Materials Science in Semiconductor Processing 24 (2014) 265–271
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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Temperature effect on the physical properties of CuIn11S17 thin films for photovoltaic applications B. Khalfallah a, N. Khemiri a,b,n, M. Kanzari a a b
Laboratoire de Photovoltaïque et Matériaux Semi-conducteurs – ENIT – Université Tunis ElManar, BP 37, Le belvédère 1002 Tunis, Tunisie Institut Préparatoire des Etudes d'Ingénieurs El Manar – Université de Tunis El Manar, BP 37, le belvédère 1002 Tunis, Tunisie
a r t i c l e i n f o
Keywords: Thin films Thermal evaporation Structural properties Optical properties
abstract CuIn11S17 compound was synthesized by horizontal Bridgman method using high-purity copper, indium and sulfur elements. CuIn11S17 thin films were prepared by high vacuum evaporation on glass substrates. The glass substrates were heated at 30, 100 and 200 1C. The structural properties of the powder and the films were investigated using X-ray diffraction (XRD). XRD analysis of thin films revealed that the sample deposited at a room temperature was amorphous in nature while those deposited on heated substrates were polycrystalline with a preferred orientation along the (311) plane of the spinel phase. Ultraviolet–visible (UV–vis) spectroscopy was used to study the optical properties of thin films. The results showed that CuIn11S17 thin films have high absorption coefficient α in the visible range (105–106 cm 1). The band gap Eg of the films decrease from 2.30 to 1.98 eV with increasing the substrate temperature (Ts) from 30 to 200 1C. We exploited the models of Swanepoel, Wemple–DiDomenico and Spitzer–Fan for the analysis of the dispersion of the refractive index n and the determination of the optical constants of the films. Hot probe method showed that CuIn11S17 films deposited at Ts ¼30 1C and Ts ¼ 100 1C are p-type conductivity whereas the sample deposited at Ts ¼200 1C is highly compensated. & 2014 Elsevier Ltd. All rights reserved.
1. Introduction Thin film solar cells based on wide-gap chalcopyrite are promising for the next generations of photovoltaic modules [1]. The standard device structure of CuInS2 based solar cells includes a thin CdS film as buffer layer (p or n type), between the absorber (CuInS2) and the transparent conductor oxide (ZnO), to create the junction with the absorber layer. The primary function of the buffer layer in a heterojunction is to form a junction with the absorber layer while admitting a maximum amount of light to the n Corresponding author at: Laboratoire de Photovoltaïque et Matériaux Semi-conducteurs - ENIT - Université Tunis ElManar, BP 37, Le belvédère 1002 Tunis, Tunisie. Tel.: þ 216 22274341. E-mail address:
[email protected] (N. Khemiri).
http://dx.doi.org/10.1016/j.mssp.2014.03.048 1369-8001/& 2014 Elsevier Ltd. All rights reserved.
junction [2]. In addition, the buffer layer should have a wide bangap (E2.5 eV), a high optical transmission in the visible range and should be capable of driving out the photogenerated carriers with minimum recombination losses and transporting the photo generated carriers to the outer circuit with minimal electrical resistance. In recent years, the maximum efficiency reported for a CuInS2-based solar cell is 12.5% for the Mo/CuInS2/CdS/ ZnO cell [3]. However, in the last decade, serious efforts to substitute the CdS buffer layer in the CuInS2-based solar cells by other nontoxic materials have been made for the following reasons: the toxic effect of the cadmium on the environment, the high resistivity of CdS thin films and the lattice mismatch between the CdS and CuInS2 [4,5]. The aim of this work is the preparation and the characterization of CuIn11S17 thin films in order to use
B. Khalfallah et al. / Materials Science in Semiconductor Processing 24 (2014) 265–271
them as buffer layer in CuInS2 based solar cells. This ternary compound belongs to the CuIn2n þ 1S3n þ 2 family with n¼ 5. In last years, CuIn2n þ 1S3n þ 2 family have received much attention because these materials do not contain any toxic elements such as Ga or Se, and this may have an advantage in comparison with other ternary materials like CuIn2n þ 1Se3n þ 2 and CuGa2n þ 1S3n þ 2. They belong to I-III2n þ 1–VI3n þ 2 ternary materials which are receiving a great deal of attention as candidate materials for visible-light and IR emitters, high-efficiency solar cells, and other semiconductor and quantum-electronic devices [6,7]. Some authors were interested in the study of some physico-chemical properties of CuIn11S17 material. Indeed, Basavaswaran et al. [8] studied the structural properties of CuIn11S17 prepared by homogeneous precipitation method and reported that the CuIn11S17 has disordered spinel structure with space groups (Fd3m) and that the lattice constant is a ¼10.73 Å. The same results were also reported by Ohachi and Pamplin [9]. Bodnar et al. reported the optical and electrical properties of CuIn11S17 monocrystal prepared by Bridgman method and mentioned that the CuIn11S17 is an n-type semiconductor with direct transition and the band gap of CuIn11S17 single crystal is near 2.23 eV [10]. In this work, CuIn11S17 thin films were elaborated, for the first time to our knowledge, using the thermal evaporation method. We have studied the effect of the substrate temperature Ts on the structural, optical and electrical properties of the films in order to use this compound as buffer layer in CuInS2 based solar cells. 2. Experimental procedure 2.1. Synthesis of CuIn11S17 crystal CuIn11S17 crystal has been synthesized by the horizontal Bridgman method. Stoichiometric amounts of high purity (99.999%) elemental copper, indium and sulfur, corresponding to the composition of the ternary compound, were placed in a quartz ampoule. After pumping down to 10 5 mbar, the ampoule was sealed off and was transferred to a programmable furnace (Nabertherm–Allemagne). For the synthesis, the temperature of the furnace was raised to 600 1C with a rate of 10 1C/h and the temperature was kept constant at 600 1C for 24 h. Then, the temperature was increased with the rate 20 1C/h up to 1000 1C. A complete homogenization could be obtained by keeping the melt at this temperature (1000 1C) for about 48 h. Finally, the temperature was lowered to 800 1C at a rate of 10 1C/h and the furnace was switched off until the tube reached room temperature. The obtained ingot was crushed in order to obtain CuIn11S17 powder.
substrate temperature Ts was measured using a thermocouple embedded in the substrate holder underneath the substrates. The glass substrates were previously cleaned with washing agents (commercial detergent, acetone, ethanol and deionized water) before being introduced into the vacuum system. The base pressure of the vacuum system was kept between 10 5 and 10 6 mbar. The crystalline phase and crystal orientation of the films were examined using a Philips X' Pert X-ray diffractometer with monochromatic CuKα radiation (λ¼ .154056 nm and 40 kV, 30 mA). Normal incidence transmittance T and reflectance R spectra were recorded at room temperature in the range of 300–1800 nm using a double-beam spectrophotometer, model SHIMADZU UV 3100S. The thickness of films was calculated using the procedure of Swanepoel [11,12] which is based on the use of the extremes of the interference fringes. The electrical properties of the CuIn11S17 thin films were examined by hot probe method and the Van der Pauw technique [13]. The ohmic contact is formed by 200 nm thick Au deposited by thermal evaporation technique before and after the deposition of the CuIn11S17 film. 3. Results and discussions 3.1. Structural properties 3.1.1. Characterization of powder Fig. 1 shows the X-ray diffraction patterns of the synthesized CuIn11S17 powder and the theoretical CuIn11S17 (JCPDS 34-797). The coincidence between both patterns confirms the existence of a single phase CuIn11S17 with a privileged orientation along the (311) peak. CuIn11S17 crystallizes in the cubic spinel structure (Fd3m). The lattice parameter a of CuIn11S17 powder was determined by using the following relation: 2
1 d
¼ 2
2
ð1Þ
where d is the interplanar spacing determined using Bragg's equation and (hkl) are the miller indices of the lattice planes. The obtained value is a¼10.70 Å. This value is in good agreement with the values reported by other authors [8,9].
JCPDS 34-797 (311)
(440) (400) (511) (111)
2.2. Film preparation CuIn11S17 thin films were prepared by thermal evaporation of CuIn11S17 powder from a Tungsten boat on heated and non-heated glass substrates under vacuum (10–6 mbar) using a high vacuum coating unit Alcatel. The substrates were placed directly above the source at a distance of 15 cm and were heated by an insulator heater system. The
2
h þk þl a2
Intensity [a.u]
266
(220) (222)
5
10
15
20
25
30
(731) (531) (533) (642) (620) (444) (711)
(422) (331) 35
40
45
50
55
60
65
70
Bragg Angle 2θ [°] Fig. 1. XRD pattern of the synthesized CuIn11S17 powder. The inset shows the XRD pattern of the theoretical CuIn11S17 (JCPDS 34-797).
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3.1.2. Characterization of thin films Fig. 2 displays XRD patterns of CuIn11S17 films elaborated at different substrate temperatures. It is clear from Fig. 2 that CuIn11S17 film deposited on unheated substrate (Ts ¼30 1C) is amorphous whereas the sample deposited at Ts ¼100 1C has a peak at 2θ¼27.671 assigned to the (311) plane of the CuIn11S17 phase. By increasing the substrate temperature to 200 1C, this peak (located at 2θ¼27.511) becomes more intense and highly oriented. The slight shift in the (311) peak position is probably due to the changes in lattice spacing and the lattice parameter resulted from the rearrangement of the atom periodicity caused by the transition from amorphous to polycrystalline CuIn11S17. The (311) peak is the preferential orientation for the polycrystalline samples. The increase of the (311) peak intensity by increasing the substrate temperature implies that the structural properties depend on Ts. Indeed, at higher substrate temperatures, the atoms have sufficient thermal energy to move into stable positions, so that the structural reorientation occurs, leading to a significant increase in the intensity of the (311) peak. We also note that the patterns do not contain any extra peaks corresponding to the elements or other secondary phases, which confirms the homogeneity of the CuIn11S17 phase. The improvement of the crystallinity of the films was also verified by the increasing of the grain sizes of the samples estimated using the Scherrer formula [14]: 0:9λ B cos θ
molecules arriving on the heated substrate surface acquire a large thermal energy and hence a large mobility. This enhances the diffusion distance of the evaporated atoms/ and as a result, the collision process initiates the nucleation and enhances the island formation in order to grow continuous films with larger grains [16]. 3.2. Optical properties 3.2.1. Optical transmittance and reflectance spectra Fig. 3a and b shows the transmittance (T) and the reflectance (R) spectra, in the wavelength range of 300– 1800 nm, of CuIn11S17 films elaborated at different substrate temperatures. All the spectra show very pronounced interference effects in the transparent region (700– 1800 nm) with a sharp fall of transmittance at the band edge. The transmittance values in the transparent region were in the range 50–75%. In addition, the values of the reflectance for all the samples were in the range 30–45% which means that no absorption occurs in the spectral range of 700–1800 nm. The thickness of films was calculated with the procedure of Swanepoel [11] which is based on the use of the extremes of the interference fringes. It was found that the thickness of the films were 460, 345– 290 nm for the films deposited at 30, 100 and 200 1C, respectively.
ð2Þ
100
where D is the average grain size, λ is the X-ray wavelength, θ is the diffraction angle of the peak and B is the value of the full width at half maximum (FWHM) of the (311) peak. The calculated values of the grain size for the films grown on heated substrates (100 and 200 1C) are 10 and 25 nm, respectively. It is clear that D increases with an increase in the substrate temperature. In general, at higher substrate temperature the formation of a larger grain size is favored due to the increase in the mobility of the surface ad-atoms [15]. These observations can also be explained by the fact that the evaporated atoms or
80
90
Transmittance (%)
D¼
267
70 60 50 40 30 20
Ts = 30 °C Ts = 100 °C Ts = 200 °C
10 0 300
600
900
1200
1500
1800
Wavelength λ (nm)
(a) Ts = 30 °C
(311)
(b) Ts = 100 °C
100
(c) Ts = 200 °C
90 80
Reflectance (%)
Intensity (a.u)
JCPDS 34-797
Ts = 30 °C Ts = 100 °C Ts = 200 °C
(c) (b) (a)
70 60 50 40 30 20 10 0
10
20
30
40
50
60
Bragg angle (°) Fig. 2. X-ray diffraction patterns of CuIn11S17 thin films deposited at different substrate temperatures.
300
600
900
1200
1500
1800
Wavelength λ (nm) Fig. 3. (a) Transmittance and (b) reflectance spectra of CuIn11S17 thin films deposited at different substrate temperatures.
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6
8.0x10
T = 30 °C 5
4.0x10
2
10
-1 2
6.0x10 (αhν) (eV cm )
Absorption coefficient α (cm-1 )
10
10
4
d
Eg = 2.30 eV
2.0x10
Ts = 30 °C Ts = 100 °C Ts = 200 °C 10
0.0
3
1.6
1.8
2.0
2.2
2.4
1.75
2.6
2.00
Energy hν (eV) Fig. 4. Absorption coefficient of the CuIn11S17 thin films deposited at different substrate temperatures.
3.2.2. Absorption coefficient The absorption coefficient of CuIn11S17 films was evaluated from the transmittance (T) and reflectance (R) data by using the following formula [17]: " # 1 ð1 RÞ2 α ¼ Ln ð3Þ ðcm 1 Þ d T where α is the absorption coefficient, d is the film thickness and R and T are the reflection and transmission coefficient, respectively. Fig. 4 shows the dependence of the absorption coefficient on photon energy for the CuIn11S17 films. It can be seen that all samples have relatively high absorption coefficients (higher than 105 cm 1 in the visible and near-IR spectral region). Though such high value of α may be useful for the fabrication of high absorptive layers of solar cell, the spectral dependence of α may affect considerably the solar energy conversion efficiency [18,19]. Also, it can be observed that the absorption coefficient α is slightly affected by the substrate temperature. At the absorption edge (λ¼ 500 nm), the absorption coefficient α increases from 1.11 105 to 2.98 105 cm 1 as the substrate temperature increases from 30 to 200 1C. The effect of substrate temperature on the absorption coefficient shows that the film deposited at 200 1C has higher absorption, which indicates that the films become more opaque at higher temperature. There is a good correlation between the absorption coefficient α and the band gap Eg of semiconductors, where typically, lower band gap values are often related to higher optical absorption coefficient [20]. Since Eg decreases with substrate temperature, the temperature dependence of α arises from the variation of Eg with the substrate temperature Ts and typically α increases with increasing Ts. These observations have been made by some authors for chalcogenide thin films [21,22]. 3.2.3. Energy gaps The absorption coefficient α is related to the energy gap Eg according to the equation [23,24]: ðαhνÞ ¼ Aðhν Eg opt Þq
ð4Þ
2.25
2.50
2.75
hν (eV) Fig. 5. Plot of (αhν)2 versus hν for CuIn11S17 films deposited at 30 1C. The inset shows the plot of (αhν)1/2 versus hν for the same sample.
Table 1 Band gap values obtained for CuIn11S17 thin films. Ts (1C)
Thickness (nm)
Direct band gap (eV)
Indirect band gap (eV)
30 100 200
460 345 290
2.30 2.15 1.98
1.92 1.77 1.68
where A is a constant, h is the Planck constant, ν is the frequency of the incident radiation and q is an index that characterizes the optical absorption process (q¼1/2 for a direct allowed transition and q¼ 2 for an indirect allowed transition). We plot (αhν)2 and (αhν)1/2 against hν (Fig. 5). Values of the direct and indirect optical energy gap Edg and Eind were obtained by extrapolating the linear regions of g the (αhν)2 and (αhν)1/2 versus hν curves to the horizontal photon energy axis. Table 1 shows a decrease in the values of the direct and indirect energy gaps of CuIn11S17 thin films by increasing the substrate temperature. In the semiconductors, several possible reasons that contribute to a decrease in band gaps have been postulated [25]. In the present study, the decrease of optical band gap could be attributed to two factors. Indeed, it may be attributed to the improvement of crystallinity and the increase in the grain size caused by increasing the substrate temperature [26] or to the presence of unsaturated defects which increase the density of localized states in the band gap [18]. Compared to CdS buffer layer with a direct optical band gap of 2.4 eV [27], the obtained values of Edg show that CuIn11S17 material could be used as an efficient buffer layer material for thin film solar cells.
3.2.4. Refractive index dispersion analysis The refractive index n(λ) of CuIn11S17 thin films can be calculated using the Swanepoel method [11]. This method is based on the approach of Manifacier et al. [28]. This approach suggests creating an upper and lower envelope of the transmission spectrum beyond the absorption edge. The refractive index can then be calculated from the
B. Khalfallah et al. / Materials Science in Semiconductor Processing 24 (2014) 265–271
relation [11]: n ¼ ½N þðN 2 S2 Þ1=2 1=2
ð5Þ
where T M T m S2 þ 1 þ 2 T MT m
the ‘centers of gravity’ of the valence and conduction bands and an indicator for the quantification of the energy gap of the material [32] and Ed is the dispersion energy and represents a measure of the average strength of interband optical transitions.
ð6Þ 0.225
0.175
-1
0.150 0.125
2
αλ k¼ 4π
0.200
(n -1)
where S is the refractive index of the glass substrate. TM and Tm are the values of the envelope of the maximum and minimum positions of the transmission spectra, respectively. The extinction coefficient k can be calculated from the formula [29]:
0.075 Ts = 30 °C Ts = 100 °C Ts = 200 °C
0.050 0.025 1.75
2.00
2.25
2.50
2.75
(hν)2 (eV)2 Fig. 7. Plot of (n2–1) 1 versus (hν)2 for CuIn11S17 thin films deposited at different substrate temperatures.
8.0 Ts = 30 °C Ts = 100 °C Ts = 200 °C
7.5
2
The variations of the refractive index n and extinction coefficient k of CuIn11S17 thin films deposited at different substrate temperature are shown in Fig. 6. The values of both n and k decrease by increasing the wavelength of the incident photon. For example, the refractive index of CuIn11S17 deposited at 200 1C decreases from a value of 3.3 at λ¼700 nm to a value of 2.7 at λ¼1200 nm and then n tends to be constant. In the other hand, the values of n and k are influenced by the substrate temperature. Indeed, n and k of CuIn11S17 thin films are found to increase by increasing the substrate temperature. We believe that this observation is a result of the increase of grain size by increasing the substrate temperature. The refractive index n of the films follows an increasing trend with the grain size, which indicates that the films become more opaque as the substrate temperature increases. Based on the idea that the refractive index of the materials in visible region is due to electron oscillation excitation between conduction and valence band (interband transitions in and around the band edge), the dispersion of the refractive index can be analyzed using the Wemple–DiDomenico relationship [30,31]:
0.100
7.0
2
ð7Þ
εr = n - k
N ¼ 2S
269
6.5
6.0
5.5
n2 ðhνÞ ¼ 1 þ
Ed E0 2
E0 ðhνÞ
1.2x10
ð8Þ
2
6
1.6x10
6
2.0x10 2
6
2.4x10
6
2
λ (nm)
where hν is the photon energy, E0 is the single oscillator energy and a measure of the energy difference between
Fig. 8. Plot of the optical dielectric constant εr ¼n2 – k2 versus λ2 for CuIn11S17 thin films deposited at different substrate temperature.
3.8 Ts = 30 °C Ts = 100 °C Ts = 200 °C
3.6
0.32 Ts = 30 °C Ts = 100 °C Ts = 200 °C
0.28 0.24
3.2 0.20
3.0
-4πχe
Refractive index n
3.4
2.8
0.16 0.12
2.6 0.08
2.4 0.04
2.2 600
800
1000
1200
1400
1600
1800
Wavelength λ (nm) Fig. 6. Refractive index n versus the wavelength for CuIn11S17 thin films deposited at different substrate temperatures. The inset shows the extinction coefficient k versus the wavelength.
0.00 0.0
5.0x10
1.0x10
1.5x10 2
2.0x10
2.5x10
3.0x10
3.5x10
2
λ (nm)
Fig. 9. Plot of ( 4πχe) versus λ2 for CuIn11S17 thin films deposited at different substrate temperatures.
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Table 2 The estimated values of optical parameters for CuIn11S17 thin film. Ts (1C)
E0 (eV)
Ed (eV)
Eg (eV)
E0/Eg
εW 1
εS1
n (0)
N/mn (kg 1 m 3)
χe (10 3)
30 100 200
4.41 3.96 3.24
19.84 19.65 16.87
2.30 2.15 1.98
1.91 1.84 1.63
5.49 5.95 6.19
5.85 6.77 7.42
2.34 2.43 2.48
.85 1047 6.86 1047 11.17 1047
2–22 26–179 32–284
Fig. 7 shows a plot (n2–1) 1 versus (hν)2 from which the values of E0 and Ed were estimated. The observed decrease in the Eo with increasing substrate temperatures can be attributed to quantum confinement in the films. As mentioned, Eo is the single oscillator energy related to the materials band gap. We find Eo is directly proportional to E0 E2Eg [33]. This is consistent with results reported in literature [34–37]. It is hence natural that the variation of Eo with the grain size is identical to that of the optical band gap. For further analysis of the optical data, the contribution from the free carrier electric susceptibility χe to the real dielectric constant is discussed according to the Spitzer–Fan model by [38]: 2
εr ¼ n2 k ¼ ε1 ½e2 =πc2 ðN=mn Þλ2 ½e2 =πc2 ðN=mn Þλ2 ¼ 4πχ e
ð9Þ ð10Þ
where ε1 is the high-frequency dielectric constant in the absence of any contribution from free carrier, χe is the electric free carrier susceptibility, N/mn is the carrier concentration to the effective mass ratio, e is the electronic charge, and c is the velocity of light. The values of N/mn and ε1 were estimated by plotting εr versus λ2 (Fig. 8). It is significant to compare the values of ε1 obtained from the Wemple–DiDomenico model (Fig. 7) with those obtained from the Spitzer–Fan model (Fig. 8), the disagreement between the values of ε1 obtained from both models may be attributed to the formation of free carriers in CuIn11S17 thin films [39]. Fig. 9 shows ( 4πχe) versus λ2. The figure depicts that χe increases in magnitude with the wavelength and becomes sufficiently large to reduce the refractive index and the dielectric constant in the nearinfrared region. A good fit to a straight line is seen from which the free carrier susceptibility values at the extremes of the investigated range were estimated. All the results determined from both the models are summarized in the Table 2. We note that the values of ε1 are practically constant in the spectral field of the visible range. The values of the oscillation energy describe the expression E0 E2Eg. We can conclude that the Wemple–DiDomenico model describes well the optical behavior of the CuIn11S17 thin films. 3.3. Electrical properties The type of conductivity of the films was determined by the hot probe method. We found that CuIn11S17 thin films deposited at Ts ¼30 1C and Ts ¼100 1C are p-type conductivity and their resistances are very low (2 and 5 MΩ, respectively). The p-type conductivity is probably due to the high concentration of the cation vacancies and the anion interstitials, such as VCu and Si, in the films [40].
Indeed, VCu and Si are defects which act as acceptors leading to p-type conductivity. The sample elaborated at Ts ¼200 1C is highly compensated and its resistance exceeds 40 MΩ. So, we can say that the increase in substrate temperature allowed the transformation of the films from the p-type state to a highly compensated state. This change may be attributed to a decrease of the concentration of copper vacancies which are responsible for the p-type conductivity, and the increase of the concentration of sulfur vacancy Vs which makes Na ENd (Na is the number of acceptors and Nd is the number of donors). Indeed, sulfur vacancies are defects which act as donors and compensate a part of the acceptor conductivity leading to the highly compensated state and consequently give rise to an increase in the resistivity. In the forthcoming work, we will try to transform the conductivity of CuIn11S17 films into n-type either by increasing Ts or by annealing the films.
4. Conclusion CuIn11S17 thin films were deposited at different substrate temperatures by vacuum thermal evaporation method. Structural analysis of CuIn11S17 thin films revealed that the substrate temperature has a significant effect on the structural properties of the films. Indeed, the asdeposited CuIn11S17 thin film is amorphous, whereas those deposited on heated substrates show a polycrystalline structure with preferred orientation along the (311) plane. The optical study has shown that all films exhibit a transmittance higher than 75% in the visible region. Strong absorption coefficients (105–106 cm 1) were observed for all films. The shift of the absorption edge to lower energies with increasing the substrate temperature causes the decrease of the band gap energies from 2.30 to 1.98 eV. The refractive index dispersion parameters (the highfrequency dielectric constant, the carrier concentration to the effective mass ratio, the electric free carrier susceptibility…) were also calculated using the models of Wemple–DiDomenico and Spitzer–Fan. CuIn11S17 films possess p-type conductivity at Ts ¼30 1C and Ts ¼100 1C and become highly compensated at Ts ¼200 1C. The characteristics of CuIn11S17 films reported in this work offer perspectives for using CuIn11S17 films in many physical applications such as buffer layer in CuInS2 based solar cells. References [1] Y. You-hua, L. Ying-chun, F. Ling, L. Zhi-chao, L. Zheng-bang, Z. Shaoxiong, Trans. Nonferr. Metals Soc. China 21 (2011) 359.
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