Abstract

Indium tin oxide (ITO) films with various thicknesses are deposited on glass substrates using a DC magnetron sputtering technique. The microstructure and chemical composition of the sputtered samples are examined by scanning electron microscopy (SEM), X-Ray Diffraction (XRD) and Energy Dispersive X-Ray Spectroscopy (EDS). Two-layer and three-layer optical models of the sputtered ITO films are constructed for fitting the experimental results of the spectroscopic ellipsometry. The results obtained from the two models for the resistivity, carrier density and carrier mobility are compared with those obtained via Hall effect measurements. Finally, the three-layer optical model is used to evaluate the refractive index and extinction coefficient spectra of the various samples. In general, the present results show that the three-layer model, in which the transition layer between the ITO film and the glass substrate is included, provides a better approximation of the SE results than the two-layer model. However, both models yield a reasonable estimate of the Hall resistivity. The results obtained using the three-layer model show that the carrier density and carrier mobility in the bulk layer are lower and higher, respectively, than those in the transition layer. In addition, it is shown that the refractive index of the bulk layer is lower than that of the transition layer in the UV and visible spectrum. Moreover, the extinction coefficient of the transition layer is significantly higher than that of the bulk layer in the near IR-region.

© 2013 Optical Society of America

1. Introduction

Indium-tin-oxide thin films have excellent conducting properties and are transparent in the visible spectrum. As a result, they are widely used throughout the optoelectronics industry for such devices as flat-panel displays, touch panels, and so on [13]. Various methods are available for coating ITO thin films on substrates, including chemical vapor deposition [1], pulsed laser deposition [4], sol-gel [2], and magnetron sputtering [5]. Of these various techniques, DC magnetron sputtering is commonly preferred for mass production due to its high reliability in producing ITO thin films with excellent electrical and optical properties [5].

Hoheisel [6] and Rogozin [7] reported that ITO thin films are characterized by a columnar structure with a clear inter-columnar boundary. The non-uniform structure is considered to correlative with film thickness, composition, and deposition conditions [4, 6]. Dudek [8] showed that the resulting inhomogeneous composition of the ITO film causes the optical constant to vary throughout the film thickness. Jung [5] demonstrated that the optical constant depends not only on the film thickness, but also on the crystallite orientation. Thus, effective methods are required for evaluating the optical properties of ITO thin films deposited in practical sputtering applications. Many researchers have demonstrated the feasibility of using spectroscopic ellipsometry (SE) to determine the thickness, dielectric function, surface roughness, refractive index and extinction coefficient of thin optical films [5, 911]. Furthermore, various dispersion models have been proposed for estimating the dielectric function of ITO films, including the Cauchy model [11], the Drude-Lorentz model [9, 10] and the Tauc-Lorentz model [12]. Among these models, the Drude-Lorenz model provides a particularly good estimate of the electrical resistivity of ITO thin films [10]. However, while the electrical and inhomogeneous optical properties of ITO thin films grown on silicon substrates are relatively well understood [5, 9, 10], those of ITO films deposited on glass substrates are less clear.

Accordingly, the present study investigates the inhomogeneous electrical and optical properties of ITO thin films deposited on glass substrates using spectroscopic ellipsometry measurement. In the proposed approach, two-layer and three-layer optical models of the ITO thin film are constructed by tuning the model parameters (e.g., the surface roughness, film thickness, and dielectric constant) such that the estimated values of the SE parameters (i.e., psi and delta) approach the experimental values. The results obtained from the two models for the electrical properties of ITO thin films with various thicknesses (i.e., the resistivity, carrier density and carrier mobility) are then compared with those obtained from experimental Hall effect measurements. Finally, the three-layer model is used to examine the optical properties (i.e., refractive index and extinction coefficient) of the bulk layer and transition layer within the ITO film. Overall, the results confirm the effectiveness of the three-layer model in predicting the electrical and optical properties of ITO thin films deposited on glass substrates.

2. Experimental details and optical models

2.1. Sample preparation and characterization

ITO thin films with thicknesses of approximately 145 nm, 180 nm and 260 nm were coated on a 370 mm x 470 mm Corning glass plates (Taiwan Foresight Corp.) using a DC magnetron sputtering technique. The sputtering process was performed at a temperature of 295°C using an ITO target with 10 wt.% SnO2. Pure argon (99.99%) with flow rate of 150 sccm was used as the sputtering gas. The chamber had a working pressure of 3 × 10−3 torr. The sputtering power of DC power supplier was 8 kW and the distance between the target and the substrate was 70 mm. Following the deposition process, the glass plates were sliced into small slides with dimensions of 20 mm x 20 mm and, for each film thickness, four slides were chosen at random for characterization purposes. The selected slides were cleaned in chloroform and then in acetone. Finally, the slides were cleaned ultrasonically in distilled water to eliminate any residual solvent traces and were then dried in an argon gas flow for 3 min.

The thickness of the various ITO thin films was measured using a field emission scanning electron microscope (FE-SEM, Model S-4700, Hitachi, Japan). The chemical composition of the ITO films was investigated using an Energy Dispersive X-ray Spectroscopy (EDS) equipped on FE-SEM. The microstructures of the various films were examined using an X-ray Diffraction (XRD) system (Model ATX-E, Rigaku) with Cu Kα radiation and a standard Bragg Brentano geometry (θ-2θ). The electrical properties of the ITO films (i.e., the resistivity (ρ), carrier density (N) and carrier mobility (μ) were determined using a Hall effect measurement system (Model HMS-3000, Ecopia, South Korea) operated with a magnetic flux of 0.51 T and a Van der Pauw configuration. Finally, the optical properties of the ITO film were investigated using a Rotating Compensator Ellipsometer (VASE M2000U, J.A. Woollam). An ellipsometry measurement provides the ratio of the polarization coefficients of the reflected and incident light. The ellipsometry equation is defined as ρ = Rp/Rs = tanΨ∙exp(iΔ), where Rp and Rs are the complex Fresnel reflection coefficient regarding to the parallel and perpendicular components of the reflected light; Ψ and Δ are the ellipsometry parameters that determine the ratio of amplitude and differential changes in phase, respectively [13]. Specifically, the SE parameters Ψ and Δ were obtained at two angles of incidence (60° and 65°) over the wavelength range of 260~1000 nm (4.77~1.24eV) in incremental steps of 5 nm.

2.2. Optical models and calculation process

In this study, the electrical and optical properties of three ITO thin films with different thicknesses were estimated using two multi-layer optical models, namely a two-layer model comprising a surface roughness layer and a bulk ITO layer, and a three-layer model comprising a surface roughness layer, a bulk ITO layer and a transition layer. For each model and each film thickness, the surface roughness and thickness of the various layers were obtained by fitting the estimated values of Ψ and Δ to the experimental SE values using WVASE32 software (Woollam Corp). The two-layer model was performed prior to the three-layer model for confirming the inhomogeneous optical constant of ITO film. In performing the fitting process, the optical properties of the bulk ITO layer for both models were assumed to have linear grade optical constant (the linear grade mode in WVASE32 software) in order to account for the inhomogeneous microstructure of each sample. However, for the transition layer analysis of the three-layer model, the linear grade property is not considered because of its small thickness. In fact, the two-layer and three-layer models without consideration of grade properties in bulk layers have been studied in this work; however they were not focused due to the relatively poor fitting results. Thus, the purpose of the linear grade bulk layer (followed by a roughness layer) connecting with a non-grade transition layer in the three-layer model is due to the consideration of non-fully linear inhomogeneous optical and electrical properties through the ITO film. Subsequently, the surface roughness layer was assumed to comprise a mixture of voids and ITO material. Thus, the complex effective dielectric function of the surface roughness layer was calculated using the Bruggeman Effective Medium Approximation (BEMA) given the assumption of 50% voids and 50% ITO [13].

The dielectric function of the bulk and transition layers of the ITO films was calculated using the Drude-Lorentz model. This model can be expressed in either a frequency form (ω) or an energy form (E), i.e., E = ħω, where ħ is the Plank constant. In spectroscopic ellipsometry, the energy form is generally preferred [8, 13]. The frequency and energy forms of the model are given respectively as [13]

ε(ω)=εωp2ω2+iωτω+j=12fjωj2ω0j2ω2+iγjω
or
ε(E)=εADE2+iBDE+j=12ALE0j2E2+iΓLE
where ε is the high-frequency dielectric constant, and ωp and ωτ are the plasma frequency and damping frequency, respectively. Furthermore, ω0j, ƒj and γj are the resonance frequency, strength factor and damping constant for the jth oscillator, respectively. The Lorentz model, i.e., the third term in the complex dielectric function (Eq. (1a)) describes the inter-band transition of electron which contributes to the light absorption in the energy range of 1.0~4.77 eV. Meanwhile, the Drude model, i.e., the second term in the complex dielectric function describes the free-carrier scattering effect in the near-IR energy spectrum caused by the high density of free electrons in the ITO film [1, 4].

Comparing Eqs. (1a) and (1b), it is seen that the amplitude of the Drude model AD is related to the plasma frequency by AD = ħ2ωp2, while the damping parameter BD is related to the damping frequency by BD = ħωτ. The plasma frequency is related to the carrier density N and effective mass of a free carrier me* by the relation ωp2 = (Ne2)/(εε0me*) where e is the charge of each electron and ε0 is the permittivity of ITO in free space [1]. The damping frequency ωτ of the Drude model is inversely proportional to the carrier mobility and is given by ωτ = e/(μme*) [1, 2]. The electrical resistivity (ρ) varies with the free carrier density (N) and mobility (μ) in accordance with ρ = 1/(Nμe) [1]. In practice, the electrical resistivity is proportional to the ratio of the damping frequency to the plasma frequency (i.e., ρ≈ωτp2). Thus, adopting the energy form of the Drude-Lorentz model (Eq. (1b)), the resistivity of the ITO film can be expressed as [10]

ρD=BDADε0
where AD and BD are the amplitude parameter and damping parameter, respectively, in the Drude model. Connecting to the amplitude parameter AD of Drude model and the plasma frequency ωp, the carrier density can be a function of effective mass and given as
N=(AD)(me*ε0εe2)
where me* is the effective mass of a free carrier. Meanwhile, linking to the damping parameter BD and the damping frequency ωτ, the carrier mobility is given as

μ=eBDme*

Various models have been proposed for determining the effective mass of a free carrier me* in ITO thin films, including the constant value model proposed in [1, 9, 14], the Hall carrier density dependent model proposed by Fujiwara [12] and the lattice orientation and composition dependent model proposed by Brewer [15].

3. Results and discussion

3.1. Composition and microstructure

Many studies have shown that the non-uniform composition and crystalline structure of ITO thin films have a significant effect on the optical properties [5, 9, 10]. The cross-sectional SEM images presented in Fig. 1(a) show that the three samples have thicknesses of approximately 145 nm (Sample A), 180 nm (Sample B) and 260 nm (Sample C), respectively. The EDS analysis results presented in the insets of Fig. 1(a) show that for all three samples, the tin content of the ITO film increases from approximately 6 wt.% near the film-substrate interface to around 8 wt.% near the film surface. The XRD analysis results presented in Fig. 1(b) show that Samples A and C have a predominantly (222) crystallite orientation. By contrast, the peaks corresponding to the (222) and (400) planes in the spectrum of Sample B have an approximately constant intensity. Literature has reported that high fraction of (400) crystalline in ITO films would affect electrical properties [14]. According to Brewer [15], the effective mass of the electron carriers in ITO thin films depends on the crystallite orientation. Thus, the results presented in Fig. 1(b) suggest that the electrical properties of the present ITO films depend strongly on the films thickness.

 

Fig. 1 (a) Cross-sectional SEM images of Samples A, B and C. (b) XRD analysis results for Samples A, B and C. Note that the insets in Fig. 1(a) show the EDS analysis results for the corresponding ITO thin film.

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3.2. Ellipsometry measurement results

Figures 2(a) and 2(b) compare the experimental and calculated values of the SE parameters Ψ and Δ for the two-layer and three-layer optical models, respectively. Table 1 shows the Mean Square Error (MSE) values of the fitting results obtained using the two models for each of the three samples. It is seen that the MSE values for the two-layer model are apparently higher than those for the three-layer model. Thus, it is inferred that while the two-layer model has the advantage of computational simplicity, the three-layer model is more precise on estimation of dielectric function of thin film. Table 1 also shows the results obtained by the two models for the surface roughness and layer thickness of each sample. It is observed that both models yield a similar result for the surface roughness and total ITO film thickness. In addition, it is noted that the predicted results for the total ITO film thickness are consistent with the SEM measurement results. Observing the results obtained using the three-layer model, it is seen that the transition layers in Samples A and B account for just 3% (approximately) of the total ITO film thickness. However, in Sample C, the transition layer accounts for almost 10% of the total film thickness. Thus, it is inferred that properties of the transition layer have more influence on Sample C than that of the other two samples.

 

Fig. 2 Optical models and corresponding SE fitting results for: (a) two-layer optical model and (b) three-layer optical model for Sample C.

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Tables Icon

Table 1. Fitting results obtained for three samples using two-layer and three-layer optical models, in which MSE and Ra represent mean square error and surface roughness, respectively.

3.3. Inhomogeneous resistivity

For the three-layer optical model, the total resistance R of the ITO thin film can be calculated as 1/R = 1/RL1 + 1/RL2, where RL1 and RL2 are the resistance values of the transition layer and bulk layer, respectively. The resistivity of electrically conductive thin films is related to the resistance as R = ρ/d, where ρ and d are the resistivity and thickness of the thin film, respectively. Thus, for the three-layer optical model, the total resistivity ρ of the ITO film can be calculated as ρ = [(k + 1)ρ1ρ2]∕(ρ1 + kρ2), where ρ1 and ρ2 are the estimated resistivities of the transition layer and bulk layer, respectively, as calculated using Eq. (2), and k = d1/d2, where d1 and d2 are the thicknesses of the two layers.

Figure 3(a) compares the experimental results for the resistivity of the three samples as determined via Hall Effect measurements (ρH) with the estimated values obtained using the two-layer optical model (ρ*S) and three-layer optical model (ρ*D) based on the Drude resistivity equation (i.e., Eq. (2)). It is seen that both models yield a reasonable general approximation of the ITO film resistivity. However, both models overestimate the resistivity given a small film thickness, but underestimate the resistivity given a large film thickness. In practice, the difference between the Hall measurement results for the resistivity and the estimated results can be attributed to various factors, including the surface contact resistivity [16, 17], grain boundary scattering effects, intrinsic defect scattering and the inhomogeneous structure of the ITO film [18, 19]. As stated above, both models enable a reasonable estimate of the ITO resistivity to be obtained. However, as shown in the following, only the three-layer model provides the means to determine the separate resistivities of the bulk and transition layers, respectively.

 

Fig. 3 (a) Comparison of Hall effect measurement of sample resistivity (ρH) with estimated results obtained using two-layer model (ρ*S) and three-layer model (ρ*D). (b) Comparison of lump sum resistivity (ρ*D) with resistivities of bulk layer (ρ*D2) and transition layer (ρ*D1).

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Figure 3(b) compares the results obtained by the three-layer model for the lump sum resistivity of the ITO thin film (ρ*D) and the separate resistivities of the bulk layer (ρ*D2) and transition layer (ρ*D1), respectively. It is seen that for all three samples, the resistivity of the transition layer is higher than that of the bulk layer. It is noted that this result is consistent with the experimental results presented by Shigesato et al. [20] for their DC magnetron sputtered ITO films. In addition, it is observed that the Drude resistivity of the bulk layer is close to that obtained using the lump sum model in all three samples. According to Fig. 1(a), the inhomogeneous resistivity is considered as a contribution of the composition changing with depth of ITO film. Finally, it is seen that the difference in resistivity of the bulk and transition layers is relatively small for Sample B. According to Qiao et al. [14], the resistivity in ITO films can vary with the peak intensity ratio of (222)/(400) depending on film thickness. As evidenced by the XRD spectra presented in Fig. 1(b), the homogeneous resistivity of Sample B is contributed by the relatively high (222)/(400) ratio.

3.4. Inhomogeneous carrier density and carrier mobility

Given knowledge of the effective mass of the free electrons in the ITO thin films, the carrier density and carrier mobility can be calculated using Eqs. (3) and (4), respectively. The literature contains three models for estimating the effective mass, namely the constant model m*C [1, 14], the Fujiwara model m*F [5] and the Brewer model m*B [15]. In the constant model, the effective mass is simply assigned a fixed value in the range of 0.25 ~0.4 me, where me is the electron mass. Meanwhile, in the Fujiwara model, the effective mass is determined from the corresponding Hall density measurement (NH) in accordance with the function m*F = (0.297 + 0.011 x 10−20 x NH) me. Finally, in the Brewer model, the effective mass varies depending on the composition and orientation of the ITO crystallite structure and the tin content. Table 2 summarizes the effective mass values of the bulk and transition layers, respectively, obtained using the three different models for each of the three samples. Note that in computing the results, m*C is simply assigned a value of 0.35 for both layers, while the values of m*B for the bulk layer and transition layer are specified as 0.45me and 0.49me, respectively, in accordance with the XRD and EDS analysis results. It is noted that only the Brewer model provides the means to assign different values of the effective mass to the free electrons in the bulk and transition layers, respectively. Thus, of the three models, the Brewer model provides the most suitable method for computing the carrier density and carrier mobility using the proposed three-layer optical model.

Tables Icon

Table 2. Effective mass values for free electrons in bulk and transition layers as determined using constant model (m*C), Fujiwara model (m*F) and Brewer model (m*B).

Figures 4(a) and 4(b) compare the estimated values of the transition layer and bulk layer carrier density, respectively, with the experimental values for each of the three samples. It is seen in Fig. 4(a) that the Drude density calculated for the transition layer using the three effective mass models is generally higher than the experimental Hall density. However, in the bulk layer, the Drude density calculated using the Brewer effective mass model is higher than the experimental Hall density, while the Drude densities calculated using the constant effective mass model and Fujiwara model, respectively, are lower than the experimental value (see Fig. 4(b)). Comparing the two figures, it is observed that the carrier density of the transition layer is greater than that of the bulk layer for Samples A and B. However, for Sample C (the thickest sample), the carrier density of the transition layer is close to or slightly lower than the bulk layer (depending on the particular effective mass model used). As shown in Table 1, the transition layer in Sample C is far thicker than that in Sample A or B. In the present study, a thicker ITO film was produced by means of a longer deposition time. The results presented in Fig. 4 for Sample C suggest that the longer deposition time prompts a greater diffusion of the free electrons away from the substrate and therefore reduces the carrier density in the transition layer region of the film. It is inferred that in Sample C, the electrical properties of the bulk layer provide a reduced contribution toward the overall electrical properties of the film due to the relatively larger thickness of the transition layer. Comparing Figs. 4(a) and 4(b), it is seen that the Drude density of the bulk layer is in better agreement with the Hall density than that of the transition layer for all three samples. This result is reasonable since the value of NH determined by Hall measurement represents the average value of the carrier density over the full ITO film thickness. The results presented in Table 1 show that the bulk layer thickness is significantly higher than the transition layer thickness in all of the samples. As a result, the carrier densities of the bulk layer are more representative of those of the full ITO film than that of the transition layer.

 

Fig. 4 Comparison of estimated results and experimental results for carrier density (N) in: (a) transition layer and (b) bulk layer of ITO films. Note that NH represents the experimental Hall measurement value, while N*F, N*C and N*B represent the carrier densities estimated by the Fujiwara model, constant model and Brewer model, respectively. Note also that subscripts 1 and 2 refer to the transition layer and bulk layer, respectively.

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It is seen in Fig. 4(b) that the Drude density of the bulk layer obtained using the Fujiwara effective mass model is very close to the Hall density for Samples A and B. In these particular samples, the transition layer accounts for just 3% of the total film thickness. In other words, the electrical properties of the films are dominated by those of the bulk layer. In the Fujiwara model, the Drude density is based on the value of NH determined by Hall measurement. Since the value of NH is determined principally by the carrier density of the bulk layer in Samples A and B, a good agreement is to be expected between the results estimated using m*F and those determined experimentally. For Sample C, the Brewer model provides the best estimate of the experimental Hall density. As shown in Table 2, the Brewer model is the only model capable of distinguishing between the effective mass of the free electrons in the bulk layer and transition layer, respectively. Thus, it is reasonable to expect that the Brewer model provides a more accurate estimation of the carrier density in the two layers.

Figures 5(a) and 5(b) compare the estimated values of the carrier mobility with the experimental values obtained via Hall measurement in the transition layer and bulk layer, respectively. It is observed that for all three samples, the carrier mobility in the transition layer is much lower than that in the bulk layer. It is noted that this finding is consistent with the results reported by Shigesato et al. [20] for early-stage sputtered ITO films. Furthermore, the present results are also consistent with the findings of [1, 5, 10, 21] that the microstructure is complex and the crystal size small at the beginning of the deposition process, and thus the carrier mobility is suppressed as a result of impurity scattering and grain boundary scattering effects. Moreover, as discussed above in relation to Fig. 4, the carrier density in the transition layer is generally higher than that in the bulk layer. As a result, the scattering effect is increased, and thus the carrier mobility is reduced [19].

 

Fig. 5 Comparison of estimated results and experimental results for carrier mobility (μ) in: (a) transition layer and (b) bulk layer of ITO films. Note that μH represents the experimental Hall measurement value, while μ*C, μ*F and μ*B represent the carrier mobilities estimated by the constant model, Fujiwara model and Brewer model, respectively. Note also that subscripts 1 and 2 refer to the transition layer and bulk layer, respectively.

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As for the case of the carrier density, the results presented in Fig. 5(b) show that the Fujiwara model provides the best estimate of the carrier mobility in the bulk layer for the samples with a small-to-medium thickness (i.e., Sample A (~145 nm) and Sample B (~180 nm)), whereas the Brewer model yields the best fit for the sample with a large thickness (Sample C (~260 nm)). In addition, it is observed that the constant effective mass model generally overestimates the Drude mobility.

3.5. Inhomogeneous optical functions

Figure 6(a) shows that the refractive index spectrum of the bulk layer is very similar in all three samples. Moreover, it is observed that the refractive index of the bulk layer is lower than that of the transition layer in the UV and visible spectrum. The higher refractive index of the transition layer is due to a greater density of ITO material in this particular region of the film [22]. It is noted that in the visible range, the refractive index spectra of the bulk and transition layers, respectively, are very similar in Sample C. Thus, it is inferred that this particular sample has a relatively homogeneous micro structure.

 

Fig. 6 (a) Refractive index spectra and (b) extinction coefficient spectra of bulk layer and transition layer in Samples A, B and C. Note that L1 denotes the transition layer and L2 denotes the bulk layer.

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Figure 6(b) shows that for all three samples, the extinction coefficient of the bulk layer has a very high value in the UV region, but reduces sharply in the visible range, before increasing slightly once again in the near-IR range. It is noted that this tendency is similar to that reported in [23] for ITO films grown on crystalline silicon substrates. The extinction coefficient of the transition layer is almost twice that of the bulk layer in the near-IR range. This finding is consistent with the assertion in [4, 22] that in the near-IR range, the incident light interacts with the free electrons as a result of the high density of free electrons within the film, thereby changing its polarization state and affecting the optical function accordingly. The absorption coefficient of a material is computed as α = 4πk/λ, where k is the extinction coefficient and λ is the wavelength of the incident light. Then, the results shown in Fig. 6 suggest that the light absorption in the ITO film is dominated by the bulk layer in the UV and near-UV range, but by the transition layer in the near-IR range.

4. Conclusions

This study has investigated the inhomogeneous electrical and optical properties of ITO thin films deposited on glass substrates using spectroscopic ellipsometry with multi-layer optical models. Two optical models have been considered, namely a two-layer model comprising a surface roughness layer and a bulk layer, and a three-layer model comprising a surface roughness layer, a bulk layer and a transition layer. For both models, the resistivity has been computed using the Drude-Lorentz dielectric function model and compared with the Hall resistivity for samples with three different thicknesses. In addition, the carrier density and carrier mobility have been estimated using the three-layer model based on three different effective mass models, namely the constant model m*C, the Fujiwara model m*F and the Brewer model m*B. Finally, the three-layer model has been used to evaluate the refractive index and extinction coefficient of the various samples.

In general, the results have shown that both optical models provide a reasonable approximation of the electrical resistivity of ITO thin films. However, only the three-layer model provides the ability to examine the difference in the resistivity, carrier density and carrier mobility in the bulk layer and transition layer, respectively. In other words, the three-layer model provides a more suitable solution for exploring the initial growth conditions during the sputtering process. The results obtained using the three-layer optical models have shown that the transition layer accounts for around 3% of the total film thickness given an ITO film thickness of around 145 nm or 180 nm. However, for an ITO film with a thickness of around 260 nm, the transition layer accounts for almost 10% of the total film thickness. The resistivity of the bulk layer is smaller than that of the transition layer for all values of the ITO film thickness and approaches that of the Hall resistivity. The effective mass model proposed by Fujiwara [5] yields the best estimate of the carrier density and carrier mobility for ITO thin films in which the electrical properties are dominated by the bulk layer (i.e., ITO films with a thickness of around 145 nm or 180 nm). However, for ITO films in which the transition layer plays a significant role in determining the overall electrical properties of the film (i.e., ITO films with a thickness of around 260 nm), the effective mass model proposed by Brewer provides a better estimate of the carrier density and carrier mobility. The carrier density in the bulk layer is slightly lower than that in the transition layer. Conversely, the carrier mobility in the bulk layer is much higher than that in the transition layer.

Irrespective of the ITO film thickness, the refractive index of the bulk layer is lower than that of the transition layer in the UV and visible spectrum. The extinction coefficient of the bulk layer is higher than that of the transition layer in the UV region. However, in the near-IR range, the extinction coefficient of the transition layer is approximately twice that of the bulk layer. Thus, it is inferred that in the UV and near-UV range, the light absorption properties of an ITO thin film is dominated by the bulk layer, whereas in the near-IR range, the absorption properties is dominated by the transition layer.

Acknowledgments

The partial support provided to this study by the National Science Council of Taiwan under Grant NSC 101-2221-E-006-028-MY3 is greatly appreciated. The authors also wish to thank Dr. Kemo Lin of Southern Taiwan University of Science and Technology for his assistance in characterizing the ITO samples used in the present study.

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14. Z. Qiao, R. Latz, and D. Mergal, “Thickness dependence of In2O3: Sn film growth,” Thin Solid Films 446(1-2), 250–258 (2004). [CrossRef]  

15. S. H. Brewer and S. Franzen, “Calculation of the electronic and optical properties of indium tin oxide by density functional theory,” Chem. Phys. 300(1-3), 285–293 (2004). [CrossRef]  

16. H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001). [CrossRef]  

17. S. Z. Tehrani, W. L. Lim, and L. Lee, “Correction factors for films resistivity measurement,” Measurement 45(3), 219–225 (2012). [CrossRef]  

18. R. Clanget, “Ionized impurity scattering in degenerate In2O3,” Appl. Phys. (Berl.) 2(5), 247–256 (1973). [CrossRef]  

19. K. Ellmer and R. Mientus, “Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide,” Thin Solid Films 516(14), 4620–4627 (2008). [CrossRef]  

20. Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000). [CrossRef]  

21. E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007). [CrossRef]  

22. C. C. Lee, J. C. Hsu, and D. H. Wong, “The characteristics of some metallic oxides prepared in high vacuum by ion beam sputtering,” Appl. Surf. Sci. 171(1-2), 151–156 (2001). [CrossRef]  

23. M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002). [CrossRef]  

References

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  1. I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: Basic optical properties and application to energy-efficient windows,” J. Appl. Phys. 60(11), R123–R160 (1986).
    [Crossref]
  2. R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: Electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998).
    [Crossref]
  3. A. N. Banerjee and K. K. Chattopadhyay, “Recent developments in the emerging field of crystalline p-type transparent conducting oxide thin films,” Prog. Cryst. Growth Ch. 50(1-3), 52–105 (2005).
    [Crossref]
  4. H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
    [Crossref]
  5. Y. S. Jung, “Spectroscopic ellipsometry studies on the optical constants of indium tin oxide films deposited under various sputtering conditions,” Thin Solid Films 467(1-2), 36–42 (2004).
    [Crossref]
  6. M. Hoheisel, A. Mitwalsky, and C. Mrotzek, “Microsturcture and Etching Properties of Sputtered Indium-Tin Oxide (ITO),” Phys. Status Solidi 123(2), 461–472 (1991).
    [Crossref]
  7. A. I. Rogozin, M. V. Vinnichenko, A. Kolitsch, and W. Moller, “Effect of deposition parameters on properties of ITO films prepared by reactive middle frequency pulsed dual magnetron sputtering,” J. Vac. Sci. Technol. 22(2), 349–355 (2004).
    [Crossref]
  8. M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
    [Crossref]
  9. M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
    [Crossref]
  10. S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
    [Crossref]
  11. R. A. Synowicki, “Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants,” Thin Solid Films 313–314, 394–397 (1998).
    [Crossref]
  12. Y. H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3: Sn studied by spectroscopic ellipsometry: Analysis of free-carrier and band-edge absorption,” Phys. Rev. B 71(7), 075109 (2005).
    [Crossref]
  13. H. Fujiwara, Spectroscopic Ellipsometry - Principle and Application (John Wiley and Sons, 2006), Chap. 4.
  14. Z. Qiao, R. Latz, and D. Mergal, “Thickness dependence of In2O3: Sn film growth,” Thin Solid Films 446(1-2), 250–258 (2004).
    [Crossref]
  15. S. H. Brewer and S. Franzen, “Calculation of the electronic and optical properties of indium tin oxide by density functional theory,” Chem. Phys. 300(1-3), 285–293 (2004).
    [Crossref]
  16. H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
    [Crossref]
  17. S. Z. Tehrani, W. L. Lim, and L. Lee, “Correction factors for films resistivity measurement,” Measurement 45(3), 219–225 (2012).
    [Crossref]
  18. R. Clanget, “Ionized impurity scattering in degenerate In2O3,” Appl. Phys. (Berl.) 2(5), 247–256 (1973).
    [Crossref]
  19. K. Ellmer and R. Mientus, “Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide,” Thin Solid Films 516(14), 4620–4627 (2008).
    [Crossref]
  20. Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000).
    [Crossref]
  21. E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
    [Crossref]
  22. C. C. Lee, J. C. Hsu, and D. H. Wong, “The characteristics of some metallic oxides prepared in high vacuum by ion beam sputtering,” Appl. Surf. Sci. 171(1-2), 151–156 (2001).
    [Crossref]
  23. M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
    [Crossref]

2012 (1)

S. Z. Tehrani, W. L. Lim, and L. Lee, “Correction factors for films resistivity measurement,” Measurement 45(3), 219–225 (2012).
[Crossref]

2009 (2)

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
[Crossref]

2008 (1)

K. Ellmer and R. Mientus, “Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide,” Thin Solid Films 516(14), 4620–4627 (2008).
[Crossref]

2007 (1)

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

2005 (2)

A. N. Banerjee and K. K. Chattopadhyay, “Recent developments in the emerging field of crystalline p-type transparent conducting oxide thin films,” Prog. Cryst. Growth Ch. 50(1-3), 52–105 (2005).
[Crossref]

Y. H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3: Sn studied by spectroscopic ellipsometry: Analysis of free-carrier and band-edge absorption,” Phys. Rev. B 71(7), 075109 (2005).
[Crossref]

2004 (4)

Z. Qiao, R. Latz, and D. Mergal, “Thickness dependence of In2O3: Sn film growth,” Thin Solid Films 446(1-2), 250–258 (2004).
[Crossref]

S. H. Brewer and S. Franzen, “Calculation of the electronic and optical properties of indium tin oxide by density functional theory,” Chem. Phys. 300(1-3), 285–293 (2004).
[Crossref]

Y. S. Jung, “Spectroscopic ellipsometry studies on the optical constants of indium tin oxide films deposited under various sputtering conditions,” Thin Solid Films 467(1-2), 36–42 (2004).
[Crossref]

A. I. Rogozin, M. V. Vinnichenko, A. Kolitsch, and W. Moller, “Effect of deposition parameters on properties of ITO films prepared by reactive middle frequency pulsed dual magnetron sputtering,” J. Vac. Sci. Technol. 22(2), 349–355 (2004).
[Crossref]

2002 (2)

M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
[Crossref]

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

2001 (2)

H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
[Crossref]

C. C. Lee, J. C. Hsu, and D. H. Wong, “The characteristics of some metallic oxides prepared in high vacuum by ion beam sputtering,” Appl. Surf. Sci. 171(1-2), 151–156 (2001).
[Crossref]

2000 (1)

Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000).
[Crossref]

1999 (1)

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

1998 (2)

R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: Electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998).
[Crossref]

R. A. Synowicki, “Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants,” Thin Solid Films 313–314, 394–397 (1998).
[Crossref]

1991 (1)

M. Hoheisel, A. Mitwalsky, and C. Mrotzek, “Microsturcture and Etching Properties of Sputtered Indium-Tin Oxide (ITO),” Phys. Status Solidi 123(2), 461–472 (1991).
[Crossref]

1986 (1)

I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: Basic optical properties and application to energy-efficient windows,” J. Appl. Phys. 60(11), R123–R160 (1986).
[Crossref]

1973 (1)

R. Clanget, “Ionized impurity scattering in degenerate In2O3,” Appl. Phys. (Berl.) 2(5), 247–256 (1973).
[Crossref]

Amassian, A.

M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
[Crossref]

Ban, T.

R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: Electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998).
[Crossref]

Banerjee, A. N.

A. N. Banerjee and K. K. Chattopadhyay, “Recent developments in the emerging field of crystalline p-type transparent conducting oxide thin films,” Prog. Cryst. Growth Ch. 50(1-3), 52–105 (2005).
[Crossref]

Barreca, D.

M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
[Crossref]

Bartolino, R.

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

Brewer, S. H.

S. H. Brewer and S. Franzen, “Calculation of the electronic and optical properties of indium tin oxide by density functional theory,” Chem. Phys. 300(1-3), 285–293 (2004).
[Crossref]

Bruno, G.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
[Crossref]

Capezzuto, P.

M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
[Crossref]

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Chattopadhyay, K. K.

A. N. Banerjee and K. K. Chattopadhyay, “Recent developments in the emerging field of crystalline p-type transparent conducting oxide thin films,” Prog. Cryst. Growth Ch. 50(1-3), 52–105 (2005).
[Crossref]

Chrisey, D. B.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Ciuchi, F.

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

Clanget, R.

R. Clanget, “Ionized impurity scattering in degenerate In2O3,” Appl. Phys. (Berl.) 2(5), 247–256 (1973).
[Crossref]

D’Elia, S.

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

De Rosa, R.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Dudek, M.

M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
[Crossref]

Ellmer, K.

K. Ellmer and R. Mientus, “Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide,” Thin Solid Films 516(14), 4620–4627 (2008).
[Crossref]

Franzen, S.

S. H. Brewer and S. Franzen, “Calculation of the electronic and optical properties of indium tin oxide by density functional theory,” Chem. Phys. 300(1-3), 285–293 (2004).
[Crossref]

Fujiwara, Y. H.

Y. H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3: Sn studied by spectroscopic ellipsometry: Analysis of free-carrier and band-edge absorption,” Phys. Rev. B 71(7), 075109 (2005).
[Crossref]

Giangregorio, M.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Gilmore, C. M.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Granqvist, C. G.

I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: Basic optical properties and application to energy-efficient windows,” J. Appl. Phys. 60(11), R123–R160 (1986).
[Crossref]

Hamberg, I.

I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: Basic optical properties and application to energy-efficient windows,” J. Appl. Phys. 60(11), R123–R160 (1986).
[Crossref]

Hoheisel, M.

M. Hoheisel, A. Mitwalsky, and C. Mrotzek, “Microsturcture and Etching Properties of Sputtered Indium-Tin Oxide (ITO),” Phys. Status Solidi 123(2), 461–472 (1991).
[Crossref]

Horwitz, J. S.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Hsu, J. C.

C. C. Lee, J. C. Hsu, and D. H. Wong, “The characteristics of some metallic oxides prepared in high vacuum by ion beam sputtering,” Appl. Surf. Sci. 171(1-2), 151–156 (2001).
[Crossref]

Inoue, K.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Ito, N.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Jung, Y. S.

Y. S. Jung, “Spectroscopic ellipsometry studies on the optical constants of indium tin oxide films deposited under various sputtering conditions,” Thin Solid Films 467(1-2), 36–42 (2004).
[Crossref]

Kafafi, Z. H.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Kaijo, A.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Kawashima, T.

Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000).
[Crossref]

Kim, H.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Klemberg-Sapieha, J. E.

M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
[Crossref]

Kolitsch, A.

A. I. Rogozin, M. V. Vinnichenko, A. Kolitsch, and W. Moller, “Effect of deposition parameters on properties of ITO films prepared by reactive middle frequency pulsed dual magnetron sputtering,” J. Vac. Sci. Technol. 22(2), 349–355 (2004).
[Crossref]

Kondo, M.

Y. H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3: Sn studied by spectroscopic ellipsometry: Analysis of free-carrier and band-edge absorption,” Phys. Rev. B 71(7), 075109 (2005).
[Crossref]

Koshi-ishi, R.

Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000).
[Crossref]

Latz, R.

Z. Qiao, R. Latz, and D. Mergal, “Thickness dependence of In2O3: Sn film growth,” Thin Solid Films 446(1-2), 250–258 (2004).
[Crossref]

Lee, C. C.

C. C. Lee, J. C. Hsu, and D. H. Wong, “The characteristics of some metallic oxides prepared in high vacuum by ion beam sputtering,” Appl. Surf. Sci. 171(1-2), 151–156 (2001).
[Crossref]

Lee, L.

S. Z. Tehrani, W. L. Lim, and L. Lee, “Correction factors for films resistivity measurement,” Measurement 45(3), 219–225 (2012).
[Crossref]

Lim, W. L.

S. Z. Tehrani, W. L. Lim, and L. Lee, “Correction factors for films resistivity measurement,” Measurement 45(3), 219–225 (2012).
[Crossref]

Liu, H. D.

H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
[Crossref]

Losurdo, M.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
[Crossref]

Martinu, L.

M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
[Crossref]

Mattoussi, H.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Mergal, D.

Z. Qiao, R. Latz, and D. Mergal, “Thickness dependence of In2O3: Sn film growth,” Thin Solid Films 446(1-2), 250–258 (2004).
[Crossref]

Mientus, R.

K. Ellmer and R. Mientus, “Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide,” Thin Solid Films 516(14), 4620–4627 (2008).
[Crossref]

Mitwalsky, A.

M. Hoheisel, A. Mitwalsky, and C. Mrotzek, “Microsturcture and Etching Properties of Sputtered Indium-Tin Oxide (ITO),” Phys. Status Solidi 123(2), 461–472 (1991).
[Crossref]

Moller, W.

A. I. Rogozin, M. V. Vinnichenko, A. Kolitsch, and W. Moller, “Effect of deposition parameters on properties of ITO films prepared by reactive middle frequency pulsed dual magnetron sputtering,” J. Vac. Sci. Technol. 22(2), 349–355 (2004).
[Crossref]

Mrotzek, C.

M. Hoheisel, A. Mitwalsky, and C. Mrotzek, “Microsturcture and Etching Properties of Sputtered Indium-Tin Oxide (ITO),” Phys. Status Solidi 123(2), 461–472 (1991).
[Crossref]

Mruarka, S. P.

H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
[Crossref]

Murata, H.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Nishimura, E.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Ohsako, J.

Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000).
[Crossref]

Ohya, Y.

R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: Electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998).
[Crossref]

Pique´, A.

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

Plá, J.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Qiao, Z.

Z. Qiao, R. Latz, and D. Mergal, “Thickness dependence of In2O3: Sn film growth,” Thin Solid Films 446(1-2), 250–258 (2004).
[Crossref]

Ramantath, G.

H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
[Crossref]

Rizzoli, R.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Roca, F.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Rogozin, A. I.

A. I. Rogozin, M. V. Vinnichenko, A. Kolitsch, and W. Moller, “Effect of deposition parameters on properties of ITO films prepared by reactive middle frequency pulsed dual magnetron sputtering,” J. Vac. Sci. Technol. 22(2), 349–355 (2004).
[Crossref]

Sasabayashi, T.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Sato, Y.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Scaramuzza, N.

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

Shigesato, Y.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000).
[Crossref]

Strangi, G.

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

Summonte, C.

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Synowicki, R. A.

R. A. Synowicki, “Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants,” Thin Solid Films 313–314, 394–397 (1998).
[Crossref]

Tahar, R. B. H.

R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: Electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998).
[Crossref]

Takahashi, Y.

R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: Electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998).
[Crossref]

Tehrani, S. Z.

S. Z. Tehrani, W. L. Lim, and L. Lee, “Correction factors for films resistivity measurement,” Measurement 45(3), 219–225 (2012).
[Crossref]

Tondello, E.

M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
[Crossref]

Utsumi, K.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Versace, C.

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

Vinnichenko, M. V.

A. I. Rogozin, M. V. Vinnichenko, A. Kolitsch, and W. Moller, “Effect of deposition parameters on properties of ITO films prepared by reactive middle frequency pulsed dual magnetron sputtering,” J. Vac. Sci. Technol. 22(2), 349–355 (2004).
[Crossref]

Wang, G. C.

H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
[Crossref]

Wong, D. H.

C. C. Lee, J. C. Hsu, and D. H. Wong, “The characteristics of some metallic oxides prepared in high vacuum by ion beam sputtering,” Appl. Surf. Sci. 171(1-2), 151–156 (2001).
[Crossref]

Yano, K.

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Zabeida, O.

M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
[Crossref]

Zhao, Y. P.

H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
[Crossref]

Appl. Phys. (Berl.) (1)

R. Clanget, “Ionized impurity scattering in degenerate In2O3,” Appl. Phys. (Berl.) 2(5), 247–256 (1973).
[Crossref]

Appl. Surf. Sci. (2)

C. C. Lee, J. C. Hsu, and D. H. Wong, “The characteristics of some metallic oxides prepared in high vacuum by ion beam sputtering,” Appl. Surf. Sci. 171(1-2), 151–156 (2001).
[Crossref]

S. D’Elia, N. Scaramuzza, F. Ciuchi, C. Versace, G. Strangi, and R. Bartolino, “Ellipsometry investigation of the effects of annealing temperature on the optical properties of indium tin oxide thin films studied by Drude–Lorentz model,” Appl. Surf. Sci. 255(16), 7203–7211 (2009).
[Crossref]

Chem. Phys. (1)

S. H. Brewer and S. Franzen, “Calculation of the electronic and optical properties of indium tin oxide by density functional theory,” Chem. Phys. 300(1-3), 285–293 (2004).
[Crossref]

J. Appl. Phys. (3)

I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: Basic optical properties and application to energy-efficient windows,” J. Appl. Phys. 60(11), R123–R160 (1986).
[Crossref]

R. B. H. Tahar, T. Ban, Y. Ohya, and Y. Takahashi, “Tin doped indium oxide thin films: Electrical properties,” J. Appl. Phys. 83(5), 2631–2645 (1998).
[Crossref]

H. Kim, C. M. Gilmore, A. Pique´, J. S. Horwitz, H. Mattoussi, H. Murata, Z. H. Kafafi, and D. B. Chrisey, “Electrical, optical, and structural properties of indium–tin–oxide thin films for organic light-emitting devices,” J. Appl. Phys. 86(11), 6451–6461 (1999).
[Crossref]

J. Vac. Sci. Technol. (1)

A. I. Rogozin, M. V. Vinnichenko, A. Kolitsch, and W. Moller, “Effect of deposition parameters on properties of ITO films prepared by reactive middle frequency pulsed dual magnetron sputtering,” J. Vac. Sci. Technol. 22(2), 349–355 (2004).
[Crossref]

J. Vac. Sci. Technol. A (1)

M. Losurdo, M. Giangregorio, P. Capezzuto, G. Bruno, R. De Rosa, F. Roca, C. Summonte, J. Plá, and R. Rizzoli, “Parameterization of optical properties of indium-tin-oxide thin films by spectroscopic ellipsometry: Substrate interfacial reactivity,” J. Vac. Sci. Technol. A 20(1), 37–42 (2002).
[Crossref]

Jpn. J. Appl. Phys. (1)

E. Nishimura, T. Sasabayashi, N. Ito, Y. Sato, K. Utsumi, K. Yano, A. Kaijo, K. Inoue, and Y. Shigesato, “Structure and internal stress of tin-doped indium oxide and indium-zinc oxide films deposited by DC magnetron sputtering,” Jpn. J. Appl. Phys. 46(12), 7806–7811 (2007).
[Crossref]

Measurement (1)

S. Z. Tehrani, W. L. Lim, and L. Lee, “Correction factors for films resistivity measurement,” Measurement 45(3), 219–225 (2012).
[Crossref]

Phys. Rev. B (1)

Y. H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3: Sn studied by spectroscopic ellipsometry: Analysis of free-carrier and band-edge absorption,” Phys. Rev. B 71(7), 075109 (2005).
[Crossref]

Phys. Status Solidi (1)

M. Hoheisel, A. Mitwalsky, and C. Mrotzek, “Microsturcture and Etching Properties of Sputtered Indium-Tin Oxide (ITO),” Phys. Status Solidi 123(2), 461–472 (1991).
[Crossref]

Prog. Cryst. Growth Ch. (1)

A. N. Banerjee and K. K. Chattopadhyay, “Recent developments in the emerging field of crystalline p-type transparent conducting oxide thin films,” Prog. Cryst. Growth Ch. 50(1-3), 52–105 (2005).
[Crossref]

Surf. Coat. Tech. (1)

M. Losurdo, D. Barreca, P. Capezzuto, G. Bruno, and E. Tondello, “Interrelation between nanostructure and optical properties of oxide thin films by spectroscopic ellipsometry,” Surf. Coat. Tech. 151–152, 2–8 (2002).
[Crossref]

Thin Solid Films (6)

K. Ellmer and R. Mientus, “Carrier transport in polycrystalline transparent conductive oxides: A comparative study of zinc oxide and indium oxide,” Thin Solid Films 516(14), 4620–4627 (2008).
[Crossref]

Y. S. Jung, “Spectroscopic ellipsometry studies on the optical constants of indium tin oxide films deposited under various sputtering conditions,” Thin Solid Films 467(1-2), 36–42 (2004).
[Crossref]

M. Dudek, A. Amassian, O. Zabeida, J. E. Klemberg-Sapieha, and L. Martinu, “Ion bombardment-induced enhancement of the properties of indium tin oxide films prepared by plasma-assisted reactive magnetron sputtering,” Thin Solid Films 517(16), 4576–4582 (2009).
[Crossref]

R. A. Synowicki, “Spectroscopic ellipsometry characterization of indium tin oxide film microstructure and optical constants,” Thin Solid Films 313–314, 394–397 (1998).
[Crossref]

Z. Qiao, R. Latz, and D. Mergal, “Thickness dependence of In2O3: Sn film growth,” Thin Solid Films 446(1-2), 250–258 (2004).
[Crossref]

H. D. Liu, Y. P. Zhao, G. Ramantath, S. P. Mruarka, and G. C. Wang, “Thickness dependent electrical resistivity of ultrathin (<40nm) Cu films,” Thin Solid Films 384(1), 151–156 (2001).
[Crossref]

Vacuum (1)

Y. Shigesato, R. Koshi-ishi, T. Kawashima, and J. Ohsako, “Early stages of ITO deposition on glass or polymer substrates,” Vacuum 59(2-3), 614–621 (2000).
[Crossref]

Other (1)

H. Fujiwara, Spectroscopic Ellipsometry - Principle and Application (John Wiley and Sons, 2006), Chap. 4.

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Figures (6)

Fig. 1
Fig. 1 (a) Cross-sectional SEM images of Samples A, B and C. (b) XRD analysis results for Samples A, B and C. Note that the insets in Fig. 1(a) show the EDS analysis results for the corresponding ITO thin film.
Fig. 2
Fig. 2 Optical models and corresponding SE fitting results for: (a) two-layer optical model and (b) three-layer optical model for Sample C.
Fig. 3
Fig. 3 (a) Comparison of Hall effect measurement of sample resistivity (ρH) with estimated results obtained using two-layer model (ρ*S) and three-layer model (ρ*D). (b) Comparison of lump sum resistivity (ρ*D) with resistivities of bulk layer (ρ*D2) and transition layer (ρ*D1).
Fig. 4
Fig. 4 Comparison of estimated results and experimental results for carrier density (N) in: (a) transition layer and (b) bulk layer of ITO films. Note that NH represents the experimental Hall measurement value, while N*F, N*C and N*B represent the carrier densities estimated by the Fujiwara model, constant model and Brewer model, respectively. Note also that subscripts 1 and 2 refer to the transition layer and bulk layer, respectively.
Fig. 5
Fig. 5 Comparison of estimated results and experimental results for carrier mobility (μ) in: (a) transition layer and (b) bulk layer of ITO films. Note that μH represents the experimental Hall measurement value, while μ*C, μ*F and μ*B represent the carrier mobilities estimated by the constant model, Fujiwara model and Brewer model, respectively. Note also that subscripts 1 and 2 refer to the transition layer and bulk layer, respectively.
Fig. 6
Fig. 6 (a) Refractive index spectra and (b) extinction coefficient spectra of bulk layer and transition layer in Samples A, B and C. Note that L1 denotes the transition layer and L2 denotes the bulk layer.

Tables (2)

Tables Icon

Table 1 Fitting results obtained for three samples using two-layer and three-layer optical models, in which MSE and Ra represent mean square error and surface roughness, respectively.

Tables Icon

Table 2 Effective mass values for free electrons in bulk and transition layers as determined using constant model (m*C), Fujiwara model (m*F) and Brewer model (m*B).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ε(ω)= ε ω p 2 ω 2 +i ω τ ω + j=1 2 f j ω j 2 ω 0j 2 ω 2 +i γ j ω
ε(E)= ε A D E 2 +i B D E + j=1 2 A L E 0j 2 E 2 +i Γ L E
ρ D = B D A D ε 0
N=( A D )( m e * ε 0 ε e 2 )
μ= e B D m e *

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