Characterization of quaternary chalcogenide As-Ge-Te-Si thin films

Investigated in this paper is the effect of replacement of Te by Si on the optical gap and some other physical operation parameters of quaternary chalcogenide As₃₀Ge₁₀Te₆₀₋xSix (where x = 0, 5, 10, 12 and 20 at.%) thin films. Thin films with the thickness 100-200 nm of As₃₀Ge₁₀Te₆₀₋xSix were pre...

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Дата:2011
Автори: Amer, H.H., Elkordy, M., Zien, M., Dahshan, A., Elshamy, R.A.
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Опубліковано: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2011
Назва видання:Semiconductor Physics Quantum Electronics & Optoelectronics
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Цитувати:Characterization of quaternary chalcogenide As-Ge-Te-Si thin films / H.H. Amer, M. Elkordy, M. Zien, A. Dahshan, R.A. Elshamy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 3. — С. 302-307. — Бібліогр.: 34 назв. — англ.

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spelling nasplib_isofts_kiev_ua-123456789-1177642025-06-03T16:28:47Z Characterization of quaternary chalcogenide As-Ge-Te-Si thin films Amer, H.H. Elkordy, M. Zien, M. Dahshan, A. Elshamy, R.A. Investigated in this paper is the effect of replacement of Te by Si on the optical gap and some other physical operation parameters of quaternary chalcogenide As₃₀Ge₁₀Te₆₀₋xSix (where x = 0, 5, 10, 12 and 20 at.%) thin films. Thin films with the thickness 100-200 nm of As₃₀Ge₁₀Te₆₀₋xSix were prepared using thermal evaporation of bulk samples. Increasing Si content was found to affect the average heat of atomization, average coordination number, number of constraints and cohesive energy of the As₃₀Ge₁₀Te₆₀₋xSix alloys. Optical absorption is due to allowed non-direct transition, and the energy gap increases with increasing Si content. The chemical bond approach has been applied successfully to interpret the increase in the optical gap with increasing silicon content. The authors would like to thank Dr. A. Abdglel, Solid State Physics Department, National Center for Radiation Research and Technology, Atomic Energy Authority, Cairo, Egypt for his help and support. 2011 Article Characterization of quaternary chalcogenide As-Ge-Te-Si thin films / H.H. Amer, M. Elkordy, M. Zien, A. Dahshan, R.A. Elshamy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 3. — С. 302-307. — Бібліогр.: 34 назв. — англ. 1560-8034 PACS 61.80.-x, 78.66.Jg https://nasplib.isofts.kiev.ua/handle/123456789/117764 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description Investigated in this paper is the effect of replacement of Te by Si on the optical gap and some other physical operation parameters of quaternary chalcogenide As₃₀Ge₁₀Te₆₀₋xSix (where x = 0, 5, 10, 12 and 20 at.%) thin films. Thin films with the thickness 100-200 nm of As₃₀Ge₁₀Te₆₀₋xSix were prepared using thermal evaporation of bulk samples. Increasing Si content was found to affect the average heat of atomization, average coordination number, number of constraints and cohesive energy of the As₃₀Ge₁₀Te₆₀₋xSix alloys. Optical absorption is due to allowed non-direct transition, and the energy gap increases with increasing Si content. The chemical bond approach has been applied successfully to interpret the increase in the optical gap with increasing silicon content.
format Article
author Amer, H.H.
Elkordy, M.
Zien, M.
Dahshan, A.
Elshamy, R.A.
spellingShingle Amer, H.H.
Elkordy, M.
Zien, M.
Dahshan, A.
Elshamy, R.A.
Characterization of quaternary chalcogenide As-Ge-Te-Si thin films
Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet Amer, H.H.
Elkordy, M.
Zien, M.
Dahshan, A.
Elshamy, R.A.
author_sort Amer, H.H.
title Characterization of quaternary chalcogenide As-Ge-Te-Si thin films
title_short Characterization of quaternary chalcogenide As-Ge-Te-Si thin films
title_full Characterization of quaternary chalcogenide As-Ge-Te-Si thin films
title_fullStr Characterization of quaternary chalcogenide As-Ge-Te-Si thin films
title_full_unstemmed Characterization of quaternary chalcogenide As-Ge-Te-Si thin films
title_sort characterization of quaternary chalcogenide as-ge-te-si thin films
publisher Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate 2011
url https://nasplib.isofts.kiev.ua/handle/123456789/117764
citation_txt Characterization of quaternary chalcogenide As-Ge-Te-Si thin films / H.H. Amer, M. Elkordy, M. Zien, A. Dahshan, R.A. Elshamy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 3. — С. 302-307. — Бібліогр.: 34 назв. — англ.
series Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv AT amerhh characterizationofquaternarychalcogenideasgetesithinfilms
AT elkordym characterizationofquaternarychalcogenideasgetesithinfilms
AT zienm characterizationofquaternarychalcogenideasgetesithinfilms
AT dahshana characterizationofquaternarychalcogenideasgetesithinfilms
AT elshamyra characterizationofquaternarychalcogenideasgetesithinfilms
first_indexed 2025-11-30T23:47:46Z
last_indexed 2025-11-30T23:47:46Z
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fulltext Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 3. P. 302-307. PACS 61.80.-x, 78.66.Jg Characterization of quaternary chalcogenide As-Ge-Te-Si thin films H.H. Amer1, M. Elkordy2, M. Zien2, A. Dahshan3, R.A. Elshamy2* 1Solid State Department, National Center for Radiation Research and Technology, Nasr City, Cairo, Egypt 2Electronics and Communication Department, Faculty of Electronic Engineering, Menofia University, Egypt 3Department of Physics, Faculty of Science, Port Said University, Port Said, Egypt 2*E-mail: randa.aly72@yahoo.com Abstract. Investigated in this paper is the effect of replacement of Te by Si on the optical gap and some other physical operation parameters of quaternary chalcogenide (where x = 0, 5, 10, 12 and 20 at.%) thin films. Thin films with the thickness 100-200 nm of were prepared using thermal evaporation of bulk samples. Increasing Si content was found to affect the average heat of atomization, average coordination number, number of constraints and cohesive energy of the alloys. Optical absorption is due to allowed non-direct transition, and the energy gap increases with increasing Si content. The chemical bond approach has been applied successfully to interpret the increase in the optical gap with increasing silicon content. xx601030 SiTeGeAs − xx601030 SiTeGeAs − xx601030 SiTeGeAs − Keywords: thin films, optical gap, Si material, radiation effects, cohesive energy. Manuscript received 09.03.11; accepted for publication 14.09.11; published online 21.09.11. 1. Introduction Chalcogenide glasses are a recognized group of inorganic glassy materials which always contain one or more chalcogen elements S, Se, or Te but not O, in conjunction with more electropositive elements as As, Sb, and Bi. Chalcogen glasses are generally less robust, weakly bonded materials than oxide glasses. Initially, glasses containing chalcogen elements were the subject of study owing to their interesting semiconducting properties, and more recently for their applications in optical recording [1, 2], technological applications, like optical imaging or storage media [3] and in the field of infrared optical transmitting materials, fiber optics and memory devices [4]. The absence of long-range order of chalcogenide glassy semiconductors allows modification of their optical properties to a specific technological application by continuously changing their chemical composition [5, 6]. Hence, studying the dependence of their optical properties on composition is important to improve technological application [7, 8]. As chalcogenide glassy semiconductors, the physical properties of SiTeAs −− and SiTeGe −− are strongly dependent on composition, thus composition is especially important in studying their physical properties. In fact, the chemical bond approach was very useful in predicting the semiconductor properties of different compounds and crystal classes [9]. The present study investigates the influence of addition of Si (0, 5, 10, 12 and 20 at.%), which is lower in atomic weight than Te, on the optical properties of new, amorphous thin films. In addition, the optical band gap (E xx601030 SiTeGeAs − g), average coordination numbers (Nco) and average heat of atomization (Hs) of the glasses have been examined theoretically. The results were interpreted in terms of the chemical bond approach used to estimate the cohesive energies of the glasses under investigation. xx601030 SiTeGeAs − 2. Experimental details Different compositions of bulk (where x = 0, 5, 10, 12, 20 at.%) chalcogenide glasses were prepared from high-purity (99.999%) As, Ge, Te xx601030 SiTeGeAs − © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 302 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 3. P. 302-307. © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine Table 1. Values of optical band gap, density, coordination number, heat of atomization (Hs), bond energy and electronegativities of As, Ge, Te, Si used for calculations. As Ge Te Si and Si by using the melt-quench technique. Appropriate proportions of the raw materials were weighed and sealed into silica ampoules under vacuum of ≈ , which were then heated gradually up to a temperature of 1125 K within 1 h and kept constant for 8 h. Throughout the heating process, the ampoules were regularly shaken to ensure homogeneity and then quenched in ice-cold water to avoid crystallization. Energy gap (eV) 1.15 0.95 0.65 1.65 Density (g/cm3) 4.7 5 6 2 Coordination number 3 4 2 4 Hs (kcal/g atom) 69 90 46 108 Bond energy (kcal/mol) 32.1 37.6 33 42.2 Electronegativity 2.18 2.01 2.1 1.8 Pa10 4− Thin films of were prepared by thermal evaporation of the bulk samples. The thermal evaporation process was performed inside the coating system Edward 306E at the pressure close to . During the deposition process (at normal incidence), substrates were suitably rotated to obtain films of uniform thickness. The film thickness was controlled within the range 100-200 nm using a quartz crystal thickness monitor Edward FTM5. The elemental compositions of the investigated specimens were checked using the energy dispersive X-ray spectroscopy (Link Analytical Edx). Deviations in the elemental composition of the evaporated thin films from the initial bulk specimens did not exceed 1.0 at.%. The amorphous state of the films was checked using an X-ray diffractometer (Philips type 1710 with Cu as a target and Ni as a filter; λ = 1.5418 Ǻ). Absence of crystalline peaks confirmed the glassy state of the prepared samples. The double beam spectrophotometer Shimadzu 2101 was used to measure reflectance and transmittance for the prepared films in the spectral wavelength range 200 to 1100 nm. xx601030 SiTeGeAs − Pa10 4− VISUV − 3. Simulation results and discussion Ioffe and Regel [10] suggested that the bonding character in the nearest neighbor region, which is described by the coordination number (the degree of cross linking), characterizes the electronic properties of the semiconducting materials. It is well known that the coordination number of covalently bonded atoms in glass is given by the so-called rule, where N is the number of outer-shell electrons [11]. The numbers of the nearest neighbor atoms for As, Ge, Te and Si are calculated and listed in Table 1. N−8 The average coordination number is defined simply as the atom-averaged covalent coordination of the constituents [12]. In the quaternary compounds AαBBβCγDλ the averaged coordination number is generalized as: ( ) ( ) ( ) ( ) λ+γ+β+α λ+γ+β+α = DNCNBNAN N cocococo co . (1) For our compound the average coordination number is given by the following 2nd relation [13] Nco = 2xTe + 3xAs + 4xGe + 4xSi. (2) The degree of cross linking has a profound effect on the thermal and mechanical properties of chalcogenide glasses, because increasing the cross linking makes the atoms become more tightly bound [14]. The determination of Nco allows estimation of the number of constraints (Ns). This parameter is closely related to the glass-transition temperature and associated properties. For a material with the coordination number Nco, Ns can be expressed as the sum of the radial and angular valence force constraints [15]: ( 32 2 −+= co co s NNN ) . (3) The calculated values of Nco and Ns for the system are given in Table 2. The parameter r, which determines the deviation of stoichiometry and is expressed by the ratio of the covalent bonding possibilities of chalcogen atoms to that of non-chalcogen atoms, was calculated using the following relation [16, 17]: xx601030 SiTeGeAs − ( ) ( ) ( ) ( ) ( )SiGe10As30 Te60 cococo co xNNN Nx r ++ − = . (4) The calculated values of r for system are also given in Table 2. xx601030 SiTeGeAs − According to Pauling [18], the heat of atomization ( )BAH s − at standard temperature and pressure of a binary semiconductor formed from atoms A and B is the sum of the heats of formation ΔH and the average of the heats of atomization and corresponding to the average non-polar bond energy of the two atoms [19, 20]: A sH B sH 303 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 3. P. 302-307. Table 2. Some of physical parameters as a function of the Si content for As30Ge10Te60–xSix (where x = 0, 5, 10, 12, 20 at.%) specimens. Composition Nco Ns R Hs ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ atomg kcal CE ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ atom eV Eg, th (eV) Hs/Nco 601030 TeGeAs 2.5 3.25 0.923 57.3 3.624 0.83 22.92 5551030 SiTeGeAs 2.6 3.5 0.733 60.4 3.848 0.88 23.23 10501030 SiTeGeAs 2.7 3.75 0.588 63.5 4.071 0.93 23.52 12481030 SiTeGeAs 2.74 3.85 0.539 64.74 4.161 0.95 23.63 20401030 SiTeGeAs 2.9 4.25 0.381 69.7 4.517 1.03 24.03 Table 3. Bond energy, probabilities and relative probabilities for formation of various bonds in As – Ge – Si – Te glasses, taking the probability of Si – Si bonds as unity. Bond Bond energy (kcal/mol) Probability Relative probability (at T = 298.15 K) Si–Si 42.20 1.03×1031 1 Ge–Si 41.16 1.77×1030 0.17 As–Si 41.13 1.69×1030 0.16 Te–Si 40.02 2.58×1029 0.02 Ge–Ge 37.60 4.30×1027 4.16×10–4 As–Ge 35.61 1.48×1026 1.43×10–5 Ge–Te 35.46 1.15×1026 1.11×10–5 Te–Te 33.00 1.79×1024 1.73×10–7 As–Te 32.70 1.08×1024 1.04×10–7 As–As 32.10 3.90×1023 3.78×10–8 ( ) ( )B s A ss HHHBAH ++Δ=− 2 1 . (5) ΔH is proportional to the square of the difference between the electronegativities χA and χB of the two atoms: ( 2 BAH χ−χ∝Δ ) . (6) ΔH that is strongly correlated with the difference in the ionicities of different atoms is small compared to the cohesive energy, because the electronegativities of the constituent elements such as As, Te, Si are very similar. In most cases, the heat of formation of chalcogenide glasses is unknown. In the few materials for which it is known, the heat of formation ΔH is about 10% of the heat of atomization and, therefore, can be neglected. To extend the idea to ternary and higher order semiconductor compounds, the average heat of atomization is defined for a compound AαB © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine BβCγDλ as [21, 22]: λ+γ+β+α λ+γ+β+α = D s C s B s A s s HHHH N . (7) The values of Hs for alloys obtained using the values of H xx601030 SiTeGeAs − s of As, Ge, Te and Sb are given in Table 2. As shown in this table, the values of Hs increase with increasing Si content. To correlate Hs with Eg in non-crystalline solids, it is reasonable to use the average coordination number instead of the isostructure of crystalline semiconductors. It was found that the variation in the theoretical values of the energy gap with composition in quaternary alloys can be described [23] by the following simple relation: thgE , ( ) ( ) BgAgABg EYEYYE −+= 1 , (8) where Y is the volume fraction of element. For quaternary alloys: ( ) ( ) ( ) ( ) ( ) , , DdECcE BbEAaEABCDE gg ggthg ++ ++= (9) where a, b, c, and d are the volume fractions of the elements A, B, C and D, respectively. Eg(A), Eg(B), Eg(C), and Eg(D) are the corresponding optical gaps. Conversion from a volume fraction to atomic percentage is made using the atomic weights and densities [24] tabulated in Table 1. The calculations of , based on the above equation for the alloys, are given in Table 2, which reveals that the addition of Si leads to a change in the considered properties. The increase in Si leads to increase in and N thgE , xx60 SiTe −1030GeAs thgE , co. The various bond energies of the expected bonds in the system are listed in Table 3. By increasing the Si content, the average bond strength of the compound decreases, and hence Eg will decrease. 304 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 3. P. 302-307. Fig. 1. X-ray diffraction patterns of the amorphous (where x = 0, 5, 10, 12, 20 at.%) thin films. xx601030 SiTeGeAs − To emphasize the relationship between Eg and the average bond strength more clearly, Eg is compared with Hs/Nco which is the average single-bond energy in the alloy. One observes that Eg, as well as Hs/Nco increase with increasing Si content, which suggests that one of the main factors determining Eg is the average single bond in the alloy [25]. Fig. 1 shows the X-ray diffraction patterns for thin films. The absence of diffraction lines in the X-ray patterns indicates that the films have amorphous structures. Transmission spectra corresponding to the amorphous thin films before and after irradiation of 1 and 15 Mrad are plotted in Figs 2, 3, 4 and show a clear ultraviolet shift of the interference-free region with increasing Si content. xx601030 SiTeGeAs − xx601030 SiTeGeAs − The values of the absorption coefficient α for the studied films were calculated from transmittance T and reflectance R using the equation: ( ) T R d 21ln1 − =α , (10) Fig. 2. Transmission spectra for (where x = 0, 5, 10, 12, 20 at.%) thin films before irradiation. xx601030 SiTeGeAs − where d is the thickness of the film. According to Tauc’s relation [26, 27] for the allowed non-direct transition, the photon energy dependence of the absorption coefficient can be described by: ( ) ( )gEhBh −= ννα 21 , (11) where B is a parameter that depends on the transition probability. Figs 5, 6 and 7 are a typical best fit of (αhν)1/2 versus photon energy hν for thin films before and after the radiation exposures 1 and 15 Mrad. The intercepts of the straight lines with the photon energy axis give the values of the optical band gap. The variation in E xx601030 SiTeGeAs − g as a function of Si content before and after the radiation exposures 1 and 15 Mrad are shown in Fig. 8. It is clear that Eg increases with increasing the Si content of the investigated films. Fig. 9 shows the density of amorphous thin film, and it is clear that density decreases with increasing the Si content. xx601030 SiTeGeAs − The possible bond distribution at various compositions may be considered using the chemically ordered network (CON) model [28]. This model assumes that: a) atoms combine more favourably with atoms of different kinds than with the same and b) bonds are formed in the sequence of bond energies. The bond energies ( )BAD − for heteronuclear bonds have been calculated by using the empirical relation [29]: Fig. 3. Transmission spectra for (where x = 0, 5, 10, 12, 20 at.%) thin films after the radiation exposure 1 Mrad. xx601030 SiTeGeAs − Fig. 4. Transmission spectra for (where x = 0, 5, 10, 12, 20 at.%) thin films after the radiation exposure 15 Mrad. xx601030 SiTeGeAs − © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 305 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 3. P. 302-307. ( ) ( ) ( )[ ] ( ) ,30 2 21 BA BBDAADBAD χ−χ+ +−⋅−=− (12) proposed by Pauling [30], where ( AAD © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine )− and are the energies of the homonuclear bonds (in units of kcal/mol) [31]: χ ( BBD − ) A and χB are the electronegatives for the involved atoms [32]. B At elevated temperatures, energy bonding effects can influence the film composition. This is because more energy is available to the atoms striking a hot substrate, and they can adjust themselves after striking to form more favorable (i.e. a higher energy) bonds. Thus, for the present material, more silicon might be incorporated into the films at higher temperatures, because it is possible for silicon to form relatively strong bonds with other constituents. This hypothesis is supported by the contents of Table 3, which lists the relative order of the bond energies of the ten possible bonds in the system. The hetero-atom single-bond energies were calculated from the average of the homo- atom single-bond energies for silicon, tellurium, arsenic and germanium, with addition of ionic contribution proportional to the square of the electronegatives difference between the elements. GeAsTeSi −−− Fig. 5. Best fit of (αhν)1/2 versus photon energy hν for (where x = 0, 5, 10, 12, 20 at.%) thin films before irradiation. xx601030 SiTeGeAs − Fig. 6. Best fit of (αhν)1/2 versus photon energy hν for (where x = 0, 5, 10, 12, 20 at.%) thin films after the radiation exposure 1 Mrad. xx601030 SiTeGeAs − Fig. 7. Best fit of (αhν)1/2 versus photon energy hν for (where x = 0, 5, 10, 12, 20 at.%) thin films after the radiation exposure 15 Mrad. xx601030 SiTeGeAs − Fig. 8. Variation in the optical band gap Eg as a function of Si content for (where x = 0, 5, 10, 12, 20 at.%). xx601030 SiTeGeAs − 0 5 10 15 20 0 1 2 3 4 5 6 D en si ty (g /c m 3 ) Si content % Fig. 9. Density dependence on the Si content for (where x = 0, 5, 10, 12, 20 at.%) glasses. xx601030 SiTeGeAs − It can be seen from Table 3 that silicon has a better chance of sticking to the growing film at elevated temperatures, as it can form strong bonds with tellurium, the major constituent. However, the bonds are relatively weak so that a deficiency of arsenic might be expected on energetic grounds. TeAs − Knowing the bond energies, we can estimate the cohesive energy (CE), i.e. the stabilized energy of an infinitely large cluster of the material per atom, by summing the bond energies over all the bonds expected 306 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 3. P. 302-307. in the system under test the CE of the prepared samples is evaluated from the following equation [33] ∑ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛= 100 iiDCCE , (13) where Ci and Di are the numbers of the expected chemical bonds and the energy of each corresponding bond, respectively. The calculated values of CE for all compositions are summarized in Table 2. CE increases with increasing the Si content. Increasing the Si content leads to an increase in the average molecular weight, which increases the rigidity (strength) of the system. This approach explains the behaviour in terms of the cohesive energy. It allows determination of the number of possible bonds and their type (heteropolar and homopolar). The energies of various possible bonds in the system are given in Table 3. Depending on the bond energy D, the relative probability of its formation was calculated [34] using the probability function exp(D/kT) and listed in Table 3. Bonds, such as , , , and TeSiGeAs −−− SiSi − GeGe − TeTe − AsAs− bonds exist with high priority in the TeSiGeAs −−− system. 4. Conclusions Optical data indicated that the allowed, non-direct gap is responsible for photon absorption in thin films. Increasing the Si content at the expense of Te atoms increases the optical gap of these films. The values for heat of atomization, coordination number, number of constraints and cohesive energy of are dependent on glass composition. The increase in Si content leads to increase in thgE , , H xx601030 SiTeGeAs − xx601030 SiTeGeAs − s/ and N © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine Nco co. Cohesive energy increases with increasing the Si content. The chemical-bond approach can be successfully applied to interpret the increase in the optical gap with increasing the Si content. Acknowledgement The authors would like to thank Dr. A. Abdglel, Solid State Physics Department, National Center for Radiation Research and Technology, Atomic Energy Authority, Cairo, Egypt for his help and support. References 1. N.A. Goryunova and B.T. Kolomiets // Zhurnal Tekhnich. Fiziki, 25, p. 984 (1955), in Russian. 2. K. Tanaka, Y. Osaka, M. Sugi, et al. // J. Non- Cryst. Solids, 12, p. 100 (1973). 3. A.E. Owen, A.P. Firth and P.J.S. Ewen // Phil. Mag. B, 52, p. 347 (1985). 4. R. Zallen, Physics of Amorphous Solids. Wiley, New York, 1983. 5. E.A. Davis // J. Non-Cryst. Solids, 71, p. 113 (1985). 6. A.H. Moharram, A.A. Othman, H.H. Amer, et al. // J. Non-Cryst. Solids, 352, p. 2187 (2006). 7. M. Yamaguchi // Phil. Mag. 51, p. 651 (1985). 8. S.S. Fouad, A. Ammar, M. Abo-Ghazala // Physica B, 229, p. 249 (1997). 9. E. Mooser, W.B. Pearson // Prog. 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