Effect of Sb on the optical properties of the Ge–Se chalcogenide thin films

Physica B 422 (2013) 40–46

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Effect of Sb on the optical properties of the Ge–Se chalcogenide thin films F. Abdel-Wahab a,b,n, N.N. Ali karar a, H.A. El Shaikh a, R.M. Salem a a b

Department of Physics, Faculty of Science, University of Aswan, Aswan, Egypt Department of Physics, Faculty of Science, Taif University, Taif, Kingdom of Saudi Arabia

art ic l e i nf o

a b s t r a c t

Article history: Received 14 December 2012 Received in revised form 4 April 2013 Accepted 5 April 2013 Available online 25 April 2013

Thin films of Ge30−xSbxSe70 (x ¼ 0, 5, 10 and 15) were prepared by thermal evaporation technique. All samples were confirmed as amorphous according to XRD results. The complex dielectric functions and optical parameters of the films determined by using the Swanepoel's method from transmittance spectra at room temperature in the range of wavelength 400–1100 nm. It has been found that by increasing Sb content, the optical band gap decreases, while the refractive index and the extinction coefficient increase. The optical energy gap of the films under test was discussed in terms of the chemically ordered model (COM) and random covalent network model (RCNM). We confirmed, using Raman spectroscopy, by addition of Sb the intensity of Ge–Ge and Ge–Se bands decreased; however, Sb–Se, and Se-chain band increased, in agreement with COM and RCNM. The results of the refractive index were studied using the Wemple equation. The variations of the refractive index and real part of dielectric constant associated with the changes of the density were examined with the well-known Lorentz–Lorenz relation. The experimental results were found to be in good agreement with those of theoretical ones. & 2013 Elsevier B.V. All rights reserved.

Keywords: Thin films Optical properties Lorentz–Lorenz relation Ordered bond network model Random bond network model

1. Introduction

2. Experimental details

Chalcogenide glasses attracted a lot of attention due to their distinguished optical and electrical properties making them efficient materials in variety of applications such as photoresistors [1,2], microelectronics [3–5], optoelectronics, ultrafast optical switches [6–8] and holographics [9,10]. Amorphous Ge–Se chalcogenide glasses have been investigated intensively including structure, glass forming area and some physical properties, the physical properties of this glassy system are found to be highly composition dependent [11]. The physical properties of these glasses may be enhanced by alloying them with Sb. Since both Ge and Sb are aliovalent ions, the basic structure of glass could alter drastically. Ganjoo et al. [12] showed that substituting Sb instead of Ge leads the glass to become a more stable structure by creating, Sb–Se bonds, and the homopolar of Ge–Ge bonds, could be converted to more stable Ge–Se bonds. In addition, it is recognized that the entity of antimony in chalcogenide glass matrix permits a faster optical storage process [13,14]. In the present work, the variation of optical properties accompanied by addition of antimony (0, 5, 10,and 15 at%) to Ge–Se are investigated, using the Swanepoel's method [15,16], based on optical transmission spectra.

Glasses of Ge30−xSbxSe70 where (x¼ 0, 5, 10 and 15) were prepared from stoichiometric mixture of high pure (99.999%) Ge, Sb and Se. The appropriate proportions in at% were weighed and sealed in quartz glass ampoules (12 mm dia.) under vacuum of 10−5 Torr. Each ampoule was slowly heated to 1000 1C and kept there for 24 h. At the maximum temperature, the tube was frequently shaken to homogenize the melt. Quenching was done in ice water to get the glassy state. The amorphous nature of the glassy alloys was verified by X-ray diffraction. The density (ρ) of the glasses under test were measured at room temperature by Archimedes technique using xylene as a buoyant liquid. The accuracy was better than 70.02 g/cm3, and the molar volume values were then calculated using the relation, VM ¼MT/(ρ), where, MT is the total molecular weight. Thin films of the prepared compositions were deposited at room temperature by thermal evaporation at a pressure of 10−5 Torr using Edwards's highvacuum coating unit model E306A. The rate of deposition was 1–2 nm s−1. Ultrasonically cleaned Corning glass was used as a substrate. The film thickness was controlled by means of an Edwards TM200 Maxtek166 high vacuum film thickness monitor. The microstructure analysis was carried out using X-ray diffractometer type Philips model PW1710. The chemical composition of the prepared films was identified from energy-dispersive X-ray analysis (EDAX) using scanning electron microscope (Philips XL30) attached with the EDAX unit. The transmittance T (λ) and reflectance R (λ) measurements were carried out using Shimadzu-UV-1650 PC UV–Visible

n Corresponding author at: Department of Physics, Faculty of Science, Taif University, Kingdom of Saudi Arabia. Tel.: +966 595410651. E-mail address: [email protected] (F. Abdel-Wahab).

0921-4526/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2013.04.010

F. Abdel-Wahab et al. / Physica B 422 (2013) 40–46

41

Table 1 Values of density (ρs), molar volume (Vm) and average coordination number (L) for Ge30−xSbxSe80 glassy alloys.

Relative intensity

x=15

10

Ge30Se70 Ge25Sb5Se70 Ge20Sb10Se70 Ge15Sb15Se70

ρs (gm/cm3)

VM (cm3/mol)

(L)

4.95 5.04 5.11 5.19

15.57 15.79 16.03 16.26

2.6 2.55 2.5 2.45

structure. It has been pointed out that, for glasses with L o2.4, the structure is ‘under-constrained’, ‘floppy’ or ‘spongy’ and for glasses with L4 2.4, the structure is over-constrained or rigid. The values of L were calculated using the standard method described in Refs. [18–20]. For the composition GexSbySez, L is given by: L ¼ xCNðGeÞ þ yCNðSbÞ þ zCNðSeÞ;

5 0

ð1Þ

where CN(Ge) ¼4, CN(Sb) ¼3 and CN(Se) ¼2, x, y and z are the ratios of Ge, Sb and Se, respectively. The calculated coordination numbers are greater than 2.4 as listed in Table 1. It can be noted from Table 1 that L decreases with the increase of Sb content. This decrease in the coordination number may be correlated with the increase of the molar volume of the structure of the Ge–Sb–Se glasses. 3.3. Optical properties of Ge–Sb–Se thin films from the transmittance spectra

20

30

40

50

60

2θ Fig. 1. XRD diagrams for Ge30−xSbxSe70 (where x¼ 0, 5, 10, and 15).

spectrophotometer (with photometric accuracy of 70.002–0.004 absorbance and 70.3% transmittance) over the wavelength range 200–2500 nm at normal incidence. A 532 nm diode laser with a power of 5–8 mW at the source was used for Raman measurements (DXR Raman microscope, Thermo Scientific). The Raman wavenumber range was set between 50 and 400 cm−1.

3. Results and discussion

3.3.1. Refractive indices, extinction coefficient and thicknesses of Ge–Sb–Se thin films by the Swanepoel's method The method suggested by Swanepoel [15,16] was used to measure the refractive index (n), extinction coefficient (k) and film thickness (d) of Ge–Sb–Se films. According to the Swanepole method, the transmittance spectra were taken at normal incidence of a beam of monochromatic light on homogeneous film of uniform thickness and complex refractive index nc ¼n−ik. The films were deposited on transparent substrate with refractive index (s), in addition, the substrate should be perfectly smooth and has a thickness of several orders of magnitude larger than the thickness of the film to avoid the optical interference effect of the substrate. The substrate and film surfaces are surrounded by air (no ¼1). The normal transmittance at different wavelength (λ) of such system is determined by the Swanepoel method as

3.1. XRD and density and molar volumes T¼ X-ray diffraction (XRD) pattern of the as-deposited Ge30 −xSbxSe70 thin films was measured in the range from 201 to 601. Fig. 1 shows the absence of any sharp diffraction peaks emphasizing the amorphous nature of the film. The EDAX analysis carried out on these films suggested that their compositions are very close to the starting materials. The density (ρ) and molar volume (VM) are essential parameters, which are correlated to other physical properties of the material as will be seen in refractive index. The measured densities (ρ) and the corresponding calculated molar volumes (VM) are summarized in Table 1 for all the samples. It can be seen from this table that both ρ and VM increase with increasing Sb content which can be due to the replacement of less denser Ge (5.32 g/cm3) having low VM (13.63 cm3) by denser Sb (6.697 g/ cm3) having high VM (18.19 cm3).

Ax ; B−CxcosðφÞ þ Dx2

where A ¼ 16n2 s;

ð3aÞ


B ¼ ðn þ 1Þ3 n þ s2 ;


C ¼ 2 n2 −1 n2 −s

Most of glass forming schemes are well-illustrated by the continuous-random-network model proposed by Zachariasen [17]. Phillips [18] and Thorpe [19] introduced the concept of average coordination number o L4 for understanding the glasses


2


D ¼ ðn−1Þ3 n−s2 ; φ¼

4πnd ; λ

;

ð3bÞ ð3cÞ ð3dÞ ð3eÞ

and x ¼ expð−αdÞ:

3.2. The average coordination number

ð2Þ

ð3fÞ

The fitting procedure for data starts with assuming that the refractive index n varies slowly with wavelength as proposed by Cauchy. nðλÞ ¼ f 0 þ

f1 ; λ2

ð4Þ

42

F. Abdel-Wahab et al. / Physica B 422 (2013) 40–46

where f's are adjusted parameters. Since, the absorption mechanism in the transparent region could be due to band transport, Urbach tail, and defect absorption then one can use the following empirical for the absorption coefficient: h1 –h0 ; λ2

ð5Þ

where h′s are adjusted parameters. All f's and h's were used to calculate the transmittance according to Eq. (2). The transmittance spectra T(λ) of Ge30−xSbxSe70 thin films in the wavelength range 400–1100 nm of normal incident light are depicted in Fig. 1 as open circles. The spectra showed many fringes due to interference of various wavelengths resulting in the transparency of the films under test. The obtained spectra from applying the model are fit to the experimental data by varying the values of the model's parameters. The solid curves in Fig. 2 represent the theoretical calculations of T(λ) using the Swanepole's method. It is clear from this figure that the theoretical calculations of transmittances are in good agreement with those obtained from experimental results of the investigated samples. Figs. 3 and 4 present the refractive index n and the extinction coefficient k (αλ/4π) of the thin films respectively as a function of wavelength taking in consideration that the data of n and k are extracted from the fitting using Eqs. (4), and (5) respectively. As it is seen, the values of k of the thin films are very small at longer wavelengths, demonstrating that the thin films under test are highly transparent. Further, both n and k increase with the increase in Sb content at any given wavelength. Huang et al. [21] observed similar composition dependence of n and k upon adding Sb into Ge–S network. The observed increase in n and k with increasing Sb can be explained in terms of variation of elements polarization [22]. As the Sb cations have higher polarizability than the Ge cations, so, the increase of Sb amount in the glass most probably causes the observed increase in the refractive index.

3.5

3.0

n

logðαÞ ¼

4.0

x= 2.5

10 5 2.0

0

400

600

800

1000

(λ/nm) Fig. 3. Plots of the refractive index, n vs. λ, for different compositions of Ge30 −xSbxSe70 thin films.

100

3.3.2. Optical band gap of Ge–Sb–Se The variation of the optical absorption near the fundamental absorption edge allowed determining the optical energy gap. In the high absorption region (α4104 cm−1), the absorption is characterized by Tauc's relation [23]: αhv ¼ Bðhv−Eg Þm ;

15

10-1

where B is the slope of the Tauc edge called the band tail parameter, Eg is the optical band gap of the material, hv is the incident photon energy and m is an integer number.

k

ð6Þ

10-2

1.0

x=

Transmittance

0.8

15

10-3

10 0.6

5 0.4 0.2

0

x =0

0.0 400

5

10

600

10-4

15

800

1000

600

800 (λ/nm)

1000

1200

Fig. 4. Plots of the extinction coefficient, k vs. λ, for different compositions of Ge30 −xSbxSe70 thin films.

(λ/nm) Fig. 2. Optical transmission spectra Ge30−xSbxSe70 thin films deposited onto thick transparent substrates as a function of, λ. Data symbols are experimental results and solid curves are calculated results according to the Swanepole's method.

Tauc and co-workers demonstrated that for crystalline state the value of m is equal to 1/2 for indirect transitions. In amorphous semiconductors, the lack of periodicity of arrangement of atoms

F. Abdel-Wahab et al. / Physica B 422 (2013) 40–46

preferred to homo-polar bonds. However, the second approach called random covalent network model (RCNM) assumes that all possible bonds exist. It should be mentioned that both models estimate that cj statistically based on local coordination of each atomic species. Following the notions of Tichý et al. [26] and Nang et al.[28], the present system can be represented as GeaSbbSer where a+b+r ¼1 with the coordination numbers of Ge, Sb and Se being 4, 3 and 2, respectively. The fraction cj of the considered bond in each model can be given as:

400

x=15

10

5

0

300

CGe–Se CSb–Se CSe–Se CGe−Ge CSb–Sb CGe–Sb

200

100

1.8

2.0 hv (eV)

2.2

2.4

2.6

Table 2 Optical band gap estimated using the Tauc's extrapolation method Eg (exp.) and Eg from Manca relation based on COM and RCMN. Eg (exp.) 7 0.05(eV)

Eg (COM) (eV)

Eg (RCNM) (eV)

2.20 2.10 1.80 1.72

2.10 2.07 2.03 1.99

1.95 1.93 1.90 1.88

removes the possibility of phonon momentum; thus the transition must be direct and m ¼2. Fig. 5 represents the relation between (αhv)1/2 and hv for all samples (open circles). In this figure, the high energy data are linearly extrapolated to zero in order to determine the band gap energy. The results are summarized in Table 2. A decrease in the optical band gap with increasing Sb concentration is observed. This variation of Eg as a function of Sb content may be interpreted in terms of the change in chemical bonds. It has been pointed out that in non crystalline materials, the values of Eg depends on composition [24,25]. Furthermore, it has been argued that the Eg depends not only on composition but also on bonds arrangement [26]. Manca [27] proposed the following relation between the bond energy (Es) and the energy gap (Eg)

8a/N 6b/N (2r−4a−3b)/N – – –

2N1/N 2N3/N (2r−N1−N3)/N (4a−N2−N1)/N (3b−N2−N3)/N 2N2/N

ð9Þ

where EAA and EBB are the energies of the homonuclear bonds, χA and χB are the electronegativity values for the involved atoms [30]. The estimated values of Eg according to COM and RCNM using the above data are presented in Table 2. On the other hand, it can be noted from Table 3 that the increase of Sb content introduces new Sb–Se chemical bonds (1.86 eV) with much smaller binding energy than that of Ge–Se (2.12 eV). Furthermore, another new type of Sb– Sb (1.31 eV) will be created at the expense of homopolar bond of Ge–Ge (1.63 eV) which may explain the decrease of Tauc energy gap with increasing Sb content. 3.3.3. Raman scattering. Table 4 It is well-known that for Se rich Ge–Sb–Se system, the structural model involves are tetrahedral GeSe4/2, pyramidal SbSe3/2 units and cross-linked by Se-chain fragments. By increasing Sb content, several aspects could be anticipated, the number of Ge–Ge and Ge–Se bonds will be decreased, however Sb–Sb bonds, Ge–Sb bonds and Se-chain fragments could be increased. In order to clear the previous aspects, we measured Raman spectra of the investigated system as shown in Fig. 6. In Fig. 6 by increasing Sb, the main band in the range 170–225 cm−1 shifts slightly to lower wave number. This shift could be due to formation of pyramidal SbSe3/2 in expense GeSe4/2 tetrahedra. Now let us consider two extreme cases in the present system, at x ¼0, a band at 170 cm−1 is attributed to the vibration of homopolar Ge–Ge bonds in the Ge2(Se1/2)6 structural units [31]. Also weak band at 219 cm−1 is designated to the vibration of Ge–Ge bonds in the GeSe2 [32]. The band at 181 cm−1 is attributed to GeSe4/2 tetrahedra [33]. The band peaking at 198 cm−1 is ascribed to the Se–Ge bonds [34]. At x ¼15,

ð7Þ

where a and b are constants. In the present study we assumed these constants to be 0 and 1, respectively. A mean bond energy (Ēs) rather than Es is assumed Ē s ¼ ∑j cj Esj ;

RCNM

EAB ¼ ðEAA EBB Þ1=2 þ 30ðχ A −χ B Þ2 ;

1.6

Fig. 5. The dependence of (αhv)1/2 on photon energy, hv, for the different composition of amorphous Ge30−xSbxSe70 thin films from which the optical band gap (Eg) is estimated (Tauc extrapolation).

Eg ¼ bðEs −aÞ;

COM

where N ¼4a+3b+2r. The values of N1, N2, and N3 are given in Eq. (5) cited in Ref. [28]. The results of fraction bond are presented in Table 3. The bond energy EAB for hetero-nuclear bonds have been calculated using the empirical relation proposed by Pauling [29],

0 1.4

Ge30Se70 Ge25Sb5Se70 Ge20Sb10Se70 Ge15Sb15Se70

43

Table 3 The results of bond fraction according to COM and RCNM. Composition COM

ð8Þ

where cj is the relative fraction bond of the j-type bonds. The problem now is to calculate cj of all possible chemical bonds. The possible bonds arrangement in the present system can be described by different approaches. The first approach is chemically ordered model (COM), where hetero-polar bonds formation are

Ge30Se70 Ge25Sb5Se70 Ge20Sb10Se70 Ge15Sb15Se70

RCNM

Ge– Se

Sb– Se

Se– Se

Ge– Se

Ge– Sb

Sb– Se

Se– Se

Ge– Ge

Sb– Sb

92.3 78.4 64.0 49.0

0.0 11.8 24.0 36.7

7.7 9.8 12.0 14.3

49.7 43.1 35.8 28.0

0.0 3.7 5.3 5.4

0.0 5.1 12.1 20.3

29.0 30.8 32.0 33.0

21.3 15.9 11.4 7.8

0.0 1.5 3.3 5.5

44

F. Abdel-Wahab et al. / Physica B 422 (2013) 40–46

0.4

Table 4 Values of dispersion energy (Ed) single oscillator energy (Eo), high frequency dielectric constant (ε∞) and films thickness in terms of Sb content. Eo (eV)

no

ε∞

NC

Film thickness (nm)

17.25 20.52 23.83 27.84

4.20 3.72 3.76 3.78

2.26 2.55 2.71 2.89

3.98 4.69 5.54 6.56

2.80 3.29 3.79 4.39

558 671 796 830

5

0.3

10

(n2-1)-1

Ge30Se70 Ge25Sb5Se70 Ge20Sb10Se70 Ge15Sb15Se70

Ed (eV)

x=0

15

0.2

0.1

0.0

0

2

4

6

8

(hv)2 (eV)2 Fig. 7. Plot of (n2−1)−1 vs. (hv)2 for Wemple–DiDomenico analysis of Ge30−xSbxSe70 thin films.

x = 15

10 5 0

50

100

150

200

250

300

350

Fig. 6. Raman spectra of Ge30−xSbxSe70 for different Sb content.

the peaks at 118, 191, and 205 cm−1 are characteristic of the Sb–Se stretching mode of the SbSe3/2 pyramidal units. [35,36]. On the other hand, the replacement of Sb instead of Ge, beside reducing the number of corner-sharing GeSe4/2, increases the number of the wrong Se–Se. The band at 250–285 cm−1 corresponding to vibration of Se, in rings and in chains with an intensity increases with the progressive introduction of Sb, in good agreement with the Raman spectrum of GeSe2 [37].Similar behaviors for the shoulders at 84 cm−1and 93 cm−1 that represents the Se8 rings as suggested by Ball and Chamberlain [38] and Ohsaka [39]. It should be mentioned that the minority homopolar Sb–Sb and heteropolar Ge–Sb bonds may not be clearly identified in the present system. 3.3.4. Refractive indices analysis of Ge–Sb–Se thin films by the Wemple–DiDomenico model The measured refractive indices were examined by using the Wemple–DiDomenico model in the region from visible to nearinfrared by the following equation [40,41]: n2 −1 ¼

Eo Ed E2o −ðhvÞ2

;

ð10Þ

where Ed is the dispersion energy which is the measure of the strength of inter-band optical transition and Eo is the single oscillator energy for electronic transition. The values of both E0 and Ed values were calculated from the slope and intercept of the straight line of the (n2−1)−1 vs. (hν)2 relation as shown in Fig. 7. The values of

Eo and Ed of the present system on Sb content were recorded in Table 2. It can be noted that both E0 and Ed decrease with increasing Sb content which might be explained in terms of the increase in the number of scattering centers due to dissolving Sb atoms in the Ge–Se glassy film matrix [42]. In addition, Ed relates to other physical parameters of the material through an empirical relation [41,43]: in the form Ed ¼βNcZaNe, where β is a constant which, for covalent crystalline and amorphous materials, has a value of 0.4 eV, Nc is the total number of valence electrons per anion, Za is the formal chemical valence of the anion and Ne is the effective number of valence electrons per anion. For GexSbySez, assuming Ne from the following equation (4x+5y+6z)/z and Za ¼2, the corresponding Nc can be calculated and these are summarized in Table 2. The static refractive index (n0) was also calculated from dispersion parameters Eo and Ed using the formula no ¼(1+Ed/Eo)1/2 and recorded in Table 2. Also the values of films thickness are summarized in Table 2. The transmission spectra of the present system can also be utilized to derive the complex dielectric function as well as the dissipation factor (tan δ) of the films. The real and imaginary parts of the dielectric function ε′ and ε″ are related to n and k by 2

ε′ ¼ n2 −k ;

ð11aÞ

ε″ ¼ 2nk;

ð11bÞ

tan d ¼

ε″ : ε′

ð11cÞ

The variations of ε′, ε″, and tan δ with wavelength λ for all samples were plotted in Figs. 8–10, respectively revealing that all of them decreased with increasing wavelength, and the values of ε′ were higher than those of ε″ for all the samples. Also, it can be noted that at a fixed wavelength, the values of ε′, ε″, and tan δ increased with increase in Sb content. On the other hand, the increase in the values of dielectric constant with increasing Sb content can be understood in terms of the nature of bonds percentage in the system, and from the values of the bond energy [44]. It is found that the increase of Sb leads to decrease in the density of stronger bonds Ge–Ge and Ge–Se and increase in the weaker bonds as Sb–Se, Sb–Sb and Ge–Sb in the network structure. It should be mentioned that the weaker bonds are easy to respond to the electric field than the stronger bonds. Thus one can say that as Sb content increases the density of the weaker bond increases.

F. Abdel-Wahab et al. / Physica B 422 (2013) 40–46

45

100

'

8 10-1

x= 15

6

5 0

4

tan(δ)

10 10-2 x= 2 400

500

600

700

800 λ/nm

900

1000

15

10-3

1100

10

Fig. 8. Plots of ε′ as a function of λ for the investigated thin films.

5

10-4

100

0

600

800 λ/mn

1000

Fig. 10. Dependence of the dissipation factor tan δ on the wavelength for the investigated thin films.

10-1 In order to calculate ΔP/P, the following relations were used [46]:

"

x =

PðωÞ ¼ εo χ ðωÞEðωÞ;

ð13Þ

where ε0 is permittivity of free space and dielectric susceptibility χ (ω) is

10-2 15

χðωÞ ¼ χ 1 ðωÞ−iχ 2 ðωÞ:

10

The components of χ(ω) are related to those of complex relative permittivity ε(ω) ¼ε′(ω)−iε″(ω)

5

χ′ðωÞ ¼ ε′ðωÞ−1

ð15aÞ

χ ″ðωÞ ¼ ε″ðωÞ

ð15bÞ

10-3

ð14Þ

At high frequency where these materials become more transparent (n»k), one can expect the following relation ΔP Δε′ ¼ : P ε′−1

0

600

800 λ/nm

Then the Lorentz–Lorenz relation can be written as   ðn2 −1Þðn2 þ 1Þ Δε′ Δρ : Δn ¼ þ 0 ε −1 ρ 6n2

1000

Fig. 9. Plots of ε″ as a function of λ for the investigated thin films.

This in turn leads to increase in dielectric constant in the investigated compositions. The results belonging to the films under test indicated that the increase in the density (ρ) was accompanied with an increase of the refractive index increase, and this can be discussed as follows. In the first approximation, the changes in the refractive index associated with the density changes can be evaluated using wellknown Lorentz–Lorenz relation [45]. This relation relates the change in refractive index (Δn) with the change in density (Δρ) of a substance and the change in polarizability (ΔP) through the following expression:   ðn2 −1Þðn2 þ 1Þ ΔP Δρ Δn ¼ þ 2 P ρ 6n

ð12Þ

ð16Þ

ð17Þ

Fig. 11 shows the variation of the refractive index with changing the wave length for different compositions (data points). The previous figure indicates that, the refractive index seem to be independent on the wavelength, whereas, Δn increase monotonically with λ at lower range of λ. It is noticed that the solid curves are the theoretical one which are calculated using Eq. (17). It can be noted from Fig. 11 that the Lorentz–Lorenz relation in its modified form Eq. (17) represents the best relation that collects refractive index, density and polarizability.

4. Conclusion The effect of addition of Sb on the optical properties of vacuum evaporated thin films of Ge30−xSbxSe70 with x¼ 0, 5, 10 and 15 has been studied using transmission spectra. The refractive and absorption

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F. Abdel-Wahab et al. / Physica B 422 (2013) 40–46

0.8

Δn

0.6

f

e

d 0.4

c b

0.2

a 600

800

1000

1200

λ/mn Fig. 11. Calculated refractive index change (Δn) from experimental data for Ge30−xSbxSe70 (where x ¼0, 5, 10, and 15) represent as data point (a) n5–n0, (b) n10–n5, (c) n15–n10, (d) n10–n0, (e) n15–n5, and (f) n15–n0. The solid curves are the theoretical fitting according to Eq. (17).

indices were computed using the Swanepoel's method. A good fitting to experimental data were obtained assuming refractive index follows Cauchy equation. The optical band gaps estimated using Manca's relation based on the COM and RCNM model are in good agreement with those obtained from Tauc's extrapolation method. The opticaldispersion data were analyzed using WDD model and, consequently, the oscillator strength, oscillator energy and static dielectric constant can be calculated. The decrease in the value of Eg and the increase in the magnitude of n are accompanied by increasing the Sb content in the glassy network. We have driven a new form for the Lorentz– Lorenz relation; by this form a plausible fitting to experimental data for various wave length was obtained. References [1] K. Petkov, J. Optoelectron. Adv. Mater. 4 (2002) 611. [2] A. Kovalskiy, M. Vlcek, H. Jain, A. Fiserova, C.M. Waits, M. Dubey, J. Non-Cryst. Solids 352 (2006) 589. [3] S.R. Ovshinsky, J. Non-Cryst. Solids 141 (1992) 200. [4] J.P. Kloock, L. Moreno, A. Bratov, S. Huachupoma, J. Xu, T. Wagner, T. Yoshinobu, Y. Ermolenko, Y.G. Vlasov, M.J. Schöning, Sensors Actuators B 118 (2006) 149.

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