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AC conductivity and dielectric properties of Sb2S3 films
Vac1=1935=Susan=Venkatachala=BG
Vacuum 59 (2000) 932}939
AC conductivity and dielectric properties of Sb S "lms A.M. Farid*, A.E. Bekheet Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Abstract Stoichometric Sb S "lms were prepared by thermal evaporation technique. X-ray di!raction patterns showed that the as-deposited Sb S "lms is in the amorphous state. The ac conductivity and dielectric properties of the amorphous Sb S "lms has been investigated in the frequency range of 100}100 kHz. The ac conductivity is found to be proportional to u1 where s(1. The temperature dependence of ac conductivity and the parameter s can be discussed with the aim of the correlated barrier-hopping (CBH) model. The maximum barrier height = calculated from dielectric measurements according to Guintini equation agrees + with the theory of hopping of charge carriers over potential barrier as suggested by Elliot in the case of chalcogenide glasses. 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Sb S exists in nature in a crystalline form known as stibnite. Its structure reported by Arun et al. [1] belongs to the orthorhombic system. Sb S in thin "lm form was prepared by several methods, namely spray pyrolysis [2,3], chemical deposition [4,5], electrodeposition [5], dip try method [7] and thermal evaporation [8,9]. It was found that amorphous "lms could be obtained by thermal evaporation of the bulk material [8]. The electrical [2,3,7,10,11], thermoelectrical [7] and optical [3,6,10,11] properties were studied for the Sb S "lms. No data concerning the ac conductivity and/or dielectric properties of the obtained material are available in literature. Measurement of ac conductivity of amorphous chalcogenide semiconductors has been extensively used to understand the conduction process in these materials. Various models, quantum}mechanical tunneling model (QMT) [12,13], small polaron tunneling model [13,14], large polaron tunneling model [14], atomic hopping model [14,15] and correlated barrier hopping (CBH) model [16}18] have been proposed to explain the ac conduction mechanism for di!erent
* Corresponding author. Fax: #20-2-4552138. E-mail address: ashraf}[email protected] (A.M. Farid). 0042-207X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 4 0 3 - 6
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
933
materials. Measurements of dielectric properties of materials are used to understand the types of polarization that exist in these materials. In this paper the temperature and frequency dependence of ac conductivity and dielectric properties are measured for Sb S "lms of di!erent thicknesses . Our results are discussed with the basis of a di!erent theory of ac conductivity of amorphous semiconductors.
2. Experimental techniques Thin "lms of di!erent thicknesses of Sb S were obtained by conventional thermal evaporation technique using a high vacuum coating unit (Edwards-type E306 A). The substrate was "xed onto a rotatable holder (up to 240 r.p.m.) to obtain homogeneous deposited "lms at a distance of 25 cm above the evaporator. The "lm thickness was measured by Tolansky's interferometric method. The "lm thickness ranged from 323 to 506 nm. X-ray di!raction analysis revealed the amorphous nature of the investigated "lms. For ac measurements, "lms were sandwiched between two Al electrodes as lower and upper electrodes. A programmable automatic RLC bridge (PM 6304 Philips) was used to measure the impedance Z, the capacitance C and the loss tangent (tan d) directly, since all samples could be represented by a resistance R connected in parallel with a capacitance C. The total conductivity was calculated from the equation: p (u)"d/ZA, where d is the thickness of the "lm and A is the cross-sectional area. The dielectric constant was calculated from the equation: e "dC/Ae , where C is the capacitance of the "lm and e is the permittivity of free space. The dielectric loss e was calculated from the equation: e "e tan d, where (d"90! ). 3. Results and discussion 3.1. Frequency and temperature dependence of ac conductivity A common feature of all the amorphous semiconductors is that the ac conductivity p (u) increases with frequency according to the equation p (u)"p (u)!p "AuQ, (1) where u is the angular frequency, s is the frequency exponent and A is a temperature-independent constant. Fig. 1 shows the frequency dependence of ac conductivity p (u) for Sb S "lm of thickness 323 nm at di!erent temperatures as a representative example. It is clear from the "gure that p (u) increases linearly with frequency. The same behavior of the frequency dependence of p (u) was obtained for all investigated "lms. Values of the frequency exponent s were obtained from the slopes of these lines of the "gure. The temperature dependence of s for the investigated "lms is shown in Fig. 2. It is clear from this "gure that, s decreases with increasing temperature. The discrepancy in the values of s for samples at each temperature indicated by vertical lines on the obtained results lie within the experimental error of $6% on average. Accordingly, s is independent of the "lm thickness in the investigated range.
Vac=1935=SK=VVC 934
A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
Fig. 1. Frequency dependence of p (u) for Sb S "lm of thickness 323 nm at di!erent temperatures.
Fig. 2. The temperature dependence of the parameter s for Sb S "lms.
According to the quantum}mechanical tunneling (QMT) model [19], the exponent s is almost equal to 0.8 and increases slightly with increasing temperature or independent of temperature. Therefore, QMT model is considered not applicable to the obtained samples. According to the overlapping-large polaron tunneling (OLPT) model [20], the exponent s is both temperature and frequency dependent. s decreases with increasing temperature from unity at room temperature to a minimum value at a certain temperature, then it increases with increasing temperature. Therefore, OLPT model is considered not applicable to the obtained samples. According to the correlated barrier-hopping (CBH) model, values of the frequency exponent s is ranged from 0.7 to 1 at room temperature and is found to decrease with increasing temperature.
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
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Fig. 3. Temperature dependence of p (u) for Sb S "lm of thickness 506 nm at di!erent frequencies.
This is in good agreement with the obtained results, so the frequency dependence of p (u) can be explained in terms of CBH model. The expression for s derived on the basis of this model is given by Elliott [16,17] as S"1!(6k¹/B),
(2)
where k is Boltzmann constant, T is temperature in kelvin and B is the optical band gap of the material. Using the previously [6] obtained value of the energy gap of Sb S "lms (1.74 eV), the value of s at room temperature is calculated using Eq. (2). The calculated value (0.911) is in good agreement with the experimental value (0.925) within 1.5%. According to the Austin}Mott formula [21], ac conductivity p (u) can be explained in terms of hopping of electrons between pairs of localized states at the Fermi level. p (u) is related to the density of states N (E ) at the Fermi level by the equation p (u)"(p/3)[N(E )]k¹ea\[ln(l /u)],
(3)
where a is the exponential decay parameter of localized states wave functions, and l is the phonon frequency. By assuming l "10 s\ and a\"10 As , the density of state is calculated. It is found that it has values of the order of 10}10 eV\ cm\ and increases with frequency and temperature. The temperature dependence of p (u) for Sb S "lm of thickness 506 nm is shown in Fig. 3 as a representative example. It is clear from the "gure that p (u) increases linearly with the reciprocal of absolute temperature. This suggested that the ac conductivity is a thermally activated process from di!erent localized states in the gap or in its tails. The activation energy of conduction is calculated at di!erent frequencies using the well-known equation p"p exp(*E /k¹). The fre N quency dependence of activation energy for Sb S "lms of di!erent thicknesses is shown in Fig. 4. It is clear that *E (u) decreases with increasing frequency. Such a decrease can be attributed to the N
Vac=1935=SK=VVC 936
A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
Fig. 4. The frequency dependence of ac activation energy for Sb S "lms.
Fig. 5. Frequency dependence of e for Sb S "lm of thickness 506 nm at di!erent temperatures.
contribution of the frequency applied to the conduction mechanism, which con"rms the hopping conduction to the dominant mechanism. The discrepancy in the values of *E (u) for samples at N each frequency indicated by vertical lines on the obtained results lie within the experimental error of $8% on average. Accordingly, *E (u) is independent on "lm thickness in the investigated N range. 3.2. Frequency and temperature dependence of dielectric constant Fig. 5 shows the frequency dependence of dielectric constant e at di!erent temperatures for Sb S "lm of thickness 506 nm as a representative example. It is clear from the "gure that e decreases with increasing frequency and increases with increasing temperature. The decrease of
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
937
e with frequency can be attributed to the fact that at low frequencies e for polar material is due to the contribution of multicomponents of polarizibility, deformational (electronic, ionic) and relaxation (orientaional an interfacial). When the frequency is increased, the orientational polarization decreases since it takes more time than electronic and ionic polarization. This decreases the value of dielectric constant with frequency reaching a constant value at high frequency due to interfacial polarization. The increase of e with temperature can be attributed to the fact that the orientational polariza tion is connected with the thermal motion of molecules, so dipoles cannot orient themselves at low temperatures. When the temperature is increased the orientation of dipoles is facilitated and this increases the value of orientational polarization and this increases e with increasing temperature. 3.3. Frequency and temperature dependence of dielectric loss The frequency dependence of dielectric loss e was studied at di!erent temperatures for Sb S "lms of di!erent thicknesses. e is found to decrease with increasing frequency and increase with increasing temperature. The obtained data of the frequency dependence of e for a "lm of thickness 223 nm is represented as ln e vs. ln u (Fig. 6) according to the equation e "Au , where A is
Fig. 6. Frequency dependence of e for Sb S "lm of thickness 323 nm at di!erent temperatures.
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A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
Fig. 7. Temperature dependence of the parameter m for Sb S "lms.
a constant. The power m, calculated from Fig. 6, is represented in Fig. 7 as m vs. T. It is clear from the "gure that m decreases linearly with temperature according to the Guintini [22] equation: m"!4k¹/= , where = is the maximum barrier height. Value of = obtained from the slope
of the line of the "gure (0.182 eV) which is in good agreement with the theory of hopping of charge carriers over a potential barrier as suggested by Elliott [16,17] in the case of chalcogenide glasses. The variation of e with temperature can be explained by Stevels [23] who divided the relaxation phenomena into three parts, conduction losses, dipole losses and vibrational losses. At low temperatures conduction losses have minimum value since it is proportional to (p/u). As the temperature increases p increases and so the conduction losses increase. This increases the value of e with increasing temperature. 4. Conclusion Amorphous Sb S "lms were prepared by thermal evaporation technique. The ac conductivity, dielectric constant and dielectric loss, is found to be frequency and temperature dependent. The frequency and temperature dependence of ac conductivity suggested the applicability of correlated barrier model (CBH) to the investigated material. Value of the maximum barrier height is estimated from the data of dielectric loss which is in good agreement with the theory of hopping of charge carriers over a potential barrier as suggested by Elliott in case of chalcogenide glasses.
References [1] [2] [3] [4] [5] [6] [7]
Arun P, Vedeshwar AG. J Mater Sci 1996;31:6507. Killedar VV, Lokhande CD, Bhosale CH. Indian J Pure Appl Phys 1998;36:33. Killedar VV, Lokhande CD, Bhosale CH. Mater Chem Phys 1997;47:104. Desai JD, Lokhande CD. Thin Solid Films 1994;237:29. Mandal KC, Mondal A. J Phys Chem Solids 1990;51:1339. Yesugade NS, Lokhande CD, Bhosale CH. Thin Solid Films 1995;263:145. Nayak BB, Acharya HN. Thin Solid Films 1984;122:93.
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939 [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
Mady KHA, El-Nahas MM, Farid AM, Soliman HS. J Mater Sci 1988;23:3636. George J, Radhakrishnan MK. Solid State Commun 1980;33:987. El Zawawi IK, Abdel-Moez A, Terra FS, Mounir M. Thin Solid Films 1998;324:300. El Zawawi IK, Abd-Moez A, Riad MA, Mounir M. Phys Low-Dim Struct 1998;7/8:155. Pollak M. Philos Mag 1971;23:519. Pollak M, Geballe TH. Phys Rev B 1961;22:1742. Pollak M, Pike GE. Phys Rev Lett 1972;28:1449. X-Lecleac'H, J Phys 1979;40:27. Elliott SR. Philos Mag B 1978;36:1291. Elliott SR. Philos Mag B 1978;37:135. Shimakawa K. Philos Mag 1982;46:123. Ghosh A. Phys Rev B 1990;41:1479. Long AR. Adv Phys 1982;31:553. Austin LG, Mott NF. Adv Phys 1969;18:41. Giuntini JC, Zancheha JV. J Non-Cryst Solids 1979;34:57. Stevels JM. The electrical properties of glasses. 1975. p. 350.
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Vacuum 59 (2000) 932}939
AC conductivity and dielectric properties of Sb S "lms A.M. Farid*, A.E. Bekheet Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Abstract Stoichometric Sb S "lms were prepared by thermal evaporation technique. X-ray di!raction patterns showed that the as-deposited Sb S "lms is in the amorphous state. The ac conductivity and dielectric properties of the amorphous Sb S "lms has been investigated in the frequency range of 100}100 kHz. The ac conductivity is found to be proportional to u1 where s(1. The temperature dependence of ac conductivity and the parameter s can be discussed with the aim of the correlated barrier-hopping (CBH) model. The maximum barrier height = calculated from dielectric measurements according to Guintini equation agrees + with the theory of hopping of charge carriers over potential barrier as suggested by Elliot in the case of chalcogenide glasses. 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Sb S exists in nature in a crystalline form known as stibnite. Its structure reported by Arun et al. [1] belongs to the orthorhombic system. Sb S in thin "lm form was prepared by several methods, namely spray pyrolysis [2,3], chemical deposition [4,5], electrodeposition [5], dip try method [7] and thermal evaporation [8,9]. It was found that amorphous "lms could be obtained by thermal evaporation of the bulk material [8]. The electrical [2,3,7,10,11], thermoelectrical [7] and optical [3,6,10,11] properties were studied for the Sb S "lms. No data concerning the ac conductivity and/or dielectric properties of the obtained material are available in literature. Measurement of ac conductivity of amorphous chalcogenide semiconductors has been extensively used to understand the conduction process in these materials. Various models, quantum}mechanical tunneling model (QMT) [12,13], small polaron tunneling model [13,14], large polaron tunneling model [14], atomic hopping model [14,15] and correlated barrier hopping (CBH) model [16}18] have been proposed to explain the ac conduction mechanism for di!erent
* Corresponding author. Fax: #20-2-4552138. E-mail address: ashraf}[email protected] (A.M. Farid). 0042-207X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 4 0 3 - 6
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
933
materials. Measurements of dielectric properties of materials are used to understand the types of polarization that exist in these materials. In this paper the temperature and frequency dependence of ac conductivity and dielectric properties are measured for Sb S "lms of di!erent thicknesses . Our results are discussed with the basis of a di!erent theory of ac conductivity of amorphous semiconductors.
2. Experimental techniques Thin "lms of di!erent thicknesses of Sb S were obtained by conventional thermal evaporation technique using a high vacuum coating unit (Edwards-type E306 A). The substrate was "xed onto a rotatable holder (up to 240 r.p.m.) to obtain homogeneous deposited "lms at a distance of 25 cm above the evaporator. The "lm thickness was measured by Tolansky's interferometric method. The "lm thickness ranged from 323 to 506 nm. X-ray di!raction analysis revealed the amorphous nature of the investigated "lms. For ac measurements, "lms were sandwiched between two Al electrodes as lower and upper electrodes. A programmable automatic RLC bridge (PM 6304 Philips) was used to measure the impedance Z, the capacitance C and the loss tangent (tan d) directly, since all samples could be represented by a resistance R connected in parallel with a capacitance C. The total conductivity was calculated from the equation: p (u)"d/ZA, where d is the thickness of the "lm and A is the cross-sectional area. The dielectric constant was calculated from the equation: e "dC/Ae , where C is the capacitance of the "lm and e is the permittivity of free space. The dielectric loss e was calculated from the equation: e "e tan d, where (d"90! ). 3. Results and discussion 3.1. Frequency and temperature dependence of ac conductivity A common feature of all the amorphous semiconductors is that the ac conductivity p (u) increases with frequency according to the equation p (u)"p (u)!p "AuQ, (1) where u is the angular frequency, s is the frequency exponent and A is a temperature-independent constant. Fig. 1 shows the frequency dependence of ac conductivity p (u) for Sb S "lm of thickness 323 nm at di!erent temperatures as a representative example. It is clear from the "gure that p (u) increases linearly with frequency. The same behavior of the frequency dependence of p (u) was obtained for all investigated "lms. Values of the frequency exponent s were obtained from the slopes of these lines of the "gure. The temperature dependence of s for the investigated "lms is shown in Fig. 2. It is clear from this "gure that, s decreases with increasing temperature. The discrepancy in the values of s for samples at each temperature indicated by vertical lines on the obtained results lie within the experimental error of $6% on average. Accordingly, s is independent of the "lm thickness in the investigated range.
Vac=1935=SK=VVC 934
A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
Fig. 1. Frequency dependence of p (u) for Sb S "lm of thickness 323 nm at di!erent temperatures.
Fig. 2. The temperature dependence of the parameter s for Sb S "lms.
According to the quantum}mechanical tunneling (QMT) model [19], the exponent s is almost equal to 0.8 and increases slightly with increasing temperature or independent of temperature. Therefore, QMT model is considered not applicable to the obtained samples. According to the overlapping-large polaron tunneling (OLPT) model [20], the exponent s is both temperature and frequency dependent. s decreases with increasing temperature from unity at room temperature to a minimum value at a certain temperature, then it increases with increasing temperature. Therefore, OLPT model is considered not applicable to the obtained samples. According to the correlated barrier-hopping (CBH) model, values of the frequency exponent s is ranged from 0.7 to 1 at room temperature and is found to decrease with increasing temperature.
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
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Fig. 3. Temperature dependence of p (u) for Sb S "lm of thickness 506 nm at di!erent frequencies.
This is in good agreement with the obtained results, so the frequency dependence of p (u) can be explained in terms of CBH model. The expression for s derived on the basis of this model is given by Elliott [16,17] as S"1!(6k¹/B),
(2)
where k is Boltzmann constant, T is temperature in kelvin and B is the optical band gap of the material. Using the previously [6] obtained value of the energy gap of Sb S "lms (1.74 eV), the value of s at room temperature is calculated using Eq. (2). The calculated value (0.911) is in good agreement with the experimental value (0.925) within 1.5%. According to the Austin}Mott formula [21], ac conductivity p (u) can be explained in terms of hopping of electrons between pairs of localized states at the Fermi level. p (u) is related to the density of states N (E ) at the Fermi level by the equation p (u)"(p/3)[N(E )]k¹ea\[ln(l /u)],
(3)
where a is the exponential decay parameter of localized states wave functions, and l is the phonon frequency. By assuming l "10 s\ and a\"10 As , the density of state is calculated. It is found that it has values of the order of 10}10 eV\ cm\ and increases with frequency and temperature. The temperature dependence of p (u) for Sb S "lm of thickness 506 nm is shown in Fig. 3 as a representative example. It is clear from the "gure that p (u) increases linearly with the reciprocal of absolute temperature. This suggested that the ac conductivity is a thermally activated process from di!erent localized states in the gap or in its tails. The activation energy of conduction is calculated at di!erent frequencies using the well-known equation p"p exp(*E /k¹). The fre N quency dependence of activation energy for Sb S "lms of di!erent thicknesses is shown in Fig. 4. It is clear that *E (u) decreases with increasing frequency. Such a decrease can be attributed to the N
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A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
Fig. 4. The frequency dependence of ac activation energy for Sb S "lms.
Fig. 5. Frequency dependence of e for Sb S "lm of thickness 506 nm at di!erent temperatures.
contribution of the frequency applied to the conduction mechanism, which con"rms the hopping conduction to the dominant mechanism. The discrepancy in the values of *E (u) for samples at N each frequency indicated by vertical lines on the obtained results lie within the experimental error of $8% on average. Accordingly, *E (u) is independent on "lm thickness in the investigated N range. 3.2. Frequency and temperature dependence of dielectric constant Fig. 5 shows the frequency dependence of dielectric constant e at di!erent temperatures for Sb S "lm of thickness 506 nm as a representative example. It is clear from the "gure that e decreases with increasing frequency and increases with increasing temperature. The decrease of
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
937
e with frequency can be attributed to the fact that at low frequencies e for polar material is due to the contribution of multicomponents of polarizibility, deformational (electronic, ionic) and relaxation (orientaional an interfacial). When the frequency is increased, the orientational polarization decreases since it takes more time than electronic and ionic polarization. This decreases the value of dielectric constant with frequency reaching a constant value at high frequency due to interfacial polarization. The increase of e with temperature can be attributed to the fact that the orientational polariza tion is connected with the thermal motion of molecules, so dipoles cannot orient themselves at low temperatures. When the temperature is increased the orientation of dipoles is facilitated and this increases the value of orientational polarization and this increases e with increasing temperature. 3.3. Frequency and temperature dependence of dielectric loss The frequency dependence of dielectric loss e was studied at di!erent temperatures for Sb S "lms of di!erent thicknesses. e is found to decrease with increasing frequency and increase with increasing temperature. The obtained data of the frequency dependence of e for a "lm of thickness 223 nm is represented as ln e vs. ln u (Fig. 6) according to the equation e "Au , where A is
Fig. 6. Frequency dependence of e for Sb S "lm of thickness 323 nm at di!erent temperatures.
Vac=1935=SK=VVC 938
A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939
Fig. 7. Temperature dependence of the parameter m for Sb S "lms.
a constant. The power m, calculated from Fig. 6, is represented in Fig. 7 as m vs. T. It is clear from the "gure that m decreases linearly with temperature according to the Guintini [22] equation: m"!4k¹/= , where = is the maximum barrier height. Value of = obtained from the slope
of the line of the "gure (0.182 eV) which is in good agreement with the theory of hopping of charge carriers over a potential barrier as suggested by Elliott [16,17] in the case of chalcogenide glasses. The variation of e with temperature can be explained by Stevels [23] who divided the relaxation phenomena into three parts, conduction losses, dipole losses and vibrational losses. At low temperatures conduction losses have minimum value since it is proportional to (p/u). As the temperature increases p increases and so the conduction losses increase. This increases the value of e with increasing temperature. 4. Conclusion Amorphous Sb S "lms were prepared by thermal evaporation technique. The ac conductivity, dielectric constant and dielectric loss, is found to be frequency and temperature dependent. The frequency and temperature dependence of ac conductivity suggested the applicability of correlated barrier model (CBH) to the investigated material. Value of the maximum barrier height is estimated from the data of dielectric loss which is in good agreement with the theory of hopping of charge carriers over a potential barrier as suggested by Elliott in case of chalcogenide glasses.
References [1] [2] [3] [4] [5] [6] [7]
Arun P, Vedeshwar AG. J Mater Sci 1996;31:6507. Killedar VV, Lokhande CD, Bhosale CH. Indian J Pure Appl Phys 1998;36:33. Killedar VV, Lokhande CD, Bhosale CH. Mater Chem Phys 1997;47:104. Desai JD, Lokhande CD. Thin Solid Films 1994;237:29. Mandal KC, Mondal A. J Phys Chem Solids 1990;51:1339. Yesugade NS, Lokhande CD, Bhosale CH. Thin Solid Films 1995;263:145. Nayak BB, Acharya HN. Thin Solid Films 1984;122:93.
Vac1=1935=SK=VVC A.M. Farid, A.E. Bekheet / Vacuum 59 (2000) 932}939 [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
Mady KHA, El-Nahas MM, Farid AM, Soliman HS. J Mater Sci 1988;23:3636. George J, Radhakrishnan MK. Solid State Commun 1980;33:987. El Zawawi IK, Abdel-Moez A, Terra FS, Mounir M. Thin Solid Films 1998;324:300. El Zawawi IK, Abd-Moez A, Riad MA, Mounir M. Phys Low-Dim Struct 1998;7/8:155. Pollak M. Philos Mag 1971;23:519. Pollak M, Geballe TH. Phys Rev B 1961;22:1742. Pollak M, Pike GE. Phys Rev Lett 1972;28:1449. X-Lecleac'H, J Phys 1979;40:27. Elliott SR. Philos Mag B 1978;36:1291. Elliott SR. Philos Mag B 1978;37:135. Shimakawa K. Philos Mag 1982;46:123. Ghosh A. Phys Rev B 1990;41:1479. Long AR. Adv Phys 1982;31:553. Austin LG, Mott NF. Adv Phys 1969;18:41. Giuntini JC, Zancheha JV. J Non-Cryst Solids 1979;34:57. Stevels JM. The electrical properties of glasses. 1975. p. 350.
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