CHIN.PHYS.LETT.
Vol. 25, No. 11 (2008) 4079
Thermally Activated Photoconduction and Alternating-Current Conduction in Se75 Ge20 Ag5 Chalcogenide Glass: Investigation of Meyer–Neldel Rule R. S. Sharma1 , N. Mehta2 , A. Kumar1** 1
Department of Physics, Harcourt Butler Technological Institute, Kanpur, India 2 Department of Physics, Banaras Hindu University, Varanasi, India
(Received 10 March 2008) We report on the observation of Meyer–Neldel rule in glassy Se75 Ge20 Ag5 alloy where Δ𝐸 is varied by two different methods. In the first approach, the intensity of light varies while measuring the photoconductivity in amorphous thin films of Se75 Ge20 Ag5 instead of changing composition of the glassy system. In the second approach, the variation of ac conductivity with temperature is found to be exponential and the activation energy is found to vary with frequency.
PACS: 61. 43. Dq, 73. 50. Pz. In the case of thermally activated electrical conduction, the electrical conductivity 𝜎 obeys the Arrhenius equation 𝜎 = 𝜎0 exp
(︁ −∆𝐸 )︁ 𝑘𝑇
,
(1)
where ∆𝐸 is called the activation energy of the thermally activated electrical conduction and 𝜎0 is called the pre-exponential factor of the electrical conduction. In most of the semiconducting materials, 𝜎0 does not depend on ∆𝐸. However in some cases 𝜎0 correlates with the activation energy ∆𝐸 as[1] 𝜎0 = 𝜎00 exp
(︁ ∆𝐸 )︁ 𝑘𝑇0
,
(2)
where 𝜎00 and 𝑘𝑇0 are constants for a given class of materials; 𝜎00 is often called the Meyer–Neldel (MN) pre-exponential factor and 𝑘𝑇0 the MN characteristic energy. Equation (2) is often refereed to as the MN rule or the compensation rule. This rule holds in disordered materials when ∆𝐸 is varied by doping, by surface absorption, light soaking or by preparing films under different conditions.[2−8] This rule has also been observed for liquid semiconductors[9] and in fullerenes.[10] The validity of the MN rule has also been reported in the case of chalcogenide glasses.[11−16] However, in the case of these glasses this rule is observed by the variation of ∆𝐸 on changing the composition of the glassy alloys in a specific glassy system. Electrical conductivity in dark is measured as a function of temperature for this purpose. Another related problem is whether the conductivity pre-factor varies in a sample of particular glassy alloy, when the activation energy is a function of position, or the MN rule is not a local property but is apparently satisfied for the sample as a whole in the case ** To
of band bending. When one changes ∆𝐸 by changing composition in a particular glassy system, there are changes in the density of defect states and its distribution with energy due to compositional disorder. Since the distribution of density of defect states may be responsible [17] for the observation of the MN rule, it is desirable to look the MN rule in a sample, which is not affected by these complications. In our earlier communication,[18] we changed ∆𝐸 by varying electric field across a particular sample and verified the MN rule. In the presence of light, the Fermi level splits into quasi Fermi levels, the positions depend on intensity.[19] The activation energy of a particular glass composition can, therefore, be changed in the presence of light by varying the intensity of light. This has the advantage that the distribution of the density of defect states in the material remains unchanged with a change of the activation energy. Another method to change the value of ∆𝐸 has recently been developed by Abdel–Wahab during ac conductivity measurements in some chalcogenide glasses.[20,21] Several interesting models have been proposed to derive the MN rule; for example, Jackson[22] reported that whenever a multi-trapping transport process is observed over a fixed distance as a function of temperature, the MN rule should be followed. Crandall attributed the MN rule to the effect of disorder within the material.[6] The nature of electron transport in amorphous materials has been a subject of curiosity among scientists as well as engineers due to their potential use in semi-conducting devices. The common factor to all these materials is the existence of a large density of localized states with high activation energy. Chalcogenide glasses are an important class of amorphous semiconductors and, therefore, the studies on electrical conductivity of these glasses are important from
whom correspondence should be addressed. Email: dr ashok
[email protected] c 2008 Chinese Physical Society and IOP Publishing Ltd ○
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application point of view as well as from the point of investigation of localized states in the mobility gap of these materials. With the above viewpoint, we have measured the temperature dependence of conductivity at different intensities in amorphous thin films of Se75 Ge20 Ag5 alloy to investigate the MN rule in thermally activated photoconduction and ac conduction. Glassy alloy of Se75 Ge20 Ag5 is prepared by the well-known quenching technique and thin films of this glass are prepared by vacuum evaporation technique Thin films samples are mounted in a specially designed sample holder. The light is exposed on films through a transparent window. A vacuum of about 10−3 Torr is maintained throughout the measurements. Interference filters are used to obtain a desired wavelength. The present measurements have been made at a wavelength of 620 nm. The intensity of light is varied by changing the voltage across the lamp and measured by a lux-meter (Testron, model 146 LX-101). The current is measured by a digital Electrometer (Keithley, model 614). The heating rate was kept quite small (0.5 K/min) for these measurements. Before measurements, the films were first annealed below glass transition temperature 𝑇𝑔 for two hours in a vacuum of about 10−3 Torr. The 𝐼 −𝑉 characteristics are found to be linear and symmetric up to 30 V in all the glasses studied. The present measurements are, however, made by applying only 10 V across the films. For ac conductivity studies, glassy Se75 Ge20 Ag5 alloy was ground to a very fine powder. Pellets (diameter of about 6 mm and thickness of about 1 mm) were obtained by compressing the powder in a die at a load of five tons.
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by subtracting the dc conductivity from the total measured conductivity 𝜎𝑇 . Three terminal measurements were performed to avoid the stray capacitances. The temperature dependence of conductivity is studied in dark as well as in the presence of light at different intensities in glassy Se75 Ge20 Ag5 alloy. The temperature dependence of photoconductivity at various intensities (0, 7000, 9400 and 12000 lx) for a particular composition Se75 Ge20 Ag5 is shown in Fig. 1.
Fig. 1. Conductivity as a function of reciprocal temperature at different light intensities for glassy Se75 Ge20 Ag5 alloy.
Table 1. Semiconduction parameters of photoconduction for amorphous thin films of Se75 Ge20 Ag5 alloy. Intensity (Δ𝐸)ph ln(𝜎0 )ph ln(𝜎0 )𝑝ℎ = ln(𝜎00 )𝑝ℎ (Lux) (eV) (Ω−1 cm−1 ) +[(Δ𝐸)𝑝ℎ /𝑘𝑇0 ] (Ω−1 cm−1 ) 0 0.650 4.94 4.50 700 0.639 3.95 4.16 9400 0.519 0.90 0.60 1200 0.391 −3.05 −3.29
The pellets were mounted between two steel electrodes of a metallic sample holder for dc conductivity measurements using a digital electrometer (Keithly, model 614). The temperature measurement was facilitated by a copper-constantan thermocouple mounted very near to the sample. A vacuum of about 10−3 Torr was maintained over the entire temperature range. For calculating the ac conductivity, conductance and capacitance were measured using a GR 1620 AP capacitance measuring assembly. The parallel conductance was measured and ac conductivity was calculated. The experimental results for the temperature dependence of the ac conductivity 𝜎𝑎𝑐 (𝜔) are obtained
Fig. 2. Plot of ln(𝜎ph )0 vs activation energy Δ𝐸ph for glassy Se75 Ge20 Ag5 alloy.
The photoconductivity 𝜎ph varies exponentially with temperature as ln 𝜎ph vs 1000/𝑇 curves are straight lines (see Fig. 1). Such behaviour is consistent with Eq. (1). From the slopes and the intercepts of Fig. 1, the values of ∆𝐸ph and (𝜎ph )0 have been calculated and these values are given in Table 1 for different intensities. Figure 2 shows a plot of ln(𝜎ph )0 vs ∆𝐸ph , which is a straight line indicating that (𝜎ph )0 varies exponentially with ∆𝐸ph following Eq. (2). The slope of ln(𝜎ph )0 vs ∆𝐸𝑝ℎ yields the values of (𝑘𝑇0 )−1 and 𝜎00 for thin films of glassy Se75 Ge20 Ag5 alloy (see
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Table 2). Using these values of (𝑘𝑇0 )−1 and 𝜎00 , the expected (𝜎ph )0 values have been calculated for the above glassy alloy and compared with the reported values (see Table 1). An overall good agreement confirms the validity of the MN rule. Table 2. Values of (𝑘𝑇0 )−1 and ln(𝜎00 ) for photoconduction of amorphous thin films of Se75 Ge20 Ag5 alloy. (𝑘𝑇0 )−1 (eV)−1 29.5
ln(𝜎00 )ph (Ω−1 cm−1 ) −14.5
Various workers have provided different models or assumptions to explain the MN rule for such thermally activated phenomena.[22−25] The concluding remarks of their models or assumptions are given in the following.
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the present case. The temperature dependence of ac conductivity in glassy Se75 Ge20 Ag5 is studied at different audio frequencies. The results are shown in Fig. 3. It is clear from this figure that ln 𝜎𝑎𝑐 vs 1000/𝑇 plots are straight lines at different frequencies for glassy Se75 Ge20 Ag5 alloy. The above results show that the variation of ac conductivity with temperature can be expressed by an exponential relation, i.e. (︁ −∆𝐸 )︁ 𝑎𝑐 𝜎𝑎𝑐 = (𝜎𝑎𝑐 )0 exp , (3) 𝑘𝑇0 where ∆𝐸𝑎𝑐 is called the activation energy for ac conduction and (𝜎𝑎𝑐 )0 is called the pre-exponential factor. As is evident from Eq. (3), the pre-exponential factor (𝜎𝑎𝑐 )0 and ac activation energy ∆𝐸𝑎𝑐 can be obtained from the semi-logarithmic plots of the ac conductivity versus reciprocal temperature. Hence, the activation energy ∆𝐸𝑎𝑐 is determined from the slope of the approximate straight lines in the resulting plots at different frequencies (see Fig. 3). These straight lines are obtained by the best fit to the experimental data using the least squares method. The intercept of line gives the value of ln(𝜎𝑎𝑐 )0 . Table 3. Semiconduction parameters of ac conduction for amorphous bulk samples of Se75 Ge20 Ag5 alloy.
Fig. 3. Plots of ln 𝜎𝑎𝑐 vs 1000/𝑇 at different audio frequencies for glassy Se75 Ge20 Ag5 alloy.
Jackson[22] proposed that whenever a multitrapping transport process is observed over fixed distances as a function of temperature, the MN rule should be observed for this transport quantity. Others[13,23,24] speculated that the MN rule arises because of the entropy of multiple excitations. This approach is very general and can not be universal explanation for this rule.[25] Fortner et al.[9] proposed that the MN rule arises from hopping conductivity. Yelon and Movaghar[23] have proposed a model of multiphonon excitation to explain the MN rule in amorphous as well as crystalline materials. The model suggests that the optical phonons are the source of the excitation energy in such process. Density of states model[6,26,27] was given by Crandall and other authors according to which the MN rule is due to the effect of disorder within the material. The above-mentioned reports show that, till now, there is no universal explanation for the MN rule. In the present work, we can not also identify the exact origin but we have shown that the MN rule is more general in chalcogenide glasses and does not depend on the way how ∆𝐸 is changed. Also, the change in physical properties due to change in composition can be ruled out in
Frequency (Δ𝐸)𝑎𝑐 ln(𝜎0 )𝑎𝑐 ln(𝜎0 )𝑎𝑐 = ln(𝜎00 )𝑎𝑐 (kHz) (eV) (Ω−1 cm−1 ) +[(Δ𝐸)𝑎𝑐 /𝑘𝑇0 ] (Ω−1 cm−1 ) 1 0.212 −8.0 −8.1 2 0.117 −11.8 −11.6 5 0.086 −12.6 −12.7 10 0.075 −13.1 −13.1
Fig. 4. Plot of ln(𝜎𝑎𝑐 )0 vs activation energy Δ𝐸𝑎𝑐 for glassy Se75 Ge20 Ag5 alloy.
The values of ∆𝐸𝑎𝑐 and ln(𝜎𝑎𝑐 )0 are given in Table 3 for glassy Se75 Ge20 Ag5 alloy. Figure 4 shows the plots of ln(𝜎𝑎𝑐 )0 vs ∆𝐸𝑎𝑐 for the present glassy alloy, which is a straight line indicating that (𝜎𝑎𝑐 )0 varies exponentially with ∆𝐸𝑎𝑐 following the relation given by Eq. (2).
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The slope of ln(𝜎𝑎𝑐 )0 vs ∆𝐸𝑎𝑐 curve yields the values of (𝑘𝑇0 )−1 and ln 𝜎00 for the present glassy alloy (see Table 4). Using these values of (𝑘𝑇0 )−1 and ln 𝜎00 , the expected 𝑙𝑛(𝜎𝑎𝑐 )0 values have been calculated for the present glassy alloy and compared with the reported values (see Table 3). An overall good agreement confirms the validity of the MN rule in this case also. However, it is clear that from Tables 1 and 2 that the change in activation energy is more significant in the case of thermally activated photoconduction process as compared to thermally activated ac conduction. Table 4. Values of (𝑘𝑇0 )−1 and ln(𝜎00 ) for ac conduction of amorphous thin films of Se75 Ge20 Ag5 alloy. (𝑘𝑇0 )−1 (eV)−1 37.1
ln(𝜎00 )ac (Ω−1 cm−1 ) −15.9
In the correlated barrier hopping (CBH) model,[28,29] the electrons in charged defect states hop over the Coulombic barrier whose height W is given as (︁ 𝑛 𝑒2 )︁ , (4) 𝑊 = 𝑊𝑚 − 𝜋 𝜀 𝜀0 𝑟 where 𝑊𝑚 is the maximum barrier height, 𝜀 is the bulk dielectric constant, 𝜀0 is the permittivity of free space, 𝑟 is the distance between hopping sites, and 𝑛 is the number of electrons involved in a hop (𝑛 = 1 and 𝑛 = 2 for the single polaron and bipolaron processes, respectively). The relaxation time 𝜏 for the electrons to hop over a barrier of height 𝑊 is given by (︁ 𝑊 )︁ 𝜏 = 𝜏0 exp , (5) 𝑘𝑇 where 𝜏0 is a characteristic relaxation time which is of the order of an atomic vibrational period, and 𝑘 is the Boltzmann constant. Recently, a new approach has been suggested for the CBH model in the chalcogenide glasses.[20,21] It is reported in this approach that the relaxation time formula is activated, and it includes the MN rule term rather than its simple activated form. The chalcogenide glassy material during ac conduction can be considered as a medium consisting of network of resistors and capacitors.[26,30−33] If the local conductivity is thermally activated, and all capacitors are assumed to be equal, then Eq. (5) yields[26,30−33] (︁ −𝑊 )︁ (︁ 𝑊 )︁ exp . (6) 𝜏 = 𝜏0 exp 𝑘𝑇 𝑘𝑇0 This is exactly the same as the MN rule formula. In the present case also, the activation energy of ac conduction decreases with increase in frequency and it satisfies MN relation with pre-exponential factor. This may be due to compensation effect in relaxation
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time as suggested by Abdel-Wahab for some chalcogenide glasses.[20,21] We find that the thermally activated photoconduction is more effective method to change the activation energy with pre-exponential factor according to the MN rule. In the present study, the activation energy is varied by changing the intensity of light in the first case and by changing the audio frequency in the second case instead of changing the composition of the glassy alloy. The observation of the MN rule in the present cases indicates that this rule, which is generally applicable, can also be applied in a particular glassy alloy without changing its composition when we change the density or distribution of defect states of a glassy system by changing the composition.
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