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Structural and electrical transport properties of CdS0.9Se0.1:In thin films: effect of film thickness
Materials Chemistry and Physics 70 (2001) 112–116
Materials science communication
Structural and electrical transport properties of CdS0.9Se0.1:In thin films: effect of film thickness G.S. Shahane a,∗ , L.P. Deshmukh b a
Department of Electronics, DBF Dayanand College of Arts and Science, Solapur 413 002, MS, India b Thin Film and Solar Studies Research Laboratory, Department of Physics (Applied Electronics), Shivaji University Centre for PG Studies, Solapur 413 003, MS, India Received 13 April 2000; received in revised form 24 July 2000; accepted 9 August 2000
Abstract Thin films of CdS0.9 Se0.1 :In (0.05 mol%) of various thicknesses have been deposited on to the clean glass substrates using a chemical deposition technique. Composition analysis showed that films were sulphur deficit. Structural investigations on these films revealed the polycrystalline nature of the films with the presence of hexagonal CdS0.9 Se0.1 and cubic CdS phases. Grain size increased with the film thickness. Electrical conductivity and thermoelectric power (TEP) measurements have been carried out in 300–550 K temperature range. The conduction activation energy is found to be thickness-dependent. TEP measurements showed n-type conduction. Carrier concentration increased with thickness. © 2001 Elsevier Science B.V. All rights reserved. Keywords: CdS Se (In) thin films; Electrical conductivity; Grain size effect
1. Introduction The II–VI semiconducting compounds, especially the cadmium chalcogenides, have been extensively studied owing to their potential applications in semiconductor devices [1–6]. It is worth mentioning that cadmium sulphide and selenide have an important place in this respect and we have already established that the solid solution/alloyed phases of the CdS1−x Sex (0 ≤ x ≤ 1) type were more promising, especially in the photoelectrochemical solar cell applications [7,8]. It has also been pointed out that the performance of photo electro chemical (PEC) cells based on these photoelectrodes were composition-dependent and most favourable results were obtained at x = 0.1 [7]. However, the conversion efficiency so far reported is low and one of the major reasons for such a low efficiency is the higher resistance of the photoelectrode material. This could effectively be reduced by doping the photoelectrode material with suitable impurity and/or by increasing the film thickness. After doping with indium, the performance of PEC cell is found to be improved and optimum performance is observed at 0.05 mol% In-doping concentration [8]. This work attempts to study the ∗ Corresponding author. E-mail address: [email protected] (G.S. Shahane).
effect of photoelectrode thickness on the electrical transport properties of chemically deposited CdS0.9 Se0.1 :In thin films. 2. Experimental The CdS0.9 Se0.1 :In (0.05 mol%) thin films with varying thickness were obtained on the glass substrates using a chemical deposition process reported elsewhere [7–10]. For deposition of the samples, cadmium acetate, thiourea and sodium selenosulphate were mixed together in a volume stoichiometric proportion. An indium trichloride was used as a source material for doping. Triethanolamine was used as a complexing agent and sodium hydroxide and aqueous ammonia were used to adjust the pH (≈10.4) of the resulting solution. The deposition was carried out at 55◦ C for 75 min. The film thickness was increased by retreating the samples, each time to fresh quantities of the solutions. The film thickness was measured by weight differencedensity consideration technique. The film composition and structure were determined by EDAX and XRD analyses, respectively. The range of 2θ angle was from 10 to 80◦ . The surface features of these samples were examined through a scanning electron microscope. The DC electrical conductivity of these samples was measured in 300–550 K temperature range. A two-probe press contact technique was used
0254-0584/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 0 ) 0 0 4 6 7 - 3
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
113
Table 1 EDAX analysis of CdS0.9 Se0.1 :In thin films of various thicknesses Thickness (m)
1.39 1.75 2.26 2.42 2.85
Composition in solution (%)
Composition in film (%)
Cd
S
Se
In
Cd
S
Se
In
50 50 50 50 50
45 45 45 45 45
5 5 5 5 5
0.05 0.05 0.05 0.05 0.05
58.76 58.06 57.52 58.34 58.18
33.42 33.65 34.84 33.32 33.35
6.08 6.55 6.06 6.74 6.61
1.74 1.74 1.58 1.66 1.86
for this purpose. The thermo emf of the films was measured by the integral method in 300–550 K temperature range.
3. Results and discussion Table 1 shows the comparison between initial composition in the bath and final composition in the film as revealed by EDAX technique. It is seen that the atomic percentage of Cd, Se and In in the films are greater than the expected values while that for S are below expectation, resulting in sulphur deficit films. These stoichiometric deviations are responsible for n-type conduction of undoped CdS0.9 Se0.1 thin films [11–13]. No appreciable change in stoichiometric ratio were observed with change in film thickness. The X-ray diffractograms were obtained for these samples and are shown in Fig. 1 for four typical film thicknesses. The peaks were identified by comparing the d-values obtained from the XRD patterns with the standard ASTM data-cards d-values. The strongest reflection is observed at d = 3.364 Å which can be indexed as (0 0 2) plane of the hexagonal CdS0.9 Se0.1 solid solution [10] 1 . Other peaks also show a good match with the ASTM values. Few reflections corresponding to cubic phase are also detected 2 . This indicates that the structure is a mixture of hexagonal CdS0.9 Se0.1 solid solution and cubic CdS, hexagonal phase being dominant [10]. For increased thickness, the diffraction peaks occur at the same position with modification in intensity and width of peaks. The grain size of the films was calculated from the X-ray diffraction pattern using the Scherrer’s relation, D=
0.9λ B cos θ
(1)
where D is the grain size, λ the wavelength, B the full width at half maximum and θ the diffraction angle. It is found that the grain size increases with increasing thickness (Table 2). The lattice parameters have been calculated and their average values are a = 4.16 Å and c = 6.78 Å for hexagonal CdS0.9 Se0.1 structure and a = 5.696 Å for cubic CdS structure. Fig. 2 shows the SEM micrographs for two typical film thicknesses. It is seen that grain structure is improved with thickness and supports the XRD observation. 1 2
ASTM card for X-ray diffraction data No. 6-0314. ASTM card for X-ray diffraction data No. 10-454.
Fig. 1. X-ray diffractograms of four typical photoelectrodes with thicknesses: (a) 1.75 m; (b) 2.26 m; (c) 2.42 m; (d) 2.85 m.
The dark electrical conductivity was measured for all the samples in 300–550 K temperature range. It is observed that room temperature electrical conductivity is found to increase with thickness. The variation of log σ with the reciprocal of temperature for four typical film thicknesses is shown in Fig. 3. The variation shows a usual Arrhenius behaviour consisting of high and low temperature regions. The activation energies of electrical conduction have been determined from these plots in both the regions and are listed in Table 2. It is found that the activation energy is thickness-dependent and decreases with increase in thickness. This can be explained due to the polycrystalline nature of the films as explained by Seto’s model [14]. A polycrystalline film material contains a large number of microcrystallites with grain boundaries between them. At the grain boundary the incomplete atomic bondings can act as trap centres. These trap centres traps the charge carriers at the grain boundaries, and hence, a space charge can be built up locally. This space charge impedes the transit of charge carriers from one crystallite to the other. Taking these effects into account Seto derived the expressions, ΦB =
qD2 n 8ε
for Dn < Qt
(2)
114
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
Table 2 Effect of thickness on various properties of CdS0.9 Se0.1 :In thin films Thickness (m)
1.39 1.75 2.26 2.42 2.85
Grain size (Å)
350 372 395 414 429
Activation energy HT (eV)
LT (eV)
0.675 0.595 0.542 0.510 0.493
0.089 0.075 0.061 0.059 0.051
Carrier concentration n (×1019 cm−3 )
Barrier height Φ B (eV)
4.82 5.63 6.30 6.47 6.52
0.629 0.562 0.529 0.493 0.480
Fig. 2. The SEM micrographs of CdS0.9 Se0.1 :In thin films with various thicknesses: (a) 1.75 m and (b) 2.26 m.
ΦB =
qQ2t 8εn
for Dn > Qt
(3)
where Φ B is the barrier height, q the electronic charge, D the grain size, n the carrier concentration, Qt the density of surface states and ε the dielectric permittivity. The
Fig. 3. The variation of log σ vs 1/T for four typical film thicknesses: (䊉): t = 1.39 m; (䊊): t = 1.75 m; (䉱): t = 2.26 m; (䊐): t = 2.42 m.
first equation suggests that as the grain size increases, the barrier height increases. But we observe that as the thickness (and hence, grain size) increases the activation energy decreases. Thus, the first condition can be ruled out and the second equation can be taken as the appropriate one. This indicates that the carrier concentration increases with thickness. This is supported by the fact that as thickness increases conductivity increases. This type of behaviour has also been observed by Damodara Das et al. [15,16] in (Bi0.6 Sb0.4 )2 Te3 and Pb0.5 Sn0.5 Te thin films. In order to have a clear understanding, attempts were made to measure the carrier concentration (n), carrier mobility (µ) and grain barrier height (Φ B ). The thermoelectric power coupled with an electrical conductivity measurement is an important tool for determination of the type of conductivity, carrier concentration, carrier mobility and grain barrier height. The thermopower measurements showed n-type conduction for all the samples. This can be ascribed to the stoichiometric deficiency of sulphur as detected from EDAX analysis and the role of indium that acts as donor [10–13]. The variation of thermoelectric power (TEP) with temperature is shown in Fig. 4. As expected, there is a general trend of decrease in TEP with increase in thickness. It is known that the TEP of the amorphous or disordered materials is high. As the thickness increases the grain size of the film increases and hence, the crystallinity and orderliness also increases (as observed form XRD and SEM studies) with thickness. This results in decrease in TEP with thickness. It is also seen from the plots that the variation of
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
Fig. 4. Dependence of TEP on temperature for (䊉): t = 1.39 m; (䊊): t = 1.75 m; (䉱): t = 2.26 m; (䊐): t = 2.42 m.
TEP with temperature is nonlinear suggesting the samples to be of nondegenerate type semiconductor whose temperature dependence of TEP is given by " ( !)# 2πm∗d kT3/2 −K A + ln 2 (4) P = e nh3 where A is the thermoelectric factor which depends on the various scattering mechanisms and other terms have their usual significance. Eq. (4) can be solved and rearranged for the value of n, the temperature dependence of carrier concentration becomes, log n =
3 2
log T − 0.005P + 15.7198
(5)
The carrier concentrations at various temperatures were determined for all the samples. It is observed that carrier concentration increases with thickness (Table 2). This also supports the observations from conductivity measurements. Carrier mobility was then determined using the standard relation, σ (6) µ= ne The mobility is found to be a function of both temperature and thickness. The temperature dependence of carrier mobility was then analysed to yield the grain barrier height by applying the Petritz’s grain boundary scattering model [17]. According to Petritz, the grain boundary scattering dependent mobility is given by, ΦB −1/2 (7) exp − µ = µ0 T kT where µ0 is the pre-exponential factor on the assumption that current over barrier flows by thermionic emission and Φ B the intergrain barrier height. Thus, the plot of log (µT1/2 ) vs 1/T should yield a straight line. Fig. 5 shows the plots of
115
Fig. 5. The variation of log (µT1/2 ) vs 1/T for (䊉): t = 1.39 m; (䊊): t = 1.75 m; (䉱): t = 2.26 m; (䊐): t = 2.42 m.
log (µT1/2 ) vs 1/T for four representative samples showing the presence of grain boundary scattering mechanism. The grain barrier heights (Φ B ’s) were calculated from the slope of these plots and the values are listed in Table 2. The grain barrier height decreases with thickness. The above observations are in good consonance with the observed variation of an electrical conductivity through the changes that are observed in the carrier concentration and mobility as a result of the grain boundary limited scattering.
4. Conclusions An attempt is made in these investigations to understand the effect of film thickness on the electrical transport properties of CdS0.9 Se0.1 :In thin films. X-ray diffraction studies revealed improvement in the crystallinity. SEM studies support the above observation. Electrical conductivity is found to be increased with thickness. The thickness dependence of activation energy is attributed to the grain boundary potential variation with grain size according to Seto’s model. The TEP measurements showed n-type conduction. The carrier concentration and mobility are found to be increased whereas grain barrier height decreased with thickness. This also explains the observed variation of conductivity.
References [1] P.J. Sebastin, Thin Solid Films 245 (1994) 132. [2] R.C. Kainthla, J.F. Mc Cann, D. Haneman, Sol. Ener. Mater. 7 (1983) 491. [3] M.A. Kenawy, H.A. Zayed, A.M. Ibrahim, Ind. J. Pure Appl. Phys. 29 (1991) 624. [4] A. Mondal, T.K. Chaudhuri, P. Pramanik, Sol. Ener. Mater. 7 (1983) 431.
116
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
[5] R.N. Noufi, P.A. Kohl, A.J. Bard, J. Electrochem. Soc. 125 (1978) 375. [6] P.K. Mahapatra, A.R. Dubey, Sol. Ener. Mater. Sol. Cells 32 (1994) 29. [7] L.P. Deshmukh, G.S. Shahane, Int. J. Electron. 83 (1997) 341. [8] L.P. Deshmukh, G.S. Shahane, K.M. Garadkar, Ind. J. Pure Appl. Phys. 35 (1997) 560. [9] G.S. Shahane, B.M. More, C.B. Rotti, L.P. Deshmukh, Mater. Chem. Phys. 47 (1997) 263. [10] G.S. Shahane, K.M. Garadkar, L.P. Deshmukh, Mater. Chem. Phys. 51 (1997) 246.
[11] L.P. Deshmukh, G.S. Shahane, D.S. Sutrave, P.P. Hankare, Solid State Phenomena 55 (1997) 68. [12] T.K. Gupta, J. Doh, Sol. Ener. Mater. Sol. Cells 27 (1992) 327. [13] G. Gordillo, Sol. Ener. Mater. Sol. Cells 25 (1992) 41. [14] J.Y.W. Seto, J. Appl. Phys. 46 (1975) 5247. [15] V. Damodara Das, P. Gopal Ganesan, Semicond. Sci. Technol. 12 (1997) 195. [16] V. Damodara Das, C. Bahulayan, Solid State Commun. 93 (1995) 949. [17] R.L. Petritz, Phys. Rev. 104 (1956) 1508.
Materials science communication
Structural and electrical transport properties of CdS0.9Se0.1:In thin films: effect of film thickness G.S. Shahane a,∗ , L.P. Deshmukh b a
Department of Electronics, DBF Dayanand College of Arts and Science, Solapur 413 002, MS, India b Thin Film and Solar Studies Research Laboratory, Department of Physics (Applied Electronics), Shivaji University Centre for PG Studies, Solapur 413 003, MS, India Received 13 April 2000; received in revised form 24 July 2000; accepted 9 August 2000
Abstract Thin films of CdS0.9 Se0.1 :In (0.05 mol%) of various thicknesses have been deposited on to the clean glass substrates using a chemical deposition technique. Composition analysis showed that films were sulphur deficit. Structural investigations on these films revealed the polycrystalline nature of the films with the presence of hexagonal CdS0.9 Se0.1 and cubic CdS phases. Grain size increased with the film thickness. Electrical conductivity and thermoelectric power (TEP) measurements have been carried out in 300–550 K temperature range. The conduction activation energy is found to be thickness-dependent. TEP measurements showed n-type conduction. Carrier concentration increased with thickness. © 2001 Elsevier Science B.V. All rights reserved. Keywords: CdS Se (In) thin films; Electrical conductivity; Grain size effect
1. Introduction The II–VI semiconducting compounds, especially the cadmium chalcogenides, have been extensively studied owing to their potential applications in semiconductor devices [1–6]. It is worth mentioning that cadmium sulphide and selenide have an important place in this respect and we have already established that the solid solution/alloyed phases of the CdS1−x Sex (0 ≤ x ≤ 1) type were more promising, especially in the photoelectrochemical solar cell applications [7,8]. It has also been pointed out that the performance of photo electro chemical (PEC) cells based on these photoelectrodes were composition-dependent and most favourable results were obtained at x = 0.1 [7]. However, the conversion efficiency so far reported is low and one of the major reasons for such a low efficiency is the higher resistance of the photoelectrode material. This could effectively be reduced by doping the photoelectrode material with suitable impurity and/or by increasing the film thickness. After doping with indium, the performance of PEC cell is found to be improved and optimum performance is observed at 0.05 mol% In-doping concentration [8]. This work attempts to study the ∗ Corresponding author. E-mail address: [email protected] (G.S. Shahane).
effect of photoelectrode thickness on the electrical transport properties of chemically deposited CdS0.9 Se0.1 :In thin films. 2. Experimental The CdS0.9 Se0.1 :In (0.05 mol%) thin films with varying thickness were obtained on the glass substrates using a chemical deposition process reported elsewhere [7–10]. For deposition of the samples, cadmium acetate, thiourea and sodium selenosulphate were mixed together in a volume stoichiometric proportion. An indium trichloride was used as a source material for doping. Triethanolamine was used as a complexing agent and sodium hydroxide and aqueous ammonia were used to adjust the pH (≈10.4) of the resulting solution. The deposition was carried out at 55◦ C for 75 min. The film thickness was increased by retreating the samples, each time to fresh quantities of the solutions. The film thickness was measured by weight differencedensity consideration technique. The film composition and structure were determined by EDAX and XRD analyses, respectively. The range of 2θ angle was from 10 to 80◦ . The surface features of these samples were examined through a scanning electron microscope. The DC electrical conductivity of these samples was measured in 300–550 K temperature range. A two-probe press contact technique was used
0254-0584/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 4 - 0 5 8 4 ( 0 0 ) 0 0 4 6 7 - 3
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
113
Table 1 EDAX analysis of CdS0.9 Se0.1 :In thin films of various thicknesses Thickness (m)
1.39 1.75 2.26 2.42 2.85
Composition in solution (%)
Composition in film (%)
Cd
S
Se
In
Cd
S
Se
In
50 50 50 50 50
45 45 45 45 45
5 5 5 5 5
0.05 0.05 0.05 0.05 0.05
58.76 58.06 57.52 58.34 58.18
33.42 33.65 34.84 33.32 33.35
6.08 6.55 6.06 6.74 6.61
1.74 1.74 1.58 1.66 1.86
for this purpose. The thermo emf of the films was measured by the integral method in 300–550 K temperature range.
3. Results and discussion Table 1 shows the comparison between initial composition in the bath and final composition in the film as revealed by EDAX technique. It is seen that the atomic percentage of Cd, Se and In in the films are greater than the expected values while that for S are below expectation, resulting in sulphur deficit films. These stoichiometric deviations are responsible for n-type conduction of undoped CdS0.9 Se0.1 thin films [11–13]. No appreciable change in stoichiometric ratio were observed with change in film thickness. The X-ray diffractograms were obtained for these samples and are shown in Fig. 1 for four typical film thicknesses. The peaks were identified by comparing the d-values obtained from the XRD patterns with the standard ASTM data-cards d-values. The strongest reflection is observed at d = 3.364 Å which can be indexed as (0 0 2) plane of the hexagonal CdS0.9 Se0.1 solid solution [10] 1 . Other peaks also show a good match with the ASTM values. Few reflections corresponding to cubic phase are also detected 2 . This indicates that the structure is a mixture of hexagonal CdS0.9 Se0.1 solid solution and cubic CdS, hexagonal phase being dominant [10]. For increased thickness, the diffraction peaks occur at the same position with modification in intensity and width of peaks. The grain size of the films was calculated from the X-ray diffraction pattern using the Scherrer’s relation, D=
0.9λ B cos θ
(1)
where D is the grain size, λ the wavelength, B the full width at half maximum and θ the diffraction angle. It is found that the grain size increases with increasing thickness (Table 2). The lattice parameters have been calculated and their average values are a = 4.16 Å and c = 6.78 Å for hexagonal CdS0.9 Se0.1 structure and a = 5.696 Å for cubic CdS structure. Fig. 2 shows the SEM micrographs for two typical film thicknesses. It is seen that grain structure is improved with thickness and supports the XRD observation. 1 2
ASTM card for X-ray diffraction data No. 6-0314. ASTM card for X-ray diffraction data No. 10-454.
Fig. 1. X-ray diffractograms of four typical photoelectrodes with thicknesses: (a) 1.75 m; (b) 2.26 m; (c) 2.42 m; (d) 2.85 m.
The dark electrical conductivity was measured for all the samples in 300–550 K temperature range. It is observed that room temperature electrical conductivity is found to increase with thickness. The variation of log σ with the reciprocal of temperature for four typical film thicknesses is shown in Fig. 3. The variation shows a usual Arrhenius behaviour consisting of high and low temperature regions. The activation energies of electrical conduction have been determined from these plots in both the regions and are listed in Table 2. It is found that the activation energy is thickness-dependent and decreases with increase in thickness. This can be explained due to the polycrystalline nature of the films as explained by Seto’s model [14]. A polycrystalline film material contains a large number of microcrystallites with grain boundaries between them. At the grain boundary the incomplete atomic bondings can act as trap centres. These trap centres traps the charge carriers at the grain boundaries, and hence, a space charge can be built up locally. This space charge impedes the transit of charge carriers from one crystallite to the other. Taking these effects into account Seto derived the expressions, ΦB =
qD2 n 8ε
for Dn < Qt
(2)
114
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
Table 2 Effect of thickness on various properties of CdS0.9 Se0.1 :In thin films Thickness (m)
1.39 1.75 2.26 2.42 2.85
Grain size (Å)
350 372 395 414 429
Activation energy HT (eV)
LT (eV)
0.675 0.595 0.542 0.510 0.493
0.089 0.075 0.061 0.059 0.051
Carrier concentration n (×1019 cm−3 )
Barrier height Φ B (eV)
4.82 5.63 6.30 6.47 6.52
0.629 0.562 0.529 0.493 0.480
Fig. 2. The SEM micrographs of CdS0.9 Se0.1 :In thin films with various thicknesses: (a) 1.75 m and (b) 2.26 m.
ΦB =
qQ2t 8εn
for Dn > Qt
(3)
where Φ B is the barrier height, q the electronic charge, D the grain size, n the carrier concentration, Qt the density of surface states and ε the dielectric permittivity. The
Fig. 3. The variation of log σ vs 1/T for four typical film thicknesses: (䊉): t = 1.39 m; (䊊): t = 1.75 m; (䉱): t = 2.26 m; (䊐): t = 2.42 m.
first equation suggests that as the grain size increases, the barrier height increases. But we observe that as the thickness (and hence, grain size) increases the activation energy decreases. Thus, the first condition can be ruled out and the second equation can be taken as the appropriate one. This indicates that the carrier concentration increases with thickness. This is supported by the fact that as thickness increases conductivity increases. This type of behaviour has also been observed by Damodara Das et al. [15,16] in (Bi0.6 Sb0.4 )2 Te3 and Pb0.5 Sn0.5 Te thin films. In order to have a clear understanding, attempts were made to measure the carrier concentration (n), carrier mobility (µ) and grain barrier height (Φ B ). The thermoelectric power coupled with an electrical conductivity measurement is an important tool for determination of the type of conductivity, carrier concentration, carrier mobility and grain barrier height. The thermopower measurements showed n-type conduction for all the samples. This can be ascribed to the stoichiometric deficiency of sulphur as detected from EDAX analysis and the role of indium that acts as donor [10–13]. The variation of thermoelectric power (TEP) with temperature is shown in Fig. 4. As expected, there is a general trend of decrease in TEP with increase in thickness. It is known that the TEP of the amorphous or disordered materials is high. As the thickness increases the grain size of the film increases and hence, the crystallinity and orderliness also increases (as observed form XRD and SEM studies) with thickness. This results in decrease in TEP with thickness. It is also seen from the plots that the variation of
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
Fig. 4. Dependence of TEP on temperature for (䊉): t = 1.39 m; (䊊): t = 1.75 m; (䉱): t = 2.26 m; (䊐): t = 2.42 m.
TEP with temperature is nonlinear suggesting the samples to be of nondegenerate type semiconductor whose temperature dependence of TEP is given by " ( !)# 2πm∗d kT3/2 −K A + ln 2 (4) P = e nh3 where A is the thermoelectric factor which depends on the various scattering mechanisms and other terms have their usual significance. Eq. (4) can be solved and rearranged for the value of n, the temperature dependence of carrier concentration becomes, log n =
3 2
log T − 0.005P + 15.7198
(5)
The carrier concentrations at various temperatures were determined for all the samples. It is observed that carrier concentration increases with thickness (Table 2). This also supports the observations from conductivity measurements. Carrier mobility was then determined using the standard relation, σ (6) µ= ne The mobility is found to be a function of both temperature and thickness. The temperature dependence of carrier mobility was then analysed to yield the grain barrier height by applying the Petritz’s grain boundary scattering model [17]. According to Petritz, the grain boundary scattering dependent mobility is given by, ΦB −1/2 (7) exp − µ = µ0 T kT where µ0 is the pre-exponential factor on the assumption that current over barrier flows by thermionic emission and Φ B the intergrain barrier height. Thus, the plot of log (µT1/2 ) vs 1/T should yield a straight line. Fig. 5 shows the plots of
115
Fig. 5. The variation of log (µT1/2 ) vs 1/T for (䊉): t = 1.39 m; (䊊): t = 1.75 m; (䉱): t = 2.26 m; (䊐): t = 2.42 m.
log (µT1/2 ) vs 1/T for four representative samples showing the presence of grain boundary scattering mechanism. The grain barrier heights (Φ B ’s) were calculated from the slope of these plots and the values are listed in Table 2. The grain barrier height decreases with thickness. The above observations are in good consonance with the observed variation of an electrical conductivity through the changes that are observed in the carrier concentration and mobility as a result of the grain boundary limited scattering.
4. Conclusions An attempt is made in these investigations to understand the effect of film thickness on the electrical transport properties of CdS0.9 Se0.1 :In thin films. X-ray diffraction studies revealed improvement in the crystallinity. SEM studies support the above observation. Electrical conductivity is found to be increased with thickness. The thickness dependence of activation energy is attributed to the grain boundary potential variation with grain size according to Seto’s model. The TEP measurements showed n-type conduction. The carrier concentration and mobility are found to be increased whereas grain barrier height decreased with thickness. This also explains the observed variation of conductivity.
References [1] P.J. Sebastin, Thin Solid Films 245 (1994) 132. [2] R.C. Kainthla, J.F. Mc Cann, D. Haneman, Sol. Ener. Mater. 7 (1983) 491. [3] M.A. Kenawy, H.A. Zayed, A.M. Ibrahim, Ind. J. Pure Appl. Phys. 29 (1991) 624. [4] A. Mondal, T.K. Chaudhuri, P. Pramanik, Sol. Ener. Mater. 7 (1983) 431.
116
G.S. Shahane, L.P. Deshmukh / Materials Chemistry and Physics 70 (2001) 112–116
[5] R.N. Noufi, P.A. Kohl, A.J. Bard, J. Electrochem. Soc. 125 (1978) 375. [6] P.K. Mahapatra, A.R. Dubey, Sol. Ener. Mater. Sol. Cells 32 (1994) 29. [7] L.P. Deshmukh, G.S. Shahane, Int. J. Electron. 83 (1997) 341. [8] L.P. Deshmukh, G.S. Shahane, K.M. Garadkar, Ind. J. Pure Appl. Phys. 35 (1997) 560. [9] G.S. Shahane, B.M. More, C.B. Rotti, L.P. Deshmukh, Mater. Chem. Phys. 47 (1997) 263. [10] G.S. Shahane, K.M. Garadkar, L.P. Deshmukh, Mater. Chem. Phys. 51 (1997) 246.
[11] L.P. Deshmukh, G.S. Shahane, D.S. Sutrave, P.P. Hankare, Solid State Phenomena 55 (1997) 68. [12] T.K. Gupta, J. Doh, Sol. Ener. Mater. Sol. Cells 27 (1992) 327. [13] G. Gordillo, Sol. Ener. Mater. Sol. Cells 25 (1992) 41. [14] J.Y.W. Seto, J. Appl. Phys. 46 (1975) 5247. [15] V. Damodara Das, P. Gopal Ganesan, Semicond. Sci. Technol. 12 (1997) 195. [16] V. Damodara Das, C. Bahulayan, Solid State Commun. 93 (1995) 949. [17] R.L. Petritz, Phys. Rev. 104 (1956) 1508.