- Email: [email protected]
Further MN rule in thermally activated a.c. conduction of Se–Te–Sb chalcogenide glasses
Vacuum 84 (2010) 1176–1179
Contents lists available at ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Short communication
Further MN rule in thermally activated a.c. conduction of Se–Te–Sb chalcogenide glasses N. Mehta a, *, A. Kumar b a b
Department of Physics, Banaras Hindu University, Varanasi, India Department of Physics, Harcourt Butler Technological Institute, Kanpur, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 October 2009 Accepted 17 January 2010
Temperature and frequency dependence of a.c. conductivity have been studied in glassy Se70Te30xSbx (4 x 10) alloys. The observation of Further Meyer–Neldel rule in case of a.c. conductivity is reported. The observation of the correlation between Meyer–Neldel pre-factor s00 and Meyer–Neldel energy is explained by multiple excitations stimulated by optical phonon energy as described by Yelon and Movaghar. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Chalcogenide glasses Meyer–Neldel rule
1. Introduction Meyer–Neldel rule (MNR) [1] can occur in any situation which involves an activated process. However, the rule is still most commonly referred to in connection with diffusion phenomena. As the rule still tends to exist in a sort of limbo between fully accepted physical law and unexplained correlation, the scientists all over world are analyzing the applicability of MNR for different thermally activated processes [2–10]. This shows that most of the huge amount of available data is unsuitable for giving a clear-cut answer concerning the significance of the MNR. A major difficulty is that such data were usually determined with some other aim in mind and are not intrinsically well-suited to the testing of the Meyer– Neldel relationship. Different laboratories, using standard methods, are very likely to obtain very similar Arrhenius parameters: too similar, in fact, to test the rule properly. Nevertheless, an extensive data-base and analysis is presented for those relatively few systems in which the rule can be tested over reasonable ranges of pre-exponential factor and activation energy values. In some cases, the rule seems to be adhered to very closely by a good number of independent data-points. Areas of semiconductors where the MNR is detected include porous and amorphous silicon [5,6], microcrystalline silicon films [4], glassy materials [7] and organic materials [8] in various devices such as charge-coupled devices [9], thin-film transistors [4] and even superconductors [10].
* Corresponding author. Tel.: þ91 542 2307308; fax: þ91 542 2368174. E-mail address: [email protected] (N. Mehta). 0042-207X/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2010.01.042
These days, our laboratories are also engaged in observing the applicability of MNR in different thermally activated electronic conduction processes. The observation of MNR for thermally activated photoconduction, high field conduction and a.c conduction is verified by us in different chalcogenide glasses in a series of papers [7,11,12]. Recently, we have reported ‘‘Further MNR’’ for thermally activated photoconduction and high field conduction in some chalcogenide glasses [12,13]. In the present work, we are reporting first time the applicability of Further MNR in thermally activated a.c conduction for glassy Se70Te30xSbx (4 x 10) alloys. 2. Material preparation Glassy alloys of Se70Te30–xSbx (4 x 10) were prepared by quenching technique. The exact proportions of high purity (99.999%) Se, Te and Sb elements, in accordance with their atomic percentages, were weighed using an electronic balance (LIBROR, AEG-120) with the least count of 104 gm. The materials were then sealed in evacuated (w 105 Torr) quartz ampoules (length w 5 cm and internal diameter w 8 mm). The ampoules containing material were heated to 800 C and were held at that temperature for 12 h. The temperature of the furnace was raised slowly at a rate of 3–4 C/min. During heating, the ampoules were constantly rocked, by rotating a ceramic rod to which the ampoules were tucked away in the furnace. This was done to obtain homogeneous glassy alloys. After rocking for about 12 h, the obtained melt was cooled rapidly by removing the ampoules from the furnace and dropping them to ice-cooled water rapidly. The quenched samples were then taken out by breaking the quartz ampoules. The glassy nature of the alloys was ascertained by X-ray diffraction (XRD) technique. The XRD pattern of glassy Se70Te20Sb10 is shown in Fig. 1. Absence of any
N. Mehta, A. Kumar / Vacuum 84 (2010) 1176–1179
1177
Se70Te24Sb6 -18 200 Hz 500 Hz 1000 Hz 10000 Hz
ln σ ac (Ohm-cm)
-1
-18.5
-19
-19.5
-20
-20.5 2.95
Fig. 1. XRD pattern of glassy Se70Te20Sb10 alloy.
sharp peak in XRD pattern in Fig. 1 confirms the glassy nature of Se70Te20Sb10 alloy. Similar XRD patterns were obtained for the other glassy alloys.
3. Experimental The glassy alloys thus prepared were ground to a very fine powder and pellets (diameter w 6 mm and thickness w 1 mm) were obtained by compressing the powder in a die at a load of 5 Tons. The pellets were coated with indium films to ensure good electrical contact between sample and the electrodes. The pellets were mounted in between two steel electrodes of a metallic sample holder for electrical conductivity measurements. The temperature measurement was facilitated by a copper-constantan thermocouple mounted very near to the sample. A vacuum of w102 Torr was maintained over the entire temperature range. For measuring a.c. conductivity, conductance and capacitance were measured using a GR 1620 AP capacitance measuring assembly. The parallel conductance was measured and a.c. conductivity was calculated. Three terminal measurements were performed to avoid the stray capacitances.
4. Results and discussion In general, above the room temperature, for a semiconducting material, the variation of a.c. conductivity with temperature can be expressed by an exponential relation:
sac ¼ s0 expðDE=kTÞ
3
3.1 3.15 -1 1000 / T (K)
3.2
3.25
3.3
Fig. 2. Temperature dependence of sac for a-Se70Te24Sb6 alloy at different audio frequencies.
From the slope and the intercepts of ln sac vs 1000/T curves, the values of DE and s0 have been calculated. Fig. 3 shows the plots of ln s0 vs DE for different alloys, which are the straight lines indicating that s0 varies exponentially with DE following the MN relation given by:
s0 ¼ s00 exp½DE=EMN ;
(2)
The slope of ln s0 vs DE curve yields the values of EMN and ln s00 for glassy Se70Te30–xSbx (4 x 10) alloys. On plotting ln s00 as a function of EMN for the present glassy system by changing the composition keeping the frequency constant, a straight line is found, which is quite consistent with Equation:
lns00 ¼ a þ b EMN
(3)
Here a and b are constants. The observation of Further MNR in present case can be explained using Yelon–Movaghar model or YM model [14,15]. This model is based on the assumption that the phonons are the source of the excitation energy in such process involve in trapping and detrapping of electrons, either by cascade or by multi-phonon process. Emin [16] has calculated the hopping rates due to multi-phonon effects, using small polaron theory and the Kubo–Greewood formula. The result is
(1)
where DE is called the activation energy for a.c. conduction and s0 is called the pre-exponential factor. These parameters are of significance to differentiate various conduction mechanisms. Generally, the pre-exponential factor parameter s0 and ac activation energy DE are obtained from the semi-logarithmic plots of the ac conductivity versus reciprocal temperature. The activation energy DE is determined from the slope of the approximate straight line in the resulting plot, which is obtained by the best fit to the experimental data using the least squares method. The intercept of line gives the value of ln s0. Fig. 2 shows the temperature dependence of a.c. conductivity in glassy Se70Te24Sb6 alloy in the temperature range above the room temperature, where sac shows strong temperature dependence. From this figure, it is clear that the a.c. conductivity (sac) varies exponentially with temperature as ln sac vs 1000/T curves are straight lines. Such behavior is consistent with eq. (1). Similar plots are obtained for other alloys.
3.05
RðDEÞfexp
DE DE lnS exp Zu0 kT
(4)
where Zu0 is the optical phonon energy. That is,
EMN ¼
Zu0 lnS
(5)
where
S ¼
2Eb Zu0
(6)
In Eq. (6), Eb is the small polaron binding energy, so that S represents a normalized coupling strength. In Eq. (5), if ln S is of the order 1 in all these cases, the typical value of optical phonon energies in materials is about 25 and 50 meV [17]. In order to understand the variation of EMN with ln s00 observed by Shimakawa and Abdel-Wahab, we begin by assuming that electron hopping induced by optical phonons and the associated
1178
N. Mehta, A. Kumar / Vacuum 84 (2010) 1176–1179
Se 70 Te 24 Sb6
Se 70 Te 26 Sb4
5
R = 0.9986 0
2 ln σ 0
ln σ 0
2
R = 0.9999
3
2
-5
-10
1 0
-15
-1 0.2
0.3
0.4 0.5 Δ Eac (eV)
0.6
0.7
Se 70 Te 22 Sb8
6
R2 = 0.9999
4 2 0 -2 -4 -6 -8 0.26
0.54
Δ Eac (eV)
0.58
0.62
Se 70 Te 20 Sb10 2
R =1
ln σ 0
4
0.5
ln σ 0
2 0
-2 -4 0.4
0.44
0.48
0.52 Δ Eac (eV)
0.56
0.6
0.32
0.38
0.44 0.5 Δ Eac (eV)
0.56
0.62
Fig. 3. ln s0 versus DE plots for glassy Se70Te30xSbx (4 x 10) alloys.
variation in s00, must be due to variation in ln S. In fact, Emin’s model predicts that the hopping rate, and as a result, the conductivity, will be extremely sensitive to variation in ln S. The most complete expression for the hopping rate at low temperatures is presented by Emin [16]. If we limit our consideration to hops upward in energy, and use the present notation, this may be written as
2 exp J RðDEÞ ¼ es 2pu0 Z 1
"
N X
DE Zu0
ðAn Þ
DE EMN
exp DE ! Zu0
DE kT
lattice-relaxation phase shift. As can be easily seen the MN energy depends upon ln S, whereas the hopping rate depends upon the exp (S). Combining Eqs. (5) and (7) leads the prediction that
Zu0 lns00 ¼ r exp ; EMN
(8)
Here it has been assumed that ‘r’ is a constant. Using the data of
# DEfn cos Zu0
(7)
s00 and EMN, curves are plotted between s00 and EMN, and values of r and Zu0 are calculated for present case (see Figs. 4 and 5). The value of Zu0 for the present case is higher (102.6 meV) as compared to that are proposed by Yelon et al. The higher values of Zu0 in the
Where J is the electron transfer integral connecting the initial and final sites, An is a lattice-relaxation amplitude function and fn is the
present case may be due to a. c conduction in the present case, whereas Yelon et al. developed above theory without applying any audio frequency. The present results, therefore supports the model given by Yelon and Movaghar to explain the observation of MN rule between s00 and EMN for a.c conduction too.
Se70Te30-xSbx
Se70Te30-xSbx
pN
-16
2.98
-16.5
2.96 2.94
-17 ln (-ln σ00)
ln σoo
-18 -18.5
R2 = 0.9552
2.9 2.88 2.86
-19
2.84
-19.5
2.82
-20 0.0288
= 103.6 meV
2.92
R2 = 0.9595
-17.5
2.8
0.029
0.0292
0.0294
0.0296
0.0298
0.03
0.0302
EMN (eV) Fig. 4. ln s00 versus EMN plot for glassy Se70Te30xSbx (4 x 10) alloys.
33
33.2
33.4
33.6
33.8
34
34.2
34.4
34.6
34.8
(EMN)-1 (eV)-1 Fig. 5. ln(–ln s00) versus (EMN)1 plot for glassy Se70Te30xSbx (4 x 10) alloys.
N. Mehta, A. Kumar / Vacuum 84 (2010) 1176–1179
5. Conclusions Temperature dependence of a.c. conductivity is measured in bulk samples of glassy Se70Te30xSbx (4 x 10) alloys. Conductivity is found to be thermally activated at all the values of frequency. The results show that the values of s00 and EMN satisfy Further MNR. This is explained by the multi-excitation character of the processes suggested by Yelon and Movaghar for MNR in chalcogenide glasses. References [1] Meyer W, Neldel H. Z Tech Phys 1937;18:588. [2] Abtew TA, Zhang MingLiang, Pan Yue, Drabold DA. J Non-Cryst Sol 2008;354:2909. [3] Sharma SK, Sagar P, Gupta H, Kumar R, Mehra RM. Sol Stat Electron 2007;51:1124.
[4] [5] [6] [7] [8] [9] [10]
[11] [12] [13] [14] [15] [16] [17]
1179
Ram SK, Kumar S, Cabarrocas PR. J Non-Cryst Sol 2008;354:2263. Lubianiker Y, Balberg I. J Non-Cryst Sol 1998;227–230:180. Kondo M, Chida Y, Matsuda A. J Non-Cryst Sol 1996;198–200:178. Mehta N, Kumar D, Kumar A. Mat Lett 2007;61:3167. Meijer EJ, Matters M, Herwig PT, de Leeuw DM, Klapwijk TM. Appl Phys Lett 2000;76:3433. Widenhorn R, Mundermann L, Rest A, Bodegom E. J Appl Phys 2001;89:8179. Makarova T. Magnetism of carbon-based materials. In: Narlikar A, editor. Studies of High-Tc superconductivity, Vol. 44/45. New York: Nova Science Publishers; 2003. Mehta N, Kumar D, Kumar A. Philos Mag 2008;88:61. Kushwaha VS, Mehta N, Kushwaha N, Kumar A, Optoelectron J. Adv Mater 2005;7:2035. Mehta N, Kushwaha VS, Kumar A. Vacuum 2009;83:1169. Yelon A, Movaghar B. Phys Rev Lett 1990;65:618. Yelon A, Movaghar B, Branz HM. Phys Rev B 1992;46:12244. Emin D. Adv Phys 1975;24:305. Abdel-Wahab F. J Appl Phys 2002;91:265.
Contents lists available at ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Short communication
Further MN rule in thermally activated a.c. conduction of Se–Te–Sb chalcogenide glasses N. Mehta a, *, A. Kumar b a b
Department of Physics, Banaras Hindu University, Varanasi, India Department of Physics, Harcourt Butler Technological Institute, Kanpur, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 October 2009 Accepted 17 January 2010
Temperature and frequency dependence of a.c. conductivity have been studied in glassy Se70Te30xSbx (4 x 10) alloys. The observation of Further Meyer–Neldel rule in case of a.c. conductivity is reported. The observation of the correlation between Meyer–Neldel pre-factor s00 and Meyer–Neldel energy is explained by multiple excitations stimulated by optical phonon energy as described by Yelon and Movaghar. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Chalcogenide glasses Meyer–Neldel rule
1. Introduction Meyer–Neldel rule (MNR) [1] can occur in any situation which involves an activated process. However, the rule is still most commonly referred to in connection with diffusion phenomena. As the rule still tends to exist in a sort of limbo between fully accepted physical law and unexplained correlation, the scientists all over world are analyzing the applicability of MNR for different thermally activated processes [2–10]. This shows that most of the huge amount of available data is unsuitable for giving a clear-cut answer concerning the significance of the MNR. A major difficulty is that such data were usually determined with some other aim in mind and are not intrinsically well-suited to the testing of the Meyer– Neldel relationship. Different laboratories, using standard methods, are very likely to obtain very similar Arrhenius parameters: too similar, in fact, to test the rule properly. Nevertheless, an extensive data-base and analysis is presented for those relatively few systems in which the rule can be tested over reasonable ranges of pre-exponential factor and activation energy values. In some cases, the rule seems to be adhered to very closely by a good number of independent data-points. Areas of semiconductors where the MNR is detected include porous and amorphous silicon [5,6], microcrystalline silicon films [4], glassy materials [7] and organic materials [8] in various devices such as charge-coupled devices [9], thin-film transistors [4] and even superconductors [10].
* Corresponding author. Tel.: þ91 542 2307308; fax: þ91 542 2368174. E-mail address: [email protected] (N. Mehta). 0042-207X/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2010.01.042
These days, our laboratories are also engaged in observing the applicability of MNR in different thermally activated electronic conduction processes. The observation of MNR for thermally activated photoconduction, high field conduction and a.c conduction is verified by us in different chalcogenide glasses in a series of papers [7,11,12]. Recently, we have reported ‘‘Further MNR’’ for thermally activated photoconduction and high field conduction in some chalcogenide glasses [12,13]. In the present work, we are reporting first time the applicability of Further MNR in thermally activated a.c conduction for glassy Se70Te30xSbx (4 x 10) alloys. 2. Material preparation Glassy alloys of Se70Te30–xSbx (4 x 10) were prepared by quenching technique. The exact proportions of high purity (99.999%) Se, Te and Sb elements, in accordance with their atomic percentages, were weighed using an electronic balance (LIBROR, AEG-120) with the least count of 104 gm. The materials were then sealed in evacuated (w 105 Torr) quartz ampoules (length w 5 cm and internal diameter w 8 mm). The ampoules containing material were heated to 800 C and were held at that temperature for 12 h. The temperature of the furnace was raised slowly at a rate of 3–4 C/min. During heating, the ampoules were constantly rocked, by rotating a ceramic rod to which the ampoules were tucked away in the furnace. This was done to obtain homogeneous glassy alloys. After rocking for about 12 h, the obtained melt was cooled rapidly by removing the ampoules from the furnace and dropping them to ice-cooled water rapidly. The quenched samples were then taken out by breaking the quartz ampoules. The glassy nature of the alloys was ascertained by X-ray diffraction (XRD) technique. The XRD pattern of glassy Se70Te20Sb10 is shown in Fig. 1. Absence of any
N. Mehta, A. Kumar / Vacuum 84 (2010) 1176–1179
1177
Se70Te24Sb6 -18 200 Hz 500 Hz 1000 Hz 10000 Hz
ln σ ac (Ohm-cm)
-1
-18.5
-19
-19.5
-20
-20.5 2.95
Fig. 1. XRD pattern of glassy Se70Te20Sb10 alloy.
sharp peak in XRD pattern in Fig. 1 confirms the glassy nature of Se70Te20Sb10 alloy. Similar XRD patterns were obtained for the other glassy alloys.
3. Experimental The glassy alloys thus prepared were ground to a very fine powder and pellets (diameter w 6 mm and thickness w 1 mm) were obtained by compressing the powder in a die at a load of 5 Tons. The pellets were coated with indium films to ensure good electrical contact between sample and the electrodes. The pellets were mounted in between two steel electrodes of a metallic sample holder for electrical conductivity measurements. The temperature measurement was facilitated by a copper-constantan thermocouple mounted very near to the sample. A vacuum of w102 Torr was maintained over the entire temperature range. For measuring a.c. conductivity, conductance and capacitance were measured using a GR 1620 AP capacitance measuring assembly. The parallel conductance was measured and a.c. conductivity was calculated. Three terminal measurements were performed to avoid the stray capacitances.
4. Results and discussion In general, above the room temperature, for a semiconducting material, the variation of a.c. conductivity with temperature can be expressed by an exponential relation:
sac ¼ s0 expðDE=kTÞ
3
3.1 3.15 -1 1000 / T (K)
3.2
3.25
3.3
Fig. 2. Temperature dependence of sac for a-Se70Te24Sb6 alloy at different audio frequencies.
From the slope and the intercepts of ln sac vs 1000/T curves, the values of DE and s0 have been calculated. Fig. 3 shows the plots of ln s0 vs DE for different alloys, which are the straight lines indicating that s0 varies exponentially with DE following the MN relation given by:
s0 ¼ s00 exp½DE=EMN ;
(2)
The slope of ln s0 vs DE curve yields the values of EMN and ln s00 for glassy Se70Te30–xSbx (4 x 10) alloys. On plotting ln s00 as a function of EMN for the present glassy system by changing the composition keeping the frequency constant, a straight line is found, which is quite consistent with Equation:
lns00 ¼ a þ b EMN
(3)
Here a and b are constants. The observation of Further MNR in present case can be explained using Yelon–Movaghar model or YM model [14,15]. This model is based on the assumption that the phonons are the source of the excitation energy in such process involve in trapping and detrapping of electrons, either by cascade or by multi-phonon process. Emin [16] has calculated the hopping rates due to multi-phonon effects, using small polaron theory and the Kubo–Greewood formula. The result is
(1)
where DE is called the activation energy for a.c. conduction and s0 is called the pre-exponential factor. These parameters are of significance to differentiate various conduction mechanisms. Generally, the pre-exponential factor parameter s0 and ac activation energy DE are obtained from the semi-logarithmic plots of the ac conductivity versus reciprocal temperature. The activation energy DE is determined from the slope of the approximate straight line in the resulting plot, which is obtained by the best fit to the experimental data using the least squares method. The intercept of line gives the value of ln s0. Fig. 2 shows the temperature dependence of a.c. conductivity in glassy Se70Te24Sb6 alloy in the temperature range above the room temperature, where sac shows strong temperature dependence. From this figure, it is clear that the a.c. conductivity (sac) varies exponentially with temperature as ln sac vs 1000/T curves are straight lines. Such behavior is consistent with eq. (1). Similar plots are obtained for other alloys.
3.05
RðDEÞfexp
DE DE lnS exp Zu0 kT
(4)
where Zu0 is the optical phonon energy. That is,
EMN ¼
Zu0 lnS
(5)
where
S ¼
2Eb Zu0
(6)
In Eq. (6), Eb is the small polaron binding energy, so that S represents a normalized coupling strength. In Eq. (5), if ln S is of the order 1 in all these cases, the typical value of optical phonon energies in materials is about 25 and 50 meV [17]. In order to understand the variation of EMN with ln s00 observed by Shimakawa and Abdel-Wahab, we begin by assuming that electron hopping induced by optical phonons and the associated
1178
N. Mehta, A. Kumar / Vacuum 84 (2010) 1176–1179
Se 70 Te 24 Sb6
Se 70 Te 26 Sb4
5
R = 0.9986 0
2 ln σ 0
ln σ 0
2
R = 0.9999
3
2
-5
-10
1 0
-15
-1 0.2
0.3
0.4 0.5 Δ Eac (eV)
0.6
0.7
Se 70 Te 22 Sb8
6
R2 = 0.9999
4 2 0 -2 -4 -6 -8 0.26
0.54
Δ Eac (eV)
0.58
0.62
Se 70 Te 20 Sb10 2
R =1
ln σ 0
4
0.5
ln σ 0
2 0
-2 -4 0.4
0.44
0.48
0.52 Δ Eac (eV)
0.56
0.6
0.32
0.38
0.44 0.5 Δ Eac (eV)
0.56
0.62
Fig. 3. ln s0 versus DE plots for glassy Se70Te30xSbx (4 x 10) alloys.
variation in s00, must be due to variation in ln S. In fact, Emin’s model predicts that the hopping rate, and as a result, the conductivity, will be extremely sensitive to variation in ln S. The most complete expression for the hopping rate at low temperatures is presented by Emin [16]. If we limit our consideration to hops upward in energy, and use the present notation, this may be written as
2 exp J RðDEÞ ¼ es 2pu0 Z 1
"
N X
DE Zu0
ðAn Þ
DE EMN
exp DE ! Zu0
DE kT
lattice-relaxation phase shift. As can be easily seen the MN energy depends upon ln S, whereas the hopping rate depends upon the exp (S). Combining Eqs. (5) and (7) leads the prediction that
Zu0 lns00 ¼ r exp ; EMN
(8)
Here it has been assumed that ‘r’ is a constant. Using the data of
# DEfn cos Zu0
(7)
s00 and EMN, curves are plotted between s00 and EMN, and values of r and Zu0 are calculated for present case (see Figs. 4 and 5). The value of Zu0 for the present case is higher (102.6 meV) as compared to that are proposed by Yelon et al. The higher values of Zu0 in the
Where J is the electron transfer integral connecting the initial and final sites, An is a lattice-relaxation amplitude function and fn is the
present case may be due to a. c conduction in the present case, whereas Yelon et al. developed above theory without applying any audio frequency. The present results, therefore supports the model given by Yelon and Movaghar to explain the observation of MN rule between s00 and EMN for a.c conduction too.
Se70Te30-xSbx
Se70Te30-xSbx
pN
-16
2.98
-16.5
2.96 2.94
-17 ln (-ln σ00)
ln σoo
-18 -18.5
R2 = 0.9552
2.9 2.88 2.86
-19
2.84
-19.5
2.82
-20 0.0288
= 103.6 meV
2.92
R2 = 0.9595
-17.5
2.8
0.029
0.0292
0.0294
0.0296
0.0298
0.03
0.0302
EMN (eV) Fig. 4. ln s00 versus EMN plot for glassy Se70Te30xSbx (4 x 10) alloys.
33
33.2
33.4
33.6
33.8
34
34.2
34.4
34.6
34.8
(EMN)-1 (eV)-1 Fig. 5. ln(–ln s00) versus (EMN)1 plot for glassy Se70Te30xSbx (4 x 10) alloys.
N. Mehta, A. Kumar / Vacuum 84 (2010) 1176–1179
5. Conclusions Temperature dependence of a.c. conductivity is measured in bulk samples of glassy Se70Te30xSbx (4 x 10) alloys. Conductivity is found to be thermally activated at all the values of frequency. The results show that the values of s00 and EMN satisfy Further MNR. This is explained by the multi-excitation character of the processes suggested by Yelon and Movaghar for MNR in chalcogenide glasses. References [1] Meyer W, Neldel H. Z Tech Phys 1937;18:588. [2] Abtew TA, Zhang MingLiang, Pan Yue, Drabold DA. J Non-Cryst Sol 2008;354:2909. [3] Sharma SK, Sagar P, Gupta H, Kumar R, Mehra RM. Sol Stat Electron 2007;51:1124.
[4] [5] [6] [7] [8] [9] [10]
[11] [12] [13] [14] [15] [16] [17]
1179
Ram SK, Kumar S, Cabarrocas PR. J Non-Cryst Sol 2008;354:2263. Lubianiker Y, Balberg I. J Non-Cryst Sol 1998;227–230:180. Kondo M, Chida Y, Matsuda A. J Non-Cryst Sol 1996;198–200:178. Mehta N, Kumar D, Kumar A. Mat Lett 2007;61:3167. Meijer EJ, Matters M, Herwig PT, de Leeuw DM, Klapwijk TM. Appl Phys Lett 2000;76:3433. Widenhorn R, Mundermann L, Rest A, Bodegom E. J Appl Phys 2001;89:8179. Makarova T. Magnetism of carbon-based materials. In: Narlikar A, editor. Studies of High-Tc superconductivity, Vol. 44/45. New York: Nova Science Publishers; 2003. Mehta N, Kumar D, Kumar A. Philos Mag 2008;88:61. Kushwaha VS, Mehta N, Kushwaha N, Kumar A, Optoelectron J. Adv Mater 2005;7:2035. Mehta N, Kushwaha VS, Kumar A. Vacuum 2009;83:1169. Yelon A, Movaghar B. Phys Rev Lett 1990;65:618. Yelon A, Movaghar B, Branz HM. Phys Rev B 1992;46:12244. Emin D. Adv Phys 1975;24:305. Abdel-Wahab F. J Appl Phys 2002;91:265.