Compositional dependence of thermal transport and optical properties of Se85 Ge15-x Pbx (0≤ x ≤10) chalcogenide glassy alloys

Optical Materials 97 (2019) 109395

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Compositional dependence of thermal transport and optical properties of Se85 Ge15-x Pbx (0≤ x ≤10) chalcogenide glassy alloys

T

Pankaj K. Mishraa, K. Singhb, A.N. Upadhyayc, H. Kumara,∗ a

Department of Physics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India School of Physical Sciences, Jawahar Lal Nehru University, New Delhi, 110067, India c Department of Ceramic Engineering, IIT (Banaras Hindu University), Varanasi, 221005, India b

A R T I C LE I N FO

A B S T R A C T

Keywords: Chalcogenide Excitons DSC Thermal-transport Uv–Vis

In the present work, the ratio of germanium (Ge) to lead (Pb) is varied keeping the concentration of selenium(Se) fixed in the glassy system, Se85 Ge15-x Pbx (0 ≤ x ≤ 10) to optimize the thermal transport and optical properties. The differential scanning calorimetry (DSC) measurements were carried out in the non-isothermal mode to know glass transition temperature (Tg), crystallization temperature (Tc) and melting temperature (Tm). DSC scans of some samples(4 ≤ x ≤ 10) exhibit two glass transition temperatures (Tg), which indicates the presence of coexisting phases in glassy samples. The values of effective thermal conductivity (λe),effective thermal diffusivity (χe) and volumetric heat capacity(QCp) have been determined using transient plane source (TPS) measurements. These parameters show a non-monotonous behavior with the variation of Pb content in the prepared series. These results are explained in terms of chemical bond approach, changes in thermal transfer processes and mechanism of phonon scattering under transitions from dilute to concentrated solid solution. Band gap and Urbach energy have been estimated using Uv–Vis spectroscopy. Optical band gap (~0.65 eV) is minimum for the sample having 4 at.% of Pb. A signature of exciton formation is obtained for this critical composition. Results are explained using structural defect model and by degree of disorder induced, as indicated by a change in intensity and position of the Raman peak corresponding to Se–Se bonds.

1. Introduction Currently, chalcogenide based glassy alloys have been become an attractive and intense field of research due to its wide range of scientific and technological application in solid state, electronic devices and holography recording media [1–9]. Low value of acoustic loss, high indices of refraction (2.5–3.0), optical transmission in infrared make them suitable for fabrication of IR detectors, Optical-fibers, acoustic delay lines and acousto-optic devices [10–13]. Enriched with relatively large optical non linear refractive index chalcogenide glasses are promising candidate for high efficiency nonlinear (the optical response of the medium do not scale linearly with the electric field of the light signal) applications. Other important non linear application includes, wave guides, sensing, Raman lasing, creation of shortest event and harmonic generation [14–16]. Wider transparency of chalcogenide fibres (over 20 μm) combined with higher nonlinearity (third order nonlinearity) in comparison to silica glass fibres makes them good candidate for super continuum generation (SC) i.e. the production of continuum of intense ultrafast broad band white-light pulses [17]. A

∗

non linear optical effect in which laser modulates its own phase as the light propagates through the glass fibre is responsible SC generation. Literature reveals that by using a 3 cm long step indexed As2Se3 fiber with~170fs pulses pumped at 9.8 μm Chen et al. [18] has achieved SC broadening of 2.0–15.1 μm. P. Zhang et al. has produced broadband mid-infrared super continuum generation in 1-meter-long As2S3- based fibre with ultra-large core diameter [19]. Selenium has been used as base chalcogen element due to its excellent glass forming ability.But poor thermal stability, low glass transition temperature, high level of intrinsic defects and low photo sensitivity limit its performance in technological applications [20]. To remove these difficulties faced in fully functionalized the selenium [21] some other elements are used as additives [22,23]. A carrier type reversal (CTR) from p to n type has been observed on incorporating the Bi/Pb in Germanium–Selenium (Ge–Se) and Indium–Selenium (In-Se) [24,25] chalcogenide glassy systems [26–28]. Discovery of CTR has led to further extensive research on Pb containing chalcogenide materials [29–31]. These are promising materials for solar cell research for example, PbSe nanocrystals or quantum dots exhibits highest measured

Corresponding author. E-mail address: [email protected] (H. Kumar).

https://doi.org/10.1016/j.optmat.2019.109395 Received 17 May 2019; Received in revised form 22 July 2019; Accepted 16 September 2019 Available online 25 September 2019 0925-3467/ © 2019 Elsevier B.V. All rights reserved.

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bulk samples were characterized using X-ray diffracto-meter (XRD): Proto X-ray diffracto-meter with CuKα (λ = 1.54 Ao). Differential scanning calorimetry (DSC) has been performed (Mettler Toledo DSC-1 with heating rate 5K/min) to knowing the glassy nature of samples. The pellets (10 mm diameter and 3 mm thickness) of these samples were prepared at the load of 6 tons. The surface of these pellets was enough smooth which insured a good thermal contact between the pellet and heating elements of Transient plane source (TPS). A TPS sensor is composed of an electrically conducting element in the spiral form. The wire used in TPS element is 10 μm thick nickel foil, having resistance of 3.26Ω. Temperature coefficient of the foil is 4.5 × 10−3 k−1. The insulating layer of Kapton, of thickness 50 μm has been placed on each side of the pattern. The theory and measurements analysis of the data has been carried out on the lines as described by Gustafson [43]. The absorption spectra (200–3000 nm) of prepared samples were recorded using a Perkin Lambda-750, Uv–Vis/NIR spectrometer in reflection mode. Kubelka-Munk transformation was used to obtain the pseudo absorption coefficient. A Renishaw RM-1000, laser Raman set up with 532 nm, laser light source was used to record the Raman spectra of the samples. For the proper focusing of laser light Olympus microscope having objective 50x was used.

photocurrents under 1‐sun conditions for nanostructured solar cells [32]. Discovery of multiple excitons generation in these chalcogenide provides ample opportunity to extend the efficiency of a single junction solar cell beyond the Shockley Quisser limit of ~33% [33,34]. Special and exotic applications of Pb containing chalcogenides, cover the area of thermo-electrics for space application, opto-electronics [35–40] and Excitonic insulators (EI) which exhibits correlated electronic phases [41]. Thermal transport properties like thermal conductivity and diffusivity etc., which give an indication of internal structure, impurities, and defects etc., are of immense use due to recent quest for high-efficiency thermoelectric materials [42]. In chalcogenide thermoelectric materials, proper compositional variation of chalcogen elements and additives may lead to sub micron thermodynamic-driven phase separation features causing reduction in thermal conductivity and hence enhanced thermoelectric figure of merit. Due to thermodynamic origin, such a sub micron phase separation is considered much more stable at elevated operating temperatures. In this work we have synthesized Se85 Ge15-x Pbx (where x = 0 ≤ x ≤ 10) glassy alloys and composition dependence of effective thermal conductivity(λe), effective thermal diffusivity(χe) and volumetric heat capacity (QCp) have been studied using Transient plane source (TPS) developed by Gustafsson [43,44]. Glassy nature of the samples was determined using DSC and XRD. Optical properties have been studied using Uv–Vis spectroscopy and applying Kubelka-Munk transformation. Structural information was extracted using Raman analysis. The glass forming region of Se-Ge-Pb system is shown in Fig. 1.

3. Result and discussion 3.1. XRD analysis The X-ray diffraction patterns of as-prepared samples, Se85Ge15-xPbx (0 ≤ x ≤ 10) are shown in Fig. 2(a) and (b). The XRD diffractograms reveal that the microstructure of all prepared samples is fully amorphous in nature and no signature of crystalline phase is evident except for Se85Ge11Pb4 sample. Presence of broad halos (more than one) in the XRD patterns indicates that more than one phase in amorphous form may be present there. The existence of more than one phase is further confirmed by the presence of two glass transition temperatures in DSC thermo-grams of the prepared samples (4 ≤ x ≤ 10) . However, in the XRD of sample Se85Ge11Pb4 some sharp structural peaks are appeared. Structural analysis of peaks reveals the nano-crystalline nature of the sample. The average crystalline size of the investigated sample is determined by the Debye-Scherrer's formula:

2. Material preparation and experimental details The bulk samples Se85 Ge15-x Pbx (x = 0, 2, 4, 6, 8, and 10) were prepared by adopting standard melt quench technique. The desired amount of elements Se, Ge and Pb of high purity (99.999%) were weighed according to their appropriate atomic percentage using an electronic balance and were sealed in evacuated (~10−6 torr) quartz ampoules (length 5 cm and internal diameter 0.8 cm). The temperature of furnace was slowly raised at the rate of 3–4 K/min up to 950 °C and kept constant at this value for 12 h. During this stage (the above mentioned period) ampoules were kept continuously rocked to ensure the homogeneity of samples. After 12 h the obtained melts were quenched by dropping the ampoules quickly into the ice-cooled water. The quenched melts were taken out by breaking the ampoules. Obtained ingots were crushed in to fine powder using a grinder. The

D = kλ / βcosθ

(1)

where λ is the wavelength (CuKα −1.54 A ) of the X-rays, K (0.9) is the Scherrer constant, β is the full width at half maximum (FWHM) of the peaks, D is the crystalline size and θ is the angle determined from peak position(2θ /2) .The calculated crystalline size lies in nano-range between 31 and 45 nm. However, three most prominent as well as weak peaks in XRD of this sample correspond to Pb–Se, associated with germanium (Ge) (PCPDF file no. 650347). This phase has a cubic facecentred (Fm3m [225]) unit cell with a = b = c = 6.130 A0 and α = β = γ = 900. o

3.2. DSC analysis The thermo-grams (DSC) of the prepared samples Se85Ge15-xPbx (0 ≤ x ≤ 10) under the non isothermal condition are represented in Fig. 3(a). Thermo-grams for samples with x = 0&2 single, while with 4 ≤ x ≤ 10 , exhibit bimodal glass transition temperatures. The glass transition temperature is one of the most attractive and intriguing phenomena which gives the reliable information about the network structure, bonding strength and thermal stability [45,46]. The temperature corresponding to the point of intersection of tangents, drawn to the base line and beyond the point of inflection in endothermic peak before crystallization is taken as Tg in this study [16]. It is evident from DSC scan that the sample Se85Ge15 is highly homogeneous in nature, has a single glass transition temperature. We rule out any possibility of phase separation. When, we incorporated small amount of lead (Pb) at

Fig. 1. Glass forming region of Se-Ge-Pb system. 2

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Fig. 2. (a) & (b) show the X-ray diffraction patterns of the samples Se85 Ge15-x Pbx (0,2,6,8,10) and (x = 4).

is phase separated [51]. Boolchand et al. [52] demonstrated that percolation threshold or rigidity transition occurs for Se − Ge glass near < r > = 2.32 which is always accompanied with critical phenomena. At Pb = 4 at. % (< r > = 2.38) infinite chains of interacting impurity atoms (cluster), extended through-out the volume of sample are formed. Due to interconnection of impurity atoms, self organisation becomes possible. Atoms form groups (clusters) as a result of interaction of them with their nearest neighbours (short range ordering) and next neighbours. Probably this is the reason XRD indicates nano-sized clusters ingrained in the glassy matrix. Boolchand also discussed the nano phase separation in chalcogenide glasses and concluded that phase separation takes placed at critical compositions and there is a abrupt change in dT composition Vs Tg curve ( g changes abruptly) at nano scale phase

2 at. % it leads to increase in configuration entropy which facilitates the impurity atoms to enter the interstices where their valences are locally satisfied [47]. Hence a single Tg (120.47 °C) is obtained. As the Ge is substituted by Pb atoms, number of Ge–Se bonds (49.41 kcal/mol) decreases while no. of Pb–Se (31.47 kcal/mol) bonds increases. The nature of Pb–Se bond is iono-covalent and that of Ge–Se is covalent. Therefore, covalent character and hence network connectivity [48–50] of the samples decreases. Thus incorporation of Pb results in decrease in cohesive energy of the samples. Which may be one of the reasons of shifting the first Tg towards lower value of temperature (4 ≤ x ≤ 10) . Further, for the composition with Pb = 4 at. %, double glass transition temperature, (Tg = 63.68 °C, 209.65 °C) with two melting temperatures and no evidence of sharp crystallization peak are noticed. Probably two crystallization peaks are merged together forming a broad peak. This indicates that probably this sample (Pb = 4)

dc

Fig. 3. (a) DSC scans of Se85Ge15-xPbx (0 ≤ x ≤ 10) samples at the heating rate, 5 K/min. 3(b) compositional dependence of two Tg (4 ≤ x ≤ 10). 3

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system and exhibit a maximum at x = 4. On further incorporation it decreases very slowly with increasing Pb content. Thermal diffusivity also follows the same trend for 0 ≤ x ≥ 8. However, it decreases rapidly from x = 4 to x = 8. Finally, it increases significantly and attains its maximum value at x = 10. Compositional dependence of mean free path is shown in Fig. 5(b). Mean free path is minimum for x = 2 and maximum at x = 10. Volumetric specific heat (QCp) shows (Fig. 5(c)) a minimum at x = 2 like thermal conductivity and diffusivity. It is well known that the vibrational modes (phonons) of the network are the main carrier of heat in glassy semiconductors. Scattering of the propagating phonons by the defects and molecular vibrations reduces the mean free path of phonons. As the concentration of free electrons in glassy semiconductors is generally very small, hence the electronic contribution to the thermal conductivity is also small and usually neglected. Structure of Se–Ge glass is a layered structure [56,57]. On the inclusion of Pb(x = 2) in Se–Ge glassy system, it acts as a network modifier and changes the chemical network of amorphous matrix and leads to weaken the inter-chain Van der Waal interaction. There for disorder increases which is also revealed by increased FWHM of 198 cm−1 in Raman spectra and broad crystallization peak in DSC scan. Increased disorder leads to reduction in specific heat as many degrees of freedom are not available to absorb energy. As thermal conductivity is directly proportional to diffusivity and volumetric specific heat (λ e = χe QCp ) and as both are decreasing therefore thermal conductivity decreases. Thermal diffusivity is linked with mean free path by the relation

Fig. 4. Raman Spectra of Se85Ge15-xPbx (0 ≤ x ≤ 10) glasses.

separation [53]. The obtained values of first Tg shows minima for Pb = 4 at. %. Therefore, this composition is expected to be phase separated as the case exists. DSC scans of samples with x = 6, 8, & 10 also consist of two Tg which indicates two amorphous phases are co-exist in these samples. Hence, these samples may be considered as solid (concentrated) solution of selenium rich and lead rich amorphous phases [45,54].

τ = 3χ / vs

(2)

where, vs is the sound velocity (for chalcogenides vs ≈ 2000m / s ). Therefore, mean free path correlates with diffusivity. Basically as described previously (sec.3.2) incorporation of impurity in small amount leads to increase in configuration entropy which facilitates the impurity atoms to enter the interstices. At this material has largest variety of defects. According to Klemens [58–59] difference in mass, the change in the force constant at the defect site and the strain field arising due to dilation or concentration of lattice around defect contribute additively to the phonon scattering. This is the reason why thermal conductivity decreases at small Pb content (Pb = 2). Let us see how the electronic contribution to the thermal conductivity decreases. In Se–Ge glasses charged defect pairs, Se+ and Se− are present. The formation of these charged defects can be represented as

3.3. Raman analysis Raman spectra of prepared samples are shown in Fig. 4. For x = 0, spectrum consist of two peaks, one centred at 195 cm−1 which is attributed to symmetric (A1) breathing vibration of Ge2Se4/2 tetrahedron, second one centred at 256 cm−1 is assigned to the Se–Se vibration of Se8 rings and chains. Sample with x = 0 is selenium rich one and can be treated as chemically order network [55] which consist of only Se–Se bonds and Ge–Se bonds, Ge–Ge bonds are forbidden also we have not obtained any peak corresponding to the same. With the incorporation of Pb intensity of the both peaks shows non-monotonic behaviour. For x = 2 intensity of both peaks (195 cm−1, 256 cm−1) decreases. For x = 4 the intensity of 256 cm−1 again increases. After that it decreases and becomes maximum again for x = 10. Intensity of Peak 195 cm−1is low and almost same for 2 ≤ x≥ 8 while it increases again for x = 10. Decreased intensity of 195 cm−1 may be due to decreased corner shared Ge2Se4/2 tetrahedral units or decreased number of Se–Ge bonds or may be due to reduction of force constant of Ge–Se bonds. Furthermore, low intensity of both peaks for x = 4 and 6, may be due to breaks of chains and weakening of Van der Waals force between layers i.e. layered structure is distorted by the Pb. For x = 10 intensity of both lines revamped and indicates establishment of layered structure again. Emergence of a new peak at 131 cm−1 after addition of Pb is due to Se–Pb bonds.

2C20 ↔ C1− + C2+

(3)

where C represents Chalcogen atom. The super script is the formal charge on Chalcogen atom and the subscript denotes the number of bonds by which the Chalcogen atom is connected to other additives. The total density of valence alteration centres (N) is given by:

N = [C1−] + [C3+]

(4)

In the absence of metallic additives like Bi, Pb and In etc., the positively and negatively charged native defects are equal in number i.e.

[C1−] = [C3+] = N0 and N= 2N0 where N0 denotes the concentration of individual native-charge defects. The concentration of native VAPs equilibrating at the quenching or glass transition temperature (Tg), is also given by

N02 = [C3+][C1−] = NA2 exp(−EVAP /kTg)

3.4. TPS analysis

(5)

where NA is the density of the chalcogens and EVAP is the energy required to create a valence alteration defect pair from a normally bonded chalcogen. If n 0 and n respectively are the electron concentration in the absence and presence of the additives, these two are related by

Thermo-physical properties of prepared samples were measured using Transient plane source technique. Variation of thermal conductivity (λe) and thermal diffusivity (χe) with Pb content is shown in Fig. 5(a). It is observed form Fig. 5(a) that the value of thermal conductivity shows a minimum on the incorporation of Pb (x = 2) in Se–Ge

n2 [C3+]/[C1−] = NC2 exp(−2εn/ kT ) = n 02 4

(6)

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Fig. 5. Fig. 5(a) and (b) represent the variation of observed thermal conductivity, thermal diffusivity and mean free path against Pb at. % of as-prepared glassy samples Se85 Ge15-x Pbx (0 ≤ x ≤ 10) by using TPS measurement technique. Fig. 5(c) Compositional dependence of observed volumetric heat capacity and calculated Specific heat capacity of glassy samples Se85 Ge15-x Pbx (0 ≤ x ≤ 10).

In the region of low Pb concentration Se3+ can be assumed to major carrier. Further the incorporation of Pb in to Se–Ge glass converts some of the positively charged Se3+ centres in to Se1− centres keeping Ge3− centres unaffected. Consequently, the number of Se3+ centres that can undergo thermal excitation decreases [60]. Conversion of Se3+ centre in to Se1− centre results in a free hole. Hence there is a decrease in the number of free holes due to the less no of available Se3+ centres for conversion. With the decrease in the Se3+ centres, the concentration of traps that can capture electrons excited in to the conduction band also decreases. Therefore the effective electron concentration in the material increases. Beside this, there is a simultaneous increase in the concentration of charged defect states, which enhances the concentration of shallow acceptors that capture holes from the valance band. The increased electron concentration reduces the phonon mean free path, which results in a decrease in the thermal conductivity (electronic contribution) and diffusivity of x = 2 glass. As the impurity concentration is further increased, the overlapping of the elastic fields of neighbouring atoms starts to become significant and produces a partial compensation of the impurity imposed elastic stresses. On reaching the percolation threshold ( x = 4, < r > = 2.38) an infinite chain of interacting impurity atoms (cluster), extended through-out the volume of sample, is formed. Compensation of stress takes on collective behaviour and facilitates the propagation of phonons reducing the phonon scattering and hence increasing the thermal conductivity and mean free path. Due to interconnection of impurity atoms, self organisation

where NC is the effective density of conduction band states and εn is the activation energy of electrons. If Eg is the mobility gap, then εn ≈ Eg /2 It is assumed that additives as Pb equilibrate at Tg and yield positive centre of concentration [A+ ], where A denotes additive. Assuming that n 0 is small compared to N0 , the defect concentration after the addition of metal atoms in to the chalcogenide glass can be estimated from.

[C1−]∗ = 1/2[A+ ] + (N02 + 1/4[A+ ]2 )1/2

(7)

[C3+]∗ = −1/2[A+ ] + (N02 + 1/4[A+ ]2 )1/2

(8)

[A+ ]

Here, is treated as an independent variable for determining [C1−]∗ and [C3+]∗ at Tg . The total concentration of VAPs after the addition of metal atoms (Nmod ) is given by

(Nmod ) = [C1−]∗ + [C3+]∗ = 2(N02 + 1/4[A+ ]2 )1/2

(9)

In order to have any appreciable effect: the value of n after the incorporation of the additive can be estimated

n2 (2N02/[A+ ] + n) = 2[A+ ] n02

(10)

For high additive concentration, Eqn. (10) simplifies to

n = (2[A+ ])1/3n02/3, whereas for low additive concentrations, it reduces to

n = [A+ ] n 0 / N0

(11) 5

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Fig. 6. (a) Tauc plots of prepared samples Se85 Ge15-x Pbx (0 ≤ x ≤ 10), 6 (b) Absorption spectra of Se85 Ge11 Pb4 sample.

increase in band gap is noticed (Δ~1 eV) that may be due to formation of most rigid topology [66]. Finally for the composition with highest lead content (x = 10) we have a reduced value of band gap (1.25 eV) in comparison to composition with x = 6, because the electro-negativities of Ge and Pb are nearly same and Pb is found to be in Pb2+ state in these glasses [67], naturally Pb2+ is likely to pull sufficient electron density around itself in the bonded state in the glass, therefore the energy levels of Pb2+ (sp3d2 band) are expected to be higher than lone -pair levels of Se and have a stabilizing effect on the electrons in lone pair band. The higher content of Pb leads to a swift growth of sp3d2 band states accompanied with a growth in Se− lone pair states. It also results in broadening of anti-bonding band levels (Anti bonding band forms from the overlapping of Ge–Ge and Ge–Se anti-bonding orbitals, which acts as a conduction band) into the band gap. Since the optical transition takes place from top of the valance band (lone pair orbitals) to the conduction band and hence higher concentration of Pb leads to a decrease in optical band gap of Se-Ge-Pb system [68]. An alternative explanation of the obtained behaviour of optical band gap of the prepared samples can be given by following the Tanaka [69]. Tanaka taking into an account of Raman spectra of chalcogenide glasses, demonstrated that shift in band gap can be attributed to the shift in position in Raman peak (shift in peak position reveals the change in medium range order) and change in normalised intensity of the peak corresponding to homo-polar bonds.

becomes possible. After elastic stress compensation over entire volume, entire volume becomes filled with “impurity liquid” and further, inclusion of impurity atoms (6 ≤ x ≤ 10) leads to the lattice distortion which in turn causes to decrease the thermal conductivity [61,62]. 3.5. UV–visible analysis Kubelka-Munk (Eqn. (12)) transformation was used to obtain the pseudo absorption coefficient [α (K/M)]:

F(R) =

(1 − R)2 K = S 2R

(12)

where R is the reflectance of an infinitely thick sample, K and S are the absorption and scattering coefficient respectively of the sample. Tauc [Eqn. (13)] has given the following relation for indirect band gap semiconductors:

(αhν )1/2 = B1/2 (hν − ETauc )

(13)

Thus by plotting (αhν)1/2 against photon energy (hν) and noting the intercept on hν axis we obtained the optical band gap (E Tauc ). Such plots are shown in Fig. 6 (a) and the values extracted are given in table-1. The optical band gap exhibits a fluctuating behaviour with the increasing Pb content in Se–Ge parent glass. The maximum optical band gap is obtained for composition with Pb = 2 at. % (i. e x = 2) and minimum is obtained for Pb = 4 at. %. Major off set in band gap is noticed for compositions with Pb = 4&8 at.%. A increase in optical band gap on the inclusion of Pb (x = 2) in Se–Ge glass is associated with the decreased inter-chain Van der Waals interaction due to replacement of Ge by Pb in chains of Se–Ge units. Abnormal behaviour is obtained for x = 4, band gap decreases sharply that may be due to presence of long range order [63,64] in this sample which is evident from XRD or may be a result of the excitons broadening of absorption edge [65] as shown in Fig. 6(b). After registering a dip in band gap value at x = 4, further alloying of Pb (x = 6) leads to reversing the trend, and a sharp

∗

Egopt = Egopt − ΔEgm − ΔEgc

ΔEgm

(14)

Egopt

expresses the change in due to modification in medium where range order and ΔEgc represents the change induced with chemical disorder. Literature review [70] reveals that the optical band gap of SeGe-Pb glasses is Eg~1.65 eV. In present study maximum obtained band gap (Eg~1.62 eV) is of same order therefore it can be taken the band gap of stabilized glass to explain the variation of band gap with Pb content in terms of intensity of Raman peaks corresponding to homopolar bonds and shifts in their position reflecting the modification in

Table 1 Pb at.% in (Se85Ge15-xPbx) alloys

Urbach Energy EU (eV)

Coordination number < r >

(eV)

Raman peak positions of ISe–Se (cm−1)

Normalise Intensity of peak (ISe–Se)

0 2 4 6 8 10

1.32 1.62 0.65 1.60 1.07 1.25

0.06063 0.0670 0.969 0.0821 0.0894 0.0655

2.30 2.34 2.38 2.42 2.46 2.50

250.90 257.60 250.89 252.19 251.98 253.00

1 0.05375 0.33705 0.15795 0.15339 0.74763

Optical Band gap Eg

6

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decreases it reveals the same nature of band gap of each composition respectively. Because EU represent the disorderness or width of band tail, when width of tail increases optical band gap decreases. 4. Conclusions Samples, Se85 Ge15-x Pbx (0 ≤ x ≤ 10) were prepared using melt quench technique. XRD of the samples reveals amorphous nature of the prepared samples except Pb = 4 at. %. DSC scans of some samples exhibit two glass transition temperatures (Tg), which indicates the presence of separate phase embedded in the glassy matrix. Degree of disorder changes with Pb concentration which is reflected in terms of intensity and shift in peak position (Raman) of Se–Se bond (ISe–Se). The optimum values of thermal parameters are obtained at x = 2&4. Uv–Vis spectroscopy and Kubelka Munk transformation gives pseudo absorption F(R) . A non monotonic behaviour of optical band gap (Tauc) is noticed, as the Pb concentration increases in the alloy. The absorption spectra for Pb = 4 at. % shows signature of exciton formation. Fig. 7. (c) Urbach energy estimation for sample Se85Ge9 Pb6.

Declaration of competing interest medium range order. The normalised intensity of Raman peak corresponding to composition x = 0, is maximum. Therefore it contains greatest number of homo-polar bonds (and hence chemical disorder). Similarly there is a shift in the values of kmax (2.7 cm−1) which shows a slight change in medium range order. Both kind of disorder affects additively and leads to reduction in band gap (Eqn. (14)). For x = 4, the normalised intensity (ISe–Se) increases by nearly 1/3rd of intensity as in case of x = 0, while there is a greatest shift (~7 cm−1) in the position of this Raman line which indicates a largest change in order of atomic structure perhaps there exist a long range structural order in this composition which is also evident from XRD of this sample. Hence we have obtained the least value of optical band gap. Further inclusion of Pb leads to a small increase in normalised intensity (~0.2 times of (ISe–Se)max) and ~5 cm−1 change in peak position so that cumulative effect of two disorder is small hence there is a small change in band gap with respect to the composition having Pb = 2 at.%. The ISe–Se peak intensity and shift in peak position for composition having x = 8 are nearly same as that of x = 6 although there is a second largest decrease in band gap value which cannot be explain on the above lines and indicates that the structural order of this composition is somewhat similar to that of composition with x = 4 which is also indicated by the presence of excitons formation signal in the absorption spectra of both the samples. For x = 10, there is considerable amount of Se–Se bonds which is indicated by Raman peak intensity. Corresponding peak position shift is ~5 cm−1 therefore both type of disorders is contributing sufficiently to reduce the band gap. For non crystalline materials Urbach suggested that absorption coefficient (α) follow the empirical rule:

hν α = α 0exp ⎛ ⎞ ⎝ EU ⎠ ⎜

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Authors are thankful to Dr. A. M. Awasthi, IUAC Indore for DSC measurements, Dr. Lokendra Kumar, University of Allahabad for XRD measurements and Prof. Ranjan Kumar Singh, Deptt of Physics BHU for Raman measurement. One of the authors, H. Kumar acknowledges the financial support received from DST-purse, UPE grant and UGC CAS programme. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.optmat.2019.109395. References [1] A. Zakery, S.R. Elliott, Optical properties and applications of chalcogenide glasses: a review, J. Non-Cryst. Solids 330 (2003) 1–12. [2] E. Lepine, Z. Yang, Y. Gueguen, J. Troles, X.-H. Zhang, B. Bureau, C. BoussardPledel, Optical microfabrication of tapers in low-loss Chalcogenide fibers, J-Ch. sangleboeuf, and P. lucas, J. Opt. Soc. Am. B 27 (2010) 966–971. [3] M.L. Anne, J. Keirsse, V. Nazabal, K. Hyodo, S. Inoue, C. Boussard-Pledel, H. Lhermite, J. Charrier, J. Charrier, K. Yanakata, O. Loreal, J. Leperson, F. Colas, C. Compere, B. bureau, Chalcogenide Glass optical wave guides for infrared biosensing, Sensors 9 (2009) 7398–7411. [4] D. Lezal, J. Pedlikova, J. Zavadil, Chalcogenide glasses for optical and photonics applications, J. Optoelectron. Adv. Mater. 6 (2004) 133–137. [5] A.R. Hilton, Chalcogenide Glasses for Infrared Optics, McGraw-Hill Professional, 2009. [6] D. Lathrop, H. Eckert, Chemical disorder in non-oxide chalcogenide glasses. Site speciation in the system phosphorus-selenium by magic angle spinning NMR at very high spinning speeds, J. Phys. Chem. 93 (1989) 7895–7902. [7] A.V. Kolobov, S.R. Elliott, Photodoping of amorphous chalcogenides by metals, Adv. Phys. 40 (1991) 625–684. [8] K.J. Rao, S.J. Balasubramaniam, A molecular dynamics study of atomic correlations in glassy B2S3, J. Phys. Chem. 98 (1994) 9216–9221. [9] S. Asokan, M.V.N. Prasad, G. Parthasarathy, E.S.R. Gopal, Mechanical and chemical thresholds in IV-VI chalcogenide glasses, Phys. Rev. Lett. 62 (7) (1889) 808–810. [10] K.J. Rao, R.J. Mohan, Glass transitions in as-Se glasses, J. Phys. Chem. 84 (1980) 1917–1919. [11] J. Nishi, S. Morimoto, I. Ingawa, R. Lizuka, T. Yamashta, Recent advances and trends in chalcogenide glass fiber technology: a review, J. Non-Cryst. Solids 140 (1992) 199–208. [12] M. Frumar, B. Frumarova, P. Nemec, T. Wagner, J. Jedelsky, M. Hrdlicka, Thin chalcogenide films prepared by pulsed laser deposition-new amorphous materials applicable in optoelectronics and chemical sensors, J. Non-Cryst. Solids 352 (2006) 544–561. [13] J.T. Krause, C.R. Kurkjian, D.A. Pinnow, E.A. Sigety, Low acoustic loss chalcogenide

⎟

(15)

Or

ln(α ) = ln(α 0) +

hν EU

(16)

where α 0 is a constant, nearly independent of photon energy, EU is the width of band tail due to localized state in band gap. For the sample with Pb = 2 at. % the behavior of ln(α) against hν near the absorption edge shown in Fig. 7(c). Similar behavior is obtained for other samples of the series. The value of Urbach energy EU is determined from the reciprocal of slope of straight line (Eqn. (16)). The values thus obtained are tabulated in table- 1. It is observed that the values of EU are also exhibit a non-monotonic behavior with the addition of Pb in Se–Ge system. The obtained values of EU are supporting to describe the nature of band gap, as the band gap increases or 7

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