Structure, optical spectroscopy and dispersion parameters of ZnGa2Se4 thin films at different annealing temperatures

Optics Communications 285 (2012) 3154–3161

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Structure, optical spectroscopy and dispersion parameters of ZnGa2Se4 thin films at different annealing temperatures M. Fadel a, I.S. Yahia a, b, c,⁎, 1, G.B. Sakr b, F. Yakuphanoglu c, S.S. Shenouda a, b a b c

Semiconductor Lab., Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt Nano-Science Lab., Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt Physics Department, Faculty of Science, Firat University, 23119, Elazığ, Turkey

a r t i c l e

i n f o

Article history: Received 30 November 2010 Accepted 24 February 2012 Available online 10 March 2012 Keywords: Defect chalcopyrite ZnGa2Se4 Optical constants Optical dispersion parameters Effect of annealing

a b s t r a c t Thin films of ZnGa2Se4 were deposited by thermal evaporation method of pre-synthesized ingot material onto highly cleaned microscopic glass substrates. The chemical composition of the investigated compound thin film form was determined by means of energy-dispersive X-ray spectroscopy. X-ray diffraction XRD analysis revealed that the powder compound is polycrystalline and the as-deposited and the annealed films at Ta = 623 and 673 K have amorphous phase, while that annealed at Ta = 700 K is polycrystalline with a single phase of a defective chalcopyrite structure similar to that of the synthesized material. The unit-cell lattice parameters were determined and compared with the reported data. Also, the crystallite size L, the dislocation density δ and the main internal strain ε were calculated. Analyses of the AFM images confirm the nanostructure of the prepared annealed film at 700 K. The refractive index n and the film thickness d were determined from optical transmittance data using Swanepoel's method. It was found that the refractive index dispersion data obeys the single oscillator model from which the dispersion parameters were determined. The electric susceptibility of free carriers and the carrier concentration to the effective mass ratio were determined according to the model of Spitzer and Fan. The analysis of the optical absorption revealed both the indirect and direct energy gaps. The indirect optical gaps are presented in the amorphous films (as-deposited, annealed at 623 and 673 K), while the direct energy gap characterized the polycrystalline film at 700 K. Graphical representations of ε1, ε2, tan δ, − Im[1/ε*] and − Im[(1/ε* + 1)] are also presented. ZnGa2Se4 is a good candidate for optoelectronic and solar cell devices. © 2012 Elsevier B.V. All rights reserved.

1. Introduction ZnGa2Se4, which is one of the family of AIIB2IIIX4IV semiconductors, is a wide-gap material with high photosensitivity and strong luminescence. Its crystal structure based on the defect chalcopyrite is characterized by a cation vacancy. It is much more possible that such structural defects result in deep levels in the forbidden band gap. The deep levels have a great influence on the electron emission, and on the photoelectric and luminescent properties [1]. ZnGa2Se4 can be used for phase change memories [2]. This compound was first studied crystallographically by Hahn et al. [3] using an X-ray method, and it was reported that the tetragonal unit cell had the space group symmetry I4 with cell parameters a = 5.485 Å and c = 10.97 Å and c/a = 2. Also, XRD measurements have been carried out on this compound by M. Morocoima et al. [4] to determine the values of a, c and c/a as well as the corresponding thermal expansion

⁎ Corresponding author at: Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt Tel.: +20 182848753, +90 5319343640; fax: +20 22581243. E-mail addresses: [email protected], [email protected], [email protected] (I.S. Yahia). 1 Permanent address: Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt. 0030-4018/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2012.02.096

coefficients in the temperature range between 300 and 700 K. The electrical properties of ZnGa2Se4 thin films have been investigated [5]. The optical properties of ZnGa2Se4 have been studied and the transition was found to be direct with optical band gap of 2.465 and 2.17 eV for bulk and thin film single crystals, respectively [6,7]. Optical applications of thin films require detailed knowledge of their optical properties. These include the optical constants (refractive index, n, and extinction coefficient, k) and the optical energy gap, Eg [8]. In the present work, we report in details the first results on the effect of annealing on the structural and optical properties of ZnGa2Se4 thin films to know the possibility of its applications as a new window for optoelectronic and solar cell devices. Some details of the structure properties of this material have been published in our previous works [9,10].

2. Experimental details Bulk ZnGa2Se4 was prepared by the melt and slowly cooled technique using different heat treatments. The constituent elements of the studied compound of high purity (5 N) were weighed according

3. Results and discussion 3.1. Structural properties 3.1.1. X-ray diffraction pattern X-ray diffraction pattern of the prepared ingot of ZnGa2Se4 in a fine powder form recorded using the X-ray diffractometer is shown in Fig. 1(a). Analysis of this pattern shows the polycrystalline nature of the tetragonal structure phase and the lattice parameters were determined using the powder X computer program [12]. The peak positions and the calculated lattice parameters (a = 5.524° A and c = 10.874° A) are in good agreement with the reported values for ZnGa2Se4, (JCPDS card No. 89–5716) with a = 5.5117 and c =10.9643° A, [13]. The good matching between the observed reflecting planes and that of the standard data revealed that the powder diffraction trace showed no extra peaks corresponding to any precipitation of elements or binary alloys along the whole measured 2θ ranges, including complete miscibility of the constituent elements. Fig. 1(b–e) illustrates the diffraction pattern carried out on the asdeposited and annealed films at annealing temperatures Ta = 623,

(204)

(312)

(e) (d) (c) (b)

10

20

30

40

50

60

70

(a) (424) (228)

(314) (323) (400),(008) (226),(217) (118) (332),(316),(413),(325)

(312) (116) (224)

(213),(105) (220),(204)

(301)

(211) (202)

(114)

(103) (200),(004)

(110)

(002) (101)

(112)

Intensity, (a.u.)

to their stoichiometric ratio and sealed into an evacuated silica tube (10 − 5 Torr) and then heated in a home-made designed oscillatory furnace. The temperature of the furnace was raised steeply up to 303 K at the rate 100 °C/h and was kept at this value for 2 h. Then, it was raised at the same rate to 490 K followed by an increase up to 693 K. Then, the furnace temperature was gradually raised by the same rate to 1423 K and kept at this temperature for 2 h. After that, the sample was gradually cooled down until it reached the following temperatures 873, 773 and 643 K and was kept constant for 1 h at each stage [4]. Finally, the sample was slowly cooled by the same rate of rising to room temperature. The long duration of synthesis and the continuity of the mechanical shaking of the mixture in the oscillatory furnace ensure the high homogeneity and quality of the investigated compound. Thin film samples of ZnGa2Se4 were prepared by a thermal evaporation technique using a high vacuum plant (Edward's E 306A) onto highly polished and cleaned microscopic glass substrates. The synthesized ingots of the proposed system were crushed into small grains. These grains were put into a cleaned dry quartz boat placed inside a helical tungsten wire as an evaporation source. The substrates were placed flat on a suitably designed holder (rotated horizontally). For the purpose of obtaining a parallel sided film on a plane substrate, it was sufficient to ensure that the pressure of the residual gas in the vacuum chamber was low enough and the distance between the source of material and the substrate holder was about 20 cm. The vacuum chamber was pumped down to 2 × 10 − 5 Torr. The temperature of the compound grains was then raised until the whole material evaporated with a deposition rate of about 2.5 nm/s. The substrate temperature was held at room temperature during the deposition process. Film thickness was controlled by thickness monitor model type (Edward FTM5), and then detected accurately by employing Tolansky's method of multiple-beam Fizeau fringes [11]. For X-ray diffraction (XRD) analysis of the investigated samples, Philips X-ray diffractometer (model X'-Pert) was used for the measurement by utilizing monochromatic CuKα radiation operated at 40 kV and 25 mA. The elemental composition of the as-deposited films was determined using scanning electron microscope (Joel-JSM 5400) with EDX unit (Oxford), operating at an accelerating voltage of 30 kV. The AFM micrographs were investigated by Park System XE-100E atomic force microscopy (AFM). The analysis of the grain size was done by Park system software. The optical transmittance T(λ) and reflectance R(λ) of the films were measured at room temperature with unpolarized light at normal incidence in the wavelength range 400–2500 nm using a double beam spectrophotometer (Type JASCO, model V-570, Rerll-00, UV–VIS-NIR).

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(112)

M. Fadel et al. / Optics Communications 285 (2012) 3154–3161

80

90

2θ Fig. 1. XRD patterns of ZnGa2Se4: (a) powder, (b) as-deposited film, annealed films at (c) Ta = 623 K, (d) Ta = 673 K, (e) Ta = 700 K.

673, and 700 K for 1 h. This figure showed that the as-deposited and the annealed films at Ta ≤673 K are amorphous. On the other hand, the annealed film at Ta =700 K revealed a polycrystalline structure. Such results indicate that the thermal annealing induced an amorphous-tocrystalline transition at Ta = 700 K. The analysis revealed that the annealed films at Ta = 700 K have a preferred orientation plane (112) parallel to the substrate. Also, minor peaks of other reflecting planes, (204) and (312), are observed. The unit cell lattice parameters for the films annealed at 700 K were determined from the obtained data for the reflecting planes (112), (204) and (312) using the following relation: h2 þ k2 l2 1 þ 2¼ 2 a2 c d

ð1Þ

It is found that the average values of a and c are 5.704 and 10.481° A, respectively. They are in good agreement with those for the powder and the reported values [13]. For a further analysis of the structure of the film annealed at 700 K, The crystallite size L can be calculated from the full width at half maximum, FWHM, of the (112) peak using Debye–Scherrer formula [14]: L¼

0:9λ β cosθ

ð2Þ

where β is the FWHM, λ is the wavelength of CuKα radiation and θ is the angle of diffraction. The crystallite size L is found to be 61 nm. Accordingly, the annealed film at 700 K showed a nanostructure. Also, the dislocation density δ and the main internal strain ε are calculated using the following equations [14]: δ¼

15β cosθ 4aL

1 ε≈ β cotθ 4

ð3Þ ð4Þ

The values of δ and ε are found to be 2.526 × 10 − 4 nm − 2 and 5.87 × 10 − 4, respectively. 3.1.2. Atomic force microscope images (AFM) The nanostructure of the ZnGa2Se4 thin film annealed at 700 K was confirmed by AFM micrographs. AFM images of 40 × 40, 4 × 4 and 1 × 1 μm 2 in two dimensional scales (2D) are shown in Fig. 2. As seen in Fig. 2, the annealed film is composed of nanoparticles having a cluster form. The type of nanostructure particles is like spherical

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M. Fadel et al. / Optics Communications 285 (2012) 3154–3161 Table 1 Elemental composition of ZnGa2Se4 in thin film form compared with the calculated values. Element

Calculated

Thin film (obs.)

Zn Ga Se

12.5555 26.7819 60.6626

12.69 26.71 60.60

the refractive index. In addition, thicker films would yield transmittance values too small to be reliably distinguished from the background noise [15]. Fig. 4(a) shows the spectral behavior of the transmittance T and the reflectance R, spectra at normal light incident in wavelength range 400–2500 nm, for as-deposited and annealed films. It is observed that the maxima of the reflectance spectra at the same wavelengths position of the minima in the transmission spectra and vice versa. This reflects the optical homogeneity of the films. T(λ) and R(λ) spectral distributions can be used to calculate the optical constants of the films.

3.1.3. Energy-dispersive X-ray spectroscopy (EDX) Fig. 3 represents the energy-dispersive X-ray spectroscopy EDX of the as-deposited films. The elemental analysis of the as-deposited thin film leads to the chemical formula Zn1.011Ga1.994Se3.995, revealing nearly stoichiometric composition (see Table 1). 3.2. Optical properties of ZnGa2Se4 thin films The optical properties of the investigated system corresponding to homogeneous and uniform thin films were deposited on transparent optical glass substrates which have refractive index ns and must be thicker enough to eliminate any resonant modes apart from those within the film. It should be pointed out that thicker films (891 nm) have been chosen in this work to study the optical properties of ZnGa2Se4 thin films. Thinner films would not yield useful information on low energy absorption and the lack of a sufficient number of interference fringes would have compounded the difficulty in extracting

a Reflectance R

shape. The average diameter of particles grain size equals 68.02 nm. The obtained value of the grain size from AFM micrographs is in good agreement with the calculated from Debye–Scherrer formula.

Transmittance T

Fig. 2. AFM micrographs of 40 × 40 μm2, 5 × 5 μm2and 1 × 1μm2 for ZnGa2Se4 thin film annealed at 700 K.

3.2.1. Determination of the refractive index n of ZnGa2Se4 thin films The refractive index and thickness of the studied films have been determined from the recorded transmission spectra using Swanepoel's method [16], which is based on that given by Manifacier et al. [17]. They

b

0.5 0.4 0.3 0.2 0.1 0.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 400

300 K 623 K 673 K 700 K

800

1200

1600

2000

2400

1.0 0.9

5.0 7.0 6.0

2.0

3.0

4.0

TM

Transmittance T

0.8 0.7 0.6

7.5 6.5

5.5

4.5

3.5

2.5

Tm

0.5 0.4 0.3 0.2 0.1 0.0 400

800

1200

1600

2000

2400

Wavelength λ, (nm)

Fig. 3. EDXS spectra of ZnGa2Se4 of the as-deposited thin film.

Fig. 4. (a) Transmittance and reflectance spectra of the as-deposited and annealed films of ZnGa2Se4. (b) Transmittance spectra with the maximum and minimum envelopes of the as-deposited film (as a representative example).

M. Fadel et al. / Optics Communications 285 (2012) 3154–3161

suggested the creation of envelopes TM and Tm around the interference maxima and minima of the transmittance spectrum as shown in Fig. 4(b) (dashed lines). Once the tangent points between the envelopes and the transmittance spectrum are known, initial approximation values for the refractive index ni can be calculated according to the expression [16]: ni ¼

rhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii  1=2 M þ M2 −ns 2

ð5Þ

the dispersion energy parameters Eo and Ed. The refractive index dispersion of the investigated material can be fitted by the WD model. The dispersion plays an important role in the search for the optical materials because it is a significant factor in optical communication and designing devices for spectral dispersion. The relation between the refractive index n and the single-oscillator strength below the band gap is given by the expression [18]: 2

n ¼1þ

where T M −T m ns 2 þ 1 þ 2 TMTm

ð6Þ

where TM and Tm are the values of the envelopes at wavelengths in which the upper and lower envelopes and the experimental transmission spectrum are tangent. The first approximation value of the film thickness di is calculated using the relation [16]: di ¼

λ1 λ2 2ðλ1 n2 −λ2 n1 Þ

ð7Þ

where n1 and n2 are the refractive indices at two adjacent maxima (or minima) at λ1 and λ2, respectively. The average values of the film thickness di are determined. These values are used together with the values of ni to calculate the “order number” mo of extremes using the basic equation for the interference fringes 2ni di ¼ mo λ. The accuracy of the film thickness is then significantly increased by taking the corresponding exact integer or half integer value of m, associated with each tangent (see Fig. 4(b)) and deriving new thickness df which in this way has a smaller dispersion. After that, the average value df is calculated and found to be in reasonable agreement with the interferometrically measured one. Using the exact values of m and df , the final values of the refractive index n are obtained (see Fig. 5). The values n can be fitted through a reasonable function such as the two-term Cauchy formula: n = b + a/λ 2 as shown in the inset of Fig. 5 which can be used for the extrapolation at shorter wavelengths [16]. From Fig. 5, it is observed that the spectral variation of the experimentally calculated refractive index n coincide with the calculated values using the two-term Cauchy relation. 3.2.2. Dispersion parameters of ZnGa2Se4 thin films Wemple and Didomenico (WD) model [18] used a single oscillator description of the frequency-dependent dielectric constant to define 3.0

2.8 2.7 2.6

2

Eo ¼

M −1 M −3

ð8Þ

2

and Ed ¼

M 3−1 M −3

ð9Þ

The values of M− 1 and M− 3 are given in Table 2. An important achievement of the WD model related to the dispersion energy Ed can be related to other physical parameters of the material through the following empirical formula [18]: 1

Ed ¼ β N c Z a N e

ð10Þ

where β 1 is a constant, and equals 0.37 ± 0.04 eV for covalent crystalline and amorphous materials [21]. Nc is the coordination number of the cation nearest neighbor to the anion, Za is the formal chemical valence of the anion which equals 2 and Ne is the effective number of valence electrons per anion, where Ne = [(2 valence electrons) × (1 Zinc cation) + (3 valence electrons) × (2 Galium cation) + (6 valence electrons) × (4 Selenium anions)] / [(4 no. of Selenium anions)] = 8. The values of the cation coordination number Nc for our samples

2.7

Refractive index, n

Refractive index, n

2.9

300 K 627 K 673 K 700 K

E o Ed E2o −ðhυÞ2

where υ is the frequency of the radiation, h is Planck's constant, Eo is the single-oscillator energy and Ed is the dispersion energy or the single-oscillator strength which serves as a measure of the strength of inter-band transitions [19]. Experimental verification of Eq. (8) can be obtained by plotting (n 2 − 1) − 1 versus (hυ) 2 as illustrated in Fig. 6 which yields a straight line for the normal behavior having the slope (EoEd) − 1 and the intercept Eo/Ed. Values of Eo and Ed are determined and given in Table 2. Eo scales with the optical energy gap (Eg), Eo ≈ 2Eg, as suggested by Tanaka [20] (see Table 2). The refractive index no at zero photon energy which is defined by the static dielectric constant εs =no2 can be deduced from the dispersion relation, i.e. no2 =1+ Ed/Eo and given in Table 2. On the other hand, the two parameters of the single oscillator model Eo and Ed are connected to M− 1 and M− 3 moments of the imaginary part of the complex dielectric constant ε2 as follows:

0.26

300 K 623 K 673 K 700 K

2.6

0.25

2.5

0.24

2.4 2.3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 2

-6

-2

1/λ x 10 , (nm )

(n2-1)-1

M ¼ 2ns

3157

0.23 0.22

2.5

0.21

2.4

0.20

2.3

0.19

2.2 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

0.18 0.0

0.2

0.4

0.6

0.8

Wavelength λ, (nm) Fig. 5. Spectral distribution of refractive index n. Inset: Fitting of the Cauchy equation for the as-deposited and annealed films of ZnGa2Se4.

1.0 2

1.2

1.4

1.6

1.8

2.0

2

(hυ) , (eV) 2

Fig. 6. Plot of (n − 1) ZnGa2Se4.

−1

2

versus (hυ) for the as-deposited and annealed films of

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M. Fadel et al. / Optics Communications 285 (2012) 3154–3161

Table 2 The calculated values of the optical parameters for the as-deposited and annealed ZnGa2Se4 thin films.

Eo(eV) Ed(eV) no εs M− 1 M− 3(eV− 2) Nc εL   −1 55 −3 N kg m 10 m 14 ωP(10 Hz) Ee(eV) αo, (cm− 1) Eg(eV) Eo/Eg

300 K

623 K

673 K

700 K

4.079 16.129 2.226 4.954 3.954 0.238 2.72 5.13 2.494 2.686 0.162 2.1 × 10− 3 2.27 1.797

4.322 19.123 2.329 5.425 4.425 0.237 3.23 5.60 2.469 2.672 0.142 1.0 × 10− 4 2.33 1.855

4.440 21.657 2.424 5.878 4.878 0.247 3.66 6.06 2.564 2.723 0.107 1.4 × 10− 7 2.42 1.835

4.530 22.526 2.444 5.973 4.973 0.242 3.81 6.15 2.505 2.692 0.075 2.4 × 10− 11 2.54 1.873

could be estimated according to Eq. (10) and given in Table 2. Furthermore, the relation between the lattice dielectric constant εL and the refractive index n can be described by the relation [15,22]: 2

ε 1 ¼ n ¼ εL −Χλ

2

2

where Χ ¼ 4π2 ce 2Nε l

 om

ð11Þ , ε1 is the real part of the dielectric constant, λ is the

wavelength, N is the free charge carrier concentration, εo is the permittivity of the free space (8.85 × 10− 12 Fm − 1), m* is the effective mass of the charge carrier and cl is the velocity of light. The plot of ε1 versus λ2 is shown in Fig. 7. It is observed that the dependence of ε1 on λ2 is linear at longer wavelengths verifying Eq. (11). Extrapolating the linear parts to zero wavelength gives the values of εL and from the slope of these lines values of N/m* are calculated according to Eq. (11) of the constant X. The obtained values of εL and N/m* are given in Table 2. The slight variation between the calculated values of the static and the lattice dielectric constants may be attributed to the free carrier contribution [15]. It is known that in the range of transparency, when the electron damping parameter γ b ω [23,24], the dielectric constant can be written as: ε1 ¼

2 ωp εL − 2

ð12Þ

ω

e2 N=m εo where

ω2p

¼ ωp is the plasma frequency and ω is the incident and light frequency. The calculated values of ωp are given in Table 2. For a further analysis of the optical data, the free carrier electric susceptibility

7.2

χc is discussed according to the Spitzer–Fan model [22,25] and given by the following equation: −4πχ c ¼

ð13Þ

Fig. 8 shows the plot of ln(−4πχc) versus lnλ in the near-infrared spectral range 1850–2500 nm. The figure depicts that χc increases with the wavelength and becomes sufficiently large as to reduce the refractive index and dielectric constant in the near-infrared region. A good fit to straight lines is seen. 3.2.3. Determination of the absorption coefficient α The absorption coefficient α was calculated by using two methods: The first method: Knowing the values of n, TM, To and d, α can be calculated using the following equation [16]:

α¼

1  −1  ln x d

ð14Þ

For the region of weak and medium absorption, the absorbance x is given in terms of the interference extremes by the following relation:  1=2  3  2 2 2 4 EM − EM − n −1 n −ns   x¼ ðn−1Þ3 n−n2s

ð15Þ

   2 where EM ¼ 8nT Mns þ n2 −1 n2 −n2s For the region of strong absorption where the interference maxima and minima converge to a single curve To, the absorbance x is given by:

x≈

  ðn þ 1Þ3 n þ n2s 16n2 ns

ð16Þ

To

The second method: The absorption coefficient α can be calculated using the measured values of transmittance T and reflectance R according to the following relation, which allows for multiple reflections in the film [26]:

300 K 623 K 673 K 700 K

6.8

  e2 N 2 λ 2 m πc

16.5 16.4

6.4

ln (-4πχc)

1

=n

2

16.3 6.0 5.6

16.2 16.1 16.0

5.2

300 K 623 K 673 K 700 K

15.9 4.8

0

10

20

30 2

40 5

50

60

2

λ x10 , (nm)

15.8 7.50

7.55

7.60

7.65

7.70

7.75

7.80

7.85

ln Fig. 7. Spectral distribution of refractive index n for as-deposited and annealed films of ZnGa2Se4.

Fig. 8. Plot of ln(−4πχc) versus lnλ for the as-deposited and annealed films of ZnGa2Se4.

M. Fadel et al. / Optics Communications 285 (2012) 3154–3161

!1=2 17

The values of α obtained from the two methods are in good agreement with each other, thus the mean value was taken into our account. The first region of the absorption edge is for the lower values of the absorption coefficient α b 10 4 cm − 1, where the absorption at lower photon energy usually follows the Urbach's rule according to the following equation [24,27,28]:   hυ α ðυÞ ¼ α o exp Ee

ð18Þ

where αo is a constant and Ee is Urbach's energy which is interpreted as the width of the tail of localized states in the band gap, and in general it represents the degree of disorder in the amorphous semiconductors [24]. The absorption of this region is due to transition between extended states in one band. From plotting logα as a function of hυ as shown in Fig. 9, the values of Ee and αo can be deduced by least square fitting of the first region and given in Table 2. It is observed that Ee decreases with increasing the annealing temperature owing to the decrease of the width of localized states tail in the band gap. Regarding the second region for the higher values of the absorption coefficient, α > 10 4 cm− 1, the optical absorption edge was analyzed by the following relation [24,29]:  p αhυ ¼ A hυ−Eg

ð19Þ

where A is the edge width parameter representing the film quality which is calculated from the linear part of this relation, Eg is the optical energy gap and p determines the type of the optical transition. The parameter p has the value 12 for the direct allowed transition and the value 2 for the indirect allowed transition. The usual methods for the determination of the values of Egind (indirect) and Egd (direct) are plotting (αhυ)1/2 and (αhυ)2 versus hυ as shown in Fig. 10(a). Plots of (αhυ)1/2 versus hυ yield straight lines for the as-deposited and annealed films at Ta =623 and 673 K. This linearity indicates existence of allowed indirect transition, while the plot of (αhυ)2 versus hυ yields a straight line for the annealed film at Ta =700 K indicating the existence of direct allowed transition. Values of the optical energy gap Egind and Egd were determined from the intercept of the extrapolation of the linear part to zero absorption with the photon energy axis as given in Table 2. It is observed that Eg increases with increasing the annealing temperature. This behavior is similar to that of CdGa2Se4 [30] which may be explained as a result

5.2

log α

4.0 3.6 3.2

300 K 623 K 673 K 700 K

2.4 2.4

2.6

2.8

3.0

300 K 623 K 673 K 700 K

25

400

20

300

15

200

10

100

5

0 2.2

2.4

2.6

2.8

0 3.2

3.0

hυ, (eV)

b

0.30 300 K 623 K 673 K 700 K

0.25

0.20

0.15

0.10

0.05

0.00 400

420

440

460

480

500

520

540

560

Wavelength λ, (nm) Fig. 10. (a) Dependence of (αhυ)1/2 and (αhυ)2 on the photon energy hυ. (b) Dependence of the extinction coefficient k on the wavelength λ for the as-deposited and annealed films of ZnGa2Se4.

of decreasing the degree of disorder in the structure. This reduces the localized energy level concentration which causes an increase in Eg [31]. The extinction coefficient k is calculated for the investigated films using the values of α and λ by the relation: αλ 4π

ð20Þ

Fig. 10(b) illustrates the dependence of the extinction coefficient k on the wavelength. Most of the optical parameters shown in Table 2 are in good agreement with that obtained for CdS thin films [32] which have been found to be the best suited window material as a heterojunction partner in CdTe thin film solar cells [33]. The band gap of ZnGa2Se4 (2.54 eV) in its polycrystalline form (annealed at 700 K) is higher than the reported value of CdS (2.42 eV) [32–34]. Throughout this study, ZnGa2Se4 can be used as a window layer of solar cells instead of CdS which has safety problems i.e. reducing the toxic nature of CdS used in thin film solar cells [34].

4.4

2.8

30

600

500

k¼

4.8

2.2

a

(αhυ)2, (x109 cm2 eV2)

ð1−RÞ4 2 þR 4T 2

(α αhv)1/2, (cm-1/2 eV1/2)

1 ð1−RÞ2 ln þ d 2T

Extenction coefficient, k

α¼

3159

3.2

hυ, (eV) Fig. 9. Dependence of logα on the photon energy hυ for the as-deposited and annealed films of ZnGa2Se4.

3.2.4. Spectral distribution of the real and imaginary parts of the dielectric constant and the dissipation factor The real ε1 and imaginary ε2 parts of the dielectric constant of the investigated films are shown in Fig. 11. It is observed that both ε1 and

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M. Fadel et al. / Optics Communications 285 (2012) 3154–3161

9

surface of the material, respectively. They are related to the real and imaginary parts of the complex dielectric constant by [36,37]:

(ε1)

8 7 6

300 K 623 K 673 K 700 K

5 4 3

(ε2)

0 2.2

2.4

2.6

2.8

3.0

ð22Þ



1 ε2 ¼ −Im ε  þ1 ðε1 þ 1Þ2 þ ε22

ð23Þ

where ε* is the complex dielectric constant. Fig. 13(a,b) illustrates the dependence of both the volume and surface energy loss functions on photon energy in the fundamental absorption region for the investigated compound. It is clear that the two functions in general increase with increasing the photon energy. In addition, the energy loss by the free charge carriers when traversing the bulk material has approximately the same value as when traversing the surface in particular for relatively lower energies.

2 1



1 ε −Im ¼  2 2 2 ε ε1 þ ε2

3.2

hυ, (eV) Fig. 11. Dependence of ε1 and ε2 on the photon energy hυ for the as-deposited and annealed films of ZnGa2Se4.

4. Conclusions

ε2 increase with increasing photon energy. The real and imaginary parts follow the same behavior while the values of the real part are higher than that of the imaginary part. Also, it is possible to calculate the values of the dissipation factor tanδ according to the following equation based on the values of ε1 and ε2 [24,27,35]:

Thin films of ZnGa2Se4 were prepared by thermal evaporation. The as-deposited and annealed films 623 and 673 K are amorphous. An amorphous-to-crystalline phase transition with a single phase of a defective tetragonal chalcopyrite structure similar to that of the synthesized material was obtained for the annealed films at 700 K. The obtained values of the grain size calculated from Debye–Scherrer formula and AFM micrographs and are in good agreement with each

ε2 ε1

ð21Þ

The dissipation factor tanδ is a measure of loss-rate of power of a mechanical mode, such as an oscillation, in a dissipative system. For example, electric power is lost in all dielectric materials, usually in the form of heat [27]. The dependence of tanδ on photon energy is shown in Fig. 12. It is found that the dissipation factor increases with increasing the photon energy. 3.2.5. Energy spectrum of volume and surface energy loss functions Energy absorbed by the material which might be due to single electron transitions or to collective effects induced within the solid can be expressed in terms of the volume, − Im[1/ε*] and surface, − Im[1/(ε* + 1)] energy loss functions which describe the probability that fast electrons will lose energy when traveling the bulk and

a Volume energy loss function

tan δ ¼

0.028 0.024

300 K 623 K 673 K 700 K

0.020 0.016 0.012 0.008 0.004 0.000 2.2

2.4

2.6

2.8

3.0

3.2

3.0

3.2

hυ υ, (eV)

b

0.24

Surface energy loss function

0.20

300 K 623 K 673 K 700 K

tan δ

0.16

0.12

0.08

0.04

0.00 2.2

2.4

2.6

2.8

3.0

3.2

hυ, (eV) Fig. 12. Dependence of dissipation factor tanδ on the photon energy hυ for the as-deposited and annealed films of ZnGa2Se4.

0.024

0.020

300 K 623 K 673 K 700 K

0.016

0.012

0.008

0.004

0.000 2.2

2.4

2.6

2.8

hυ, (eV) Fig. 13. Volume energy loss (a) and surface energy loss (b) as functions of hυ for the asdeposited and annealed films of ZnGa2Se4.

M. Fadel et al. / Optics Communications 285 (2012) 3154–3161

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