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Study of dielectric relaxation and thermally activated a.c. conduction in multicomponent Ge10−xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses using CBH model
Accepted Manuscript Study of dielectric relaxation and thermally activated a.c. conduction in multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses using CBH model Pravin Kumar Singh, S.K. Sharma, S.K. Tripathi, D.K. Dwivedi PII: DOI: Reference:
S2211-3797(18)32452-5 https://doi.org/10.1016/j.rinp.2018.11.048 RINP 1817
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
12 October 2018 15 November 2018 15 November 2018
Please cite this article as: Singh, P.K., Sharma, S.K., Tripathi, S.K., Dwivedi, D.K., Study of dielectric relaxation and thermally activated a.c. conduction in multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses using CBH model, Results in Physics (2018), doi: https://doi.org/10.1016/j.rinp.2018.11.048
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Study of dielectric relaxation and thermally activated a.c. conduction in multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses using CBH model Pravin Kumar Singh1, S. K. Sharma2, S.K. Tripathi3, D. K. Dwivedi1* 1 Amorphous Semiconductor Researcher Lab Department of Applied Sciences, M. M. M. University of Technology, Gorakhpur-273010 (India) 2 Department of Physics, Harcourt Butler Technical University, Kanpur-208002(India) 3 Department of Physics, Punjab University, Chandigarh, India *E.mail: [email protected] Ph: 09415712163 Abstract Amorphous Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses were prepared by melt quench technique. Surface morphology with the chemical composition of the prepared glass was examined using SEM and EDS analysis respectively. Dielectric properties and a.c. conductivity of the multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses have been examined in the frequency range 100Hz to 1MHz and temperature range 303 to 328K. It was noticed that dielectric constant and dielectric loss decreases with the increase of frequency and increases with the increase of temperatures. Frequency and temperature dependence of dielectric constant was explained by orientational polarization. The variation of dielectric loss with frequency and temperature was explained by conduction loss and theory of single polaron hopping of charge carriers suggested by Elliot and Shimakawa for chalcogenide glasses. The experimental results show that a.c. conductivity follows the power law
where s<1 and value of s decreases with
the increase of temperature. The present findings of a.c. conductivity and variation of s with temperatures are reasonably well interpreted in terms of CBH model.
Keywords: Chalcogenide glasses, a c conductivity, dielectric relaxation, CBH model, activation energy.
1. Introduction Nowadays new phenomena, new materials, and many advanced technologies are used for the scientific and technical advancement. The science of glasses is developed gradually to cater above needs. Glasses are the most common ancient natural vitreous solid that can be prepared artificially for the fundamental research and application point of view[1-3]. The heart of present electronic devices is the components made by silicon. The optimization and improvisation of silicon-based devices are of great advantage regarding the requirement of power for processing, the threshold in design complexity, dissipation of heat and memory through sinks, energy consumption etc. This has led to a quest for new materials. One of such fields of materials is chalcogenide glasses which exhibit attractive properties and have applications in different domains[4-8]. Chalcogenide glasses are amorphous semiconductor which is
applicable in many
electronic, and optoelectronic devices like rewritable optical recording[9-10], solar energy conversion[11-13], optical mass memories[14], holography[15], infrared detectors[16], holographic data storage and programmable metallization cell (PMC) memory[17], optical fibers[18] and ultrasonic delay lines[19]. The wide range of applications of these glasses is available because of some unique property like photodarkening or bleaching[20], photo-induced structural transformation[21] etc. An amorphous semiconductor (especially, chalcogenide glasses) has received a great attention of many researchers towards it due to the existence of localized state between conduction band valence band. Recently these glasses are widely used in military areas, civil and medical such as determining inorganic pollutants in river water, monitoring corrosion process and control of food stuff[22]. Infrared chalcogenide fibers are
utilized for the infrared fingerprints of human lung cells in various metabolic conditions and biosensing like tumor detection, serum analysis, liver metabolism [21-27]. Selenium-based compounds are extremely important because of its ongoing development in different solid state devices. Recent studies show that selenium-rich compound is very useful as compared to pure selenium. The mixing of doping elements like Te, Ga, Bi, Sb, Pb and As with disordered selenium has a noticeable effect on change in structure & conduction mechanism and it also provides the smaller aging effect, higher photosensitivity and crystallization temperature[28-32]. Tellurium is used as a doping element in pure Se to minimize its drawbacks. The Se-Te glassy alloys are a commercial product and have technological and scientific importance. The drawback of such binary alloy is its thermal instability leading to crystallization, so a third element Ge has been added to enhance the thermal stability of Se-Te binary alloys. From literature survey, we have found that different ternary glasses consists of indium as a modifier while to the best of author’s knowledge no study has as yet been reported on the synthesis and characterization of indium-doped quaternary glass which may enlarge the utility of these glasses. The addition of indium as a fourth element generates compositional and configurational disorder in the system, also, it enhances the glass-forming region[33-35]. In past few decades, an increasing interest has been observed to examine the dielectric relaxation and ac conductivity of chalcogenide glassy system for both academic and application point of view. These glassy alloys show higher ionic conductivity than their oxide counterparts because of its high polarizability. The insulating and conductive behavior of the materials can be described by dielectric analysis. The ability to store an electric charge is known as insulating behavior while the ability to transfer the charge is known as the conductive behavior of the
materials. Measurement of ac conductivity gives a basic approach to explain the defect centers along with the behavior of conduction mechanism existing in chalcogenide glasses. To study the conduction mechanism in chalcogenide glasses different models have been suggested like quantum mechanical tunneling (QMT) [36] model, overlapping large polaron tunneling (OLPT) [37] model, non-overlapping small polaron tunneling (NSPT)[38] model and correlated barrier hopping (CBH) [39,40] model. CBH model has extensively applied the model in chalcogenide glassy semiconductors. In this paper frequency and temperature dependence of dielectric constant, dielectric loss and ac conductivity have been measured and examined to investigate the dielectric properties and conduction process for multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glass.
2. Experimental details 2.1.Material Synthesis The bulk glassy alloys of Ge10-xSe60Te30Inx (x=0, 2, 4 & 6) was developed by a wellknown melt quench techniques. A simple step for material preparation is material crushing, weighing, ampoule sealing, heating and rocking then rapid cooling as shown in figure 1. The powder of high purity (99.999%) elements of Germanium(Ge), Selenium(Se), Tellurium(Te) and Indium(In) were weighed in order of their stoichiometric ratio using an electronic balance(LIBROR, AGE-120, least count=10-4gm ). The prepared sample was put in quartz ampoule (internal diameter=8cm, length=5cm) and squeezing it in the tube of a high vacuum unit to remove the air from the sample. The quartz ampoule containing mixture was then sealed under a high vacuum (10−5 mbars) using High Vacuum Unit (Vacuum Tech. Pvt. Ltd. Banglore, Model No: VT-ACG- 03, 2013). Evacuated
quartz ampoules (with the sample in it) were sealed by LPG-Oxygen flame. Sealed ampoules having constituent elements were hooked up in the ceramic rod with the help of nichrome wire and placed in a muffle furnace. The temperature of the furnace was increased steadily up to 800oC with constant steps of about 20 K/15 min and retained this temperature for 14h. Intermittently rocking of ampoule was done by gyrating the ceramic rod. A constant mechanical shaking was done in the muffle furnace to get a homogeneous sample. To find glassy samples the ampoules were quenched in icy water after 14 hours. After that, a very fine powder was obtained by grinding the prepared sample using a mortar. 2.2. Characterization The XRD pattern of the prepared glassy alloys was recorded by X-ray diffractometer(XPERT-PRO Cu-Kα radiation λ=1.54Ǻ). The tube was maintained at 45kV and 40mA. The XRD patterns of Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses are shown in figure 2. From XRD patterns it is found that there are no sharp structural peaks which confirms the amorphous nature of the sample. Surface morphology has been done by JEOL Field Emission Scanning Microscopy (Model/Supplier: JSM-7100F). The magnification was 2000x.
Energy dispersive X-ray
spectroscopy (EDS) analysis of prepared sample has been done to check the elemental composition of Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) bulk glassy alloys. To investigate the dielectric measurements a digital LCR meter (Wayne Kerr Electronics, Model: 43100) was used. Fine powders of the prepared sample were compressed into cylindrical pellets (diameter = 8mm and thickness = 1.3mm) by an applied load of 5tons using a hydraulic press to investigate the dielectric relaxation and a.c. conductivity. A copper-constantan thermocouple placed extremely close to the sample is used for measuring the temperature range
303K-328K. During entire temperature range (303-323K) vacuum of 10-3 torr was kept constant. The parallel capacitance (C), dissipation factor (tan (δ)) and impedance (Z) were estimated directly in the frequency span 100kHz-1MHz for the studied samples. Where and
denotes the phase angle. The parallel capacitance C and dissipation factor tan (δ)
were used to evaluate the dielectric constant
and dielectric loss
.
The a.c. conductivity of the material was evaluated by the relation , where f represents frequency. 3. Theoretical basis Giuntini et al [41] offered a suitable model to describe the dielectric relaxation in chalcogenide glass. Mott et al [5]. assumptions were the basis of this model; they proposed that electron hop between localized states within the sight of the electric field. In these states, the moving charge carriers hop from donor to an acceptor state. So every pair creates a dipole and a set of dipoles are used to explain the dielectric behavior of chalcogenide glasses with temperature. This model suggests that the relaxation time of each dipole depends on activation energy[42], further it can refer to the existence of potential barrier over which the carrier hop. The dielectric loss in terms of frequency and temperature according to Giuntini theory can be indicated by the relation [41] (1) where the static dielectric constant is
, a number of hopping electron is n, localized state
density is N, dielectric constant at high frequency is
, angular frequency is ω and maximum
barrier height is Wm. At a particular temperature, the dielectric loss equation 1.
obeys the power law according to
(2) Where the frequency exponent of dielectric loss m can be shown by the relation m= -4kT/ Wm
(3)
The value of m can be obtained by taking slope between log
versus logω.
The percentage of covalent character is obtained by Pauling relation[43] Percentage covalent character Where the electronegativity of atom A and B are
(4) and
respectively
In amorphous semiconductor a.c. conductivity has been determined through pair approximation as suggested in CBH model. Since localized state are supposed to be randomly distributed in space, therefore pairs may have different relaxation time. It has been proposed that localized states are randomly distributed and electrons move back and forth through a rigorous relaxation time between a pair of two localized states. The total a.c. conductivity of the material is the sum of all pair’s contributions. In amorphous materials and ceramic glasses, many authors have reported that ac conductivity obey the following relation[44] σac(ω) = Aωs
(5)
where s denotes frequency exponent and angular frequency is ω. The frequency exponent s in CBH model is expressed as follows
(6)
Where relaxation time is
represents the Boltzmann constant, absolute temperature is T, the characteristic . The vibrational period of an atom (
) is the approximate value of
. Maximum barrier height at infinite intersite separation is Wm which is known as binding energy of the carrier in its localized sites[44,45]. When
is large above equation can be rewritten as (7)
The value of
can be calculated by taking the slope of 1-s against T plot.
The electron relaxation time
hop over a maximum barrier height
can be
calculated at various temperatures by a well-known relation (8) Where characteristic relaxation time is
and has the value in the order of atomic vibrational
period. The relation between a.c. conductivity
and temperature at different frequencies
can be indicated as follows (9) Where
is a pre-exponential factor. The value of ac activation energy
obtained by the slopes of
can be
versus 1000/T.
4. Results and discussion: 4.1. Surface morphological analysis The Scanning Electron Micrograph(SEM) of the prepared sample is displayed in figure 3. From the SEM images of Ge10-xSe60Te30Inx (x=0, 2, 4 & 6) it is clearly observed that some structural inhomogeneities present in the prepared sample which is because of partial nano-phase separation. The Energy Dispersive Spectroscopy (EDS) spectrum of bulk glassy alloys of Ge10xSe60Te30Inx
(x=0, 2, 4 & 6) is depicted in figure 4. Figure 4 shows the respective peaks of
elements present in Ge10-xSe60Te30Inx (x=0, 2, 4 & 6) chalcogenide glass. EDS quantification
shown in Table 1 confirmed that the composition has no impurity elements in the prepared samples. 4.2. Study of dielectric relaxation Dielectrics are the substances which do not have free electric charges under ordinary circumstances but their reaction to the applied electric field is significant. Dielectric constant is an important property of dielectric substances which tells the extent to which it concentrates the electrostatic lines of flux. For a given media dielectric constant depends on the frequency and temperature and for different media, it depends on the nature of bonding, crystal structure, structural defects etc. Another property of a dielectric substance is a dielectric loss which tells the ability to support an electrostatic field while dissipating minimum energy as a consequence of heat. 4.2.1. Frequency and temperature dependence of dielectric constant The variation of dielectric constant
with frequency for prepared multicomponent
Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses are depicted in figure 5. Figure. 5 clearly shows that dielectric constant decreasing trend of
reduces with increase of the applied frequency. The
as a function of frequency can be described with the help of four types of
polarization such as electronic, ionic, orientational(or dipolar), and space charge[46-47]. At frequency up, to 1016 Hz electronic polarization occurs and it arises due to the shifting of the valence electrons with respect to the positive nucleus. At a frequency of 1013Hz ionic polarization arises and it occurs because of displacement of opposite ions relative to each other. At frequency up, to 1010 Hz orientational polarization arises and it occurs because of the existence of molecules having permanent electrical dipole moments that can alter direction into the orientation of the applied electric field. Between frequency range 1-103 Hz space charge
polarization occurs and it arises because of impedance mobile charge carriers by interfaces. So, the addition of the above mentioned all polarization serves as the total polarization of the dielectric material, which influences the dielectric constant directly. In our case, ionic polarization does not demonstrate an articulated impact in total polarization, where the degree of covalency is estimated by Pauling[43] relation shown in Eq 4. Table 2 shows that the bonding is predominantly covalent in the Ge-Se-Te-In sample. Decreasing trend of dielectric constant with frequency is because of the reduction of the orientational polarization since it requires more time than the other kind of polarization and the dipoles cannot have the capacity to rotate adequately rapidly so that their oscillations lag behind those of the field. On further increment of frequency, the dipole will be absolutely unable to follow the field and the orientational polarization stopped; so dielectric constant reduces and approach a constant value at a higher frequency because of space charge polarization only[4850]. The temperature dependence of dielectric constants is depicted in figure 6. Figure 6 clearly shows the increase of dielectric constant with increasing temperature in all studied frequency range. The increasing trend of dielectric constant with temperature can be credited to the way that at low temperatures, the dipole in the polar materials cannot orient themselves. When the temperature is increased dipole existing in the material, attain some freedom, i.e. the orientation of dipole is facilitated, and consequently, it increases the amount of orientational polarization thereby increasing the dielectric constant. The similar results were reported by other workers [51-54].
4.2.2. Frequency and temperature dependence of dielectric loss The variation of dielectric loss with frequency at various temperatures for Ge10xSe60Te30Inx
(0 ≤ x ≤ 6) chalcogenide glassy alloys is depicted in figure 7. Figure 7 clearly shows
that increasing applied frequency reduces the dielectric loss and the behavior varies for different temperatures. The dielectric loss at low frequency is because of migration of ion in the material. At low and medium frequencies, dielectric loss is higher, and this occurs because of the jumping of ions, conduction losses due to ion migration and ionic polarization losses. The ion vibration is the only cause for dielectric loss at a higher temperature. The variation of dielectric loss with frequency can be described by Mott et al [5]; they proposed that hopping of electron occurs between the localized sites in the presence of an external electric field. Because of hopping of the charge carriers from a donor to an acceptor state, each pair of sites produces a dipole. Hence, it can be observed that dielectric properties of materials can be obtained by assuming them as a set of dipoles but only for higher temperatures. Experimentally it was observed that at definite temperatures the dielectric loss was independent of temperatures. It was supposed that each dipole has its relaxation time which depends on its activation energy, which can be essentially assigned to the existence of potential barrier Wm over which the charge carriers must hop. Elliot[40] assumed that potential barrier Wm is because of coloumbic interaction between the neighboring sites producing a dipole. The variation of dielectric loss with the temperature at different frequencies is displayed in figure 8. From figure 8 It can conclude that dielectric loss increases as a function of temperature. Stevels[55] categorized the dielectric relaxation phenomenon in three section i.e. conduction
losses, vibrational losses, and dipole losses. The ion migration in the large distances is connected by conduction losses. In the glassy network, ion jumps excess of the highest potential. When the ions move some of its energy is given to the lattice in the form of heat and heat loss per cycle is proportional to σac(ω)/ω [55]. Hence, the temperature of the sample increases above the room temperature which results in an increase in σac(ω)/ω value, thereby ac conduction losses increase by increasing the temperature. Dielectric losses exhibit minimum value at low temperatures just because of the low value of all the three losses viz. dipole, vibrational and conduction but these three losses contribute to the dielectric loss at higher temperatures. Hence it causes an increase in the dielectric loss with the increase in temperature. According to Guintini’s theory from equation 3, the value of frequency exponent of dielectric loss m is evaluated by the slopes of the linear region of
versus
plot at
different temperatures for all investigated samples. The variation of m as a function of temperature is shown in figure 9. 4.3. Analysis of thermally activated a.c. conduction 4.3.1. Frequency dependence of a.c. conductivity (σac) The total conductivity in the amorphous semiconductor is the sum of dc and ac component of conductivity. Generally, the dc component is very small as compare to ac conductivity so it can be neglected and the measured value of total conductivity is considered to be a.c. conductivity. Figure 10 shows the plot of ln(σac) against frequency at different temperatures for Ge10xSe60Te30Inx
(0 ≤ x ≤ 6) multicomponent glassy alloys. From figure 10 it is observed that they
obey the power law relation mentioned in equation 5. The evaluated frequency exponent s with
temperature for the studied composition is shown in figure 11. It is found that the value of s decreases with the increase of temperature and it is less than unity. The noticed behavior of frequency exponent s is in good agreement with CBH model. S. R. Elliott[44] proposed a correlated barrier hopping (CBH) model to explain the a.c. conduction in an amorphous semiconductor. This model assumes that a bipolaron hopping process occurs when two electrons concurrently hop over a potential barrier between two defect states namely D+ and D-. The barrier height depends on Colombian interaction. Moreover, Shimakawa [42] proposed that Do states are thermally produced at higher temperatures from D+ and D- states and single polaron hopping process become dominant. 4.3.2. Temperature dependence of a.c. conductivity (σac) The ac conductivity as a function of temperature for different samples at different frequencies is investigated and shown in figure 12. Figure 12 shows that a.c. conductivity decrease with increasing reciprocal of the temperature. The decrease ln(σac) with temperature tells that σac(ω) is a thermally activated process with a single activation energy from different localized states in the bandgap. At different frequencies, the a.c. the activation energy of conduction has been evaluated by a well-known Arrhenius relation shown in equation 9. The a.c. activation energy as a function of temperature is depicted in figure 13. From figure 13 it is observed that
decreases as a function of frequency. When increasing the
applied frequency, the electronic jump between the localized states increases which is responsible for the decrease in the a.c. activation energy
. The obtained value of dielectric
constant, dielectric loss and a.c. activation energy of conduction for Ge10-xSe60Te30Inx (0, 2, 4 & 6) glassy alloys at particular frequency is shown in table 3. Our results show better agreement with most recently reported work by other workers [51-54].
4.4. Compositional dependence of dielectric constant ( ), dielectric loss ( ) and a.c. conductivity (σac) Effect of incorporation of Indium on the dielectric constant and dielectric loss of Ge-SeTe alloys has been studied. It is observed that in Ge10-xSe60Te30Inx(0≤x≤6) multicomponent glasses dielectric constant ( ) and dielectric loss ( ) increases with increasing the In concentration. The variation of
and
with glass composition at a particular temperature is
shown in figure 13(a)-(b). Similar behavior has been observed at other temperatures for the studied samples. The change in
and
with composition has been described in the succeeding
paragraph. The prepared glassy matrix becomes heavily cross-linked with increase in Indium content. Also, the steric hindrance increases with increasing In concentration. Since Se-In exhibit higher bond energy as compared to the Ge–Ge bond shown in table (3) so, in the prepared Ge10xSe60Te30Inx(0≤x≤6)
glasses weak bond of Ge–Ge will be replaced by stronger bond of Se–In
since In has been incorporated on the cost of Ge, hence, the adhesive energy of the glassy matrix increases with increasing In content which results into increase of dielectric constant and dielectric loss with addition of In in the parent ternary glass. The density of defect states increases with the incorporation of iso-electronic atom Te into a-Se[43]. This consideration can be interpreted in terms of structural defect model where it is presumed that Te form positively charged impurities because of low electro-negativity value of Te as compared to Se[43]. When Ge atom is incorporated into binary Se–Te system, it forms positively charged defect impurities because Ge has low electro-negativity as compared to Se and Te atoms [43]. When In is added in the ternary Ge-Se–Te system at the cost of Ge, one can predict that further positive charged defects states would be generated because In have less
electro-negativity in comparison to Ge. This causes an increase in the density of defect states in the glassy network of quaternary alloys in comparison to host ternary alloy. From the above discussion, one can conclude that incorporation of In into host Ge-Se-Te glass increases the number of charged defect states, which enhances the dielectric properties of the Ge10xSe60Te30Inx(0≤x≤6)
materials.
The calculated values of ac conductivity are shown in figure 13(c) and found to increase with increasing In concentration. Variation in ac conductivity with glass composition has been explained as follows: It is well known that amorphous materials have broad band edges due to the lack of a long-range order as well as the presence of defects. The incorporation of In leads to an increase in the density of localized states which results into increase in ac conductivity. Increase in ac conductivity with In incorporation could be attributed to rupturing of Ge-Ge weak bonds and the formation of Se-In strong bonds. This process changes the concentration of density of state in band tail. The incorporation of conducting element in dielectric may have an extremely huge effect on its electrical response. The existence of an additive might enhance the concentration of charge carriers and there may be a shift of the Fermi level[48,51]. Our results are in good agreement with recent results reported by other workers[51-54]. 5. Conclusions The variation of dielectric constant( ), dielectric loss( ) and a.c. conductivity(σac) with frequency and temperature are studied for multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) glassy alloys, in the frequency range 100Hz - 1MHz and temperature range 303K-323K. It is noticed that dielectric constant ( ), and dielectric loss ( ) decrease with the increase in frequency and increases with the increase of temperature. The frequency and temperature dependence of
dielectric constant was linked to orientation polarization. The variation of dielectric loss with frequency and temperature can be attributed to the conduction loss. In the present case, it is found that a.c. conductivity follows the power law relation i.e.
where s≤1 . The results of a.c.
conductivity (σac), the value of frequency exponent s and its variation with temperature are in a good agreement with CBH model for the studied compositions. Temperature dependence of a.c. conductivity (σac) is a thermally activated process, with a.c. activation energy
having
decreasing trend with an increase in frequency. Dielectric constant and loss both increase with increasing In content in the Ge-Se-Te composition. It has also been observed that a.c. conductivity increases with increasing the In content into the parent composition. This happens due to the cross linking after inclusion of In content into the parent alloy leading to the increase in the adhesive energy of quaternary composition which results into increase in
,
and σac .
Acknowledgment Authors are thankful to Prof. R.K. Shukla HBTU Kanpur for his guidance and acquiring data for dielectric measurements and ACMS IIT Kanpur for SEM and EDS analysis. The authors are also grateful to UGC-DAE-CSR Indore, India for providing the facility and financial assistance for XRD measurements. References
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Figure caption Figure 1. A simple step for material preparation is (i) material crushing (ii) weighing (iii) ampoule sealing, (iv)heating and rocking (v) rapid cooling Figure 2. XRD patterns of Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses Figure 3. SEM images for the multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses Figure 4. Energy dispersive X-ray analysis EDS for glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 5. Frequency dependence of dielectric constant for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 6. Temperature dependence of dielectric constant for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 7. Frequency dependence of dielectric loss for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 8. Temperature dependence of dielectric loss for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 9. Temperature dependence of frequency exponent m of dielectric loss for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys. Figure 10. Frequency dependence of ac conductivity for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 11. Temperature dependence of frequency exponent s of ac conduction for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 12. The variation of ln(σac) against 1000/T for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 13. Compositional dependence of dielectric constant, dielectric loss and ac conductivity in
Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) multicomponent glasses at 315K temperature. Figure 14. The variation of ac activation energy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys
against
for the glassy
(2)
(1)
(3)
(5)
(4)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
(a)
(b)
(c) Fig. 13.
Fig. 14.
Table 1 The compositional analysis of multicomponent Ge10-xSe60Te30Inx (0, 2, 4 & 6) chalcogenide glassy alloys Sample
Ge10Se60Te30 Ge8Se60Te30In2 Ge6Se60Te30In4 Ge4Se60Te30In6
at% Ge 9.2 7.2 5.1 4.4
Se 60.0 59.9 59.9 58.1
Te 30.8 29.7 30.8 29.8
wt% In --3.2 4.2 7.7
Total 100 100 100 100
Ge 7.15 5.56 3.89 3.33
Se 50.75 50.26 49.72 47.82
Te 42.10 40.27 41.32 39.63
In --3.91 5.07 9.22
Total 100 100 100 100
Table 2. Calculated covalent & ionic character of bonds and their bond energies for Ge10xSe60Te30Inx (0, 2, 4 & 6) glassy alloys Bond type
% Covalent
% Ionic
Bond energy
character
character
(kJ/mole)
Ge-Ge
100
0
188
Ge-Se
92.96
7.04
484.7
Ge-Te
99.79
0.21
396.7
Ge-In
98.68
1.32
137.31
Se-Se
100
0
172
Se-Te
95.06
4.94
293.3
Se-In
86.22
13.78
245.2
Te-Te
100
0
259.8
Te-In
97.47
2.53
215.5
In-In
100
0
100
Table 3. Dielectric constant, dielectric loss and a.c. activation energy of conduction for Ge10xSe60Te30Inx (0, 2, 4 & 6) glassy alloys at particular frequency Sample
Dielectric constant ( ) 10kHz, 318K
Dielectric loss ( ) 10kHz, 318K
a.c. activation energy ) 10kHz
Ge10Se60Te30 Ge8Se60Te30In2 Ge6Se60Te30In4 Ge4Se60Te30In6
13.16 40.45 72.41 104.44
2.56 113.74 115.21 160.12
0.86 0.79 0.60 0.38
S2211-3797(18)32452-5 https://doi.org/10.1016/j.rinp.2018.11.048 RINP 1817
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
12 October 2018 15 November 2018 15 November 2018
Please cite this article as: Singh, P.K., Sharma, S.K., Tripathi, S.K., Dwivedi, D.K., Study of dielectric relaxation and thermally activated a.c. conduction in multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses using CBH model, Results in Physics (2018), doi: https://doi.org/10.1016/j.rinp.2018.11.048
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Study of dielectric relaxation and thermally activated a.c. conduction in multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses using CBH model Pravin Kumar Singh1, S. K. Sharma2, S.K. Tripathi3, D. K. Dwivedi1* 1 Amorphous Semiconductor Researcher Lab Department of Applied Sciences, M. M. M. University of Technology, Gorakhpur-273010 (India) 2 Department of Physics, Harcourt Butler Technical University, Kanpur-208002(India) 3 Department of Physics, Punjab University, Chandigarh, India *E.mail: [email protected] Ph: 09415712163 Abstract Amorphous Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses were prepared by melt quench technique. Surface morphology with the chemical composition of the prepared glass was examined using SEM and EDS analysis respectively. Dielectric properties and a.c. conductivity of the multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses have been examined in the frequency range 100Hz to 1MHz and temperature range 303 to 328K. It was noticed that dielectric constant and dielectric loss decreases with the increase of frequency and increases with the increase of temperatures. Frequency and temperature dependence of dielectric constant was explained by orientational polarization. The variation of dielectric loss with frequency and temperature was explained by conduction loss and theory of single polaron hopping of charge carriers suggested by Elliot and Shimakawa for chalcogenide glasses. The experimental results show that a.c. conductivity follows the power law
where s<1 and value of s decreases with
the increase of temperature. The present findings of a.c. conductivity and variation of s with temperatures are reasonably well interpreted in terms of CBH model.
Keywords: Chalcogenide glasses, a c conductivity, dielectric relaxation, CBH model, activation energy.
1. Introduction Nowadays new phenomena, new materials, and many advanced technologies are used for the scientific and technical advancement. The science of glasses is developed gradually to cater above needs. Glasses are the most common ancient natural vitreous solid that can be prepared artificially for the fundamental research and application point of view[1-3]. The heart of present electronic devices is the components made by silicon. The optimization and improvisation of silicon-based devices are of great advantage regarding the requirement of power for processing, the threshold in design complexity, dissipation of heat and memory through sinks, energy consumption etc. This has led to a quest for new materials. One of such fields of materials is chalcogenide glasses which exhibit attractive properties and have applications in different domains[4-8]. Chalcogenide glasses are amorphous semiconductor which is
applicable in many
electronic, and optoelectronic devices like rewritable optical recording[9-10], solar energy conversion[11-13], optical mass memories[14], holography[15], infrared detectors[16], holographic data storage and programmable metallization cell (PMC) memory[17], optical fibers[18] and ultrasonic delay lines[19]. The wide range of applications of these glasses is available because of some unique property like photodarkening or bleaching[20], photo-induced structural transformation[21] etc. An amorphous semiconductor (especially, chalcogenide glasses) has received a great attention of many researchers towards it due to the existence of localized state between conduction band valence band. Recently these glasses are widely used in military areas, civil and medical such as determining inorganic pollutants in river water, monitoring corrosion process and control of food stuff[22]. Infrared chalcogenide fibers are
utilized for the infrared fingerprints of human lung cells in various metabolic conditions and biosensing like tumor detection, serum analysis, liver metabolism [21-27]. Selenium-based compounds are extremely important because of its ongoing development in different solid state devices. Recent studies show that selenium-rich compound is very useful as compared to pure selenium. The mixing of doping elements like Te, Ga, Bi, Sb, Pb and As with disordered selenium has a noticeable effect on change in structure & conduction mechanism and it also provides the smaller aging effect, higher photosensitivity and crystallization temperature[28-32]. Tellurium is used as a doping element in pure Se to minimize its drawbacks. The Se-Te glassy alloys are a commercial product and have technological and scientific importance. The drawback of such binary alloy is its thermal instability leading to crystallization, so a third element Ge has been added to enhance the thermal stability of Se-Te binary alloys. From literature survey, we have found that different ternary glasses consists of indium as a modifier while to the best of author’s knowledge no study has as yet been reported on the synthesis and characterization of indium-doped quaternary glass which may enlarge the utility of these glasses. The addition of indium as a fourth element generates compositional and configurational disorder in the system, also, it enhances the glass-forming region[33-35]. In past few decades, an increasing interest has been observed to examine the dielectric relaxation and ac conductivity of chalcogenide glassy system for both academic and application point of view. These glassy alloys show higher ionic conductivity than their oxide counterparts because of its high polarizability. The insulating and conductive behavior of the materials can be described by dielectric analysis. The ability to store an electric charge is known as insulating behavior while the ability to transfer the charge is known as the conductive behavior of the
materials. Measurement of ac conductivity gives a basic approach to explain the defect centers along with the behavior of conduction mechanism existing in chalcogenide glasses. To study the conduction mechanism in chalcogenide glasses different models have been suggested like quantum mechanical tunneling (QMT) [36] model, overlapping large polaron tunneling (OLPT) [37] model, non-overlapping small polaron tunneling (NSPT)[38] model and correlated barrier hopping (CBH) [39,40] model. CBH model has extensively applied the model in chalcogenide glassy semiconductors. In this paper frequency and temperature dependence of dielectric constant, dielectric loss and ac conductivity have been measured and examined to investigate the dielectric properties and conduction process for multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glass.
2. Experimental details 2.1.Material Synthesis The bulk glassy alloys of Ge10-xSe60Te30Inx (x=0, 2, 4 & 6) was developed by a wellknown melt quench techniques. A simple step for material preparation is material crushing, weighing, ampoule sealing, heating and rocking then rapid cooling as shown in figure 1. The powder of high purity (99.999%) elements of Germanium(Ge), Selenium(Se), Tellurium(Te) and Indium(In) were weighed in order of their stoichiometric ratio using an electronic balance(LIBROR, AGE-120, least count=10-4gm ). The prepared sample was put in quartz ampoule (internal diameter=8cm, length=5cm) and squeezing it in the tube of a high vacuum unit to remove the air from the sample. The quartz ampoule containing mixture was then sealed under a high vacuum (10−5 mbars) using High Vacuum Unit (Vacuum Tech. Pvt. Ltd. Banglore, Model No: VT-ACG- 03, 2013). Evacuated
quartz ampoules (with the sample in it) were sealed by LPG-Oxygen flame. Sealed ampoules having constituent elements were hooked up in the ceramic rod with the help of nichrome wire and placed in a muffle furnace. The temperature of the furnace was increased steadily up to 800oC with constant steps of about 20 K/15 min and retained this temperature for 14h. Intermittently rocking of ampoule was done by gyrating the ceramic rod. A constant mechanical shaking was done in the muffle furnace to get a homogeneous sample. To find glassy samples the ampoules were quenched in icy water after 14 hours. After that, a very fine powder was obtained by grinding the prepared sample using a mortar. 2.2. Characterization The XRD pattern of the prepared glassy alloys was recorded by X-ray diffractometer(XPERT-PRO Cu-Kα radiation λ=1.54Ǻ). The tube was maintained at 45kV and 40mA. The XRD patterns of Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses are shown in figure 2. From XRD patterns it is found that there are no sharp structural peaks which confirms the amorphous nature of the sample. Surface morphology has been done by JEOL Field Emission Scanning Microscopy (Model/Supplier: JSM-7100F). The magnification was 2000x.
Energy dispersive X-ray
spectroscopy (EDS) analysis of prepared sample has been done to check the elemental composition of Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) bulk glassy alloys. To investigate the dielectric measurements a digital LCR meter (Wayne Kerr Electronics, Model: 43100) was used. Fine powders of the prepared sample were compressed into cylindrical pellets (diameter = 8mm and thickness = 1.3mm) by an applied load of 5tons using a hydraulic press to investigate the dielectric relaxation and a.c. conductivity. A copper-constantan thermocouple placed extremely close to the sample is used for measuring the temperature range
303K-328K. During entire temperature range (303-323K) vacuum of 10-3 torr was kept constant. The parallel capacitance (C), dissipation factor (tan (δ)) and impedance (Z) were estimated directly in the frequency span 100kHz-1MHz for the studied samples. Where and
denotes the phase angle. The parallel capacitance C and dissipation factor tan (δ)
were used to evaluate the dielectric constant
and dielectric loss
.
The a.c. conductivity of the material was evaluated by the relation , where f represents frequency. 3. Theoretical basis Giuntini et al [41] offered a suitable model to describe the dielectric relaxation in chalcogenide glass. Mott et al [5]. assumptions were the basis of this model; they proposed that electron hop between localized states within the sight of the electric field. In these states, the moving charge carriers hop from donor to an acceptor state. So every pair creates a dipole and a set of dipoles are used to explain the dielectric behavior of chalcogenide glasses with temperature. This model suggests that the relaxation time of each dipole depends on activation energy[42], further it can refer to the existence of potential barrier over which the carrier hop. The dielectric loss in terms of frequency and temperature according to Giuntini theory can be indicated by the relation [41] (1) where the static dielectric constant is
, a number of hopping electron is n, localized state
density is N, dielectric constant at high frequency is
, angular frequency is ω and maximum
barrier height is Wm. At a particular temperature, the dielectric loss equation 1.
obeys the power law according to
(2) Where the frequency exponent of dielectric loss m can be shown by the relation m= -4kT/ Wm
(3)
The value of m can be obtained by taking slope between log
versus logω.
The percentage of covalent character is obtained by Pauling relation[43] Percentage covalent character Where the electronegativity of atom A and B are
(4) and
respectively
In amorphous semiconductor a.c. conductivity has been determined through pair approximation as suggested in CBH model. Since localized state are supposed to be randomly distributed in space, therefore pairs may have different relaxation time. It has been proposed that localized states are randomly distributed and electrons move back and forth through a rigorous relaxation time between a pair of two localized states. The total a.c. conductivity of the material is the sum of all pair’s contributions. In amorphous materials and ceramic glasses, many authors have reported that ac conductivity obey the following relation[44] σac(ω) = Aωs
(5)
where s denotes frequency exponent and angular frequency is ω. The frequency exponent s in CBH model is expressed as follows
(6)
Where relaxation time is
represents the Boltzmann constant, absolute temperature is T, the characteristic . The vibrational period of an atom (
) is the approximate value of
. Maximum barrier height at infinite intersite separation is Wm which is known as binding energy of the carrier in its localized sites[44,45]. When
is large above equation can be rewritten as (7)
The value of
can be calculated by taking the slope of 1-s against T plot.
The electron relaxation time
hop over a maximum barrier height
can be
calculated at various temperatures by a well-known relation (8) Where characteristic relaxation time is
and has the value in the order of atomic vibrational
period. The relation between a.c. conductivity
and temperature at different frequencies
can be indicated as follows (9) Where
is a pre-exponential factor. The value of ac activation energy
obtained by the slopes of
can be
versus 1000/T.
4. Results and discussion: 4.1. Surface morphological analysis The Scanning Electron Micrograph(SEM) of the prepared sample is displayed in figure 3. From the SEM images of Ge10-xSe60Te30Inx (x=0, 2, 4 & 6) it is clearly observed that some structural inhomogeneities present in the prepared sample which is because of partial nano-phase separation. The Energy Dispersive Spectroscopy (EDS) spectrum of bulk glassy alloys of Ge10xSe60Te30Inx
(x=0, 2, 4 & 6) is depicted in figure 4. Figure 4 shows the respective peaks of
elements present in Ge10-xSe60Te30Inx (x=0, 2, 4 & 6) chalcogenide glass. EDS quantification
shown in Table 1 confirmed that the composition has no impurity elements in the prepared samples. 4.2. Study of dielectric relaxation Dielectrics are the substances which do not have free electric charges under ordinary circumstances but their reaction to the applied electric field is significant. Dielectric constant is an important property of dielectric substances which tells the extent to which it concentrates the electrostatic lines of flux. For a given media dielectric constant depends on the frequency and temperature and for different media, it depends on the nature of bonding, crystal structure, structural defects etc. Another property of a dielectric substance is a dielectric loss which tells the ability to support an electrostatic field while dissipating minimum energy as a consequence of heat. 4.2.1. Frequency and temperature dependence of dielectric constant The variation of dielectric constant
with frequency for prepared multicomponent
Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses are depicted in figure 5. Figure. 5 clearly shows that dielectric constant decreasing trend of
reduces with increase of the applied frequency. The
as a function of frequency can be described with the help of four types of
polarization such as electronic, ionic, orientational(or dipolar), and space charge[46-47]. At frequency up, to 1016 Hz electronic polarization occurs and it arises due to the shifting of the valence electrons with respect to the positive nucleus. At a frequency of 1013Hz ionic polarization arises and it occurs because of displacement of opposite ions relative to each other. At frequency up, to 1010 Hz orientational polarization arises and it occurs because of the existence of molecules having permanent electrical dipole moments that can alter direction into the orientation of the applied electric field. Between frequency range 1-103 Hz space charge
polarization occurs and it arises because of impedance mobile charge carriers by interfaces. So, the addition of the above mentioned all polarization serves as the total polarization of the dielectric material, which influences the dielectric constant directly. In our case, ionic polarization does not demonstrate an articulated impact in total polarization, where the degree of covalency is estimated by Pauling[43] relation shown in Eq 4. Table 2 shows that the bonding is predominantly covalent in the Ge-Se-Te-In sample. Decreasing trend of dielectric constant with frequency is because of the reduction of the orientational polarization since it requires more time than the other kind of polarization and the dipoles cannot have the capacity to rotate adequately rapidly so that their oscillations lag behind those of the field. On further increment of frequency, the dipole will be absolutely unable to follow the field and the orientational polarization stopped; so dielectric constant reduces and approach a constant value at a higher frequency because of space charge polarization only[4850]. The temperature dependence of dielectric constants is depicted in figure 6. Figure 6 clearly shows the increase of dielectric constant with increasing temperature in all studied frequency range. The increasing trend of dielectric constant with temperature can be credited to the way that at low temperatures, the dipole in the polar materials cannot orient themselves. When the temperature is increased dipole existing in the material, attain some freedom, i.e. the orientation of dipole is facilitated, and consequently, it increases the amount of orientational polarization thereby increasing the dielectric constant. The similar results were reported by other workers [51-54].
4.2.2. Frequency and temperature dependence of dielectric loss The variation of dielectric loss with frequency at various temperatures for Ge10xSe60Te30Inx
(0 ≤ x ≤ 6) chalcogenide glassy alloys is depicted in figure 7. Figure 7 clearly shows
that increasing applied frequency reduces the dielectric loss and the behavior varies for different temperatures. The dielectric loss at low frequency is because of migration of ion in the material. At low and medium frequencies, dielectric loss is higher, and this occurs because of the jumping of ions, conduction losses due to ion migration and ionic polarization losses. The ion vibration is the only cause for dielectric loss at a higher temperature. The variation of dielectric loss with frequency can be described by Mott et al [5]; they proposed that hopping of electron occurs between the localized sites in the presence of an external electric field. Because of hopping of the charge carriers from a donor to an acceptor state, each pair of sites produces a dipole. Hence, it can be observed that dielectric properties of materials can be obtained by assuming them as a set of dipoles but only for higher temperatures. Experimentally it was observed that at definite temperatures the dielectric loss was independent of temperatures. It was supposed that each dipole has its relaxation time which depends on its activation energy, which can be essentially assigned to the existence of potential barrier Wm over which the charge carriers must hop. Elliot[40] assumed that potential barrier Wm is because of coloumbic interaction between the neighboring sites producing a dipole. The variation of dielectric loss with the temperature at different frequencies is displayed in figure 8. From figure 8 It can conclude that dielectric loss increases as a function of temperature. Stevels[55] categorized the dielectric relaxation phenomenon in three section i.e. conduction
losses, vibrational losses, and dipole losses. The ion migration in the large distances is connected by conduction losses. In the glassy network, ion jumps excess of the highest potential. When the ions move some of its energy is given to the lattice in the form of heat and heat loss per cycle is proportional to σac(ω)/ω [55]. Hence, the temperature of the sample increases above the room temperature which results in an increase in σac(ω)/ω value, thereby ac conduction losses increase by increasing the temperature. Dielectric losses exhibit minimum value at low temperatures just because of the low value of all the three losses viz. dipole, vibrational and conduction but these three losses contribute to the dielectric loss at higher temperatures. Hence it causes an increase in the dielectric loss with the increase in temperature. According to Guintini’s theory from equation 3, the value of frequency exponent of dielectric loss m is evaluated by the slopes of the linear region of
versus
plot at
different temperatures for all investigated samples. The variation of m as a function of temperature is shown in figure 9. 4.3. Analysis of thermally activated a.c. conduction 4.3.1. Frequency dependence of a.c. conductivity (σac) The total conductivity in the amorphous semiconductor is the sum of dc and ac component of conductivity. Generally, the dc component is very small as compare to ac conductivity so it can be neglected and the measured value of total conductivity is considered to be a.c. conductivity. Figure 10 shows the plot of ln(σac) against frequency at different temperatures for Ge10xSe60Te30Inx
(0 ≤ x ≤ 6) multicomponent glassy alloys. From figure 10 it is observed that they
obey the power law relation mentioned in equation 5. The evaluated frequency exponent s with
temperature for the studied composition is shown in figure 11. It is found that the value of s decreases with the increase of temperature and it is less than unity. The noticed behavior of frequency exponent s is in good agreement with CBH model. S. R. Elliott[44] proposed a correlated barrier hopping (CBH) model to explain the a.c. conduction in an amorphous semiconductor. This model assumes that a bipolaron hopping process occurs when two electrons concurrently hop over a potential barrier between two defect states namely D+ and D-. The barrier height depends on Colombian interaction. Moreover, Shimakawa [42] proposed that Do states are thermally produced at higher temperatures from D+ and D- states and single polaron hopping process become dominant. 4.3.2. Temperature dependence of a.c. conductivity (σac) The ac conductivity as a function of temperature for different samples at different frequencies is investigated and shown in figure 12. Figure 12 shows that a.c. conductivity decrease with increasing reciprocal of the temperature. The decrease ln(σac) with temperature tells that σac(ω) is a thermally activated process with a single activation energy from different localized states in the bandgap. At different frequencies, the a.c. the activation energy of conduction has been evaluated by a well-known Arrhenius relation shown in equation 9. The a.c. activation energy as a function of temperature is depicted in figure 13. From figure 13 it is observed that
decreases as a function of frequency. When increasing the
applied frequency, the electronic jump between the localized states increases which is responsible for the decrease in the a.c. activation energy
. The obtained value of dielectric
constant, dielectric loss and a.c. activation energy of conduction for Ge10-xSe60Te30Inx (0, 2, 4 & 6) glassy alloys at particular frequency is shown in table 3. Our results show better agreement with most recently reported work by other workers [51-54].
4.4. Compositional dependence of dielectric constant ( ), dielectric loss ( ) and a.c. conductivity (σac) Effect of incorporation of Indium on the dielectric constant and dielectric loss of Ge-SeTe alloys has been studied. It is observed that in Ge10-xSe60Te30Inx(0≤x≤6) multicomponent glasses dielectric constant ( ) and dielectric loss ( ) increases with increasing the In concentration. The variation of
and
with glass composition at a particular temperature is
shown in figure 13(a)-(b). Similar behavior has been observed at other temperatures for the studied samples. The change in
and
with composition has been described in the succeeding
paragraph. The prepared glassy matrix becomes heavily cross-linked with increase in Indium content. Also, the steric hindrance increases with increasing In concentration. Since Se-In exhibit higher bond energy as compared to the Ge–Ge bond shown in table (3) so, in the prepared Ge10xSe60Te30Inx(0≤x≤6)
glasses weak bond of Ge–Ge will be replaced by stronger bond of Se–In
since In has been incorporated on the cost of Ge, hence, the adhesive energy of the glassy matrix increases with increasing In content which results into increase of dielectric constant and dielectric loss with addition of In in the parent ternary glass. The density of defect states increases with the incorporation of iso-electronic atom Te into a-Se[43]. This consideration can be interpreted in terms of structural defect model where it is presumed that Te form positively charged impurities because of low electro-negativity value of Te as compared to Se[43]. When Ge atom is incorporated into binary Se–Te system, it forms positively charged defect impurities because Ge has low electro-negativity as compared to Se and Te atoms [43]. When In is added in the ternary Ge-Se–Te system at the cost of Ge, one can predict that further positive charged defects states would be generated because In have less
electro-negativity in comparison to Ge. This causes an increase in the density of defect states in the glassy network of quaternary alloys in comparison to host ternary alloy. From the above discussion, one can conclude that incorporation of In into host Ge-Se-Te glass increases the number of charged defect states, which enhances the dielectric properties of the Ge10xSe60Te30Inx(0≤x≤6)
materials.
The calculated values of ac conductivity are shown in figure 13(c) and found to increase with increasing In concentration. Variation in ac conductivity with glass composition has been explained as follows: It is well known that amorphous materials have broad band edges due to the lack of a long-range order as well as the presence of defects. The incorporation of In leads to an increase in the density of localized states which results into increase in ac conductivity. Increase in ac conductivity with In incorporation could be attributed to rupturing of Ge-Ge weak bonds and the formation of Se-In strong bonds. This process changes the concentration of density of state in band tail. The incorporation of conducting element in dielectric may have an extremely huge effect on its electrical response. The existence of an additive might enhance the concentration of charge carriers and there may be a shift of the Fermi level[48,51]. Our results are in good agreement with recent results reported by other workers[51-54]. 5. Conclusions The variation of dielectric constant( ), dielectric loss( ) and a.c. conductivity(σac) with frequency and temperature are studied for multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) glassy alloys, in the frequency range 100Hz - 1MHz and temperature range 303K-323K. It is noticed that dielectric constant ( ), and dielectric loss ( ) decrease with the increase in frequency and increases with the increase of temperature. The frequency and temperature dependence of
dielectric constant was linked to orientation polarization. The variation of dielectric loss with frequency and temperature can be attributed to the conduction loss. In the present case, it is found that a.c. conductivity follows the power law relation i.e.
where s≤1 . The results of a.c.
conductivity (σac), the value of frequency exponent s and its variation with temperature are in a good agreement with CBH model for the studied compositions. Temperature dependence of a.c. conductivity (σac) is a thermally activated process, with a.c. activation energy
having
decreasing trend with an increase in frequency. Dielectric constant and loss both increase with increasing In content in the Ge-Se-Te composition. It has also been observed that a.c. conductivity increases with increasing the In content into the parent composition. This happens due to the cross linking after inclusion of In content into the parent alloy leading to the increase in the adhesive energy of quaternary composition which results into increase in
,
and σac .
Acknowledgment Authors are thankful to Prof. R.K. Shukla HBTU Kanpur for his guidance and acquiring data for dielectric measurements and ACMS IIT Kanpur for SEM and EDS analysis. The authors are also grateful to UGC-DAE-CSR Indore, India for providing the facility and financial assistance for XRD measurements. References
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Figure caption Figure 1. A simple step for material preparation is (i) material crushing (ii) weighing (iii) ampoule sealing, (iv)heating and rocking (v) rapid cooling Figure 2. XRD patterns of Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses Figure 3. SEM images for the multicomponent Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) chalcogenide glasses Figure 4. Energy dispersive X-ray analysis EDS for glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 5. Frequency dependence of dielectric constant for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 6. Temperature dependence of dielectric constant for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 7. Frequency dependence of dielectric loss for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 8. Temperature dependence of dielectric loss for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 9. Temperature dependence of frequency exponent m of dielectric loss for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys. Figure 10. Frequency dependence of ac conductivity for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 11. Temperature dependence of frequency exponent s of ac conduction for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 12. The variation of ln(σac) against 1000/T for the glassy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys Figure 13. Compositional dependence of dielectric constant, dielectric loss and ac conductivity in
Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) multicomponent glasses at 315K temperature. Figure 14. The variation of ac activation energy Ge10-xSe60Te30Inx (0 ≤ x ≤ 6) alloys
against
for the glassy
(2)
(1)
(3)
(5)
(4)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
(a)
(b)
(c) Fig. 13.
Fig. 14.
Table 1 The compositional analysis of multicomponent Ge10-xSe60Te30Inx (0, 2, 4 & 6) chalcogenide glassy alloys Sample
Ge10Se60Te30 Ge8Se60Te30In2 Ge6Se60Te30In4 Ge4Se60Te30In6
at% Ge 9.2 7.2 5.1 4.4
Se 60.0 59.9 59.9 58.1
Te 30.8 29.7 30.8 29.8
wt% In --3.2 4.2 7.7
Total 100 100 100 100
Ge 7.15 5.56 3.89 3.33
Se 50.75 50.26 49.72 47.82
Te 42.10 40.27 41.32 39.63
In --3.91 5.07 9.22
Total 100 100 100 100
Table 2. Calculated covalent & ionic character of bonds and their bond energies for Ge10xSe60Te30Inx (0, 2, 4 & 6) glassy alloys Bond type
% Covalent
% Ionic
Bond energy
character
character
(kJ/mole)
Ge-Ge
100
0
188
Ge-Se
92.96
7.04
484.7
Ge-Te
99.79
0.21
396.7
Ge-In
98.68
1.32
137.31
Se-Se
100
0
172
Se-Te
95.06
4.94
293.3
Se-In
86.22
13.78
245.2
Te-Te
100
0
259.8
Te-In
97.47
2.53
215.5
In-In
100
0
100
Table 3. Dielectric constant, dielectric loss and a.c. activation energy of conduction for Ge10xSe60Te30Inx (0, 2, 4 & 6) glassy alloys at particular frequency Sample
Dielectric constant ( ) 10kHz, 318K
Dielectric loss ( ) 10kHz, 318K
a.c. activation energy ) 10kHz
Ge10Se60Te30 Ge8Se60Te30In2 Ge6Se60Te30In4 Ge4Se60Te30In6
13.16 40.45 72.41 104.44
2.56 113.74 115.21 160.12
0.86 0.79 0.60 0.38