ARTICLE IN PRESS
Journal of Crystal Growth 280 (2005) 425–435 www.elsevier.com/locate/jcrysgro
High-temperature conductivity in chemical bath deposited copper selenide thin films M. Dhanam, P.K. Manoj, Rajeev.R. Prabhu Department of Physics, Kongunadu Arts and Science College (affiliated to Bharathiar University), Coimbatore-641029, Tamilnadu, India Received 27 September 2004; accepted 26 January 2005 Available online 23 May 2005 Communicated by R. James
Abstract This paper reports high-temperature (305–523 K) electrical studies of chemical bath deposited copper (I) selenide (Cu2xSe) and copper (II) selenide (Cu3Se2) thin films. Cu2xSe and Cu3Se2 have been prepared on glass substrates from the same chemical bath at room temperature by controlling the pH. From X-ray diffraction (XRD) profiles, it has been found that Cu2xSe and Cu3Se2 have cubic and tetragonal structures, respectively. The composition of the chemical constituent in the films has been confirmed from XRD data and energy-dispersive X-ray analysis (EDAX). It has been found that both phases of copper selenide thin films have thermally activated conduction in the high-temperature range. In this paper we also report the variation of electrical parameters with film thickness and the applied voltage. r 2005 Elsevier B.V. All rights reserved. PACS: 81.5.Ln; 68.55.a; 68.55.Nq; 74.25.Gz; 73.50.h Keywords: A1. Characterization; A3. Liquid phase epitaxy; B2. Semiconducting materials
1. Introduction Thin film solar cells based on chalcopyrite thin films have gained increasing attraction due to steady progress in conversion efficiencies [1]. Thin film heterojunction solar cells play an important role as low cost, high-efficiency devices in solar energy conversions [2]. Copper selenide thin films Corresponding author. Tel.: +91 0422 2642095;
fax: +91 0422 2644452. E-mail address:
[email protected] (M. Dhanam).
finds applications as solar cell materials [3–5], optical filters, super ionic conductors [4–6], electro optical devices [7], thermo electric converters [2], microwave shield coatings [8] and transparent layers in high-speed detectors [2,9]. The attraction of copper selenide also lies in the feasibility of producing ternary material CuInSe2 by incorporating indium into this binary compound. Copper (II) selenide in the Cu3Se2 form has been reported as an impurity along with copper (I) selenide [6,10] and in copper-rich CuInSe2 [11]. The relative stability of copper (I) selenide and copper (II)
0022-0248/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2005.01.111
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selenide phases is of great relevance in the context of p-copper selenide/n-cadmium sulphide [5] or pCu2xSe/n-Si solar cells [4]. Current research efforts are directed towards identifying a low-cost deposition technique for copper selenide thin films from which solar cell grade CuInSe2 can be produced [9]. Copper selenide thin films are reported as interesting precursors for the preparation of CuInSe2 [11–14]. Copper selenide is a metal chalcogenide semiconductor with a wide range of stoichiometric compositions (CuSe, Cu2Se, Cu3Se2, Cu7Se4, Cu5Se4, Cu2Se, etc.) and non-stoichiometric composition (Cu2xSe) [3,9,15]. Cu2xSe, Cu2Se, etc. are treated as copper (I) selenide and CuSe, Cu3Se2, CuSe2 etc. are treated as copper (II) selenide [2,4,5,10,16,17]. The various crystallographic forms of copper selenide thin films include orthorhombic [6,15,18,19], monoclinic [20], cubic [2,6,8,9,15,16,18,20,21], tetragonal [15,16,20] and hexagonal [9,17,20]. All these advantages made this material to be selected as an ideal candidate for the present study. Copper selenide thin films can be obtained by a variety of techniques such as vacuum evaporation [14,22,23], electrodeposition [12,24,25], flash evaporation [26,27], solid-state reaction [28,29], electroless deposition [3,8,30], cathodic deposition [31], selenization [32,33] and chemical bath deposition [2,6,7,9,15–18]. Of the various techniques, the chemical bath deposition technique, which is a non-vacuum electroless technique, has many advantages such as simplicity, no requirement for sophisticated instruments, minimum material waste, economical way of large-area deposition, no need of handling poisonous gases like H2Se or Se vapour and the possibility of room temperature deposition. Keeping these advantages in mind, chemical bath deposition technique has been employed in the present work for the preparation of copper selenide thin films. To the best of our knowledge, earlier workers have prepared copper (I) selenide and copper (II) selenide from different reaction mixtures and also at elevated temperatures. In this paper we report the preparation of Cu2xSe and Cu3Se2 thin films from the same reaction mixture at room temperature. This paper also deals with the structural and high-
temperature electrical conductivity of copper (I) selenide and copper (II) selenide thin films in detail.
2. Experimental details In the present work a selenosulfate method [2,9,16] has been adopted for the chemical bath deposition of Cu2xSe and Cu3Se2 thin films at room temperature from the same reaction mixture just by varying the pH value. 2.1. Chemicals used Chemicals used for the preparation of copper selenide thin films were copper (II) sulphate penta hydrate (CuSO4 5H2OX99% purity-Merk), trisodium citrate (TSC: C6H5Na3O7 2H2OX99% purity-Merk), sodium sulfite anhydrous purified (Na2SO3495% purity-Merk) and selenium powder (Se499.5% purity-Loba). 2.2. Preparation of solutions All solutions were prepared in double distilled water. The reaction mixture contained 50 ml (0.2 M) CuSO4 solution, 50 ml (0.3 M) TSC solution and suitable quantity of (0.25 N) Na2SeSO3. Sodium selenosulfate (0.25 N) was prepared by refluxing selenium with sodium sulfite in 100 ml double distilled water for about 3 h at 80 1C [34]. A digital pH meter (model 101E-Electronic India) has been used to adjust the pH of the reaction mixture. The pH meter was standardized using buffer solutions of pH 4+0.05 and 9.2+0.05. 2.3. Optimization of deposition parameters The substrates used for the deposition of films were suspended closer to the inner wall of the deposition beaker for better uniformity and adherence of the film on substrate and to avoid shaking of substrates during deposition. The depositions were carried out at room temperature (29 1C). A constant and very slow stirring is provided while adding the different solutions of the reacting mixture: 50 ml of CuSO4 solution was
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taken in a 250 ml beaker, 50 ml TSC solution is then added drop-by-drop to it, and finally the Na2SeSO3 solution is added drop-by-drop using a burette. The pH of the reaction mixture was varied from 5.75 to 6.90, and the pH was optimized at 6.2 to obtain uniform Cu2xSe thin films, and for Cu3Se2 thin films the optimized pH was 6.3. The deposition time was varied from 5 min to 5 h to obtain films of different thickness. After deposition, the substrates were taken out and washed in deionized water and dried naturally. The prepared thin films were annealed at 323 K for 30 min and then used for the analysis. The annealing stimulates crystallization and does not cause phase transformation [2]. The structural characterization of the deposited copper (I) selenide and copper (II) selenide films were made using Shimadzu (Lab X-6000) X-ray diffract( line in 2y ometer with Cu Ka (l ¼ 1:54056 A) range from 201 to 601. Compositions of the prepared Cu3Se2 thin film have been determined by EDAX (LEICA S440i) analysis. Electrical measurements were carried out in the temperature range of 303–503 K and voltage range of 8–20 V.
427
3.2. Cu3Se2 thin film formation mechanism In the reaction mixture of pH 6.3, the reaction occurred as a result of Eq. (1) becomes [16] Cu2þ þ 2Na2 SeSO3 þ 4OH ! 3Cu1þ þ 2Na2 SO4 þ 2Se2 þ 2H2 O;
(4)
Cu1þ þ 2Se2 ! Cu3 Se2 :
(5)
The deposited Cu3Se2 films were uniform, adherent, greenish brown in colour and have higher thickness. 3.3. Structural analysis 3.3.1. XRD analysis of Cu2xSe thin films The X-ray diffraction (XRD) pattern of a representative CBD Cu2xSe thin film of thickness 2420 A˚ is shown in Fig. 1, which was found to be polycrystalline in nature. From the diffraction profiles the diffraction angles and the intensity of lines are measured with greater accuracy. Possible directions in which the film diffracted the beam of monochromatic X-rays are determined by the
3. Results and discussion 3.1. Film formation mechanism
95
3.1.1. Cu2xSe thin film formation mechanism In the reaction mixture of pH 6.2, the unstable Na2SeSO3 compound yields Se2 and SO2 ions 3 that react with Cu+ ions to get Cu2xSe [2,16]:
85
! 2Naþ þ Se2 þ SO4 2 þ H2 O þ 2e1 ;
(1)
75 Intensity (cps)
Na2 SeSO3 þ 2OH
(111)
(200) 65 55 (220)
2Naþ þ SO4 2 ! Na2 SO4
45
and 2Cu2þ þ 2e1 ! 2Cu1þ ;
(2)
35
ð2 xÞCu1þ þ Se2 ! Cu2x Se:
(3)
(311)
The deposited Cu2xSe films were uniform, adherent, reddish brown in colour and have remarkable thickness.
25 25
30
35
40
45
50
55
2θ (degree) Fig. 1. X-ray diffractogram of CBD Cu2xSe thin film of thickness 2420 A˚.
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Bragg condition [35], nl ¼ 2d sin y,
(6)
where n is the order of diffraction, l is the wavelength of incident X-ray, d is the distance between planes parallel to the axis of the incident beam and y is the angle of incidence relative to the plane in question. The observed d-spacing and h k l planes (1 1 1), (2 0 0), (2 2 0) and (3 1 1) of the prepared film coincide very well with Cu2xSe phase in JCPDS file 6-680 (Berzelianate) and earlier reports [9,11–13] which confirmed the cubic (fcc) structure of the film. From the h k l planes the lattice constants were evaluated using the formula [35,36] 1 ¼ d2
h2 þ k 2 þ l 2 . a2
(7)
Here, d is the d-spacing and a is the lattice constant. The lattice constant a has been determined from the most prominent peak (1 1 1) and was found to be 5.826 A˚, which is in agreement with the JCPDS data (6-680) and earlier reports [2,16]. The individual crystallite size (Dc ) has been determined as 370.32 A˚ using Scherrer’s formula [1] Dc ¼
klx . b cos y
(8)
Here, k is the Scherrer’s constant and it is the reference value corresponding to the quality factor of the apparatus measured with a reference single crystal, lx is the wavelength of the X-ray used, b is the full-width half-maximum (FWHM) and y is the Bragg’s angle. Using the size of the crystallites (Dc ), dislocation density (rD ) has been estimated as 7.292 1014 lines/m2 using the relation [1] rD ¼
as
1 . D2c
(9)
The number of crystallites N has been estimated 47.652 1014/unit area (m2) using the
relation [1] t N ¼ 3, Dc
(10)
where t is the thickness of the film. The strain has been determined using the expression [34] 1 lx s¼ ðb cos yÞ (11) sin y Dc and it has been found to be 1.179 108. The estimated structural parameters are given in Table 1. 3.3.2. XRD analysis of Cu3Se2 thin films The XRD pattern of a representative Cu3Se2 film of thickness 10500 A˚ is shown in Fig. 2, which is also found to be polycrystalline in nature. The observed d-spacing and h k l planes of this film coincide very well with the standard values for Cu3Se2 phase in JCPDS file 19-402 (Umangite) and earlier report [16], which confirmed the tetragonal structure of the film. The lattice parameters a and c of the deposited tetragonal Cu3Se2 film were calculated using the standard formula [34–36] 1 ðh2 þ k2 Þ l 2 ¼ þ 2. (12) 2 a2 c d ( The estimated lattice parameters are a ¼ 6:56 A ( and c ¼ 4:41 A; which are in good agreement with the JCPDS values and earlier reported value [16]. The grain size, dislocation density, number of crystallites/unit area, volume of the unit cell and strain in the film were determined using the relations (8)–(11) and are given in Table 2. The polycrystalline nature of the as-deposited Cu2xSe films and Cu3Se2 films are found to be important in the field of polycrystalline thin film solar cells [5,14]. 3.3.3. Compositional analysis of Cu2xSe thin films Compositional analysis of the deposited Cu2xSe thin film has been determined from XRD data using Shafizade plot and Ellis plot analysis. Cubic Cu2xSe films with non-stoichiometric factor, x up to 0.20 is considered as the most stable form [2]. Earlier workers [10,27]
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Strain 108
M. Dhanam et al. / Journal of Crystal Growth 280 (2005) 425–435
110
(101)
1.179
(200)
90 Number of crystallites 1014 per unit area
429
(210)
Intensity (cps)
Dislocation density 1014 (lines/m2)
47.625
(111)
70 (201)
7.292
(220) (311)
50
5.739 5.826 100 70 49 38
JCPDS
3.33 2.03 2.88 1.729
Observed
3.363 2.047 2.902 1.709
111 200 220 311
94 66 46 36
Observed Observed
JCPDS
Lattice constant (A˚) Relative intensities (I=I o ) hkl planes d-spacing (A˚)
Table 1 Structural parameters of CBD Cu2xSe thin film of thickness 2420 A˚
JCPDS
197.75
Volume of unit cell (A˚)3
370.39
Grain size (A˚)
(202) (321) (212)
30 20
25
30
35 40 45 2θ (degree)
50
55
60
Fig. 2. X-ray diffractogram of CBD Cu3Se2 thin film of thickness 10500 A˚.
reported that lattice constant a- and d-spacing for (0 2 2) plane of Cu2xSe films are linearly dependent on the composition. For cubic Cu2xSe phase, the lattice constant a is a strong function of x, and a varies from 5.86 to 5.74 A˚ for x values from 0.00 to 0.20, respectively [2]. Ellis [27] has reported the determination of film composition (by electron diffraction) and showed the linear dependence of lattice constant on nonstoichiometric factor x for Cu2xSe phase. Using Ellis plot, the compositional analysis of the deposited representative Cu2xSe film having ( has been carried out lattice constant a ¼ 5:826 A (Fig. 3). The value of x obtained using Ellis plot was 0.042, which corresponds to the Cu1.96Se phase of the film. The value of x or Cu:Se ratio in the as-prepared Cu2xSe film has also been confirmed from the Shafizade plot of linear dependence of d-spacing for (0 2 2) plane on composition [10] (Fig. 4). The observed value of x estimated from Shafizade plot for the same film of thickness 2420 A˚ was 0.04 or the Cu:Se ratio was 1.96. These two analyses confirmed the chemical constituents in the deposited Cu2xSe film as Cu 66% and Se 34%. The value of x or the composition of the film can be
ARTICLE IN PRESS M. Dhanam et al. / Journal of Crystal Growth 280 (2005) 425–435
5.86
Dislocation density 1014 (lines/m2)
Lattice parameter, a (Å)
135.142
Number of crystallites 1014 per unit area
3.927
Strain 108
430
5.84 5.82 5.80 5.78 5.76 5.74 0
0.05 0.10 0.15 0.20 Non-stochiometric factor, x
Fig. 3. Ellis plot of CBD Cu2xSe thin film of thickness 2420 A˚.
426.7
Grain size (A˚)
5.492
5.72
d-spacing (Å)
c ¼ 4:282
a ¼ 6:406
2.04 2.02 2.00
c ¼ 4:41
1.96 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 ←Cu/Se→ CuzSe CuSe Fig. 4. Shafizade plot of CBD Cu2xSe thin film of thickness 2420 A˚.
controlled by varying the copper–selenium concentration in the reaction mixture [16].
JCPDS
3.55 3.2 3.11 2.865 2.564 2.264 1.831 1.78 1.715 1.639
Observed
3.66 3.28 3.18 2.934 2.562 2.295 1.851 1.796 1.738 1.649
101 200 111 210 201 220 311 202 212 321
100 55 61 19 20 51 63 47 — —
a ¼ 6:56
1.98
100 94 77 83 53 51 47 40 36 40
Observed Observed
JCPDS
Lattice constant (A˚) Relative intensities (I=I o ) hkl planes d-spacing (A˚)
Table 2 Structural parameters of CBD Cu3Se2 thin film of thickness 10500 A˚
JCPDS
189.78
Volume of unit cell (A˚)3
2.06
3.3.4. Compositional analysis of Cu3Se2 thin film Ellis and Shafizade plots analysis can be employed to confirm the chemical constituents of the Cu2xSe films but cannot be applicable to the Cu3Se2 films. Energy-dispersive X-ray analysis (EDAX) has been used to determine the composition of Cu3Se2 films. EDAX pattern for the representative Cu3Se2 film of thickness 10500 A˚ is given in Fig. 5. The analysis confirms the presence of copper and selenium in the deposited film with
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Si
150
100 cps
O Se 50 Cu
Cu
0 0
2
4
6
8
Energy (KeV) Fig. 5. EDAX pattern of CBD Cu3Se2 thin film of thickness 10500 A˚.
Cu 57% and Se 43%, so the composition is Cu2.7Se2. The slight variation in composition might be due to the fact that EDAX takes into account occasional odd compositions in the film, unlike XRD which takes into account the whole composition of the film [22]. The possible compositions and structure of chemically deposited copper selenide films can vary widely, and it is due to the variation of pH value. Alternatively, it may due to the presence of reducing agents such as sulphite, selenosulfate, etc. in the reaction mixture as reported earlier [21]. The appearances of silicon (Si) and oxygen (O) peaks in the EDAX pattern are due to the glass substrates used in the analysis. 3.4. Electrical properties 3.4.1. Electrical properties of Cu2xSe thin films Electrical studies on Cu2xSe thin films have been carried out by earlier researchers [2,8,9,14–16,18,19,21,27,28]. Electrical resistivity of Cu2xSe films have been measured in the temperature range of 303–503 K and a voltage range of 8–20 V. Fig. 6 shows the variation of conductivity with inverse absolute temperature for Cu2xSe thin films of different thickness (4030 and 6450 A˚) at four different voltages. The plot shows a unique increase in film conductivity with increase in temperature, which indicates the semiconducting nature of the film [2]. The linear characteristics
431
of the plot indicate the presence of only one type of conduction mechanism. A similar behaviour has been reported by earlier workers [2,29,32] for Cu2xSe films. Since our experimental data fit into the relation s ¼ s0 expðE a =kTÞ [2], high-temperature conductivity is a thermally activated mechanism, which is attributed to the thermal excitation of charge carriers from grain boundaries to the neutral region of the grains. A plot of activation energy versus different voltages for the films of two different thickness (Fig. 7) confirms the decrease in activation energy with increase in voltages. From this plot, zero activation energies of Cu2xSe films having thickness 4030 and 6450 A˚ were found to be 0.765 and 0.685 eV, respectively. It can be concluded that the activation energy of CBD Cu2xSe films is inversely proportional to the applied voltages and film thickness. The significant decrease in activation energy with the increase in film thickness also proves the semiconducting nature of these films. The decrease in activation energy also suggests that the grain boundary scattering contribution reduces significantly as thickness increases. The estimated hightemperature electrical parameters are presented in Table 3. 3.4.2. Electrical properties of Cu3Se2 films No reports have been found related to hightemperature electrical conductivity of Cu3Se2 thin films. High-temperature electrical studies on CBD Cu3Se2 thin films have been carried out in the temperature range of 343–443 K and in the voltage range of 8–20 V. A plot of log (s) versus (1000/T) for a representative film of thickness 4580 A˚ at four different voltages is shown in Fig. 8. This plot indicates the semiconducting nature of the film with thermally activated conduction, and the linearity of the entire curve also confirms the presence of only one type of conduction mechanism. Summarized results of the study are presented in Table 4. Fig. 9 confirms the decrease in activation energy with increase in voltage. From this plot, zero activation energy of Cu3Se2 thin film of thickness 4580 A˚ has been found to be 0.0395 eV. It has been found that Cu2xSe thin films are more conducting than Cu3Se2 thin films. The result agrees very well with Gracia et al. [9]
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432
-0.5
-0.5 t = 6450 Å (8V)
-1.5
t = 4030 Å (8V)
-3.5
log (σ)
log (σ)
-2.5
-4.5
t = 6450 Å (12V)
-2.5
t = 4030 Å (12V)
-3.5 -4.5
-5.5
-5.5
-6.5
-6.5
-7.5 1.9
2.3 2.7 3.1 1000/T (K-1)
-7.5
3.5
1.9
-0.5 -1.5
t = 6450 Å (16V)
-1.5
-2.5
t = 4030 Å (16V)
-2.5
-3.5 -4.5
3.1
3.5
-6.5
-6.5 2.7 3.1 1000/T (K-1)
3.5
t = 4030 Å (20V)
-4.5 -5.5
2.3
t = 6450 Å (20V)
-3.5
-5.5
-7.5 1.9
2.3 2.7 1000/T (K-1)
-0.5
log (σ)
log (σ)
-1.5
-7.5 1.9
2.3
2.7 3.1 1000/T (K-1)
3.5
Fig. 6. A plot of log(s) vs. (103/T) of CBD Cu2xSe thin films of different thicknesses.
Activation Energy (eV)
0.9 0.85
t = 4030 Å
0.8
I = 6450 Å
who have reported that copper (II) selenide (CuSe) thin films are less conducting than copper (I) selenide (Cu2xSe) thin films.
0.75
4. Conclusions
0.7 0.65 0.6 0.55 0.5
0
2
4
6
8 10 12 14 Voltage (Volts)
16
18
20
Fig. 7. Plot of activation energy (Ea) vs. voltage for CBD Cu2xSe thin films of different thicknesses.
(1) Cubic Cu2xSe and tetragonal Cu3Se2 thin films have been prepared from the same reaction mixture at room temperature by slightly varying the pH. No earlier researchers have prepared Cu2xSe and Cu3Se2 thin films from the same reaction mixture and also at room temperature. (2) XRD analysis confirmed the structure of Cu2xSe thin films as cubic and that of Cu3Se2
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Table 3 Summarized results of the electrical properties of CBD Cu2xSe thin films Film thickness (A˚)
Voltage (V)
(s0 ) 104 (O1m1)
Activation energy (E a ) (eV)
Zero activation energy (DE a ) (eV)
4030
8 12 16 20
5.623 5.011 4.467 3.981
0.6896 0.6448 0.6104 0.5668
0.765
6540
8 12 16 20
2.818 2.512 2.239 1.995
0.6265 0.5952 0.5668 0.541
0.685
1.55
1.55 8V
12V 1.5
log (σ)
log (σ)
1.5
1.45
1.45
1.4
1.4
1.35 1.9
2.4
2.9
3.4
1000/T (K-1)
(a)
1.35 1.9 (b)
1.55
2.4 1000/T
2.9
1.55 20V
16V 1.5
log (σ)
log (σ)
1.5
1.45
1.4
1.35 1.3 (c)
3.4
(K-1)
1.45
1.4
2.4 2.9 1000/T (K-1)
1.35 1.9
3.4 (d)
2.4 2.9 1000/T (K-1)
3.4
Fig. 8. A plot of log(s) vs. (103/T) of CBD Cu3Se2 thin film of thickness 4580 A˚.
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Table 4 Summarized results of the electrical properties of CBD Cu3Se2 thin film Film thickness (A˚)
Voltage (V)
(s0 ) 101 (O1 m1)
Activation energy (E a ) (eV)
Zero activation energy (DE a ) (eV)
4580
8 12 16 20
6.8391 6.5313 5.2481 4.3152
0.02976 0.02587 0.02284 0.01587
0.0395
(5) The composition of Cu2xSe films has been confirmed as Cu1.96Se using Spectro compositional analysis. (6) High-temperature electrical studies on Cu2xSe and Cu3Se2 thin films confirm the thermally activated conduction in both the films. (7) Cu2xSe films are more conductive than Cu3Se2 films.
0.05 0.045
Activation Energy (eV)
0.04 0.035 0.03 0.025 0.02
Acknowledgements
0.015 0.01 0.005 0 0
2
4
6
8
10 12 14 16 18 20
Voltage (Volts) Fig. 9. Plot of activation energy (E a ) vs. voltage for CBD Cu3Se2 thin films of thicknesses 4580 A˚.
thin films as tetragonal. Various structural parameters such as lattice constant, volume of the unit cell, crystallite size, dislocation density, number of crystallites per unit area and strain in the film have been estimated for both phases of copper selenide thin films. (3) Films with considerable thickness have been obtained in the present study. Therefore, the prepared films can be used for the fabrication of solar cells. (4) Chemical constituent of Cu3Se2 thin film has been confirmed by energy-dispersive analysis using X-rays, and the composition of the film has been found as Cu2.7Se2.
The authors are highly thankful to the Secretary, Principal and HOD of Physics, Kongunadu Arts and Science College—Coimbatore for providing the laboratory facilities and constant encouragement. The authors acknowledge the Central Power Research Institute—Bangalore for recording EDAX patterns, PSG College of Technology—Coimbatore for recording XRD patterns and the Indian Institute of Science—Bangalore for providing the reference facilities.
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