1 Introduction

Chalcogenide glasses are one of the most widely known families of glasses, and great attention has been given to them over the past few decades because of their interesting properties and wide applications. Among all the amorphous chalcogenide alloys, mostly selenium (Se)-based materials are preferred due to its commercial and technological importance. Amorphous selenium has various device applications such as rectifiers, photocells, xerography, switching and memory which make it attractive, but pure Se has disadvantages like short life time and low sensitivity. This problem can be overcome by alloying Se with some impurity atoms such as Ge and Te which gives high sensitivity, greater hardness, high crystallization temperature and small aging effects as compared to pure Se glass [1, 2].

Generally, undoped chalcogenide glasses show low values of electrical conductivity; therefore, certain additives are used to improve their properties. It was believed earlier that impurities have little effect on the properties of amorphous semiconductors as each impurity atom can satisfy its valance requirement by adjusting its nearest neighbor environment [3]. The addition of third element acts as a chemical modifier which expands the glass-forming region and also creates the compositional and configurational disorder in the material which will be helpful in understanding the structural and electrical properties of chalcogenide glasses [4–6].

Structural studies of these glasses are very important for better understanding of transport mechanism. The study of dielectric properties of chalcogenide glasses is predictable to reveal structural information, which, in fact, can be useful for the understanding of conduction mechanism in these materials. In addition, study of temperature and frequency dependence of dielectric parameters, particularly in the high frequency range where dielectric dispersion can be of very much importance for the understanding of the nature as well as the origin of the various losses happening in the materials [2, 6].

In the present work, we have reported and discussed the effect of addition of Sb content on the Se–Te binary alloy in details. The aim of this work is to analyze the frequency and temperature dependence of AC conductivity, dielectric constant and dielectric loss for the amorphous Se80−x Te20Sb x (x = 1, 2, 4, 6 and 10) chalcogenide alloys.

2 Experimental details

The bulk samples of chalcogenide Se80−x Te20Sb x (x = 1, 2, 4, 6 and 10) glassy alloys have been prepared using the melt quenching technique. 5N pure materials are weighed according to their atomic percentages and sealed in a quartz ampoule (length ~5 cm, diameter ~12 mm) under a vacuum of 10−5 Torr. The sealed ampoules were kept inside a furnace where the temperature is raised to 1000 °C at a rate of 3–4 °C/min. The ampoules are rocked frequently for 10 h at maximum temperature to make the melt homogenous. The quenching is done in the ice-cooled water very rapidly to prevent crystallization. The amorphous nature of glassy alloys has been verified by X-ray diffraction. The absence of any prominent peak in X-ray diffraction pattern indicates amorphous nature of the investigated samples.

The glassy alloys thus prepared are ground to a very fine powder, and pellets (diameter ~10 mm and thickness ~1 mm) are obtained by compressing the powder in a die at a load of 5 tons. The pellets are coated with silver paste to assure good electrical contact between the sample and electrode. The parallel capacitance and dissipation factor are measured using the impedance analyzer (Wayne Kerr 6500B).

3 Results and discussion

3.1 Frequency and temperature dependence of dielectric constant

Dielectric analysis may be used to determine the capacitive nature of the material. Frequency dependence of dielectric constant is measured at room temperature in the frequency range from 20 Hz to 1 MHz for various glassy alloys Se80−x Te20Sb x (x = 1, 2, 4, 6 and 10) studied in the present case. The value of dielectric constant is calculated using the relation ε′ = Cd/ε 0 , where C is the parallel capacitance of the pellet, A is the area of the pellet, d is the thickness of pellet, and ε 0 is the permittivity of free space. The variation of dielectric constant with frequency at room temperature is shown in Fig. 1. It is clear from the figure that dielectric constant decreases with frequency. The decrease is fast at low frequency as compared to higher frequencies. This is due to the electrode polarization effects [7, 8]. The decrease in ε′ at low frequencies is explained by the contribution of multi-component of polarization electronic, ionic, dipolar and space charge [9]. The total polarization is the sum of these four polarizations [10]:

$$P = P_{e} + P_{i} + P_{d} + P_{s}$$
(1)
Fig. 1
figure 1

Frequency dependence of dielectric constant in Se80−x Te20Sb x (x = 1, 2, 4, 6, 10) glassy alloys

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First, electronic polarization occurs at frequencies up to 1016 Hz. Second, ionic polarization occurs due to the displacement of negative and positive ions with respect to each other and this polarization occurs at 1013 Hz. Third, dipolar polarization takes place due to the presence of molecules with permanent electrical dipole moments that can change its direction of rotation into that of the applied electric field and this polarization occurs up to about 1010 Hz. Last, space charge polarization occurs at frequencies ranging between 1 and 103 Hz and it takes place due to impedance mobile charge carriers by interfaces.

Dielectric material exhibits at least one of these polarization types. This depends upon the structure and bonding of the material and the frequency [11]. When the applied field frequency is increased, the dipoles will no longer be able to rotate sufficiently rapidly, so that their oscillations begin to lag behind those of the field. As the frequency is further raised, the dipoles will be completely unable to follow the field and orientation polarization stopped, so ε′ decreases approaching a constant value at a higher frequency due to space charge polarization [12].

The temperature dependence of dielectric constant is measured in various frequency ranges from 10 kHz to 1 MHz and temperature ranges from 350 to 500 K for various glassy alloys studied in the present case. The values of dielectric constant increase with the increase in temperature, and the increase in temperature is being different at different frequencies. This behavior has been reported by various researchers in chalcogenide glasses [13]. This behavior can be attributed to the fact that orientational polarization is associated with the thermal motion of molecules. The orientation of the molecules of dipoles increases as the thermal energy increases, leading to the increase in dielectric constant. Temperature dependence of dielectric constant for Se78Te20Sb2 is shown in Fig. 2.

Fig. 2
figure 2

Temperature dependence of dielectric constant in Se78Te20Sb2 glassy alloys

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3.2 Temperature and frequency dependence of dielectric loss

The imaginary part of dielectric constant, i.e., dielectric loss, is given by:

$$\varepsilon^{\prime\prime} = \varepsilon^{{_{\prime } }} \tan \delta$$
(2)

The tan δ is equivalent to the dissipation factor D which is taken from impedance analyzer. The variation of dielectric loss with temperature is plotted in Fig. 3. The figure shows clearly that the dielectric loss increases with the increase in temperature. At low temperatures, conduction, dipole and vibration losses have minimum value, whereas, at higher temperatures, all these losses contribute to the dielectric loss.

Fig. 3
figure 3

Temperature dependence of dielectric loss at various frequencies for Se78Te20Sb2

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In Se80−x Te20Sb x (x = 1, 2, 4, 6 and 10) glassy alloys, dielectric loss obeys the power law with angular frequency given by [14]:

$$\varepsilon^{\prime\prime} = \, Bw^{m}$$
(3)

where B is a constant. The value of m is calculated from the slope of the graph between ln(ω) and ln(ε″). The values of m obtained are given in Table 1 and found to be negative which is consistent with the earlier values of m obtained for other chalcogenide glasses [15]. Figure 4 shows the frequency dependence of dielectric loss at room temperature.

Table 1 Values of frequency exponent (s) and maximum barrier height (W m ) and (m) for various glassy alloys
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Fig. 4
figure 4

Frequency dependence of dielectric loss at room temperature for Se80-x Te20Sb x

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It is clear from the figure that dielectric loss decreases with frequency. This decrease is due to the migration of ions. Accordingly, ε″ at low and moderate frequencies is characterized by its high value due to the conduction losses of ion jump, ion migration and ion polarization, whereas at higher frequencies ion vibrations may be the only source of dielectric loss, so dielectric loss decreases and becomes constant. According to Guintini’s equation [16] based on Elliott’s model [17], the dielectric loss ε″ at a particular frequency is given by:

$$\varepsilon^{\prime\prime} = (\varepsilon_{0} - \varepsilon_{\infty } ){\kern 1pt} 2\pi r^{2} \left( {n{\text{e}}^{2} /\varepsilon_{0} } \right)^{3} kT\tau_{0}^{m} W_{m}^{ - 4} w^{m}$$
(4)

where

$$m \, = - 4KT/W_{m}$$
(5)

where W m is the maximum barrier height. Values of W m are given in Table 1. The obtained values of W m are in accordance with the theory of hopping of charge carriers over potential barrier in case of chalcogenide glasses [18, 19].

3.3 Temperature dependence of AC conductivity

A measurement of AC conductivity of amorphous semiconductors is used to understand the conduction process in these materials [22]. The AC conductivity exhibits universal behavior common to dielectric which is disordered [20]. The AC conductivity shows a temperature dependence for the studied Se80−x Te20Sb x (x = 1, 2, 4, 6 and 10) glassy system at different frequencies. Figure 5 shows the plot of ln σ ac(ω) versus 1000/T for the investigated glassy alloys. It is clear from the figure that AC conductivity increases with the increase in temperature and shows that AC conductivity is a thermally activated process. The AC conductivity is found to obey the relation:

Fig. 5
figure 5

Temperature dependence of AC conductivity for Se78Te20Sb2 glassy alloy

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$$\sigma_{\text{ac}} (\omega ) \, = \sigma_{0} \exp \left[ { -\Delta E/k_{B} T} \right]$$
(6)

The activation energy is calculated from the slope of the plot ln[σ ac(ω)] versus 1000/T. The AC activation energy decreases with the increase in frequency as is found for other amorphous materials [21]. The increase in frequency of the applied field enhances the charge carrier’s jump between the localized states, and hence, the AC activation energy decreases (Fig. 6) [16].

Fig. 6
figure 6

Composition dependence of activation energy in Se80−x Te20Sb x (x = 1, 2, 4, 6, 10) glassy alloys

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3.4 Frequency dependence of AC conductivity

The frequency dependence of AC conductivity in semiconductors and other disordered systems is due to conduction in localized states. The AC conductivity of the investigated system has been calculated from the data of dielectric constant ε′(ω) and loss factor tan δ using the following relation:

$$\sigma_{\text{ac}} = \varepsilon^{{\prime }} \varepsilon_{0} \omega \tan \delta$$
(7)

For amorphous semiconductors AC conductivity σ ac(ω) changes with frequency according to the following relation [16]:

$$\sigma_{\text{ac}} = A_{o} \omega^{s}$$
(8)

where A o is a constant dependent on temperature, ω is the angular frequency, and the exponent s denotes the frequency dependence of σ ac(ω), and it is generally less than or equal to unity. Figure 7 shows the frequency dependence of σ ac(ω) at room temperature for all the investigated compositions. According to Eq. (8), the plot between ln(σ ac) and ln(ω) should be straight line. The exponent s is calculated from the slope of the curve plotted in Fig. 8.

Fig. 7
figure 7

Frequency dependence of AC conductivity in Se80−x Te20Sb x (x = 1, 2, 4, 6, 10) glassy alloys

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Fig. 8
figure 8

The plot between ln(σ ac) and ln(ω) for Se80−x Te20Sb x (x = 1, 2, 4, 6, 10) glassy alloys

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The obtained values of s are listed in Table 1 for the investigated alloys. The value of AC conductivity is found to increase with increasing frequency. The increase in the value of AC conductivity with frequency is due to relaxation caused by the motion of electrons or atoms. Such motion can involve hopping or tunneling between equilibrium sites. Actually, increase in the frequency of the applied field enhances the charge carriers to jump between the localized states and activation energy decreases. Hence, AC conductivity ln(σ ac) increases with increasing the ln(ω) frequency. The frequency dependence of AC conductivity can be explained on the basis of correlated barrier hopping (CBH) [16, 22].

4 Conclusions

Dielectric properties and AC conductivity measurements have been made for Se80−x Te20Sb x (x = 1, 2, 4, 6 and 10) glassy alloys at different frequencies and temperature. Dielectric constant and dielectric loss are found to decrease with frequency at room temperature in the investigated system, whereas dielectric loss is found to increase with temperature. However, AC conductivity is found to increase with the increase in temperature for the studied alloys. The frequency dependence of AC conductivity can be explained on the basis of CBH model. The results of the dielectric constant and dielectric loss measurements show that Guintini’s theory of dielectric dispersion of two electrons hopping over a potential barrier is applicable in the present case.