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Optical characterization of SnO2:F films by spectroscopic ellipsometry
Journal of Non-Crystalline Solids 356 (2010) 2192–2197
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Optical characterization of SnO2:F films by spectroscopic ellipsometry F. Atay a,⁎, V. Bilgin b, I. Akyuz a, E. Ketenci c, S. Kose a a b c
Eskisehir Osmangazi University, Department of Physics, 26480 Eskisehir, Turkey Canakkale Onsekiz Mart University, Department of Physics, 17100 Canakkale, Turkey Eskisehir Osmangazi University, Graduate School of Science, 26480 Eskisehir, Turkey
a r t i c l e
i n f o
Article history: Received 2 July 2009 Received in revised form 2 July 2010 Available online 14 August 2010 Keywords: SnO2:F films; Ultrasonic spray pyrolysis; Spectroscopic ellipsometry (SE); UV
a b s t r a c t Spectroscopic ellipsometry (SE), which is a non-destructive and a non-contact optical technique used in characterization of thin films, is widely used to determine thickness, microstructure and optical constants. In this work, the effect of F incorporation on optical properties of SnO2 films grown by ultrasonic spray pyrolysis technique (USP) is presented. The reflections, refractive indices and thicknesses of the films were investigated using room temperature spectroscopic ellipsometry. The optical constants and the thicknesses of the films were fitted according to Cauchy–Urbach model, and ellipsometric angle Ψ was used as source point for optical characterizations. Besides, transmittance spectra of the films were taken from UV spectrometer, and the optical method was used to determine the band gaps. Also, band tailing resulting from defects or impurities was investigated. From the results obtained from the optical analyses, the application potential of SnO2:F films for solar cell devices was searched. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Transparent conducting oxide (TCO) thin films such as zinc oxide, indium oxide, tin oxide, indium tin oxide and cadmium oxide have attracted considerable attention because of their low resistivity and high optical transmittance [1]. Due to their optical and electrical properties, TCOs are used for photovoltaic solar cells, phototransistors, liquid crystal displays, optical heaters, gas sensors, transparent electrodes and other optoelectronic devices [2–9]. Among these TCOs, SnO2 films are inexpensive, chemically stable in acidic and basic solutions, thermally stable in oxidizing environments at high temperatures and also mechanically strong, which are important attributes for the fabrication and operation of solar cells [10–12]. SnO2 has a tetragonal structure, similar to the rutile structure with the wide energy gap of Eg = 3.6–4.0 eV and behaves as an n-type semiconductor [13–15]. Antimony (Sb), arsenic (As), phosphorus (P), indium (In), molybdenum (Mo), fluorine (F) and chlorine (Cl) have been selected as doping elements for SnO2 films [16–23]. SnO2 thin films are produced by different techniques such as thermal evaporation, sputtering, spray pyrolysis, sol–gel and hydrothermal [24–33]. Among these, spray pyrolysis is well suited for the preparation of doped tin oxide thin films because of its simple and inexpensive experimental arrangement, ease of adding various doping materials, reproducibility, high growth rate and mass production capability for uniform large area coatings [1,34]. Ultra-
⁎ Corresponding author. E-mail address: [email protected] (F. Atay). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.07.007
sonic spray pyrolysis (USP) technique includes an ultrasonic atomizer which is connected to an oscillator. This ensures the solution to be sprayed with better atomizing using ultrasonic waves, and these results in decreasing of droplet size and production of more homogeneous materials [35,36]. The aim of this work is to investigate the effect of F incorporation on the optical properties of SnO2 films produced by USP technique with spectroscopic ellipsometry (SE) and UV spectrometry. 2. Experimental procedure 2.1. Sample preparation and optical measuremets SnO2 and SnO2:F (at the F percentages of 1, 3 and 5) films were produced onto glass substrates (10 × 10 mm2) by USP technique at a substrate temperature of 350 ± 5 °C. Details of the USP technique were given in our previous works [37–39]. The ultrasonic oscillator frequency was 100 kHz, and the droplet size was 20 μm. The spraying solution contains SnCl2.2H2O (0.025 M) and NH4F (0.1 M) dissolved in deionized water. The glass substrates were heated by an electrical heater, and the substrate temperature was measured using an ironconstantan thermo-couple. The solution flow rate was kept at 5 cm3 min−1 by a flowmeter. Totally 100 cm3 of solution was used to produce all films and sprayed for 20 mins. Nitrogen was used as the carrier gas (0.2 kg cm−2). The produced SnO2:F films were named as S0, S1, S3 and S5 depending on the increasing F incorporation. SE measurements were carried out by a SC620 Spectroscopic Ellipsometer over a spectrum range of 250–2300 nm. But, the investigation of SnO2:F films has been performed in the wavelength
F. Atay et al. / Journal of Non-Crystalline Solids 356 (2010) 2192–2197
range of 500–1100 nm where Cauchy-Urbach model has been used to obtain the optical constants. This wavelength range corresponds to a region where all films are transparent or weakly absorbing. So, CauchyUrbach model can be applied to these films in this wavelength range. The thicknesses, reflections and optical constants (refractive index and extinction coefficient, n and k) of the films were obtained by analyzing the measured ellipsometric spectra through the Cauchy-Urbach model. Besides, the optical transmittance spectra of the films were taken from a Perkin Elmer UV/VIS Lambda 2S spectrometer, and the optical energy gaps of the films were calculated using the optical method. Also, band tailing resulting from defects or impurities was investigated.
where n1, n2 and n represent the refractive index of air, substrate and film, respectively. φ and λ represent the incident angle and wavelength of incident light, respectively. d and k the thickness and extinction coefficient of thin film [40]. Ellipsometry does not measure optical constants or film thickness directly; however Ψ and Δ can be represented as mathematical functions relating these material characteristics. Hence, a mathematical analysis called model-dependent analysis must be performed to determine real parameters from the measured ellipsometric data. Numerous material parameters can potentially be determined through
2.2. Spectroscopic ellipsometry technique Ellipsometer is much more of an analytical tool that is used to measure, not only single-layer thickness and refractive index with maximum precision, but also to extract microstructural and compositional information from complicated multi-layered films. One of the most important techniques is SE, which has been found favorably for characterization of thin solid films and bulk materials, especially semiconductors. This technique is a non-destructive, powerful and accurate technique [40,41] and is based on the polarized light [42]. SE is able to measure the thickness and dielectric function of a multi-layer system simultaneously [43–45]. So, it is a powerful technique to explore the band structure of nanometric semiconductor through the determination of the complex dielectric function [42]. SE, which is sensitive to films and surfaces, is widely used to determine optical constants in nearultraviolet, visible and near-infrared range (6–1.5 eV) [45]. This technique is also sensitive to film anisotropy and can be determined if the crystals in the film are randomly oriented or have preferential orientation, in which case the film becomes optically anisotropic [46]. Besides, this technique is very sensitive to surface irregularities such as surface roughness, interdiffusion and interlayer formation in multi-layer thin film systems [47–49]. The complete optical constants (n and k) can be obtained synchronously by this technique without Kramers–Kronig transformation [45,50,51]. This technique is widely used to investigate optical properties and microstructures of ferroelectric films on various substrates [52,53]. SE can be successfully characterize the microstructure and optical properties of nanocrystaline diamond films [54]. Moreover, ellipsometry allows the determination of the optical constants of the organic materials and their knowledge contributes to the understanding and optimization of the organic-based devices [41,55]. Ellipsometry name derives from the fact that when linearly polarized light that is neither perpendicular nor parallel polarized is incident on a medium at oblique angle, the reflected light is elliptically polarized [42,51]. Its polarization state can be described by two ellipsometric parameters: amplitude ratio (tan ψ) and phase shift difference(Δ)of two mutually orthogonal polarized components of the reflected waves (Rs and Rp for p- and s-polarized light) [51]. An ellipsometer yields two measurable quantities, Psi (Ψ) and Delta (Δ), at each wavelength and angle of incidence, which describes the change in the polarization state of light when it is allowed to interact with the sample under investigation [56]. Ψ and Δ parameters are related to the optical and structural properties of the sample through the following expression: ρ=
Rp = tan Ψ expðiΔÞ Rs
ð1Þ
where Rp and Rs are the complex reflection coefficients for the light polarized parallel (p) and perpendicular (s) to the plane of incidence respectively [50,55,57–64]. The fundamental equation for the complex reflectance ratio ρ is also described as follows: ρ = f ðn1 ; n2 ; n; ϕ; d; λ; kÞ
ð2Þ
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Fig. 1. SE spectra of SnO2:F films.
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F. Atay et al. / Journal of Non-Crystalline Solids 356 (2010) 2192–2197
Table 1 The thicknesses and the best-fit model parameters of SnO2:F films. Material
Code
d (nm)
A
B (nm2)
C (nm4) α
β (nm) MSE
SnO2:F SnO2:F SnO2:F SnO2:F
S0 S1 S3 S5
103.31 116.20 97.57 96.48
1.98 2.06 2.00 1.96
0.026 0.029 0.032 0.030
0.015 0.016 0.017 0.016
0.072 0.023 0.081 0.092
(at 0%) (at 1%) (at 3%) (at 5%)
0.085 0.106 0.098 0.082
0.11 0.29 0.09 0.06
SE analysis, including layer thickness, surface and/or interfacial roughness, optical constants and void fraction, using optical physics (Fresnel reflection coefficients, Snell's law, etc.) [41].
In order to extract useful information about a sample (thicknesses and optical constants of the layers) the experimental data are compared with the data generated using a model which describes the structure of the sample and its optical response [55,57,61]. For a given sample there are three unknown parameters: thickness t, refractive index n and extinction coefficient k, which have to be determined from only two ellipsometric parameters Ψ and Δ. By performing measurements at different wavelengths, more sets of Ψ and Δ data are available, and the problem can be solved numerically. The problem can be further simplified by analyzing the data in the spectral region where the film is transparent (k ≅ 0). In this spectral region, the optical response of the transparent films can be described by a Cauchy– Urbach dispersion relation for the refractive index and extinction coefficient [51,55,65], B C + 4 λ2 λ
ð3Þ
1 1 − κðλÞ = α exp β 12; 400 λ γ
ð4Þ
nðλÞ = A +
where A, B, C, α, β and γ are model parameters. 3. Results SE spectra of SnO2:F films are shown in Fig. 1. The optical response of the transparent or weakly absorbing SnO2:F films can be described by a Cauchy–Urbach dispersion relation. So, the experimental data were analyzed by using the Cauchy–Urbach model, and an appropriate fit is found between the model and experimental data as shown in Fig. 1. Fitting the experimental ellipsometric spectra of Ψ allowed the determination of the film thickness (d), spectra of refractive index (n) and extinction coefficient (k) of all films. The thicknesses determined by fitting the experimental ellipsometric spectra and the best-fit model parameters of SnO2:F films are listed in Table 1. Reflection (R) spectra of SnO2:F films are shown in Fig. 2. It was determined that the average reflection value of S0 films is about 23%, and this value remarkably decreases with the F incorporation. Refractive index (n) spectra of SnO2:F films are shown in Fig. 3. All films showed similar behavior in refractive index spectra. There is a little increase in refractive index value for S1 and S3 films. Refractive index values of the samples are nearly constant (~ 2.0–2.1) at long wavelengths. Fig. 4 shows the extinction coefficients (k) of SnO2:F films which are derived from model fitting the experimental spectroscopic ellipsometric data.
Fig. 2. Reflection (R) spectra of SnO2:F films.
Fig. 3. Refractive index (n) spectra of SnO2:F films.
F. Atay et al. / Journal of Non-Crystalline Solids 356 (2010) 2192–2197
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Fig. 4. Extinction coefficient (k) spectra of SnO2:F films.
The transmittance spectra of SnO2:F films taken by a UV/VIS spectrometer are shown in Fig. 5. It was determined that S0 films have an average T value of ~ 75% in the visible region. For S1 and S3 films, there is a small increase in T values depending on the F incorporation, but the T values of S5 films decreased in the visible region. Optical method has been used to determine the band gap values of SnO2:F films. (αhν)2 ~ hν variations of the films are shown in Fig. 6. It was determined that all films have direct band gap structure, and this property is suitable for solar cell applications. The band gap values have been calculated by extrapolating the linear portions to (αhν)2 = 0. The band gap values are given in Table 2. It is a well-known fact that semiconductors represent band tails due to the deformation and high carrier concentration. Defects in structure lead to local electric fields that affect the band tails, and band tailing is a result of impurity, disorder or any other defects. The absorption coefficient α(ν) in the low-energy range follows the wellknown exponential law, that is, the Urbach tail expressed by, αðνÞ = α0 expðhν = E0 Þ
ð5Þ
where α0 is a constant, and E0 denotes an energy which is constant or weakly dependent on temperature and is often interpreted as the width of the tail of localized states in the band gap [66–68]. E0 values were estimated from the slopes of the linear relationship lnα against hν using Eq. (5) just below the band edge. The calculated E0 values are given in Table 2. 4. Discussion It was determined that there are some deviations on fitted Ψ values (Fig. 1). Especially for S1 films, when the wavelength of incident light is higher than 600 nm, a visible deviation between the fitting and the experimental results was observed. We think that the deviations of Ψ values result from USP technique which is used to produce the SnO2:F films (because films produced by USP have not absolutely uniform and homogeneous surfaces) and low absorption in the given wavelength, (iii) roughness, grain boundaries and morphology of the films. Moreover, the rough surface and backsides of the films may affect the reflection of light. Besides, the grain boundaries and morphologies would depolarize the incident polarized light, resulting deviated experimental ellipsometric parameters and deteriorating the SE fitting. Also, backside reflection of transparent glass substrates may also affect the experimental SE data. We think that decrease of reflectance results from the surface roughness, grain boundaries and morphology of the F-doped films as
Fig. 5. Transmittance spectra of SnO2:F films.
these properties affect the intensity of the reflected light. Because of this information, we can say that the sample S0, which has the highest average reflection value, has a uniform surface structure and lower roughness as compared with others. It was determined that all films have a similar k variation belonging to wavelength of polarized light, and a similar tendency was observed according the curves of refractive index. The extinction coefficient of a material is directly related to its absorption characteristic. As shown in Fig. 4, the k values are very small at long wavelengths where all films are nearly transparent.
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F. Atay et al. / Journal of Non-Crystalline Solids 356 (2010) 2192–2197 Table 2 The band gap (Eg) and Urbach energy (E0) values of SnO2:F films. Material
Eg (eV)
E0 (meV)
S0 S1 S3 S5
3.95 3.94 3.95 3.95
270 275 270 241
5. Conclusion In this work, SnO2 and SnO2:F (at the percentages of 1, 3 and 5) films were produced by USP technique, which is a simple and economical technique and useful for large area thin film deposition with low cost. Their optical properties were studied by a spectroscopic ellipsometer and UV/VIS spectrometer. The thicknesses, refractive indices and extinction coefficients of the films were obtained by fitting the experimental spectroscopic data (Ψ) by using Cauchy–Urbach model. The numerical values of reflection remarkably decreased depending on the F incorporation, so we think that this could mean an improvement in solar cell efficiency due to a higher number of photons crossing F doped SnO2. All films have showed similar n and k variations with small differences for samples S1 and S3. From the analysis of SE results, it was concluded that the reflection and optical constants (n and k) highly depend on the production technique, surface roughness, grain boundaries and morphologies of the produced films, and these properties changed with F doping. It was determined from the transmittance spectra taken by a UV/VIS spectrometer that undoped SnO2 films have an average T value of 75% in the visible region, and there is a small increase with F doping (1% and 3%). The band gaps of the films were calculated by the optical method. To evaluate the near band gap edge characteristics of the films, we can interpret the absorption behavior by the Urbach rule. With respect to this aim, we have calculated the Urbach energy E0, which is interpreted as the width of the tails of localized states in the band gap. S5 films were found to have the lowest E0 value among others. This probably means there is lower disorder in SnO2 films when doped with F at 5%. Acknowledgements This work was supported by Eskisehir Osmangazi University Scientific Research Projects Committee under the project number 200719011. References
Fig. 6. (αhν)2 ~ hν variations of SnO2:F films.
The regions with a sharp decrease in T values indicate the fundamental absorption regions of the films. These regions correspond to nearly same wavelength range for all films, so we can say that there is not a dramatic effect of the F incorporation on the band gap of the films. It was seen from Table 2 that the band gap value of S0 films is not remarkably changed with F incorporation, and there is not a considerable effect of the F incorporation on the band gap of the films. The estimated direct band gap energies of the films were found to agree with the previously reported values [13–15].
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Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Optical characterization of SnO2:F films by spectroscopic ellipsometry F. Atay a,⁎, V. Bilgin b, I. Akyuz a, E. Ketenci c, S. Kose a a b c
Eskisehir Osmangazi University, Department of Physics, 26480 Eskisehir, Turkey Canakkale Onsekiz Mart University, Department of Physics, 17100 Canakkale, Turkey Eskisehir Osmangazi University, Graduate School of Science, 26480 Eskisehir, Turkey
a r t i c l e
i n f o
Article history: Received 2 July 2009 Received in revised form 2 July 2010 Available online 14 August 2010 Keywords: SnO2:F films; Ultrasonic spray pyrolysis; Spectroscopic ellipsometry (SE); UV
a b s t r a c t Spectroscopic ellipsometry (SE), which is a non-destructive and a non-contact optical technique used in characterization of thin films, is widely used to determine thickness, microstructure and optical constants. In this work, the effect of F incorporation on optical properties of SnO2 films grown by ultrasonic spray pyrolysis technique (USP) is presented. The reflections, refractive indices and thicknesses of the films were investigated using room temperature spectroscopic ellipsometry. The optical constants and the thicknesses of the films were fitted according to Cauchy–Urbach model, and ellipsometric angle Ψ was used as source point for optical characterizations. Besides, transmittance spectra of the films were taken from UV spectrometer, and the optical method was used to determine the band gaps. Also, band tailing resulting from defects or impurities was investigated. From the results obtained from the optical analyses, the application potential of SnO2:F films for solar cell devices was searched. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Transparent conducting oxide (TCO) thin films such as zinc oxide, indium oxide, tin oxide, indium tin oxide and cadmium oxide have attracted considerable attention because of their low resistivity and high optical transmittance [1]. Due to their optical and electrical properties, TCOs are used for photovoltaic solar cells, phototransistors, liquid crystal displays, optical heaters, gas sensors, transparent electrodes and other optoelectronic devices [2–9]. Among these TCOs, SnO2 films are inexpensive, chemically stable in acidic and basic solutions, thermally stable in oxidizing environments at high temperatures and also mechanically strong, which are important attributes for the fabrication and operation of solar cells [10–12]. SnO2 has a tetragonal structure, similar to the rutile structure with the wide energy gap of Eg = 3.6–4.0 eV and behaves as an n-type semiconductor [13–15]. Antimony (Sb), arsenic (As), phosphorus (P), indium (In), molybdenum (Mo), fluorine (F) and chlorine (Cl) have been selected as doping elements for SnO2 films [16–23]. SnO2 thin films are produced by different techniques such as thermal evaporation, sputtering, spray pyrolysis, sol–gel and hydrothermal [24–33]. Among these, spray pyrolysis is well suited for the preparation of doped tin oxide thin films because of its simple and inexpensive experimental arrangement, ease of adding various doping materials, reproducibility, high growth rate and mass production capability for uniform large area coatings [1,34]. Ultra-
⁎ Corresponding author. E-mail address: [email protected] (F. Atay). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.07.007
sonic spray pyrolysis (USP) technique includes an ultrasonic atomizer which is connected to an oscillator. This ensures the solution to be sprayed with better atomizing using ultrasonic waves, and these results in decreasing of droplet size and production of more homogeneous materials [35,36]. The aim of this work is to investigate the effect of F incorporation on the optical properties of SnO2 films produced by USP technique with spectroscopic ellipsometry (SE) and UV spectrometry. 2. Experimental procedure 2.1. Sample preparation and optical measuremets SnO2 and SnO2:F (at the F percentages of 1, 3 and 5) films were produced onto glass substrates (10 × 10 mm2) by USP technique at a substrate temperature of 350 ± 5 °C. Details of the USP technique were given in our previous works [37–39]. The ultrasonic oscillator frequency was 100 kHz, and the droplet size was 20 μm. The spraying solution contains SnCl2.2H2O (0.025 M) and NH4F (0.1 M) dissolved in deionized water. The glass substrates were heated by an electrical heater, and the substrate temperature was measured using an ironconstantan thermo-couple. The solution flow rate was kept at 5 cm3 min−1 by a flowmeter. Totally 100 cm3 of solution was used to produce all films and sprayed for 20 mins. Nitrogen was used as the carrier gas (0.2 kg cm−2). The produced SnO2:F films were named as S0, S1, S3 and S5 depending on the increasing F incorporation. SE measurements were carried out by a SC620 Spectroscopic Ellipsometer over a spectrum range of 250–2300 nm. But, the investigation of SnO2:F films has been performed in the wavelength
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range of 500–1100 nm where Cauchy-Urbach model has been used to obtain the optical constants. This wavelength range corresponds to a region where all films are transparent or weakly absorbing. So, CauchyUrbach model can be applied to these films in this wavelength range. The thicknesses, reflections and optical constants (refractive index and extinction coefficient, n and k) of the films were obtained by analyzing the measured ellipsometric spectra through the Cauchy-Urbach model. Besides, the optical transmittance spectra of the films were taken from a Perkin Elmer UV/VIS Lambda 2S spectrometer, and the optical energy gaps of the films were calculated using the optical method. Also, band tailing resulting from defects or impurities was investigated.
where n1, n2 and n represent the refractive index of air, substrate and film, respectively. φ and λ represent the incident angle and wavelength of incident light, respectively. d and k the thickness and extinction coefficient of thin film [40]. Ellipsometry does not measure optical constants or film thickness directly; however Ψ and Δ can be represented as mathematical functions relating these material characteristics. Hence, a mathematical analysis called model-dependent analysis must be performed to determine real parameters from the measured ellipsometric data. Numerous material parameters can potentially be determined through
2.2. Spectroscopic ellipsometry technique Ellipsometer is much more of an analytical tool that is used to measure, not only single-layer thickness and refractive index with maximum precision, but also to extract microstructural and compositional information from complicated multi-layered films. One of the most important techniques is SE, which has been found favorably for characterization of thin solid films and bulk materials, especially semiconductors. This technique is a non-destructive, powerful and accurate technique [40,41] and is based on the polarized light [42]. SE is able to measure the thickness and dielectric function of a multi-layer system simultaneously [43–45]. So, it is a powerful technique to explore the band structure of nanometric semiconductor through the determination of the complex dielectric function [42]. SE, which is sensitive to films and surfaces, is widely used to determine optical constants in nearultraviolet, visible and near-infrared range (6–1.5 eV) [45]. This technique is also sensitive to film anisotropy and can be determined if the crystals in the film are randomly oriented or have preferential orientation, in which case the film becomes optically anisotropic [46]. Besides, this technique is very sensitive to surface irregularities such as surface roughness, interdiffusion and interlayer formation in multi-layer thin film systems [47–49]. The complete optical constants (n and k) can be obtained synchronously by this technique without Kramers–Kronig transformation [45,50,51]. This technique is widely used to investigate optical properties and microstructures of ferroelectric films on various substrates [52,53]. SE can be successfully characterize the microstructure and optical properties of nanocrystaline diamond films [54]. Moreover, ellipsometry allows the determination of the optical constants of the organic materials and their knowledge contributes to the understanding and optimization of the organic-based devices [41,55]. Ellipsometry name derives from the fact that when linearly polarized light that is neither perpendicular nor parallel polarized is incident on a medium at oblique angle, the reflected light is elliptically polarized [42,51]. Its polarization state can be described by two ellipsometric parameters: amplitude ratio (tan ψ) and phase shift difference(Δ)of two mutually orthogonal polarized components of the reflected waves (Rs and Rp for p- and s-polarized light) [51]. An ellipsometer yields two measurable quantities, Psi (Ψ) and Delta (Δ), at each wavelength and angle of incidence, which describes the change in the polarization state of light when it is allowed to interact with the sample under investigation [56]. Ψ and Δ parameters are related to the optical and structural properties of the sample through the following expression: ρ=
Rp = tan Ψ expðiΔÞ Rs
ð1Þ
where Rp and Rs are the complex reflection coefficients for the light polarized parallel (p) and perpendicular (s) to the plane of incidence respectively [50,55,57–64]. The fundamental equation for the complex reflectance ratio ρ is also described as follows: ρ = f ðn1 ; n2 ; n; ϕ; d; λ; kÞ
ð2Þ
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Fig. 1. SE spectra of SnO2:F films.
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Table 1 The thicknesses and the best-fit model parameters of SnO2:F films. Material
Code
d (nm)
A
B (nm2)
C (nm4) α
β (nm) MSE
SnO2:F SnO2:F SnO2:F SnO2:F
S0 S1 S3 S5
103.31 116.20 97.57 96.48
1.98 2.06 2.00 1.96
0.026 0.029 0.032 0.030
0.015 0.016 0.017 0.016
0.072 0.023 0.081 0.092
(at 0%) (at 1%) (at 3%) (at 5%)
0.085 0.106 0.098 0.082
0.11 0.29 0.09 0.06
SE analysis, including layer thickness, surface and/or interfacial roughness, optical constants and void fraction, using optical physics (Fresnel reflection coefficients, Snell's law, etc.) [41].
In order to extract useful information about a sample (thicknesses and optical constants of the layers) the experimental data are compared with the data generated using a model which describes the structure of the sample and its optical response [55,57,61]. For a given sample there are three unknown parameters: thickness t, refractive index n and extinction coefficient k, which have to be determined from only two ellipsometric parameters Ψ and Δ. By performing measurements at different wavelengths, more sets of Ψ and Δ data are available, and the problem can be solved numerically. The problem can be further simplified by analyzing the data in the spectral region where the film is transparent (k ≅ 0). In this spectral region, the optical response of the transparent films can be described by a Cauchy– Urbach dispersion relation for the refractive index and extinction coefficient [51,55,65], B C + 4 λ2 λ
ð3Þ
1 1 − κðλÞ = α exp β 12; 400 λ γ
ð4Þ
nðλÞ = A +
where A, B, C, α, β and γ are model parameters. 3. Results SE spectra of SnO2:F films are shown in Fig. 1. The optical response of the transparent or weakly absorbing SnO2:F films can be described by a Cauchy–Urbach dispersion relation. So, the experimental data were analyzed by using the Cauchy–Urbach model, and an appropriate fit is found between the model and experimental data as shown in Fig. 1. Fitting the experimental ellipsometric spectra of Ψ allowed the determination of the film thickness (d), spectra of refractive index (n) and extinction coefficient (k) of all films. The thicknesses determined by fitting the experimental ellipsometric spectra and the best-fit model parameters of SnO2:F films are listed in Table 1. Reflection (R) spectra of SnO2:F films are shown in Fig. 2. It was determined that the average reflection value of S0 films is about 23%, and this value remarkably decreases with the F incorporation. Refractive index (n) spectra of SnO2:F films are shown in Fig. 3. All films showed similar behavior in refractive index spectra. There is a little increase in refractive index value for S1 and S3 films. Refractive index values of the samples are nearly constant (~ 2.0–2.1) at long wavelengths. Fig. 4 shows the extinction coefficients (k) of SnO2:F films which are derived from model fitting the experimental spectroscopic ellipsometric data.
Fig. 2. Reflection (R) spectra of SnO2:F films.
Fig. 3. Refractive index (n) spectra of SnO2:F films.
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Fig. 4. Extinction coefficient (k) spectra of SnO2:F films.
The transmittance spectra of SnO2:F films taken by a UV/VIS spectrometer are shown in Fig. 5. It was determined that S0 films have an average T value of ~ 75% in the visible region. For S1 and S3 films, there is a small increase in T values depending on the F incorporation, but the T values of S5 films decreased in the visible region. Optical method has been used to determine the band gap values of SnO2:F films. (αhν)2 ~ hν variations of the films are shown in Fig. 6. It was determined that all films have direct band gap structure, and this property is suitable for solar cell applications. The band gap values have been calculated by extrapolating the linear portions to (αhν)2 = 0. The band gap values are given in Table 2. It is a well-known fact that semiconductors represent band tails due to the deformation and high carrier concentration. Defects in structure lead to local electric fields that affect the band tails, and band tailing is a result of impurity, disorder or any other defects. The absorption coefficient α(ν) in the low-energy range follows the wellknown exponential law, that is, the Urbach tail expressed by, αðνÞ = α0 expðhν = E0 Þ
ð5Þ
where α0 is a constant, and E0 denotes an energy which is constant or weakly dependent on temperature and is often interpreted as the width of the tail of localized states in the band gap [66–68]. E0 values were estimated from the slopes of the linear relationship lnα against hν using Eq. (5) just below the band edge. The calculated E0 values are given in Table 2. 4. Discussion It was determined that there are some deviations on fitted Ψ values (Fig. 1). Especially for S1 films, when the wavelength of incident light is higher than 600 nm, a visible deviation between the fitting and the experimental results was observed. We think that the deviations of Ψ values result from USP technique which is used to produce the SnO2:F films (because films produced by USP have not absolutely uniform and homogeneous surfaces) and low absorption in the given wavelength, (iii) roughness, grain boundaries and morphology of the films. Moreover, the rough surface and backsides of the films may affect the reflection of light. Besides, the grain boundaries and morphologies would depolarize the incident polarized light, resulting deviated experimental ellipsometric parameters and deteriorating the SE fitting. Also, backside reflection of transparent glass substrates may also affect the experimental SE data. We think that decrease of reflectance results from the surface roughness, grain boundaries and morphology of the F-doped films as
Fig. 5. Transmittance spectra of SnO2:F films.
these properties affect the intensity of the reflected light. Because of this information, we can say that the sample S0, which has the highest average reflection value, has a uniform surface structure and lower roughness as compared with others. It was determined that all films have a similar k variation belonging to wavelength of polarized light, and a similar tendency was observed according the curves of refractive index. The extinction coefficient of a material is directly related to its absorption characteristic. As shown in Fig. 4, the k values are very small at long wavelengths where all films are nearly transparent.
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F. Atay et al. / Journal of Non-Crystalline Solids 356 (2010) 2192–2197 Table 2 The band gap (Eg) and Urbach energy (E0) values of SnO2:F films. Material
Eg (eV)
E0 (meV)
S0 S1 S3 S5
3.95 3.94 3.95 3.95
270 275 270 241
5. Conclusion In this work, SnO2 and SnO2:F (at the percentages of 1, 3 and 5) films were produced by USP technique, which is a simple and economical technique and useful for large area thin film deposition with low cost. Their optical properties were studied by a spectroscopic ellipsometer and UV/VIS spectrometer. The thicknesses, refractive indices and extinction coefficients of the films were obtained by fitting the experimental spectroscopic data (Ψ) by using Cauchy–Urbach model. The numerical values of reflection remarkably decreased depending on the F incorporation, so we think that this could mean an improvement in solar cell efficiency due to a higher number of photons crossing F doped SnO2. All films have showed similar n and k variations with small differences for samples S1 and S3. From the analysis of SE results, it was concluded that the reflection and optical constants (n and k) highly depend on the production technique, surface roughness, grain boundaries and morphologies of the produced films, and these properties changed with F doping. It was determined from the transmittance spectra taken by a UV/VIS spectrometer that undoped SnO2 films have an average T value of 75% in the visible region, and there is a small increase with F doping (1% and 3%). The band gaps of the films were calculated by the optical method. To evaluate the near band gap edge characteristics of the films, we can interpret the absorption behavior by the Urbach rule. With respect to this aim, we have calculated the Urbach energy E0, which is interpreted as the width of the tails of localized states in the band gap. S5 films were found to have the lowest E0 value among others. This probably means there is lower disorder in SnO2 films when doped with F at 5%. Acknowledgements This work was supported by Eskisehir Osmangazi University Scientific Research Projects Committee under the project number 200719011. References
Fig. 6. (αhν)2 ~ hν variations of SnO2:F films.
The regions with a sharp decrease in T values indicate the fundamental absorption regions of the films. These regions correspond to nearly same wavelength range for all films, so we can say that there is not a dramatic effect of the F incorporation on the band gap of the films. It was seen from Table 2 that the band gap value of S0 films is not remarkably changed with F incorporation, and there is not a considerable effect of the F incorporation on the band gap of the films. The estimated direct band gap energies of the films were found to agree with the previously reported values [13–15].
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