Optical band gap and refractive index dispersion parameters of As x Se 70 Te 30 x (0 x 30 at.%) amorphous films

Appl Phys A (2010) 99: 913 919 DOI 10.1007/s00339-010-5680-6 Optical band gap and refractive index dispersion parameters of As x Se 70 Te 30 x (0 x 30 at.%) amorphous films Kamal A. Aly Received: 15 March 2010 / Accepted: 19 March 2010 / Published online: 16 April 2010 Springer-Verlag 2010 Abstract Amorphous As x Se 70 Te 30 x thin films with (0 x 30 at.%) were deposited onto glass substrates by using thermal evaporation method. The transmission spectra T(λ)of the films at normal incidence were measured in the wavelength range 400 2500 nm. A straightforward analysis proposed by Swanepoel based on the use of the maxima and minima of the interference fringes has been used to drive the film thickness, d, the complex index of refraction, n, and the extinction coefficient, k. The dispersion of the refractive index is discussed in terms of the single-oscillator Wemple and DiDomenico model (WDD). Increasing As content is found to affect the refractive index and the extinction coefficient of the As x Se 70 Te 30 x films. With increasing As content the optical band gap increases while the refractive index decreases. The optical absorption is due to allowed indirect transition. The chemical bond approach has been applied successfully to interpret the increase of the optical gap with increasing As content. to have an insight into their optical and electronic properties. The addition of an impurity has a pronounced effect on the conduction mechanism and the structure of the amorphous glass and this effect can be widely different for different impurities [9]. Therefore, the ternary compounds involving As Se Te have interesting properties as well as technological applications because they form a wide range of glassy region. Although it is possible to find in the literature more papers dealing with As Se Te thin films [10 16] but, to the best of our knowledge, the effect of As content on the optical constants of As Se Te have not been reported. The present work deals with investigation of the optical properties of the As x Se 70 Te 30 x (0 x 30 at.%) thin films. The well-known Swanepoel s method [17, 18] is used to accurately determination of the refractive index and film thickness in the weakly absorbing and transparent regions of the spectrum. Also, the absorption coefficient, and therefore the extinction coefficient, has been determined in the strong absorption region of the transmission spectra. 1 Introduction Chalogenide glasses have been recognized as promising materials for infrared optical element, infrared optical fibers, and for the transfer of information [1 3]. They have also found applications in xerography switching and memory devices, photolithographic process, and in the fabrication of inexpensive solar cells and more recently as reversible phase change optical recorders [4 8]. This has made it important K.A. Aly ( ) Physics Department, Faculty of Science, Al-Azhar University, Assiut, Egypt e-mail: kamalaly2001@gmail.com 2 Experimental details Different compositions of bulk As x Se 70 Te 30 x (0 x 30 at.%) chalcogenide glasses were prepared from their components of high purity (99.999%) by the usual melt quenching technique. The elements were heated together in an evacuated silica ampoule up to 1200 K and then the ampoule temperature kept constant for about 20 h. During the course of heating, the ampoule was shaken several times to maintain the uniformity of the melt. Finally, the ampoule was quenched into ice-cooled water to avoid the crystallization process. The amorphous thin films were deposited by evaporating the alloys from a resistance-heat quartz glass crucible

914 K.A. Aly Fig. 1 X-ray diffraction patterns of as prepared As x Se 70 Te 30 x with (0 x 30 at.%) thin films onto clean glass substrates kept at room temperature and a vacuum of about 2 10 6 Torr using a conventional coating unit (Denton Vacuum DV 502 A). The evaporation rate as well as the film thickness was controlled using a quartz crystal DTM 100 monitor. Mechanical rotation of the substrate holder ( 30 rpm) during deposition-produced homogeneous film. The temperature rise of the substrate due to radiant heating from crucible was negligible. The amorphous nature of the as-deposited films was checked using a Philips X-ray diffractometer (1710). The chemical compositions of the as-deposited films were measured using an energy dispersive X-ray spectroscopy (Link analytical EDS). The compositions so determined agreed with those of the starting materials to within ±0.35 at.%. The optical transmittance at normal incidence was measured in the wavelength range 400 2500 nm using a doublebeam computer-controlled spectrophotometer (Jasco V-630 combined with PC). The spectrophotometer was set with a slit width of 1 nm and as this was much smaller than the line widths it was unnecessary to make slit-width corrections. The line width is simply taken to be the separation of two adjacent interference maxima and minima. Without a glass substrate in the reference beam, the measured transmittance spectra were used to calculate the optical constants by applying the envelope method suggested by Swanepoel [17]. 3 Results and discussion Figure 1 represents the XRD patterns for As x Se 70 Te 30 x (0 x 30) thin films; as shown in this figure the films did not reveal discrete or any sharp peaks but the characteristic broad humps of the amorphous materials. 3.1 Calculation of the refractive index and film thickness Figure 2a shows the measured transmittance (T)spectra for different compositions of As x Se 70 Te 30 x thin films. From Fig. 2 (a) Transmission spectra for different compositions of As x Se 70 Te 30 x with (0 x 30 at.%) thin films. (b) Transmission spectra for Se 70 Te 30 thin films. The T M,T m,andt α curves according to the text, T s is the transmission of the substrate alone this figure one can note that the addition of As content at the expense of Te content shifts the optical transmittance to the higher energies (i.e., blueshift of the optical absorption edge). Figure 2b as a comparative example, shows the measured transmittance (T), the created envelopes, T M and T m,(both the envelopes being computer-generated using the Origin Lab version 7 program), and the geometric mean, T α = T M T m, in the spectral region with interference fringes [18] for Se 70 Te 30 thin film. According to Swanepoel s method based on the idea of Manifacier et al. [19], the first approximate value of the refractive index of the film, n 1, in the spectral region of medium and weak absorption can be calculated as well as detailed in Ref. [18]. Using the values of, n 1, and taking into account the basic equation for the interference fringes: 2nd = m o λ (1) where the order number, m o, is an integer for maxima and a half-integer for minima the first approximate value of the film thickness, d 1, can be expressed as: d 1 = λ 1.λ 2 2(n c2 λ 1 n c1.λ 2 ) where, n c1, and, n c2, are the refractive indices at two adjacent maxima (or minima) at, λ 1, and, λ 2. The last value deviates considerably from the other values and must consequently be rejected. This deviation is an indication that n c1 is not accurate enough due to the departure of the hypothesis of transparency behind the application of the envelope method [17].Theaveragevalue(d 1 ) of d 1 (ignoring the last value) can now be used along with n 1 to calculate m o for the different maxima and minima using (1). The accuracy (2)

Optical band gap and refractive index dispersion parameters of As x Se 70 Te 30 x (0 x 30 at.%) 915 Fig. 3 The plots of l/2 vs.n/λ, in order to determine the film thickness and the first-order number m 1 for As x Se 70 Te 30 x with (0 x 30 at.%) thin films of the film thickness can now be significantly increased by taking the corresponding exact integer or half-integer values of m o associated with each extreme point (see Fig. 2b) and deriving a new thickness, d 2,using(1), again using the values n 1. The values of the thickness in this way have a smaller dispersion. It should be emphasized that the accuracy of the final thickness, d 2, is better than 1% as well as reported elsewhere [18]. With the accurate values of m o and (d = d 2 ) expression (1) can then be solved for n at each λ and, thus, the final values of the refractive index, n 2, are obtained. Furthermore, a simple complementary graphical method for deriving the first-order number m 1 and the film thickness d, based on (1), was also used. For this purpose (1) is rewritten as follows for the successive maxima and minima, starting from the long-wavelength end [18]: ( ) l n 2 = 2d m 1, l = 0, 1, 2, 3,... (3) λ where, m 1 is the order number of the first (l = 0) extreme considered, an integer for a maximum and a half integer for a minimum. Therefore, by plotting (l/2) versus (n/λ) a straight line with slope 2d and cut-off on the Y -axis at m 1. Figure 3 shows this plot, in which the values obtained for (d = d 2 = 0.5 slope value) and m 1 for each sample of the As x Se 70 Te 30 x thin films as well as denoted on the same graph. Now the values of n 2 can be fitted to a reasonable function such as the two-term Cauchy dispersion relationship [18]: n(λ) = a + b/λ 2 (4) where a and b are constants, then (4) can be used to extrapolate the wavelength dependence beyond the range of measurement [17, 18]. Figure 4 illustrates the dependence of the refractive index, n, on wavelength for different compositions of the amorphous As x Se 70 Te 30 x thin films. The relative error in n, n/n, does not exceed the precision of

916 K.A. Aly Fig. 4 Refractive index dispersion spectra for As x Se 70 Te 30 x with (0 x 30 at.%) thin films. The solid curves were determined according to Cauchy dispersion relationship [18] the measurements T /T (±1%). The least-squares fit of n 2 values (solid lines of Fig. 3) for the different samples, yields n = 3.21 + (3.31 10 5 /λ 2 ), n = 3.02 + (3.07 10 5 /λ 2 ), n = 2.90 + (2.53 10 5 /λ 2 ), n = 2.74 + (2.12 10 5 /λ 2 ), n = 2.62 + (1.98 10 5 /λ 2 ), n = 2.49 + (1.87 10 5 /λ 2 ), and n = 2.41 + (1.55 10 5 /λ 2 ) for x = 0, 5, 10, 15, 20, 25, and 30 at.%, respectively. As shown in Fig. 4 the refractive index, n, decreases with increasing wavelength of the incident photon, while at higher wavelengths the refractive index, n, tends to be constant for all compositions under study. Here the values of refractive index for all compositions can be fitted according to the Wemple DiDomenico (WDD) dispersion relationship [20]; n 2 (hν) = 1 + E 0E d E 2 0 (hν)2 (5) where E 0 is the single-oscillator energy and E d is the dispersion energy or single-oscillator strength where the refractive index factor (n 2 1) 1 can be plotted as a function of (hν) 2 and fitting straight lines as shown in Fig. 5, the values of the E 0 and E d can be determined from the intercept E 0 /E d and the slope (E 0 E d ) 1. As mentioned before by Tanaka [21] that the oscillator energy (E 0 ) is an average energy gap and to a good approximation, scales with the optical band gap (E g ), E 0 2E g as shown in Table 1. Figure 5 also shows the values of the refractive index n(0) at hν = 0oftheAs x Se 70 Te 30 x thin films. The obtained values of E 0, E d, and n(0) are listed in Table 1. It was observed that the single-oscillator energy E 0 increases while both the dispersion energy E d and n(0) decrease with the increase of As content. An important achievement of the WDD model is that it relates the dispersion energy, E d,to other physical parameters of the material through the following empirical relationship [20]: E d = βn c Z a N e (ev) (6) Fig. 5 Plots of refractive index factor (n 2 1) 1 vs. (hν) 2 for As x Se 70 Te 30 x with (0 x 30 at.%) thin films where N c is the effective coordination number of the cation nearest neighbor to the anion, Z a is the formal chemical valency of the anion, N e is the effective number of valence electrons per anion, and β is a two-valued constant with either an ionic or a covalent value (β i = 0.26 ± 0.03 ev and β c = 0.37 ± 0.04 ev, respectively). Therefore, in order to account for the compositional trended of E d it is suggested that the observed decrease in E d with increasing As content is primarily due to the change in the ionicities (homopolar Se Se bonds are introduced together with extra Se atoms), which decreases with increasing As content (see Table 1). The values of the single-oscillator energy, the dispersion energy, the static refractive index, and the excess of Se Se homopolar bonds for the As x Se 70 Te 30 x thin films are listed in Table 1. In addition, the fundamental electron excitation spectrum of a substance is generally described in terms of a frequency-dependent complex electronic dielectric constant (ε(ω) = ε 1 (ω) + iε 2 (ω)) either the real part ε 1 (ω) or the imaginary part ε 2 (ω) contains all desired response information since causality arguments relate the real and imaginary parts. Therefore, the single-oscillator and dispersion energy parameterization given by (5) are defined by Ref. [22], E 2 0 = M 1 M 3 and E 2 d = M3 1 M d (7) The oscillator energy E 0 is independent of the scale of ε 2 and is consequently an average energy gap, whereas E d depends on the scale of ε 2 and thus serves an interband strength parameter. Since the M 1 and M 3 moments are involved in computation of E 0 and E d,ε 2 spectrum is weighted most heavily near the interband absorption threshold. As a result, the dispersion energy may depend upon the detailed charge distribution within each unit cell, consequently, would then be closely related to chemical bonding that may lie within a nearly localized orbital theory.

Optical band gap and refractive index dispersion parameters of As x Se 70 Te 30 x (0 x 30 at.%) 917 Table 1 The Wemplee DiDomenico dispersion parameters, E 0, E d, M 1, M 3, the values of the refractive index, n(0), extrapolated at hν = 0, the average coordination number, N co, the excess of Se Se homopolar bonds, the optical band gap, E g, E 0 /E g ratio, and the cohesive energy, CE, for As x Se 70 Te 30 x with (0 x 30 at.%) thin films Composition ev n(0) N co Excess of E g E g /E 0 CE E 0 E d M 1 M 3 Se Se (ev) (ev/atom) Se 70 Te 30 2.924 27.58 9.188 1.075 3.23 2.00 80 1.40 2.094 1.911 As 5 Se 70 Te 25 2.939 24.39 8.410 0.974 3.05 2.05 75 1.44 2.041 1.942 As 10 Se 70 Te 20 3.094 22.92 8.069 0.843 2.90 2.10 70 1.49 2.073 1.974 As 15 Se 70 Te 15 3.233 21.33 7.691 0.736 2.76 2.15 65 1.56 2.075 2.006 As 20 Se 70 Te 10 3.382 20.25 7.429 0.650 2.64 2.20 60 1.64 2.062 2.038 As 25 Se 70 Te 5 3.450 18.24 6.929 0.582 2.51 2.25 55 1.72 2.007 2.070 As 30 Se 70 3.622 17.75 6.805 0.519 2.43 2.3 50 1.81 1.997 2.102 3.2 Determination of the extinction coefficient and optical band gap Since the values of the refractive index, n, are already known over the whole spectral range 400 2500 nm, the absorbance x a (λ) can be calculated using the interference-free transmission spectrum T α (see Fig. 2) using the well-known equation suggested by Connell and Lewis [23]: X a = P +[P 2 + 2QT α (1 R2 R 3 )] Q (8) where P = (R 1 1)(R 2 1)(R 3 1) and Q = 2T α (R 1 R 2 R 1 R 3 2R 1 R 2 R 3 ), R 1 is the reflectance of the air film interface (R 1 =[(1 n)/(1 + n)] 2 ), R 2 is the reflectance of film substrate interface (R 2 =[(n s)/(n + s)] 2 ), and R 3 is the reflectance of the substrate air interface (R 3 = [(s l)/(s + 1)] 2 ). Moreover, since d is known, the relation x a = exp( αd) can then be solved for the values of the absorption coefficient, α. In order to complete the calculation of the optical constants, the extinction coefficient, k, is calculated using the values of α and λ through the alreadymentioned formula, k = αλ/4π. Figure 6 illustrates the dependence of the absorption coefficient, α, on the wavelength for As x Se 70 Te 30 x (0 x 30 at.%) thin films. For α 10 5 cm 1, the imaginary part of the complex index of refraction is much less than n, so that the previous expressions used to calculate the reflectance is valid. In the region of strong absorption, the interference fringes disappear; in other words, for a very large α, the three curves T M,T α, and T m converge to a single curve. According to Tauc s relation [24, 25] for allowed indirect transitions, the photon energy dependence of the absorption coefficient can be described by (αhν) 1/2 = B 1/2 (hν E g ) (9) where B is a parameter that depends on the transition probability and E g is the optical energy gap. Figure 7 shows the Fig. 6 The absorption coefficient, α, as a function of the wavelength, λ,foras x Se 70 Te 30 x with (0 x 30 at.%) thin films Fig. 7 The absorption coefficient in the form of (αhν) 1/2 versus photon energy (hν) for As x Se 70 Te 30 x with (0 x 30 at.%) thin films. from which the optical band gap (E g ) is estimated (Tauc s extrapolation) absorption coefficient in the form of (αhν) 1/2 versus hν for the As x Se 70 Te 30 x thin films. The intercepts of the straight lines with the photon energy axis yield values of the optical band gap, E g.

918 K.A. Aly Table 2 Bond energies and the relative probabilities of formation of various bonds in As Se Te glasses, taking the probability of Se Te bond as unity Bond Bond energy Relative probability (kcal mol 1 ) (att = 298.15 K) Se Te 44.197 1 Se Se 44.04 0.763 As Se 41.71 0.015 Te Te 33.00 5.872 10 9 As Te 32.74 3.782 10 9 As As 32.10 1.28 10 9 According to the chemical-bond approach [26, 27], bonds are formed in the sequence of decreasing bond energy until the available valence of atoms is satisfied. The bond energies D(A F)for heteronuclear bonds have been calculated by using the empirical relation; D(A F)=[D(A A) D(F F)] 1/2 +30(χ A χ F ) 2 (10) proposed by Pauling [28], where D(A A) and D(F F) are the energies of the homonuclear bonds (44.04, 30.22, and 33 kcal/mol for As, Se, and Te, respectively) [18, 29], χ A and χ F are the electronegativity values for the involved atoms [28]. The energies of various possible bonds in the As Se Te system are given in Table 2. Depending on the bond energy (D), the relative probability of its formation was calculated [30] using the probability function exp(d/kt )and listed in Table 2. Bonds such as Te Te, As Te and As As have insignificant probability of formation because of their low bond energies. Therefore, only Se Te, As Se, and Se Se bonds exist with high priority in the As Se Te system. The observed increase of the E g with increasing the As content can be attributed to the formation of As Se bonds (E g = 1.55 ev) increases at the expense of Se Te bonds (E g = 1.3 ev) and also a shortage of homopolar Se Se bonds. Knowing the bond energies we can estimate the cohesive energy (CE), i.e., the stabilization energy of an infinitely large cluster of the material per atom, by summing the bond energies over all the bonds expected in the system under test. The CE of the prepared samples is evaluated from the following equation [31]; CE = (C i D i /100) (11) where C i and D i are the numbers of the expected chemical bonds and the energy of each corresponding bond, respectively. The calculated values of the cohesive energies for all compositions are presented in Table 1. It is observed that the values of CE increases with the increase of As content. The increase in the CE with increasing As content is due to the decrease in the excess of Se Se homopolar bonds (see Table 1). This result is in a good agreement with many authors [32, 33]. 4 Conclusions Optical characterization of As x Se 70 Te 30 x thin films with (0 x 30 at.%) have been analyzed using the Swanepoel s method, which is based on the generation of the envelopes of the interference maxima and minima of the transmission spectrum. Allowed indirect electronic transitions are mainly responsible for the photon absorption in the investigated films. Fitting of the refractive indices according to the single-oscillator model Wemple DiDomenico (WDD) relationship results in the dispersion of parameters that are directly related to the structure of these films. It was found that the optical band gap (E g ) and the single oscillator energy (E 0 ) increase, while the refractive index (n) and the dispersion energy (E d ) decrease on increasing the As content. A chemical-bond approach has been applied successfully to interpret the increase of the optical gap of the As x Se 70 Te 30 x films with increasing As content. Acknowledgements The author wish to thank the Optics Lap. at the Physics Department of the Faculty of Science, Al-Azhar University, Assuit, Branch, for achieving the optical measurements and the financial support for the (XRD) measurements, also the Author would like to acknowledge Dr. A. Dahshan Dep. of Phys., Faculty of Science, Suez Canal University, Port Said, Egypt, for his help and advice throughout this work. References 1. E. Marquez, J.M. Gonzalez-Leal, R. Jimenez-Garay, M. Vlcek, Thin Solid Films 396, 183 (2001) 2. T. Ohta, J. Opto-electron. Adv. Mater. 3, 609 (2001) 3. E. Marquez, P. Villars, R. Jimenez-Garay, J. Mater. Res. 3, 314 (1988) 4. A. Zakery, S.R. Elliott, J. Non-Cryst. Solids 330, 1 (2003) 5. S.R. Ovshinsky, Phys. Rev. Lett. 21, 1450 (1986) 6. N.F. Mott, Philos. Mag. 24, 911 (1971) 7. D.E. Carlson, C.R. Wronski, Appl. Phys. Lett. 28, 671 (1976) 8. J. Fusong, M. Okuda, Jpn. J. Appl. Phys. 30, 97 (1991) 9. N.E. Mott, Philos. Mag. 19, 835 (1969) 10. M.M. El-Nahass, M.B. El Den, Opt. Laser Technol. 33, 31 (2001) 11. M.B. El-Den, M.M. El-Nahass, Opt. Laser Technol. 35, 335 (2003) 12. V. Lyubin, T. Tada, M. Klebanov, N.N. Smirnov, A.V. Kolobov, K. Tanaka, Mater. Lett. 30, 79 (1997) 13. L.A. Wahab, S.A. Fayek, Solid State Commun. 100, 345 (1996) 14. R.A. Ligero, M. Casas-Ruiz, A. Orozco, M.P. Trujillo, R. Jimènez, Thermochim. Acta 249, 221 (1995) 15. M. Roilos, J. Non-Cryst. Solids 6, 5 (1971) 16. T. Takahashi, J. Non-Cryst. Solids 34, 307 (1979) 17. R. Swanepoel, J. Phys. E 16, 1214 (1983) 18. A. Dahshan, H.H. Amer, K.A. Aly, J. Phys., D. Appl. Phys. 41, 215401 (2008) (7pp)

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