Electrical properties of amorphous Ge26InxSe74-x chalcogenide thin films

Amorphous Ge26InxSe74-x (1 ≤ × ≤ 5) chalcogenide thin films have been deposited by thermal evaporation technique. The temperature-dependence of DC conductivity and the temperature and frequency dependence of AC conductivity have been studied in the temperature range 295–523 K and in the frequency range 4–8 MHz. The study of the temperature-dependent of DC conductivity refers to the presence of two distinct conduction mechanisms; the activation energies for each were calculated and it was observed that their values decrease by increasing In content. Besides, in the low-temperature region, the variation of the conductivity against temperature was further analyzed according to the variable-range hopping model based on Mott’s relation, whereby the hopping parameters were evaluated. For all investigated compositions, the variation of the AC conductivity against frequency at the studied temperatures was interpreted according to the correlated barrier hopping (CBH) model which based on Jonscher’s power law, whereby the potential barrier height, WM, and the theoretical optical bandgap, Eg, were calculated.


Introduction
Thin films of chalcogenide glassy materials gained great interest over the past several decades due to their applications in potential in several technological devices. The common feature of this class of glassy materials is the presence of the localized states in the mobility edge as a result of the presence of the short-range order as well as the various inherent defects [1][2][3]. Previous works have been established that the physical properties of the chalcogenide glassy materials are highly dependent on the atomic ratios of the elements present in the chemical formula [4,5].
The Ge-In-Se ternary system belongs to the chalcogenide glassy materials. Where it forms glasses through average compositions of a range extending from a coordination number Z = 2.4 to Z = 2.67 which are considered critical values according to Philips [6]. The system possesses interesting physical properties, such as high infrared transmission spectra, high refractive index, and fast characterization, which make the system attractive for many technological applications, such as IR detector [7], telecommunications [8], acousto-optic devices [9], switching and memory devices [10]. The thermal stability of the thermally evaporated Ge 15 Se 85-x ln x deposited films increases with increasing the In content [11], while the amorphous to the crystalline state of Se 70 In 15 Ge 15 has occurred at 413 K [12]. The optical properties of the ternary system Ge 30 Se 70−x In x [13], Ge x Se 92-x In 8 [14], Ge 20 Se 80−x In x [15], Ge 10 Se 90−x In x [16], and Ge 26 In x Se 74-x [17] have been reported. In addition, the DC electrical conductivity of Ge 20 In 5 Se 74 [18], Ge 20 Se 80-x In x [19][20][21], Ge 40-x In x Se 60 [22], and Se 70 In 15 Ge 15 [12] has been reported, while there are only two reports concerning the AC conductivity and dielectric properties of the ternary Ge-In-Se system. The first reports the frequency and temperature dependence of the dielectric properties of Se 90 Ge 10-x In x thin films at Low Temperature (78-260 K) [23], while the other reports the AC conductivity and dielectric properties of Ge 20 Se 75 In 5 films (300-423 K) [24].
In the previous work, the authors have studied the linear and non-linear optical properties of the amorphous 3 Results and discussion

DC conductivity
The temperature-dependence of DC conductivity of the investigated samples with exact chemical compositions (a) Ge 26 . 6 Fig. 1. The figure depicts that the conductivity increases with increasing temperature through the entire temperature range indicating a semiconductor behavior, with two different conduction mechanisms. The first is in the high-temperature range (T > 380 K) that can be represented through the thermally activated process across the extended states. While the other is in the low-temperature range (at T < 380 K) that can be represented through a less thermally activated process and represented by Mott's formula for the hopping conduction through the localized states. The variation of the conductivity through the extended states follow the Arrhenius relation [20,25]: where σ o is the pre-exponential factor, ∆E DC is the activation energy and K is the Boltzman's constant. The values of the pre-exponential factor, σ 0 , the activation energy, ∆E DC , and the room temperature conductivity, σ RT , for such regions as a function of In content which is calculated from Fig. 1 are listed in Table 1. It is noticed that, by increasing the In content, the conductivity increases, while the activation energy decreases. This decrease in ∆E DC is due to the reduction of average binding energy and formation of defect centers by adding In [19,26,27]. On the other hand, the value of ∆E DC was found less than the half value of the optical bandgap calculated in our previous work [17] for the samples of the same composition, which indicates the presence of impurities within the gap. Therefore, the value of ∆E DC in the present work indicates that the Fermi level is most probably displaced from the center of the gap towards the valence band [12,16]. The calculated values of ∆E DC of investigated films are in agreement with other works, as shown in Table 1.

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The measured conductivity is the sum of two components: where σ hop and σ ext, are the conduction contribution due to hopping between the nearest localized states and the conduction contribution between the extended states, respectively. In the high-temperature region, the linearity denoted that σ DC is a thermally activated process [27] according to Eq. 1. As the temperature decreases, the activated Arrhenius behavior is replaced by a power law relationship between the logarithm of conductivity and temperature. The low-temperature variable range hopping conductivity is characterized by Mott's variable-range hopping relation [14,25,28]: where T 0 is the hopping parameter that is given as where σ ho is the pre-exponential factor of the hopping conduction, N (E F ) is the density of states at the Fermi level, α −1 is the decay length of a localized wave function at the Fermi level which is taken as 10 −9 m for electrons and K is the Boltzman's constant.
The linear variation of σ hop √T vs. (1/T) 1/4 as shown in Fig. 2 confirms that in this region the transport is due to variable range hopping of charge carriers in the localized states near the Fermi level and is characterized by relation (3). The values of T 0 , σ h0 as well as the density of states at the Fermi level N(E F ) determined from Fig. 2 are listed in Table 2.
Two other hopping parameters can be calculated according to Mott [28,29], which are the hopping distance R (cm) and the average hopping energy W (eV), given by and The calculated values of R and W for the investigated compositions are also listed in Table 2. It is observed that both values of R and W decrease by increasing In content. In addition, W · KT and αR · 1 indicate that the variation of conductivity at a low temperature of the investigated samples obey the condition of Mott's model of variable-range hopping (VRH) process [25,28,30].on the other hand, the value of N(E F ) increases by adding In and this confirms the increase of conductivity due to the increase of localized states in the gap. The determined values of R, W, and N(E F ) for Ge 26 In 5 Se 69 are in agreement with those reported for Ge 20 In 8 Se 72 [14].

AC conductivity a) Frequency dependence of AC conductivity
The measurements of the AC conductivity provide significant information about the conduction mechanism of glassy systems. The real part of AC conductivity is due to trapped  where σ DC is the DC conductivity, A is a temperaturedependent constant that determines the strength of the polarizability and S is the frequency exponent that 0 < s < 1. Figure 3 shows the frequency dependence of AC conductivity for the investigated Ge 26 In x Se 74-x films compositions at room temperature. It is observed that for all compositions, there are two distinct regions; the low-frequency region, where the conductivity is frequency independent and attributed to the DC conductivity resulting from the effect of the electrode polarization, followed by the dispersion region at which the conductivity increases rapidly at high frequencies obeys the power-law relation [33,34]. This increment of the AC conductivity is attributed to the hopping or tunneling of charge carriers as the applied electric field frequency increases [35]. In addition, the AC conductivity increases by increasing In content. This is due to the formation of localized states in the band tail whose density increases by increasing In content and hence increases conductivity [36]. Figure 4 shows the frequency dependence of AC conductivity for Ge 26 In x Se 74-x thin films at different temperatures. It is found that the conductivity increases by increasing (7) � AC ( ) = DC + AC ( ) = DC + A S frequency according to Eq. 7. In addition, the conductivity increases by increasing temperature for all investigated samples due to thermally activated polaron hopping [37]. The values of the frequency exponent S for different compositions and temperatures are calculated from the slopes of the linear part in Fig. 4. Figure 5 represents the temperature dependence of the frequency exponent S for Ge 26 In x Se 74-x thin films. It is clear that the value of S decreases as the temperature increases for all compositions. It is also clear that S decreases with the increase of the In content in the investigated compositions. This means that the obtained experimental results can be interpreted according to the correlated barrier hopping CBH model [38,39].
In the CBH model, it is proposed that electrons transfer over a barrier between two defect sites by thermal activation, where each site has a coulombic potential well associated with it. For two adjacent sites separated by distance R, the coulomb wells overlap and hence the effective barrier W M will reduce to W which is given by [38,39] where W M is the maximum potential barrier height, e is the electronic charge, ε' is the real part of dielectric constant, ε 0 is the permittivity of the free space and n is the number of electrons that hop science n = 1 or 2 for a single polaron and bipolaron processes, respectively. The frequency exponent S according to this model obeys the relation [36,40]: where k B is the Boltzman constant, T is the absolute temperature and τ 0 is the characteristic relaxation time. At lower temperatures, W M > > > K B Tln(ωτ 0 ) hence the value of S is approximately given by [36]: For the case of single polaron hopping, the value of W M is typically one-quarter of optical bandgap E g, while W M is equal to E g for bipolaron hopping [41]. The values of  compositions are compatible with those determined experimentally in the earlier work [17].

b) Temperature dependence of AC conductivity
The AC conductivity exhibits temperature-dependence and obeys the relation: where ΔE AC is the activation energy for the AC conductivity. Figure 6 shows the plot between lnσ AC (ω) and 1000/T which shows semiconductor behavior as the AC conductivity increases by increasing temperature for all compositions. In addition, the AC conductivity shows the same behavior as the DC conductivity that increases by increasing In content. This is owing to the short-range order of the investigated samples as well as the formation of defects which increases the density of localized states in the band tail [43]. In other words, the formation of the hetero-polar In-Se bond at the expense of the homo-polar Se-Se bond causes the reduction of band energy and consequently, increases the AC conductivity [44,45]. In addition, there are two slopes for all compositions in the frequency range 10 Hz-10 3 Hz, while there is one slope at higher frequencies. From the slope of the straight line, AC activation energy ΔE AC can be calculated. Table 4 demonstrates the values of ΔE AC for Ge 26 In x Se 74-x at different frequencies. It is noticed that the values of ΔE AC decrease by increasing frequency for all investigated samples. This decrease may be due to the increase of the applied electric field that enhances the electronic jump between the localized states [46,47] and the small value of ΔE AC confirms that hopping conduction is the dominant mechanism [48]. In addition, the value of ΔE AC is lower than that of ΔE DC for all compositions. This is due to the charge carriers The variation of the DC conductivity in the temperature range 295-523 K exhibits a semiconductor behavior in the entire temperature range with two conduction mechanisms. The first was observed in the high-temperature range (T > 380 K), where the conduction is due to the thermally activated process through the extended states with single activation energy. The corresponding electrical parameters (activation energy, ΔE, and pre-exponential factors, σ o ) of the Arrhenius relation were calculated for each composition and found that the activation energy decreases from 0.709 to 0.466 eV by increasing In content. While the second is in the low-temperature range (T < 380 K), where the conduction is due to be less thermally activated and can be represented by the hopping conduction through the localized states according to the Mott variable range hopping model. The density of the localized states and the hopping parameter were calculated.
The AC conductivity, measured in the temperature range 295-523 K and over the frequency range 4-8 MHz, reveals that the conductivity in the dispersion region follows the Jonscher's power-law, σ(ω)α ω s . In addition, the value of the exponent s decreases with increasing temperature as well as with increasing In content. So, the results were interpreted according to the correlated barrier hopping CBH model. The potential barrier height, W M , and the theoretical optical bandgap, E g , at room temperature for the investigated compositions were evaluated. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.