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Appl Phys A (2010) 99: 913919DOI 10.1007/s00339-010-5680-6

Optical band gap and refractive index dispersion parametersof As x Se70 Te 30 x (0 x 30 at.%) amorphous lms

Kamal A. Aly

Received: 15 March 2010 / Accepted: 19 March 2010 / Published online: 16 April 2010 Springer-Verlag 2010

Abstract Amorphous As x Se70Te30

x thin lms with (0

x 30 at.%) were deposited onto glass substrates by us-ing thermal evaporation method. The transmission spectraT () of the lms at normal incidence were measured in thewavelength range 4002500 nm. A straightforward analysisproposed by Swanepoel based on the use of the maxima andminima of the interference fringes has been used to drive thelm thickness, d , the complex index of refraction, n , and theextinction coefcient, k. The dispersion of the refractive in-dex is discussed in terms of the single-oscillator Wemple andDiDomenico model (WDD) . Increasing As content is foundto affect the refractive index and the extinction coefcient of the As x Se70Te30

x lms. With increasing As content the op-

tical band gap increases while the refractive index decreases.The optical absorption is due to allowed indirect transition.The chemical bond approach has been applied successfullyto interpret the increase of the optical gap with increasingAs content.

1 Introduction

Chalogenide glasses have been recognized as promising ma-terials for infrared optical element, infrared optical bers,

and for the transfer of information [ 13]. They have alsofound applications in xerography switching and memory de-vices, photolithographic process, and in the fabrication of in-expensive solar cells and more recently as reversible phasechange optical recorders [ 48]. This has made it important

K.A. Aly ( )Physics Department, Faculty of Science, Al-Azhar University,Assiut, Egypte-mail: kamalaly2001@Gmail.com

to have an insight into their optical and electronic proper-ties. The addition of an impurity has a pronounced effecton the conduction mechanism and the structure of the amor-phous glass and this effect can be widely different for differ-ent impurities [ 9]. Therefore, the ternary compounds involv-ing AsSeTe have interesting properties as well as tech-nological applications because they form a wide range of glassy region. Although it is possible to nd in the literaturemore papers dealing with AsSeTe thin lms [ 1016] but,to the best of our knowledge, the effect of As content on theoptical constants of AsSeTe have not been reported. Thepresent work deals with investigation of the optical proper-ties of the As x Se70 Te30

x (0

x

30 at.%) thin lms. The

well-known Swanepoels method [ 17, 18] is used to accu-rately determination of the refractive index and lm thick-ness in the weakly absorbing and transparent regions of thespectrum. Also, the absorption coefcient, and therefore theextinction coefcient, has been determined in the strong ab-sorption region of the transmission spectra.

2 Experimental details

Different compositions of bulk As x Se 70 Te 30x (0 x 30 at.%) chalcogenide glasses were prepared from theircomponents of high purity (99.999%) by the usual meltquenching technique. The elements were heated together inan evacuated silica ampoule up to 1200 K and then the am-poule temperature kept constant for about 20 h. During thecourse of heating, the ampoule was shaken several times tomaintain the uniformity of the melt. Finally, the ampoulewas quenched into ice-cooled water to avoid the crystalliza-tion process.

The amorphous thin lms were deposited by evaporat-ing the alloys from a resistance-heat quartz glass crucible

mailto:kamalaly2001@Gmail.commailto:kamalaly2001@Gmail.com

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914 K.A. Aly

Fig. 1 X-ray diffraction patterns of as prepared As x Se70 Te30x with(0 x 30 at.%) thin lms

onto clean glass substrates kept at room temperature and avacuum of about 2 106 Torr using a conventional coat-ing unit (Denton Vacuum DV 502 A). The evaporation rateas well as the lm thickness was controlled using a quartzcrystal DTM 100 monitor. Mechanical rotation of the sub-strate holder ( 30 rpm) during deposition-produced homo-geneous lm. The temperature rise of the substrate due toradiant heating from crucible was negligible.

The amorphous nature of the as-deposited lms waschecked using a Philips X-ray diffractometer (1710). Thechemical compositions of the as-deposited lms were mea-sured using an energy dispersive X-ray spectroscopy (Link analytical EDS). The compositions so determined agreedwith those of the starting materials to within 0.35 at.%.

The optical transmittance at normal incidence was mea-sured in the wavelength range 4002500 nm using a double-beam computer-controlled spectrophotometer (Jasco V-630combined with PC). The spectrophotometer was set with aslit width of 1 nm and as this was much smaller than the linewidths it was unnecessary to make slit-width corrections.The line width is simply taken to be the separation of twoadjacent interference maxima and minima. Without a glasssubstrate in the reference beam, the measured transmittancespectra were used to calculate the optical constants by ap-plying the envelope method suggested by Swanepoel [ 17].

3 Results and discussion

Figure 1 represents the XRD patterns for As x Se 70Te 30x(0 x 30) thin lms; as shown in this gure the lms didnot reveal discrete or any sharp peaks but the characteristicbroad humps of the amorphous materials.

3.1 Calculation of the refractive index and lm thickness

Figure 2a shows the measured transmittance ( T ) spectra fordifferent compositions of As x Se 70 Te 30x thin lms. From

Fig. 2 (a ) Transmission spectra for different compositions of Asx Se70 Te30x with (0 x 30 at.%) thin lms. ( b ) Transmissionspectra for Se 70 Te 30 thin lms. The T M , T m , and T curves accordingto the text, T s is the transmission of the substrate alone

this gure one can note that the addition of As contentat the expense of Te content shifts the optical transmit-tance to the higher energies (i.e., blueshift of the optical ab-sorption edge). Figure 2b as a comparative example, showsthe measured transmittance ( T ) , the created envelopes, T M and T m , ( both the envelopes being computer-generated us-ing the Origin Lab version 7 program), and the geometricmean, T = T M T m , in the spectral region with interferencefringes [ 18] for Se 70 Te30 thin lm.

According to Swanepoels method based on the idea of Manifacier et al. [ 19], the rst approximate value of therefractive index of the lm, n1 , in the spectral region of medium and weak absorption can be calculated as well asdetailed in Ref. [ 18]. Using the values of, n1 , and takinginto account the basic equation for the interference fringes:

2nd =mo (1)where the order number, m o , is an integer for maxima anda half-integer for minima the rst approximate value of thelm thickness, d 1 , can be expressed as:

d 1

=

1 . 2

2(n c2 1 n c1 . 2)(2)

where, nc1 , and, nc2 , are the refractive indices at two ad- jacent maxima (or minima) at, 1 , and, 2 . The last valuedeviates considerably from the other values and must conse-quently be rejected. This deviation is an indication that n c1is not accurate enough due to the departure of the hypoth-esis of transparency behind the application of the envelopemethod [ 17]. The average value ( d 1) of d 1 (ignoring the lastvalue) can now be used along with n1 to calculate mo forthe different maxima and minima using ( 1). The accuracy

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Optical band gap and refractive index dispersion parameters of As x Se70 Te30x (0 x 30 at.%) 915Fig. 3 The plots of l/ 2 vs. n/ ,in order to determine the lmthickness and the rst-ordernumber m1 for As x Se70 Te30xwith (0 x 30 at.%) thinlms

of the lm thickness can now be signicantly increased bytaking the corresponding exact integer or half-integer val-ues of mo associated with each extreme point (see Fig. 2b)and deriving a new thickness, d 2 , using (1), again using thevalues n1 . The values of the thickness in this way have asmaller dispersion. It should be emphasized that the accu-racy of the nal thickness, d 2 , is better than 1% as well asreported elsewhere [ 18]. With the accurate values of mo and(d =d 2) expression ( 1) can then be solved for n at each and, thus, the nal values of the refractive index, n2 , are ob-tained.

Furthermore, a simple complementary graphical methodfor deriving the rst-order number m1 and the lm thick-ness d , based on ( 1), was also used. For this purpose ( 1) isrewritten as follows for the successive maxima and minima,starting from the long-wavelength end [ 18]:

l2 =2d

n m1 , l =0, 1, 2, 3, . . . (3)

where, m 1 is the order number of the rst ( l =0) extremeconsidered, an integer for a maximum and a half integerfor a minimum. Therefore, by plotting (l/ 2) versus (n/)a straight line with slope 2 d and cut-off on the Y -axis at

m1 . Figure 3 shows this plot, in which the values obtainedfor (d =d 2 =0.5 slope value) and m1 for each sample of the As x Se70 Te 30x thin lms as well as denoted on the samegraph.

Now the values of n 2 can be tted to a reasonable func-tion such as the two-term Cauchy dispersion relationship[18]:

n() =a +b/ 2 (4)where a and b are constants, then ( 4) can be used to ex-trapolate the wavelength dependence beyond the range of measurement [ 17, 18]. Figure 4 illustrates the dependenceof the refractive index, n , on wavelength for different com-positions of the amorphous As x Se 70Te 30x thin lms. Therelative error in n , n/n , does not exceed the precision of

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916 K.A. Aly

Fig. 4 Refractive index dispersion spectra for As x Se70 Te 30x with(0 x 30 at.%) thin lms. The solid curves were determined ac-cording to Cauchy dispersion relationship [ 18]

the measurements T /T ( 1% ) . The least-squares t of n2values (solid lines of Fig. 3) for the different samples, yields

n =3.21 + (3.31 105 / 2) , n =3.02 + (3.07 105 / 2) ,n =2.90 + (2.53 105 / 2) , n =2.74 + (2.12 105 / 2) ,n =2.62 + (1.98 105 / 2) , n =2.49 + (1.87 105 / 2) ,and n =2.41 +(1.55 105 / 2) for x =0, 5, 10 , 15 , 20 , 25,and 30 at.%, respectively. As shown in Fig. 4 the refractiveindex, n , decreases with increasing wavelength of the inci-dent photon, while at higher wavelengths the refractive in-dex, n , tends to be constant for all compositions under study.Here the values of refractive index for all compositions canbe tted according to the WempleDiDomenico (WDD) dis-persion relationship [ 20];

n2(h) =1 +E

0E

dE 20 (h) 2

(5)

where E 0 is the single-oscillator energy and E d is the disper-sion energy or single-oscillator strength where the refractiveindex factor (n 2 1)1 can be plotted as a function of (h) 2and tting straight lines as shown in Fig. 5, the values of theE 0 and E d can be determined from the intercept E 0/E d andthe slope (E 0E d)1 . As mentioned before by Tanaka [ 21]that the oscillator energy ( E 0) is an average energy gap andto 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 indexn( 0) at h =0 of the As x Se70 Te30x thin lms. The ob-tained values of E 0 , E d , and n( 0) are listed in Table 1. Itwas observed that the single-oscillator energy E 0 increaseswhile both the dispersion energy E d and n( 0) decrease withthe increase of As content. An important achievement of theWDD model is that it relates the dispersion energy, E d , toother physical parameters of the material through the fol-lowing empirical relationship [ 20]:

E d =N cZ aN e (eV ) (6)

Fig. 5 Plots of refractive index factor (n 2 1)1 vs. (h) 2 forAsx Se70 Te30x with (0 x 30 at.%) thin lms

where N c is the effective coordination number of the cationnearest neighbor to the anion, Z a is the formal chemical va-lency of the anion, N e is the effective number of valenceelectrons per anion, and is a two-valued constant with ei-ther an ionic or a covalent value ( i =0.26 0.03 eV and c =0.37 0.04 eV, respectively). Therefore, in order toaccount for the compositional trended of E d it is suggestedthat the observed decrease in E d with increasing As contentis primarily due to the change in the ionicities (homopolarSeSe 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 en-ergy, the static refractive index, and the excess of SeSe ho-mopolar bonds for the As x Se 70 Te 30x thin lms are listedin Table 1. In addition, the fundamental electron excitationspectrum of a substance is generally described in terms of afrequency-dependent complex electronic dielectric constant(() = 1() + i 2()) either the real part 1() or theimaginary part 2() contains all desired response informa-tion since causality arguments relate the real and imaginaryparts. Therefore, the single-oscillator and dispersion energyparameterization given by ( 5) are dened by Ref. [ 22],

E 20 =M 1M 3

and E 2d =M 31M d

(7)

The oscillator energy E 0 is independent of the scale of 2 and is consequently an average energy gap, whereasE d depends on the scale of 2 and thus serves an inter-band strength parameter. Since the M 1 and M 3 momentsare involved in computation of E 0 and E d , 2 spectrum isweighted most heavily near the interband absorption thresh-old. As a result, the dispersion energy may depend uponthe detailed charge distribution within each unit cell, conse-quently, would then be closely related to chemical bondingthat may lie within a nearly localized orbital theory.

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Optical band gap and refractive index dispersion parameters of As x Se70 Te30x (0 x 30 at.%) 917Table 1 The WempleeDiDomenico dispersion parameters, E 0 , E d , M 1 , M 3 , the values of the refractive index, n( 0) , extrapolated at h =0,the average coordination number, N co , the excess of SeSe homopolar bonds, the optical band gap, E g , E 0 /E g ratio, and the cohesive energy, CE ,for As x Se70 Te30x with (0 x 30 at.%) thin lmsComposition eV n( 0) N co Excess of E g E g /E 0 CE

E 0 E d M 1 M 3 SeSe (eV) (eV/atom)

Se70Te30 2.924 27.58 9.188 1.075 3.23 2.00 80 1.40 2.094 1.911

As5Se70 Te 25 2.939 24.39 8.410 0.974 3.05 2.05 75 1.44 2.041 1.942

As10Se70Te20 3.094 22.92 8.069 0.843 2.90 2.10 70 1.49 2.073 1.974

As15Se70Te15 3.233 21.33 7.691 0.736 2.76 2.15 65 1.56 2.075 2.006

As20Se70Te10 3.382 20.25 7.429 0.650 2.64 2.20 60 1.64 2.062 2.038

As25Se70Te5 3.450 18.24 6.929 0.582 2.51 2.25 55 1.72 2.007 2.070

As30Se70 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 coefcient and opticalband gap

Since the values of the refractive index, n , are already known

over the whole spectral range 4002500 nm, the absorbancexa() can be calculated using the interference-free transmis-sion spectrum T (see Fig. 2) using the well-known equationsuggested by Connell and Lewis [ 23]:

X a =P + [P 2 +2QT (1 R 2R 3)]

Q(8)

where P =(R 1 1)(R 2 1)(R 3 1) and Q =2T (R 1R 2 R 1R 3 2R 1R 2R 3), R 1 is the reectance of the airlminterface (R 1 = [(1 n)/( 1 + n) ]2), R 2 is the reectanceof lmsubstrate interface (R 2 = [(n s)/(n + s) ]2) , andR

3 is the reectance of the substrateair interface (R

3 =[(s l)/(s +1)]2) . Moreover, since d is known, the rela-tion xa =exp (d) can then be solved for the values of theabsorption coefcient, . In order to complete the calcula-tion of the optical constants, the extinction coefcient, k, iscalculated using the values of and through the already-mentioned formula, k =/ 4 .

Figure 6 illustrates the dependence of the absorption co-efcient, , on the wavelength for As x Se 70Te30x (0 x 30 at.%) thin lms. For 105 cm1 , the imaginary part of the complex index of refraction is much less than n , so thatthe previous expressions used to calculate the reectance is

valid. In the region of strong absorption, the interferencefringes disappear; in other words, for a very large , thethree curves T M , T , and T m converge to a single curve.According to Taucs relation [ 24, 25] for allowed indirecttransitions, the photon energy dependence of the absorptioncoefcient can be described by

(h) 1/ 2 =B1/ 2(h E g) (9)

where B is a parameter that depends on the transition prob-ability and E g is the optical energy gap. Figure 7 shows the

Fig. 6 The absorption coefcient, , as a function of the wavelength, , for As x Se70 Te 30x with (0 x 30 at.%) thin lms

Fig. 7 The absorption coefcient in the form of ( h) 1/ 2 versus pho-ton energy ( h) for As x Se70 Te 30x with (0 x 30 at.%) thin lms.from which the optical band gap ( E g) is estimated (Taucs extrapola-tion)

absorption coefcient in the form of (h) 1/ 2 versus h forthe As x Se 70Te30x thin lms. The intercepts of the straightlines with the photon energy axis yield values of the opticalband gap, E g .

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918 K.A. Aly

Table 2 Bond energies and the relative probabilities of formation of various bonds in AsSeTe glasses, taking the probability of SeTebond as unity

Bond Bond energy Relative probability

(kcalmol 1) (at T =298 .15 K)SeTe 44.197 1

SeSe 44.04 0.763

AsSe 41.71 0.015

TeTe 33.00 5 .872 109AsTe 32.74 3 .782 109AsAs 32.10 1 .28 109

According to the chemical-bond approach [ 26, 27],bonds are formed in the sequence of decreasing bond en-ergy until the available valence of atoms is satised. Thebond energies D(A F ) for heteronuclear bonds have beencalculated by using the empirical relation;

D(A F ) = [D(A A) D(F F ) ]1/ 2

+30( A 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], A and F are the electronegativity values for the involvedatoms [ 28].

The energies of various possible bonds in the AsSeTesystem are given in Table 2. Depending on the bond en-ergy (D) , the relative probability of its formation was cal-culated [ 30] using the probability function exp (D/kT ) andlisted in Table 2. Bonds such as TeTe, AsTe and AsAshave insignicant probability of formation because of theirlow bond energies. Therefore, only SeTe, AsSe, and SeSe bonds exist with high priority in the AsSeTe system.The observed increase of the E g with increasing the Ascontent can be attributed to the formation of AsSe bonds(E g =1.55 eV ) increases at the expense of SeTe bonds(E g = 1 .3 eV) and also a shortage of homopolar SeSebonds.

Knowing the bond energies we can estimate the cohe-sive energy ( CE ), i.e., the stabilization energy of an innitelylarge 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 fol-lowing equation [ 31];

CE = (C i D i / 100 ) (11)where C i and D i are the numbers of the expected chemicalbonds and the energy of each corresponding bond, respec-tively. The calculated values of the cohesive energies for allcompositions are presented in Table 1. It is observed that thevalues of CE increases with the increase of As content. The

increase in the CE with increasing As content is due to thedecrease in the excess of SeSe homopolar bonds (see Ta-ble 1). This result is in a good agreement with many authors[32, 33].

4 Conclusions

Optical characterization of As x Se70 Te30x thin lms with(0 x 30 at.%) have been analyzed using the Swanepoelsmethod, which is based on the generation of the envelopesof the interference maxima and minima of the transmis-sion spectrum. Allowed indirect electronic transitions aremainly responsible for the photon absorption in the investi-gated lms. Fitting of the refractive indices according to thesingle-oscillator model WempleDiDomenico (WDD) rela-tionship results in the dispersion of parameters that are di-rectly related to the structure of these lms. It was foundthat the optical band gap (E g) and the single oscillator

energy (E 0) increase, while the refractive index (n) andthe dispersion energy (E d) decrease on increasing the Ascontent. A chemical-bond approach has been applied suc-cessfully to interpret the increase of the optical gap of theAs x Se70 Te30x lms with increasing As content.

Acknowledgements The author wish to thank the Optics Lap. at thePhysics Department of the Faculty of Science, Al-Azhar University,Assuit, Branch, for achieving the optical measurements and the nan-cial support forthe (XRD)measurements, also the Author would like toacknowledge Dr. A. Dahshan Dep. of Phys., Faculty of Science, SuezCanal University, Port Said, Egypt, for his help and advice throughoutthis work.

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