex electric modulus at low temperatures below <330 K (Fig. 6a), showed the presence
812
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
Fig. 5. The equivalent circuit used to represent the electrical properties of bulk and grain boundary effects.
Fig. 6. The complex electric modulus plots at different temperatures for the Cd0.4 Zn0.6 Te thin films deposited at room temperature.
of one semicircular arcs, indicating parallel RC elements originating from the grain boundaries. However, at higher sample temperatures around and above 330 K (Fig. 6b), overlapping of two semicircular arcs were visualised and the response was attributed due to grain–grain boundaries. The first arc in the low-frequency region, passing through the origin is due to the parallel combination of grain boundary resistance (R1 ) and grain boundary capacitance (C1 ) and the second arc in the high frequency region is due to the parallel combination of bulk grain resistance (R2 ) and bulk grain capacitance (C2 ). The two semicircular arcs suggest that the distribution of various relaxation times from various grains and grain boundaries in the Cd0.4 Zn0.6 Te thin films. It is interesting to note that the size of the high-frequency arc at higher sample temperatures (>390 K) decreases (Fig. 6c) and disappears completely above 445 K (Fig. 6d); only the low-frequency arc passing through the origin is visualised. There was a small uplink deviated from the semicircle on the low-frequency side, which implied the presence of grain boundary and/or film electrode interface effects. The arc intercepts the real axis at C1 and C1 + C2 . The value of grain the boundary capacitance (due to the low-frequency arc) on the M axis was 1.7 nF at 330 K and the bulk capacitance is 12 pF and are found to be independent of temperature. Hence, the net effect would be considered to the bulk as well as the grain boundary combination. The regions are thin as indicated by their large capacitance value of few nF are deduced to be grain boundaries, while in the case of very low capacitance values of the order pF and are attributed to be due to the presence of grains [20,21]. It was found that, at lower temperatures, the semicircle was more perfect than the high-temperature ones. This confirms that at low temperatures the sample behaved more like a Debye-type element, where as the temperature is increased a departure from the ideal Debye type was noticed. The modulus plots show up the smallest capacitive elements, whereas the impedance plots show the more resistive one. For instance, if one of the capacitances is much larger than the other, its associated peak and semicircle will effectively disappear from the modulus plot. When the relaxation of different processes differs as a consequence of different capacitive components, the complex impedance is used to understand them. Fig. 7 shows the variation of the imaginary component of impedance as a function of frequency at different temperatures for the films deposited at 473 K. The imaginary component of impedance (Z ) showed peak
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
813
Fig. 7. Variation of the imaginary component of impedance as a function of frequency at different temperatures for the films deposited at 473 K.
maxima at different measured temperatures. These peak positions were shifted to higher frequencies, indicating the net relaxation time was decreasing with rise in measured temperatures. Also, it is apparent from Fig. 7 that, irrespective of the measured temperatures, all the curves at higher frequencies are merging with one another. This type of temperature and frequency dependence is well known in charge carrier systems. At higher frequencies, the bulk grain dispersion predominates due to the diminishing of the space charge effects, as their relaxation times are very high compared to the bulk grains. For the most common case of a capacitor with finite conductance, the electrical impedance can be written in the form Z∗ =
R 1 + iωτ
(1)
This equation, when plotted in a complex plane, takes the shape of a semicircle whose centre lies on the real axis. The intercept of this circle with the real axis gives the value of R, and the maxima on that curve corresponds to the situation when ωτ = 1, i.e. when the frequency of the driving voltage is just inverse of the relaxation time constant. When more than one such regions exists, differing in relaxation times, the semicircle splits up and another semicircle appears in the low-frequency scale. This is, however, a highly idealised situation where the inherent frequency dependence of the individual elements (R and C) is neglected. This is most often not the situation in the real case, and it is difficult to define a unique relaxation time (τ ). In such cases a distribution of the relaxation time is assumed, and the equation describing is modified according to the equation Z∗ =
R (1 + iωτ )1−α
(2)
where τ is an average relaxation time and α is a parameter that characterises the departure of a real semicircle from an ideal one (Cole–Davidson relation). With these particular materials, electrode-sample contacts do not have a significant impedance and can be ignored since the high frequency arc passes through the origin. Fig. 8 shows a typical com-
Fig. 8. Complex impedance response of Cd0.6 Zn0.4 Te thin films deposited at 473 K.
plex impedance response of Cd0.4 Zn0.6 Te thin films of a typical thickness of 500 nm for the film deposited at 473 K. For temperatures below 350 K, complex impedance plots showed the presence of two semicircular arcs. The first arc in the high-frequency region, passing through the origin, is due to the parallel combination of bulk resistance and bulk capacitance, and the second arc at low frequencies is due to the parallel combination of grain boundary resistance and grain boundary capacitance. It is interesting to note that the size of the high-frequency arc, corresponding to the bulk effect, decreases with increase of temperature and only one arc passing through the origin is obtained above 350 K. This arc is due to the parallel combination of grain boundary resistance and grain boundary capacitance of Cd0.4 Zn0.6 Te thin films. The second semicircular arc has not been resolved. This indicates that the resistance of the grains is very high in comparison to the grain boundary resistance. It is observed that the centre of each arc either lies on the real axis or very close to the real axis, i.e. the angle of depression is negligible. In polycrystalline materials, using the complex impedance analysis, it is possible to resolve the respective resistance values due to the grains and the grain boundaries from the intercept on the real axis. The intercept made by the semicircle at the high frequency end corresponds to the resistance offered by the grains and the intercept due to the low-frequency arc corresponds to the combined resistance of various grains and grain boundaries.
4. The ac conductivity The temperature dependence of the ac conductivity was calculated, using the relation σac = ωε0 ε 1 tan δ where ε 0 is the absolute permittivity, ω the angular frequency. Fig. 9 presents the frequency dependence of the ac conductivity deposited at different substrate temperatures of Cd0.4 Zn0.6 Te thin films. For the films deposited at substrate temperatures
814
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
Fig. 9. Frequency dependence of the conductivity of Cd0.4 Zn0.6 Te thin films deposited at room temperature.
Fig. 10. Arrhennius plot of σ for Cd0.6 Zn0.4 Te thin films deposited at different substrate temperatures for a fixed frequency of 1 MHz.
of 300 and 373 K at low frequencies, we observe an electrode contribution in which charges are not transferred across the electrode film interface. In the intermediate-frequency region the conductivity is almost frequency independent. In the higher-frequency domain the conductivity increases as the frequency increases. However, at very high frequencies (>1 MHz) the conductivity is observed to be independent of temperature, which is in good agreement as observed by various investigators [22,23] on semiconducting thin films. The conductivity values around the relaxation frequency are found to satisfy the Argall–Jonscher empirical relation [24], σ (ω) = Sωm , where S is a constant and m a function of temperature, and was found to be decreased with increase in the measuring temperature in the intermediate-frequency region. This can be explained with the temperature dependence of the parameter m, which is on the basis of the many-body interaction models. The interaction between all dipoles participating in the polarisation process is characterised by the parameter m. A unit value of m implies a pure Debye case, where the interaction between the neighbouring dipoles is almost negligible and the only conductive element is the dc resistance. This is normally the case at very low temperatures. As the temperature increases, the interaction increases, leading to a decrease in m. From Fig. 9 it is clear that for films deposited at a high substrate temperatures (473 K), the ac conductivity showed little dependence on frequency in the low frequency regime. This frequency independence is a characteristic of dc electrical conduction. Thus, the total conductivity can be expressed as σtotal = σdc + Aωm , where σ dc is the dc electrical conductivity, which is independent of frequency. It is observed that m varies between 0.54 < m < 0.88 for the films deposited at room temperature as well at higher substrate temperatures. The dispersion in conductivity at low frequencies can be explained as due to a non-adiabatic hopping of the charge carriers between the impurity sites. If hopping takes place between a random distribution of localised charge states, then m lies between 0.5 and 1.0. The lower value of m occurs for multiple hops while the higher value occurs for single hops. Hence in the present investigations, the Pollack–Geballe theory [25] holds good at higher temperatures and at high frequencies.
This theory also predicts a decrease in activation energy at high temperatures with a corresponding decrease in the frequency dependence. Our results for Cd0.4 Zn0.6 Te thin films satisfy all the major predictions of the theory of the randomly distributed hopping states. The square law dependence of the conductivity at higher frequencies has been explained by Argall and Jonscher [24], based on the two-centre hopping. A linear between the total conductivity and the inverse absolute temperature could be written as σ = σ0 exp(−Ea /kT)
(3)
Fig. 10 shows an Arrhennius plot of the conductivity for films deposited at different substrate temperatures. The activation energy is seen to decrease with increase in substrate temperature from 0.41 to 0.29 eV in the temperature range 300–473 K. These activation energy values are very low compared to the values calculated from the modulus and tan δ plots. This difference might have been due to the difference in the activation energies involved for the carrier transport mechanism in the grain and grain boundaries. The observed behaviour together with the frequency dependence of conductance suggests that the conduction mechanism in Cd0.6 Zn0.4 Te thin films may be due to the hopping of charge carriers.
5. Conclusions The complex electric modulus and impedance spectroscopic technique was used to characterise Cd0.4 Zn0.6 Te thin films. This technique provides a powerful and easy route to explain the phenomena of the conduction process within the thin films. Since impedance spectroscopy adds to the voluminous data obtained from other parametric variations, all presumptions may be considered redundant. The effect of different parts of the thin film, such as grains, grain boundaries and film electrode interfaces, can be clearly distinguished. The results could be correlated to the film microstructure related to the growth conditions and the absence of an electrode interface depletion layer. The analysis
K. Prabakar et al. / Materials Chemistry and Physics 78 (2003) 809–815
proved that distributed relaxation times are present, which are originating from different grain and grain boundary combinations. The relaxation times were decreasing with the rise in the measuring temperatures, suggesting that the net relaxation phenomenon is also associated with the charge carrier transport mechanism. The activation energies calculated from the spectroscopic plot varies between 0.64 and 0.51 eV. From the conductivity measurement, it is observed that the capacitance increases towards low frequency that suggests the possibility that charge carriers are blocked at the electrodes. The variation of the conductivity as a function of temperature and frequency reveals a non-adiabatic hopping of the charge carriers between the impurity sites in the low-dispersion region. The activation energy decreases with increase in frequency and substrate temperature.
References [1] T.L. Chu, S.S. Chu, C. Ferekides, J. Britt, J. Appl. Phys. 71 (1992) 5635. [2] S.B. Qadri, J.H. Dinan, Appl. Phys. Lett. 47 (1985) 1066. [3] R.D. Feldman, R.F. Austin, A.H. Daymem, E.H. Westerwick, Appl. Phys. Lett. 49 (1986) 797. [4] S.A. Ringel, R. Sudharsanan, A. Rohatgi, W.B. Carter, J. Electron. Mater. 19 (1990) 259. [5] Y. Fukuda, A.K. Numuta, A. Nishimura, J. Appl. Phys. 33 (1994) 5255.
815
[6] M.S. Tsai, T.Y. Tseng, Mater. Chem. Phys. 57 (1998) 47. [7] C. Ang, Z. Yu, L.E. Cross, Phys. Rev. B 62 (2000) 228. [8] S. Upadhyay, O.M. Parkash, D. Kumar, J. Mater. Sci. 12 (2001) 165. [9] M.A. Alim, M.A. Seitz, R.W. Hirthe, J. Appl. Phys. 63 (1988) 2337. [10] C. Ang, J.R. Jurado, Z. Yu, M.T. Colomer, J.R. Frade, J.L. Baptissta, Phys. Rev. B 57 (1998) 11858. [11] R. Waser, T. Baiatu, K.H. Hardtl, J. Am. Ceram. Soc. 73 (1990) 3008. [12] R.M. Hill, Thin Solid Films 125 (1985) 277. [13] S. Ezhilvalavan, M.S. Tsai, T.Y. Tseng, J. Phys. D: Appl. Phys. 33 (2000) 1137. [14] A. Nasar, M. Shamsuddin, J. Mater. Sci. 35 (2000) 1465. [15] J.G. Simmons, G.S. Nadkarni, M.C. Lancaster, J. Appl. Phys. 41 (1970) 538. [16] S.S.N. Bharadwaja, S.B. Krupanidhi, Mater. Sci. Eng. B 78 (2000) 75. [17] E. Iguchi, K. Ueda, W.H. Wang, Phys. Rev. 54 (1996) 17431. [18] S. Saha, S.B. Krupanidhi, J. Appl. Phys. 87 (2000) 849. [19] A.K. Jonscher, Dielectric Relaxation of Solids, Chelsea Dielectric Press, London, 1981. [20] D.C. Singclair, A.R. West, J. Appl. Phys. 66 (1989) 3850. [21] I.M. Hodge, M.D. Ingram, A.R. West, J. Electrochem. Soc. 74 (1976) 125. [22] P. Suguna, D. Mangalaraj, S.K. Narayandass, P. Meena, Phys. Status Solidi A 155 (1996) 405. [23] P. Meena, C. Balasubramanian, S.K. Narayandass, D. Mangalaraj, Thin Solid Films 252 (1994) 67. [24] F. Argall, A.K. Jonscher, Thin Solid Films 2 (1968) 185. [25] M. Pollack, T.H. Geballe, Phys. Rev. 122 (1961) 1974.