- Email: [email protected]
Influence of the film thickness on structural and optical properties of CdTe thin films electrodeposited on stainless steel substrates
Materials Chemistry and Physics 142 (2013) 432e437
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Influence of the film thickness on structural and optical properties of CdTe thin films electrodeposited on stainless steel substrates J. Pantoja Enriquez a, *, N.R. Mathews b, G. Pérez Hernández c, Xavier Mathew b a
Centro de Investigación y Desarrollo Tecnológico en Energías Renovables, Universidad de Ciencias y Artes de Chiapas, Libramiento Norte No 1150, Col. Lajas Maciel, 29039 Tuxtla Gutiérrez, Chiapas, Mexico b Instituto de Energías Renovables, Universidad Nacional Autónoma de México, 62580 Temixco, Morelos, Mexico c Universidad Juárez Autónoma de Tabasco, Avenida Universidad S/N, Zona de la Cultura, Col. Magisterial, Villahermosa, Centro, Tabasco 86040, México
h i g h l i g h t s CdTe of different thicknesses is deposited by electrodeposition on stainless steel. Structural parameters D, a, d and 3 show a noticeable dependence on film thickness. Optical constants Eg, n, ke, 3 r and 3 i strongly depend on film thickness.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 September 2012 Received in revised form 14 May 2013 Accepted 29 July 2013
CdTe thin films of different thicknesses were deposited by electrodeposition on stainless steel substrates (SS). The dependence of structural and optical properties on film thickness was evaluated for thicknesses in the range 0.17e1.5 mm. When the film is very thin the crystallites lack preferred orientation, however, thicker films showed preference for (111) plane. The results show that structural parameters such as crystallite size, lattice constant, dislocation density and strain show a noticeable dependence on film thickness, however, the variation is significant only when the film thickness is below 0.8 mm. The films were successfully transferred on to glass substrates for optical studies. Optical parameter such as absorption coefficient (a), band gap (Eg), refractive index (n), extinction coefficient (ke), real (3 r) and imaginary (3 i) parts of the dielectric constant were studied. The results indicate that all the optical parameters strongly depend on film thickness. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Thin films Semiconductors Microstructure Optical properties
1. Introduction Cadmium telluride (CdTe) is one of the most investigated semiconductors for photovoltaic applications in the past four decades and is one of the promising photovoltaic materials due to low fabrication cost, nearly optimum band gap (1.5 eV) for efficient photo conversion, high optical absorption coefficient (>104 cm1) at band edge and the variety of techniques available for its deposition as thin films. The conventional, thin film solar cells are manufactured on glass substrates having the disadvantage of weight and fragile nature of the modules. In this context, CdTe devices based on flexible metallic substrates are interesting due to its light weight and damage free nature of the device structures. * Corresponding author. Fax: þ52 9616170440. E-mail addresses: [email protected], [email protected] Enriquez).
(J.
0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.07.043
Pantoja
There are good number of reports [1e3] on the growth and characterization of the CdTe thin films on flexible metallic substrates. CdTe thin films have been extensively studied for its structural, optical, optoelectronic and electrochemical properties [4e13]. Despite the fact that CdTe has been investigated extensively as an absorber layer in solar cells, there are however many issues that still need to be understood to optimize the optical and electrical properties of CdTe films. The structural and optical properties of CdTe film influence the device performance. In photovoltaic applications, the thickness of the film is an important parameter since the thickness affects the microstructure of the film as well as the optical and electrical characteristics. No conclusive studies have been reported demonstrating the dependence of structural properties on thickness of the films. In this paper we discuss the influence of the thickness on the structural and optical properties of CdTe thin films prepared by electrodeposition on stainless steel substrate.
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
2. Experimental All the films used in this study were electrodeposited potentiostatically from an acidic bath consisting of 1 M CdSO4 and 100e 200 ppm of TeO2 as Cd and Te source respectively. The films were deposited on stainless steel foils of 0.05 mm thick at identical conditions applying a potential of 580 mV with respect to Ag/AgCl reference electrode. The electrodeposition details can be found elsewhere [4,14,15]. The thicknesses of all the films were calculated using two different methods; total charge flowed during deposition, and weighing. In some cases a third method; from the maxima and minima of interference patterns, was also employed. The thickness values obtained from these three methods are close to each other, and the mean value is reported. Films with thickness in the range 0.17e1.5 mm were used in this study. The XRD measurements were performed using a Rigaku X-ray diffractometer with Cu Ka source with l ¼ 1.5418 A. The various structural parameters such as lattice constant, grain size, dislocation density, strain and texture coefficient have been evaluated. The cross sectional composition of the film was studied by conducting the AUGER depth profile analysis of a representative film. The transmittance (T%) of the films was measured in the spectral range of 300e2500 nm, using a Shimadzu UVeVISeNIR double beam spectrophotometer. The absorption coefficient, band gap, refractive index, extinction coefficient, real and imaginary parts of the dielectric constant were determined from transmittance for CdTe samples of different thickness. The transmittance measurements were realized by transferring the films on to glass substrates using a transparent epoxy. This technique has been successfully applied for transferring CdTe films from opaque substrates and reliable results has been reported [2]. The transmittance spectra were recorded and the absorption of the glass and epoxy, were compensated by placing a glass/epoxy structure in the reference beam. 3. Results and discussion 3.1. Structural properties Fig. 1 shows the XRD spectra of CdTe thin films with different thicknesses and the inset shows the intensity of (111) peak. The spectra were obtained by scanning qe2q in the range of 20e65 .
Fig. 1. XRD patterns of CdTe thin films with different thicknesses. The inset is the (111) peak of the films.
433
Diffraction analysis suggests that all CdTe samples are polycrystalline and have a cubic zinc-blende structure, with reflections corresponding to (111), (220), (311) and (331) plane orientations, according to JCPDS data file: CdTecubic-15-0770. Since the deposition conditions are kept constant, no variation in the film stoichiometry is expected. The XRD patterns show that the peak intensity increases as the film thickness increases and this is due to the amount of material involved in the X-ray diffraction process [16]. In order to analyse the evolution of the preferential orientation during the film growth, the two parameters; texture coefficient (Ci), and the degree of preferred orientation (s) have been calculated using the following relations [17,18].
N IIi Ci ¼ PN i0
Ii i ¼ 1 Ii0
(1)
where the subscript i stands for a particular plane, Ii is the measured integral intensity, Ii0 is the integral intensity of the JCPDS powder diffraction pattern of the corresponding plane i, and N is the number of reflections in the X-ray diffraction pattern considered for the analysis. Ci is unity for each reflection in the case of a randomly oriented sample and values of Ci greater than unity indicate preferred orientation of the crystallites in that particular direction. The degree of preferred orientation s of the sample as a whole can be assessed by estimating the standard deviation of all Ci values calculated for the sample [17,18].
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 i ¼ 1 ðCi Ci0 Þ s¼ N
(2)
where Ci0 is the texture coefficient of the powder sample, which is always unity. The value of s is an indicator of the degree of orientation of a sample and can be used to compare different samples. A value of zero for s indicates that the sample is completely at random orientation and the sample with higher value of s has better preferential orientation. Fig. 2 shows the degree of preferred orientation of CdTe thin films with different thicknesses. The inset is the variation of texture coefficient with the film thickness. From Fig. 2 it can be seen that the value of s increase from 0.16 to 1.2 as the film thickness vary from 0.17 to 1.5 mm; this means that there is a strong relationship
Fig. 2. Degree of preferred orientation of CdTe thin films with different thicknesses. The inset is the variation of texture coefficient with the film thickness.
434
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
between the degree of preferred orientation and film thickness. Moreover, from the texture coefficient (see inset of Fig. 2), we can see that in all samples Ci is greater than unity for the (111) plane, indicating that the preferred growth plane is (111).The average diameter of the CdTe grains and the residual strain are calculated from the fullwidth at half-maximum (FWHM) using the relation [19].
b cos q ¼
Kl þ 43 sin q D
(3)
where q is the Bragg angle and; b2 ¼ (FWHM)2 b2, where FWHM is the full width at half maximum of the peaks, l ¼ 1.54056 A corresponds to the Cu Ka radiation, D is the average size of the grains, K is the shape factor which is approximately unity and 3 is the residual strain of the films. The integral breadth b, was obtained from a powder sample of polycrystalline silicon. A plot of bcos(q) versus sin(q) will give a straight line and the grain size D and the strain 3 can be calculated from the intercept and slope, respectively. The results of the above calculations are presented in Fig. 3. When the thickness increases from 0.17 to 1.5 mm, the grain size increases from 0.03 to 0.06 mm approximately, and the strain decreases from 4.5 103 to 2.0 104. One can see from Fig. 3, that the grain growth has two stages, in the initial stage the grain size has a strong dependence on film thickness and the grain size increases with film thickness until the film thickness attains a value greater than 0.5 mm. Beyond this thickness the grain size remains more or less constant. Strain (stress) affects the mechanical properties of the films such as the stability of microstructure, the adhesion between film and substrate and the opto-electronic properties of the deposited films. Stress in films can be intrinsic, caused by the conditions prevailing during deposition (temperature, pH of solution, deposition rate, electric field between counter and working electrodes, impurities, etc.). On the other hand stress can be extrinsic to the film, but intrinsic to the composite film-substrate system, caused by the difference in the thermal expansion coefficients [20]. From Fig. 3 we can see that the strain-thickness relation has three distinct zones; when the film is very thin the strain is high and more or less remains same up to a thickness of 0.3 mm, in the thickness range 0.3e0.8 mm the strain decreases almost linearly and attains saturation when thickness is above 0.8 mm. The decrease in strain indicates a decrease in the concentration of lattice imperfections as the film thickness increases. This implies that as the grains grow in size the grain boundaries decrease and hence the stress induced due to the grain boundaries also decreases.
Fig. 3. Variation of the grain size and strain with film thickness.
The lattice parameter, a0; of the samples was calculated from the peak positions in the XRD patterns and using the method developed by Nelson and Taylor [21,22]. In this method the lattice parameter (a0) calculated from different peaks is plotted against. cos2 q(sin1 þ q1). The graph is linear and the intercept at cos2 q(sin1 þ q1) ¼ 0, gives the lattice constant of the sample. The dependence of the lattice parameter on the film thickness is shown in Fig. 4. The lattice value is high when the films are thinner and decreases as films grow in thickness, finally attains a value close to the stress free sample (6.481 A). The dislocation density (d), defined as the length of dislocation lines per unit volume of the crystal was evaluated from the formula suggested by Williamson and Smallman [23].
d¼
1 D2
(4)
where D is grain size of the sample. The relation between dislocation density and thickness is shown in Fig. 5. As expected the dislocation density and strain decrease as the films grow in thickness. The above observations imply that as the films grow in thickness, the grain size increases and the crystalline quality of the film improves. The AFM analysis (Fig. 6) revealed a void free, rough surface with cauliflower like morphology. The cross-sectional composition (AUGER depth profile) of a film with thickness 0.7 mm is shown in Fig. 7. It can be observed that the composition is uniform throughout the thickness of the film. The oxygen in the bulk of the film may be incorporated from the electrodeposition bath which contains dissolved oxygen. The stoichiometry of the film is maintained throughout the thickness including in the layers close to the substrate, indicating that the stoichiometry of the film is independent of the thickness. However, the stoichiometry at the film surface is different from that of the bulk; which is expected due to the exposure to the atmospheric humidity and oxygen. The decrease in Cd content and the increase in oxygen concentration at the film surface are indications of the formation of trace amounts of oxides of tellurium. 3.2. Optical properties Fig. 8 shows the transmittance spectra of six CdTe samples with different thicknesses in the wavelength range 300e2500 nm. The
Fig. 4. The dependence of lattice constant on film thickness.
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
435
Fig. 5. Dependence of dislocation density on the film thickness.
absorption edge shifts towards higher wavelength region with the increase of film thickness.
Lnð1=TÞ a ¼ d
(5)
where T ¼ It/Ii is the transmittance. The absorption coefficient of the films was calculated from the transmittance spectra near the absorption edge using the relation; The absorption coefficient a of the material can be related to the incident photon energy hn through the relation [24e28];
ahv ¼ A hv Eg
1 2
(6)
where A is a constant, h is the Planck’s constant, n is the frequency and Eg is the band gap. The band gap of the films was determined by plotting (ahn)2 vs. hn. The intercept of the straight-line portion of the graph on the hn axis gives the value of Eg. The dependence of the band gap of CdTe films on the film thickness is presented in the inset of Fig. 8. It can be seen that the band gap decreases from 1.53 to 1.49 eV as the film thickness increases from 0.17 to 1.5 mm. The observed decrease in the band gap with increase of film thickness is in good agreement with the earlier investigations on CdTe thin films [29e31]. This variation can be due to the influence of different factors such as grain size, structural parameters, carrier concentration, presence of impurities, deviation from
Fig. 6. AFM image of a CdTe film of thickness 0.7 mm deposited on stainless steel substrate.
Fig. 7. AUGER depth profile of a CdTe film of thickness 0.7 mm deposited on stainless steel substrate.
stoichiometry of the film, dislocation density, lattice strain, etc. [32e35]. However, the lattice parameters, grain size and the strain have a direct dependence on the film thickness. Hence, we consider that the observed decrease in Eg with increasing thickness is due to the decrease in lattice strain and increase of grain size. The refractive index “n” was determined from the transmission spectra using the method suggested by Swanepoel and Manifacier et al. [36e38]. The envelopes around the interference maxima and minima of the transmittance spectra are considered to be continuous functions of l. According to this method, the value of refractive index, n, can be calculated using the expression [36e39],
n ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nþ
N2 n2s
(7)
where N and ns are given by
N ¼
1 þ n2s 2ns ðTmax Tmin Þ þ Tmax Tmin 2
(8)
Fig. 8. Optical transmittance spectra of six CdTe thin films of different thickness. The inset is the variation of band gap with thickness.
436
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
Fig. 11. Variation of the real (3 r) and imaginary (3 i) parts of the dielectric constant against the photon wavelength for different thickness of CdTe thin films.
Fig. 9. Dependence of refractive index n on CdTe film thickness.
The refractive index of the substrate ns is obtained from the transmittance spectrum of the substrate, Ts, using the equation [40]:
1 ns ¼ þ Ts
sffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 Ts
Ke ¼ (9)
The refractive index of the film has been evaluated from the transmittance and were fitted using Cauchy dispersion relationship, n(l) ¼ a þ b/l2 (where a and b are constants), which was used for extrapolating the data in the wavelength range 400e3100 nm [41]. The calculated values of n are plotted as a function of photon wavelength and are shown in Fig. 9. The value of the refractive index is found to decrease with the increase of wavelength, while, the refractive index increases with increasing film thickness. The increase in the refractive index with thickness is attributed to an increase in the crystallinity of the films. This tendency is consistent with the results reported [6,42,43]. The complex relative dielectric constant (3 c), the extinction coefficient (ke), and the real (3 r) and imaginary (3 i) parts of the
Fig. 10. Variation of CdTe extinction coefficient ke with film thickness.
dielectric constant for the CdTe thin films have been estimated from transmittance using the following relations [44e46]:
al
4p
3c
¼
3r
¼ n2 Ke2
(12)
3i
¼ 2nk
(13)
3r
þ i3 i
(10) (11)
Fig. 10 shows the variation of extinction coefficient ke, as a function of wavelength and thickness. It is shown that the ke, decreases with the film thickness. Fig. 11 shows a plot of the real (3 r) and imaginary (3 i) parts of the dielectric constant against the photon wavelength for CdTe thin films with different thickness. It is found that the dependence of (3 r) on thickness and wavelength is the same as that of n, because
Fig. 12. 1/(n2 1) vs. (hv)2 plot for CdTe thin films with different thickness.
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437 Table 1 The estimated values of various optical parameters of CdTe thin films, the data corresponds to films with thickness in the range 0.17e1.5 mm. Thickness d (mm)
E0 (eV)
Ed (eV)
Eg (eV)
Eg (eV) from Fig. 8
0.17 0.27 0.58 0.71 1.10 1.50
3.21 3.20 3.16 3.13 3.05 3.05
12.08 13.85 16.72 17.42 17.94 18.45
1.60 1.59 1.57 1.56 1.52 1.51
1.53 1.525 1.52 1.51 1.50 1.49
0.01 0.01 0.01 0.01 0.01 0.01
n(0)
3N
2.18 2.28 2.50 2.56 2.62 2.65
4.76 5.26 6.29 6.56 6.88 7.05
437
single oscillator model shows that these values depend on film thickness. Acknowledgements This work at CIE-UNAM was partially supported by the projects SENER-CONACyT 117891, SEP-CONACYT 83960 and ICyTDF 318/ 2009. Authors acknowledge the support of M. Luisa Ramon Garcia in XRD measurements. References
2
k2e ,
n [ on the other hand the imaginary part decreases with the film thickness and increase with the wavelength similar to that of ke. The dispersion of the refractive index was evaluated according to the single effective oscillator model proposed by Wemple and Di Domenico [47,48]. According to the dispersion theory, in the low absorption region, the index of refraction n is given in the single oscillator model by the relation;
n2 ðhvÞ ¼ 1 þ
Ed E0 E02 ðhvÞ2
(14)
where Ed is the optical dispersion energy inside the bulk, and E0 is the oscillation energy between valence and conduction bands of the semiconductor. Ed is a measure of the intensity of the inter-band transitions and is obtained from the slope of the straight line portion of 1/(n2 1) vs. (hv)2. A plot 1/(n2 1) of vs. (hv)2 for CdTe thin films with different thickness is shown in Fig. 12. The oscillator energy, E0, is approximately twice the energy gap (E0 z 2Eg). The value of refractive index n(0) and dielectric constant 3 N ¼ n(0)2 for hn / 0 were estimated from the graphs. The values of E0, Ed, Eg, n(0) and 3 N are shown in Table 1. For a comparison the values of Eg estimated from E0 and determined from Fig. 8 are presented in Table 1. From the table it is clear that all the optical parameters has certain dependence on film thickness; the strength of the oscillator E0, decrease from 3.21 to 3.03 eV, the optical dispersion energy Ed, increase from 12.08 to 18.45 eV, the refractive index n(0) increase from 2.18 to 2.65 and dielectric constant 3 N increase from 4.76 to 7.05 as the film thickness increases from 0.17 to 1.5 mm. 4. Conclusions We have studied the dependence of structural and optical properties of electrodeposited CdTe thin films on the thickness of films. The crystallite sizes in the films as measured using XRD data are found to be in the range of 0.03e0.06 mm when the film thickness vary from 0.17 to 1.5 mm. The structural parameters such as crystallite size, lattice constant, dislocation density and strain show a non-linear dependence on film thickness; in all cases the variation is significant when the film thickness is below 0.8 mm. The optical parameters such as absorption coefficient, band gap, refractive index and extinction coefficient were calculated from the transmittance spectra. The results indicate that refractive index n, extinction coefficient ke, and the real (3 r) and imaginary (3 i) parts of the dielectric constant strongly depend on film thickness. The change in optical band gap with film thickness is attributed to the decrease in lattice strain and increase of grain size. The oscillator strength and the optical dispersion energy determined using the
[1] Vijay P. Singh, John C. McClure, G.B. Lush, W. Wang, X. Wang, G.W. Thompson, E. Clark, Sol. Energy Mater. Sol. Cells 59 (1999) 145. [2] Xavier Mathew, P.J. Sebastian, Sol. Energy Mater. Sol. Cells 59 (1999) 85. [3] Xavier Mathew, Gerald W. Thompson, V.P. Singh, J.C. McClure, S. Velumani, N.R. Mathews, P.J. Sebastian, Sol. Energy Mater. Sol. Cells 76 (2003) 293. [4] M. Bulent, Basol Sol. Cells 23 (1988) 69. [5] Ting L. Chu, Shirley S. Chu, Solid State Electron. 38 (1995) 533. [6] S. Saha, U. Pal, A.K. Chaudhuri, V.V. RAO, H.D. BANERJEE, Phys. Status Solidi A 114 (1989) 721. [7] D. Kindi, J. Touskova, Phys. Status Solidi A 106 (1988) 297. [8] S.S. Ou, O.M. Stafsudd, B.M. Basol, Thin Solid Films 112 (1984) 301. [9] H.R. Moutinho, F.S. Hasoon, F. Abulfotuh, L.L. Kazmerski, J. Vac. Sci. Technol. A 13 (1995) 2877. [10] Brian E. McCandless, Robert W. Birkmire, Sol. Cells 31 (1991) 527. [11] James Sites, Jun Pan, Thin Solid Films 515 (2007) 6099. [12] S. Vatavu, H. Zhao, V. Padma, R. Rudaraju, D.L. Morel, P. Gas¸in, Iu. Caraman, C.S. Ferekides, Thin Solid Films 515 (2007) 6107. [13] N. Armani, G. Salviati, L. Nasi, A. Bosio, S. Mazzamuto, N. Romeo, Thin Solid Films 515 (2007) 6184. [14] M.P.R. Panicker, M. Knaster, F.A. Kroger, J. Electrochem. Soc. 125 (1978) 556. [15] F.A. Kroger, R.L. Rod, M.P.R. Panicker, Photovoltaic Power Generating Means and Methods, U.S. Patent 4400244, 1983. [16] N. El-Kadry, A. Ashour, S.A. Mahmoud, Thin Solid Films 269 (1995) 112. [17] K.H. Kim, J.S. Chun, Thin Solid Films 141 (1986) 287. [18] Charles S. Barrett, T.B. Massalski, in: Structureof Metals: Crystallographic Methods, Principles and Data, third ed., McGraw Hill, NY, 1966. [19] E. Lifshin, X-ray Characterization of Materials, Wiley-VCH, New York, 1999. [20] K.N. Tu, R. Rosenberg, Analytical Techniques for Thin Films, Academy Press Inc., San Diego CA, 1988. [21] A. Taylor, H. Sinclair, Proc. Phys. Soc. 57 (1945) 126. [22] J.B. Nelson, D.P. Riley, Proc. Phys. Soc. 57 (1945) 160. [23] G. Williamson, R. Smallman, Philos. Mag 1 (1956) 34. [24] J. Tauc, Amorphous and Liquid Semiconductors, Plenum, New York, 1974. [25] N.F. Mott, E.A. Davis, Electronic Processes in Non-crystalline Materials, Calendron Press, Oxford, 1979. [26] J.J. Pankove, Optical Processes in Semiconductors, Prentice-Hall, Englewood Cliffs, NJ, 1971. [27] P.W. Davis, T.S. Shilliday, Phys. Rev. 118 (1960) 1020. [28] J.I. Pankove, Optical Processes in Semiconductors, Dover, New York, 1971. [29] U. Pal, D. Samanta, S. Ghorai, A.K. Chaudri, J. Appl. Phys. 74 (1993) 6368. [30] S. Lalitha, R. Sathyamoorthy, S. Senthilarasu, A. Subbarayan, K. Natarajan, Sol. Energy Mater. Sol. Cells 82 (2004) 187. [31] R. Sathyamoorthy, S. Narayandass, D. Mangalaraj, Sol. Energy Mater. Sol. Cells 76 (2003) 339. [32] A.E. Rakhshani, A.S. Al-Azab, J. Phys. Condens. Matter 12 (2000) 8745. [33] S.A. Al Kuhaimi, Vacuum 51 (1998) 349. [34] K.L. Chopra, Thin Film Phenomena, McGraw-Hill, New York, 1969, p. 266. [35] M. Pattabi, J. Uchil, Sol. Energy Mater. Sol. Cells 63 (2000) 309. [36] R. Swanepoel, J. Phys. E Sci. Instrum. 16 (1983) 121. [37] R. Swanepoel, J. Phys. E Sci. Instrum. 17 (1984) 896. [38] J.C. Manifacer, J. Gasiot, J.P. Fillard, J. Phys. E Sci. Instrum. 9 (1976) 1002. [39] E.R. Shaaban, N. El-Kabnay, A.M. Abou-sehly, N. Afify, Physica B 381 (2006) 24. [40] T.S. Moss, Optical Properties of Semiconductors, Butterworths, London, 1959. [41] E. Márquez, J.M. González-Leal, A.M. Bernal-Oliva, R. Jiménez Garay, T. Wagner, J. Non-Cryst. Solids 354 (2008) 503. [42] S.S. Patil, P.H. Pawar, J. Chem. Bio. Phy. Sci. Sec. C. 2 (2012) 968. [43] E.R. Shaaban, N. Afify, A. El-Taher, J. Alloys Compd. 482 (2009) 400. [44] A. Milnes, D. Feucht, Heterojunctions and MetalSemiconductor Junctions, Academic Press, New York, NY, USA, 1972. [45] L. Kazmerski, Polycrystalline and Amorphous Thin Films and Devices, Materials Science and Technology Series, Academic Press, New York, NY, USA, 1980. [46] S.S. Li, Semiconductor Physical Electronics, second ed., Springer-Verlag, 2006. [47] S.H. Wemple, Di Domenico, Phys. Rev. B 7 (1971) 1338. [48] S.H. Wemple, Phys. Rev. B 7 (1973) 3767.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Influence of the film thickness on structural and optical properties of CdTe thin films electrodeposited on stainless steel substrates J. Pantoja Enriquez a, *, N.R. Mathews b, G. Pérez Hernández c, Xavier Mathew b a
Centro de Investigación y Desarrollo Tecnológico en Energías Renovables, Universidad de Ciencias y Artes de Chiapas, Libramiento Norte No 1150, Col. Lajas Maciel, 29039 Tuxtla Gutiérrez, Chiapas, Mexico b Instituto de Energías Renovables, Universidad Nacional Autónoma de México, 62580 Temixco, Morelos, Mexico c Universidad Juárez Autónoma de Tabasco, Avenida Universidad S/N, Zona de la Cultura, Col. Magisterial, Villahermosa, Centro, Tabasco 86040, México
h i g h l i g h t s CdTe of different thicknesses is deposited by electrodeposition on stainless steel. Structural parameters D, a, d and 3 show a noticeable dependence on film thickness. Optical constants Eg, n, ke, 3 r and 3 i strongly depend on film thickness.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 September 2012 Received in revised form 14 May 2013 Accepted 29 July 2013
CdTe thin films of different thicknesses were deposited by electrodeposition on stainless steel substrates (SS). The dependence of structural and optical properties on film thickness was evaluated for thicknesses in the range 0.17e1.5 mm. When the film is very thin the crystallites lack preferred orientation, however, thicker films showed preference for (111) plane. The results show that structural parameters such as crystallite size, lattice constant, dislocation density and strain show a noticeable dependence on film thickness, however, the variation is significant only when the film thickness is below 0.8 mm. The films were successfully transferred on to glass substrates for optical studies. Optical parameter such as absorption coefficient (a), band gap (Eg), refractive index (n), extinction coefficient (ke), real (3 r) and imaginary (3 i) parts of the dielectric constant were studied. The results indicate that all the optical parameters strongly depend on film thickness. Ó 2013 Elsevier B.V. All rights reserved.
Keywords: Thin films Semiconductors Microstructure Optical properties
1. Introduction Cadmium telluride (CdTe) is one of the most investigated semiconductors for photovoltaic applications in the past four decades and is one of the promising photovoltaic materials due to low fabrication cost, nearly optimum band gap (1.5 eV) for efficient photo conversion, high optical absorption coefficient (>104 cm1) at band edge and the variety of techniques available for its deposition as thin films. The conventional, thin film solar cells are manufactured on glass substrates having the disadvantage of weight and fragile nature of the modules. In this context, CdTe devices based on flexible metallic substrates are interesting due to its light weight and damage free nature of the device structures. * Corresponding author. Fax: þ52 9616170440. E-mail addresses: [email protected], [email protected] Enriquez).
(J.
0254-0584/$ e see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matchemphys.2013.07.043
Pantoja
There are good number of reports [1e3] on the growth and characterization of the CdTe thin films on flexible metallic substrates. CdTe thin films have been extensively studied for its structural, optical, optoelectronic and electrochemical properties [4e13]. Despite the fact that CdTe has been investigated extensively as an absorber layer in solar cells, there are however many issues that still need to be understood to optimize the optical and electrical properties of CdTe films. The structural and optical properties of CdTe film influence the device performance. In photovoltaic applications, the thickness of the film is an important parameter since the thickness affects the microstructure of the film as well as the optical and electrical characteristics. No conclusive studies have been reported demonstrating the dependence of structural properties on thickness of the films. In this paper we discuss the influence of the thickness on the structural and optical properties of CdTe thin films prepared by electrodeposition on stainless steel substrate.
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
2. Experimental All the films used in this study were electrodeposited potentiostatically from an acidic bath consisting of 1 M CdSO4 and 100e 200 ppm of TeO2 as Cd and Te source respectively. The films were deposited on stainless steel foils of 0.05 mm thick at identical conditions applying a potential of 580 mV with respect to Ag/AgCl reference electrode. The electrodeposition details can be found elsewhere [4,14,15]. The thicknesses of all the films were calculated using two different methods; total charge flowed during deposition, and weighing. In some cases a third method; from the maxima and minima of interference patterns, was also employed. The thickness values obtained from these three methods are close to each other, and the mean value is reported. Films with thickness in the range 0.17e1.5 mm were used in this study. The XRD measurements were performed using a Rigaku X-ray diffractometer with Cu Ka source with l ¼ 1.5418 A. The various structural parameters such as lattice constant, grain size, dislocation density, strain and texture coefficient have been evaluated. The cross sectional composition of the film was studied by conducting the AUGER depth profile analysis of a representative film. The transmittance (T%) of the films was measured in the spectral range of 300e2500 nm, using a Shimadzu UVeVISeNIR double beam spectrophotometer. The absorption coefficient, band gap, refractive index, extinction coefficient, real and imaginary parts of the dielectric constant were determined from transmittance for CdTe samples of different thickness. The transmittance measurements were realized by transferring the films on to glass substrates using a transparent epoxy. This technique has been successfully applied for transferring CdTe films from opaque substrates and reliable results has been reported [2]. The transmittance spectra were recorded and the absorption of the glass and epoxy, were compensated by placing a glass/epoxy structure in the reference beam. 3. Results and discussion 3.1. Structural properties Fig. 1 shows the XRD spectra of CdTe thin films with different thicknesses and the inset shows the intensity of (111) peak. The spectra were obtained by scanning qe2q in the range of 20e65 .
Fig. 1. XRD patterns of CdTe thin films with different thicknesses. The inset is the (111) peak of the films.
433
Diffraction analysis suggests that all CdTe samples are polycrystalline and have a cubic zinc-blende structure, with reflections corresponding to (111), (220), (311) and (331) plane orientations, according to JCPDS data file: CdTecubic-15-0770. Since the deposition conditions are kept constant, no variation in the film stoichiometry is expected. The XRD patterns show that the peak intensity increases as the film thickness increases and this is due to the amount of material involved in the X-ray diffraction process [16]. In order to analyse the evolution of the preferential orientation during the film growth, the two parameters; texture coefficient (Ci), and the degree of preferred orientation (s) have been calculated using the following relations [17,18].
N IIi Ci ¼ PN i0
Ii i ¼ 1 Ii0
(1)
where the subscript i stands for a particular plane, Ii is the measured integral intensity, Ii0 is the integral intensity of the JCPDS powder diffraction pattern of the corresponding plane i, and N is the number of reflections in the X-ray diffraction pattern considered for the analysis. Ci is unity for each reflection in the case of a randomly oriented sample and values of Ci greater than unity indicate preferred orientation of the crystallites in that particular direction. The degree of preferred orientation s of the sample as a whole can be assessed by estimating the standard deviation of all Ci values calculated for the sample [17,18].
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 i ¼ 1 ðCi Ci0 Þ s¼ N
(2)
where Ci0 is the texture coefficient of the powder sample, which is always unity. The value of s is an indicator of the degree of orientation of a sample and can be used to compare different samples. A value of zero for s indicates that the sample is completely at random orientation and the sample with higher value of s has better preferential orientation. Fig. 2 shows the degree of preferred orientation of CdTe thin films with different thicknesses. The inset is the variation of texture coefficient with the film thickness. From Fig. 2 it can be seen that the value of s increase from 0.16 to 1.2 as the film thickness vary from 0.17 to 1.5 mm; this means that there is a strong relationship
Fig. 2. Degree of preferred orientation of CdTe thin films with different thicknesses. The inset is the variation of texture coefficient with the film thickness.
434
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
between the degree of preferred orientation and film thickness. Moreover, from the texture coefficient (see inset of Fig. 2), we can see that in all samples Ci is greater than unity for the (111) plane, indicating that the preferred growth plane is (111).The average diameter of the CdTe grains and the residual strain are calculated from the fullwidth at half-maximum (FWHM) using the relation [19].
b cos q ¼
Kl þ 43 sin q D
(3)
where q is the Bragg angle and; b2 ¼ (FWHM)2 b2, where FWHM is the full width at half maximum of the peaks, l ¼ 1.54056 A corresponds to the Cu Ka radiation, D is the average size of the grains, K is the shape factor which is approximately unity and 3 is the residual strain of the films. The integral breadth b, was obtained from a powder sample of polycrystalline silicon. A plot of bcos(q) versus sin(q) will give a straight line and the grain size D and the strain 3 can be calculated from the intercept and slope, respectively. The results of the above calculations are presented in Fig. 3. When the thickness increases from 0.17 to 1.5 mm, the grain size increases from 0.03 to 0.06 mm approximately, and the strain decreases from 4.5 103 to 2.0 104. One can see from Fig. 3, that the grain growth has two stages, in the initial stage the grain size has a strong dependence on film thickness and the grain size increases with film thickness until the film thickness attains a value greater than 0.5 mm. Beyond this thickness the grain size remains more or less constant. Strain (stress) affects the mechanical properties of the films such as the stability of microstructure, the adhesion between film and substrate and the opto-electronic properties of the deposited films. Stress in films can be intrinsic, caused by the conditions prevailing during deposition (temperature, pH of solution, deposition rate, electric field between counter and working electrodes, impurities, etc.). On the other hand stress can be extrinsic to the film, but intrinsic to the composite film-substrate system, caused by the difference in the thermal expansion coefficients [20]. From Fig. 3 we can see that the strain-thickness relation has three distinct zones; when the film is very thin the strain is high and more or less remains same up to a thickness of 0.3 mm, in the thickness range 0.3e0.8 mm the strain decreases almost linearly and attains saturation when thickness is above 0.8 mm. The decrease in strain indicates a decrease in the concentration of lattice imperfections as the film thickness increases. This implies that as the grains grow in size the grain boundaries decrease and hence the stress induced due to the grain boundaries also decreases.
Fig. 3. Variation of the grain size and strain with film thickness.
The lattice parameter, a0; of the samples was calculated from the peak positions in the XRD patterns and using the method developed by Nelson and Taylor [21,22]. In this method the lattice parameter (a0) calculated from different peaks is plotted against. cos2 q(sin1 þ q1). The graph is linear and the intercept at cos2 q(sin1 þ q1) ¼ 0, gives the lattice constant of the sample. The dependence of the lattice parameter on the film thickness is shown in Fig. 4. The lattice value is high when the films are thinner and decreases as films grow in thickness, finally attains a value close to the stress free sample (6.481 A). The dislocation density (d), defined as the length of dislocation lines per unit volume of the crystal was evaluated from the formula suggested by Williamson and Smallman [23].
d¼
1 D2
(4)
where D is grain size of the sample. The relation between dislocation density and thickness is shown in Fig. 5. As expected the dislocation density and strain decrease as the films grow in thickness. The above observations imply that as the films grow in thickness, the grain size increases and the crystalline quality of the film improves. The AFM analysis (Fig. 6) revealed a void free, rough surface with cauliflower like morphology. The cross-sectional composition (AUGER depth profile) of a film with thickness 0.7 mm is shown in Fig. 7. It can be observed that the composition is uniform throughout the thickness of the film. The oxygen in the bulk of the film may be incorporated from the electrodeposition bath which contains dissolved oxygen. The stoichiometry of the film is maintained throughout the thickness including in the layers close to the substrate, indicating that the stoichiometry of the film is independent of the thickness. However, the stoichiometry at the film surface is different from that of the bulk; which is expected due to the exposure to the atmospheric humidity and oxygen. The decrease in Cd content and the increase in oxygen concentration at the film surface are indications of the formation of trace amounts of oxides of tellurium. 3.2. Optical properties Fig. 8 shows the transmittance spectra of six CdTe samples with different thicknesses in the wavelength range 300e2500 nm. The
Fig. 4. The dependence of lattice constant on film thickness.
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
435
Fig. 5. Dependence of dislocation density on the film thickness.
absorption edge shifts towards higher wavelength region with the increase of film thickness.
Lnð1=TÞ a ¼ d
(5)
where T ¼ It/Ii is the transmittance. The absorption coefficient of the films was calculated from the transmittance spectra near the absorption edge using the relation; The absorption coefficient a of the material can be related to the incident photon energy hn through the relation [24e28];
ahv ¼ A hv Eg
1 2
(6)
where A is a constant, h is the Planck’s constant, n is the frequency and Eg is the band gap. The band gap of the films was determined by plotting (ahn)2 vs. hn. The intercept of the straight-line portion of the graph on the hn axis gives the value of Eg. The dependence of the band gap of CdTe films on the film thickness is presented in the inset of Fig. 8. It can be seen that the band gap decreases from 1.53 to 1.49 eV as the film thickness increases from 0.17 to 1.5 mm. The observed decrease in the band gap with increase of film thickness is in good agreement with the earlier investigations on CdTe thin films [29e31]. This variation can be due to the influence of different factors such as grain size, structural parameters, carrier concentration, presence of impurities, deviation from
Fig. 6. AFM image of a CdTe film of thickness 0.7 mm deposited on stainless steel substrate.
Fig. 7. AUGER depth profile of a CdTe film of thickness 0.7 mm deposited on stainless steel substrate.
stoichiometry of the film, dislocation density, lattice strain, etc. [32e35]. However, the lattice parameters, grain size and the strain have a direct dependence on the film thickness. Hence, we consider that the observed decrease in Eg with increasing thickness is due to the decrease in lattice strain and increase of grain size. The refractive index “n” was determined from the transmission spectra using the method suggested by Swanepoel and Manifacier et al. [36e38]. The envelopes around the interference maxima and minima of the transmittance spectra are considered to be continuous functions of l. According to this method, the value of refractive index, n, can be calculated using the expression [36e39],
n ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nþ
N2 n2s
(7)
where N and ns are given by
N ¼
1 þ n2s 2ns ðTmax Tmin Þ þ Tmax Tmin 2
(8)
Fig. 8. Optical transmittance spectra of six CdTe thin films of different thickness. The inset is the variation of band gap with thickness.
436
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437
Fig. 11. Variation of the real (3 r) and imaginary (3 i) parts of the dielectric constant against the photon wavelength for different thickness of CdTe thin films.
Fig. 9. Dependence of refractive index n on CdTe film thickness.
The refractive index of the substrate ns is obtained from the transmittance spectrum of the substrate, Ts, using the equation [40]:
1 ns ¼ þ Ts
sffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 Ts
Ke ¼ (9)
The refractive index of the film has been evaluated from the transmittance and were fitted using Cauchy dispersion relationship, n(l) ¼ a þ b/l2 (where a and b are constants), which was used for extrapolating the data in the wavelength range 400e3100 nm [41]. The calculated values of n are plotted as a function of photon wavelength and are shown in Fig. 9. The value of the refractive index is found to decrease with the increase of wavelength, while, the refractive index increases with increasing film thickness. The increase in the refractive index with thickness is attributed to an increase in the crystallinity of the films. This tendency is consistent with the results reported [6,42,43]. The complex relative dielectric constant (3 c), the extinction coefficient (ke), and the real (3 r) and imaginary (3 i) parts of the
Fig. 10. Variation of CdTe extinction coefficient ke with film thickness.
dielectric constant for the CdTe thin films have been estimated from transmittance using the following relations [44e46]:
al
4p
3c
¼
3r
¼ n2 Ke2
(12)
3i
¼ 2nk
(13)
3r
þ i3 i
(10) (11)
Fig. 10 shows the variation of extinction coefficient ke, as a function of wavelength and thickness. It is shown that the ke, decreases with the film thickness. Fig. 11 shows a plot of the real (3 r) and imaginary (3 i) parts of the dielectric constant against the photon wavelength for CdTe thin films with different thickness. It is found that the dependence of (3 r) on thickness and wavelength is the same as that of n, because
Fig. 12. 1/(n2 1) vs. (hv)2 plot for CdTe thin films with different thickness.
J. Pantoja Enriquez et al. / Materials Chemistry and Physics 142 (2013) 432e437 Table 1 The estimated values of various optical parameters of CdTe thin films, the data corresponds to films with thickness in the range 0.17e1.5 mm. Thickness d (mm)
E0 (eV)
Ed (eV)
Eg (eV)
Eg (eV) from Fig. 8
0.17 0.27 0.58 0.71 1.10 1.50
3.21 3.20 3.16 3.13 3.05 3.05
12.08 13.85 16.72 17.42 17.94 18.45
1.60 1.59 1.57 1.56 1.52 1.51
1.53 1.525 1.52 1.51 1.50 1.49
0.01 0.01 0.01 0.01 0.01 0.01
n(0)
3N
2.18 2.28 2.50 2.56 2.62 2.65
4.76 5.26 6.29 6.56 6.88 7.05
437
single oscillator model shows that these values depend on film thickness. Acknowledgements This work at CIE-UNAM was partially supported by the projects SENER-CONACyT 117891, SEP-CONACYT 83960 and ICyTDF 318/ 2009. Authors acknowledge the support of M. Luisa Ramon Garcia in XRD measurements. References
2
k2e ,
n [ on the other hand the imaginary part decreases with the film thickness and increase with the wavelength similar to that of ke. The dispersion of the refractive index was evaluated according to the single effective oscillator model proposed by Wemple and Di Domenico [47,48]. According to the dispersion theory, in the low absorption region, the index of refraction n is given in the single oscillator model by the relation;
n2 ðhvÞ ¼ 1 þ
Ed E0 E02 ðhvÞ2
(14)
where Ed is the optical dispersion energy inside the bulk, and E0 is the oscillation energy between valence and conduction bands of the semiconductor. Ed is a measure of the intensity of the inter-band transitions and is obtained from the slope of the straight line portion of 1/(n2 1) vs. (hv)2. A plot 1/(n2 1) of vs. (hv)2 for CdTe thin films with different thickness is shown in Fig. 12. The oscillator energy, E0, is approximately twice the energy gap (E0 z 2Eg). The value of refractive index n(0) and dielectric constant 3 N ¼ n(0)2 for hn / 0 were estimated from the graphs. The values of E0, Ed, Eg, n(0) and 3 N are shown in Table 1. For a comparison the values of Eg estimated from E0 and determined from Fig. 8 are presented in Table 1. From the table it is clear that all the optical parameters has certain dependence on film thickness; the strength of the oscillator E0, decrease from 3.21 to 3.03 eV, the optical dispersion energy Ed, increase from 12.08 to 18.45 eV, the refractive index n(0) increase from 2.18 to 2.65 and dielectric constant 3 N increase from 4.76 to 7.05 as the film thickness increases from 0.17 to 1.5 mm. 4. Conclusions We have studied the dependence of structural and optical properties of electrodeposited CdTe thin films on the thickness of films. The crystallite sizes in the films as measured using XRD data are found to be in the range of 0.03e0.06 mm when the film thickness vary from 0.17 to 1.5 mm. The structural parameters such as crystallite size, lattice constant, dislocation density and strain show a non-linear dependence on film thickness; in all cases the variation is significant when the film thickness is below 0.8 mm. The optical parameters such as absorption coefficient, band gap, refractive index and extinction coefficient were calculated from the transmittance spectra. The results indicate that refractive index n, extinction coefficient ke, and the real (3 r) and imaginary (3 i) parts of the dielectric constant strongly depend on film thickness. The change in optical band gap with film thickness is attributed to the decrease in lattice strain and increase of grain size. The oscillator strength and the optical dispersion energy determined using the
[1] Vijay P. Singh, John C. McClure, G.B. Lush, W. Wang, X. Wang, G.W. Thompson, E. Clark, Sol. Energy Mater. Sol. Cells 59 (1999) 145. [2] Xavier Mathew, P.J. Sebastian, Sol. Energy Mater. Sol. Cells 59 (1999) 85. [3] Xavier Mathew, Gerald W. Thompson, V.P. Singh, J.C. McClure, S. Velumani, N.R. Mathews, P.J. Sebastian, Sol. Energy Mater. Sol. Cells 76 (2003) 293. [4] M. Bulent, Basol Sol. Cells 23 (1988) 69. [5] Ting L. Chu, Shirley S. Chu, Solid State Electron. 38 (1995) 533. [6] S. Saha, U. Pal, A.K. Chaudhuri, V.V. RAO, H.D. BANERJEE, Phys. Status Solidi A 114 (1989) 721. [7] D. Kindi, J. Touskova, Phys. Status Solidi A 106 (1988) 297. [8] S.S. Ou, O.M. Stafsudd, B.M. Basol, Thin Solid Films 112 (1984) 301. [9] H.R. Moutinho, F.S. Hasoon, F. Abulfotuh, L.L. Kazmerski, J. Vac. Sci. Technol. A 13 (1995) 2877. [10] Brian E. McCandless, Robert W. Birkmire, Sol. Cells 31 (1991) 527. [11] James Sites, Jun Pan, Thin Solid Films 515 (2007) 6099. [12] S. Vatavu, H. Zhao, V. Padma, R. Rudaraju, D.L. Morel, P. Gas¸in, Iu. Caraman, C.S. Ferekides, Thin Solid Films 515 (2007) 6107. [13] N. Armani, G. Salviati, L. Nasi, A. Bosio, S. Mazzamuto, N. Romeo, Thin Solid Films 515 (2007) 6184. [14] M.P.R. Panicker, M. Knaster, F.A. Kroger, J. Electrochem. Soc. 125 (1978) 556. [15] F.A. Kroger, R.L. Rod, M.P.R. Panicker, Photovoltaic Power Generating Means and Methods, U.S. Patent 4400244, 1983. [16] N. El-Kadry, A. Ashour, S.A. Mahmoud, Thin Solid Films 269 (1995) 112. [17] K.H. Kim, J.S. Chun, Thin Solid Films 141 (1986) 287. [18] Charles S. Barrett, T.B. Massalski, in: Structureof Metals: Crystallographic Methods, Principles and Data, third ed., McGraw Hill, NY, 1966. [19] E. Lifshin, X-ray Characterization of Materials, Wiley-VCH, New York, 1999. [20] K.N. Tu, R. Rosenberg, Analytical Techniques for Thin Films, Academy Press Inc., San Diego CA, 1988. [21] A. Taylor, H. Sinclair, Proc. Phys. Soc. 57 (1945) 126. [22] J.B. Nelson, D.P. Riley, Proc. Phys. Soc. 57 (1945) 160. [23] G. Williamson, R. Smallman, Philos. Mag 1 (1956) 34. [24] J. Tauc, Amorphous and Liquid Semiconductors, Plenum, New York, 1974. [25] N.F. Mott, E.A. Davis, Electronic Processes in Non-crystalline Materials, Calendron Press, Oxford, 1979. [26] J.J. Pankove, Optical Processes in Semiconductors, Prentice-Hall, Englewood Cliffs, NJ, 1971. [27] P.W. Davis, T.S. Shilliday, Phys. Rev. 118 (1960) 1020. [28] J.I. Pankove, Optical Processes in Semiconductors, Dover, New York, 1971. [29] U. Pal, D. Samanta, S. Ghorai, A.K. Chaudri, J. Appl. Phys. 74 (1993) 6368. [30] S. Lalitha, R. Sathyamoorthy, S. Senthilarasu, A. Subbarayan, K. Natarajan, Sol. Energy Mater. Sol. Cells 82 (2004) 187. [31] R. Sathyamoorthy, S. Narayandass, D. Mangalaraj, Sol. Energy Mater. Sol. Cells 76 (2003) 339. [32] A.E. Rakhshani, A.S. Al-Azab, J. Phys. Condens. Matter 12 (2000) 8745. [33] S.A. Al Kuhaimi, Vacuum 51 (1998) 349. [34] K.L. Chopra, Thin Film Phenomena, McGraw-Hill, New York, 1969, p. 266. [35] M. Pattabi, J. Uchil, Sol. Energy Mater. Sol. Cells 63 (2000) 309. [36] R. Swanepoel, J. Phys. E Sci. Instrum. 16 (1983) 121. [37] R. Swanepoel, J. Phys. E Sci. Instrum. 17 (1984) 896. [38] J.C. Manifacer, J. Gasiot, J.P. Fillard, J. Phys. E Sci. Instrum. 9 (1976) 1002. [39] E.R. Shaaban, N. El-Kabnay, A.M. Abou-sehly, N. Afify, Physica B 381 (2006) 24. [40] T.S. Moss, Optical Properties of Semiconductors, Butterworths, London, 1959. [41] E. Márquez, J.M. González-Leal, A.M. Bernal-Oliva, R. Jiménez Garay, T. Wagner, J. Non-Cryst. Solids 354 (2008) 503. [42] S.S. Patil, P.H. Pawar, J. Chem. Bio. Phy. Sci. Sec. C. 2 (2012) 968. [43] E.R. Shaaban, N. Afify, A. El-Taher, J. Alloys Compd. 482 (2009) 400. [44] A. Milnes, D. Feucht, Heterojunctions and MetalSemiconductor Junctions, Academic Press, New York, NY, USA, 1972. [45] L. Kazmerski, Polycrystalline and Amorphous Thin Films and Devices, Materials Science and Technology Series, Academic Press, New York, NY, USA, 1980. [46] S.S. Li, Semiconductor Physical Electronics, second ed., Springer-Verlag, 2006. [47] S.H. Wemple, Di Domenico, Phys. Rev. B 7 (1971) 1338. [48] S.H. Wemple, Phys. Rev. B 7 (1973) 3767.