Study of oxide/metal/oxide thin films for transparent electronics and solar cells applications by spectroscopic ellipsometry

“Al.I.Cuza”

We showed in our previous studies [17] that the quantity of ITO can be divided by four if the ITO films (150 nm) are replaced by ITO (20 nm)/metal (7 nm)/ITO (20 nm) films by maintaining the same figures of merit of the electrodes as that one's of single layer films. Moreover, subsequent studies of Kubis [18] and Berny [19] show the excellent mechanical properties and robustness of these films for large scale applications.
At present the research on founding alternative transparent conducting films for the replacement of ITO is mostly done by many experimental trials. Ellipsometry is a non-destructive, non-invasive non-contact, very precise, reproducible and very sensitive technique for study the ultra-thin films. Spectroscopic ellipsometry (SE) provides a widely applicable method for determining accurate characterization of optical and electrical transport properties of thin films multi-layers structures, in particularly when the multilayer of device structure, is of critical importance to their effective implementation [20,21].
However, the difficulty consists to discern between two or more ellipsometric models which both fits well the same data. In the most reported data in literature, the ellispometric models studied are considered enough good if the experimental data of the global refractive index (n) and extinction coefficient (k) fits well with the dispersion curves. Nevertheless we remarked for a large number of our experiments and data, that models which fits well with the experimental data for the global n and k they are not necessarily consistent with the other optical parameters, such as the transmission or reflection coefficient.
The purpose of this article is to provide a comprehensive study of the spectroscopic ellipsometric measurements of single oxide films and oxide/metal/oxide multi-layers thin film using a two-modulator generalized ellipsometer by continuing the study much further than usual given in literature and by also comparing the calculated the transmission coefficient from ellipsometry with the experimental values obtained from direct spectrophotometry measurements. This procedure allows establishing in a more accurate way the best dispersion model for each sample.
Given the fact that the characterization of optical and electrical properties of transparent oxide thin films such as ITO, ZnO:Al (Aluminium doped Zinc Oxide-AZO), TiO 2 , Bi 2 O 3 or multi-layers thin films Oxide/Au/Oxide of the above mentioned oxide is of considerable interest in multiple applications , we compare the results of multiple techniques for correlating all these properties.
The good correlations obtained between the electrical and optical properties determined experimentally by different techniques and the electrical and optical characteristics obtained by theoretical ellipsometric simulations, indicate that high accurate ellipsometric modelling approach, can give the possibility in the future to predict the appropriate device architecture in function of the desired optical and electrical properties.

Materials and Method
The oxide thin films were deposited on glass substrates by sputtering in reactive atmosphere using In:Sn (90%:10%), Zn:Al (98%:2%), Ti and Bi metallic targets from Kurt Lesker and respectively Mateck for the last two. The gold interlayer thin film for the oxide/metal/oxide multilayers films was deposited in argon atmosphere. The substrates were placed in a vertical targetsubstrate configuration onto a rotating disk kept at room temperature. The target-substrate distance was of about 70 mm. The deposition parameters are given in Table 1. The deposition rates were 12 nm/min for ITO films, 10 nm/min for AZO films, 7.5 nm/min for TiO 2 thin films, 30 nm/min for Bi 2 O 3 thin films and 30 nm/min for gold films. The optimized values of the films thickness were chosen in correlation with literature data and in the range for which we obtained, after many trials, simultaneously good optical and electrical properties. The glass substrate thickness was of 1.1 mm and the refractive index n = 1.52. Films thickness measurements were done by profilometry using a Dektak profilometer and as well by ellipsometry. The total thickness of oxide/metal/oxide multi-layer structures ranged between 60 and 300 nm.
Samples structures were investigated by X-ray diffraction (XRD) using D8 Advance Brucker diffractometer CuKα 1.2 (λ = 1.5406 Å), equipped with a linear Vantec super speed detector and by scanning electron microscopy (SEM) using a JEOL microscope.
Optical properties studied were made on single layer oxide thin film and also oxide/Au/oxide three layers films. The investigations of optical properties were made by spectroscopic ellipsometry (SE) technique using a UVVISELTM ellipsometer from Horiba Jobin Yvon, with a 75 W high discharge Xe lamp in the spectral range from 260 to 2100 nm. All the spectra were recorded at room temperature, at an incident angle of 70°. The configuration chosen for the modulator (M), analyzer (A) and polarizer (P) positions were: M = 0°, A = 45° respectively. After the relatively fast recording of  and  spectra, the next step was the construction of an appropriate optical model for the samples in order to fit the experimental values. These investigations were coupled with the recording of absorption/transmission spectra using a double beam spectrophotometer LAMBDA 950 UV/Vis/NIR spectrophotometer in the same spectral range from 260 to 2100 nm. Figure 1 present the architecture of the studied samples oxide and oxide/metal/oxide deposited on glass substrates and Figure 2 present the SEM micrographs for single oxide layers (named here bottom layer) and then of subsequently oxide layers of the structure oxide/Au/oxide (named top layer). Surfaces are smooth and, generally, small differences were observed between the surface morphology of bottom oxide layer and top oxide layer.

Results and Discussions
The apparently phase-separation like morphology for the TiO 2 /Au/TiO 2 sample can be attributed to the fact that the top TiO 2 film is very thin, much thinner, compared to the other samples, hence due to the scanning electron microscopy penetration depth, the top image of the three layer sample, the partially image of the gold layer can be visible through the top layer. From other analysis like AFM (not shown here), we did not remark significant differences on the morphology of the top oxide layer compared to the bottom layer. Figures 3(a-d) show the X-ray diffraction patters of as deposited oxide single layers films and oxide/metal/oxide films. As one can see all single oxide layers are amorphous. The oxide/metal/oxide layers are also amorphous except AZO/Au/AZO sample which shows small peak corresponding to (002)   In ellipsometry, the variation of the amplitude and the phase difference between the perpendicular (p) and the parallel (s) components of the reflected light polarized, with respect to the plane of incidence, are measured. In general, reflection causes a change in the relative phase of p and s waves and in the ratio of their amplitudes. According to the fundamental equation of ellipsometry the relation between the ellipsometric angles  and  is given by [44]: where, R p /R s is the complex ratio of the Fresnel reflection coefficients. -measure the amplitude ratio and -measure the relative phase change.
The measured ellipsometric spectra are fitted by minimizing the squared difference  2 between the measured and calculated values of the ellipsometric parameters I s and I c . I s and I c are given by: and where, N is the number of data points and P the number of model parameters [45]. A fit is considered enough good if  2 < 10. Ellipsometry is an indirect method. The difficulty is that one that is not sufficient to obtain a good fit of  and  spectra with very low values of  2 . Many dispersion models can fits well and the difficulty is to know what model is the most suitable. That means that once a model is tested and a good fit is obtained the results should be compared with other data measurements and the model should be improve until a good coherence between all the data is obtained. For this reason we conduct our study furthermore than usually presented in literature, by comparing the transmittance spectra calculated from ellipsometry with the transmittance spectra obtained by direct measurements from spectrophotometry.
The refractive index and extinction coefficient for a bulk (substrate) material are related to  and  by the following formula and can be calculated directly by separating the real and imaginary part of this equation and solving the two equation system [46].
The DeltaPsi2 software of Horiba Jobin Yvon allows to fit the spectra of  and , I s and I c by minimizing the values of  2 . The software calculates also a "global" refractive index and a "global" extinction coefficient of the samples including the substrate + layer(s) and allows to calculate the global transmittance (T%) and reflectance (R%). The individual refractive index, n, and individual extinction coefficient, k, for each layer should be extracted from the model on the basis of the dispersion formula which gives the best fit.
The direct measurement of n and k on the basis of Eq. (5) can be compared with the theoretical values given by the known dispersions models (Adachi-Forouhi, Cauchy, Tauc-Lorentz, Kato-Adachi, Sellmeier, etc.) of different materials from the data basis of the DeltaPsi2 software, and good fits between the measured n and k and calculated n (n-fit) and k (k-fit) can be obtained, for more than one dispersion model.
The theoretical spectral transmittance (T) and reflectance (R) of a thin film deposited on a substrates are functions of n, k, d and , where d is the film thickness and  the wavelength of incident light. The certainty of the appropriate model is achieved when the calculated values T, R and d coincides with the direct measured values of T ex , R ex and d ex , from spectrophotometry for T ex , R ex and profilometry, SEM or other methods for d ex [47]:    Figure 5 gives the experimental and calculated values for the "global" refractive index for all the samples: single oxide layers and three layers oxide/metal/oxide films deposited on glass substrates. The optimization of the models was done by comparing the calculated transmittance coefficient from ellipsometry model with the experimental values obtained from spectrophotometry ( Figure 6). From curves given in Figure 4 and Figure 5, we remark a very good fit between the calculated data (lines) and experimental values (dots) but the optimization was done on the basis of successive comparison with the transmittance spectra obtained by spectrophotometry. Figure 6 presents the best fits of the calculated transmittance spectra from ellipsometry with transmittance spectra obtained by spectrophotometry. Figure 5. Samples global refractive index n, for single layer oxide on glass and three layers oxide/metal/oxide layers on glass substrate (experimental-dots and fit-line).
If the thickness d of a film, its refractive index n, and extinction coefficient k are known, it is possible to derive its reflectance R and transmittance T. Basic equations have been derived by Heavens [48] and are detailed for a single layer on a substrate of refractive index n 1 and extinction coefficient k 1 in [49]. In the same way calculations can be made for samples with multiple layers. A computer solution can also be carried out by successive approximations using Newton's method [3,49,50]. The DeltaPsi2 software allows such calculations and gives the values of the transmission and reflection coefficients.
In agreement with [54] the best dispersion model founded for Al:ZnO doped films corresponds to Kato-Adachi dispersion model:  Figure 7. Ellipsometric models.
The new amorphous dispersion formula for TiO 2 is a rewriting of original Forouhi-Bloomer formula [55]: Tauc-Lorentz for Bi 2 O 3 films [50,51]: Drude: The dispersion models parameters corresponding hence to the best fit of the experimental data are given in Tables 2-6.     Table 7 gives the thickness values for single and three layer samples. We remark a good correlation between the values obtained by profilometry and ellipsometry for the samples for which the transmission curves in Figure 6 (ITO/Au/ITO, AZO and Bi 2 O 3 ) obtained by the two techniques are closer. As confirmed, ellipsometry analysis is performed from fitting using an optical model. Nevertheless, an optical model used in ellipsometry analysis simply represents an approximated sample structure, and obtained results are not necessarily correct even when the fit is sufficiently good. This is the greatest disadvantage of the ellipsometry technique and accordingly, ellipsometry results must be justified by using other measurement methods [50]. The novelty of this paper consist in refining the modelling of optical properties by additionally fitting the transmission coefficients by two different techniques, moreover than the usual method presented in literature, which consist only on the fit of experimental  and  angles. By this deeper analysis of the optical models we can see that even after refining by this procedure and very good fits of  and  angles, or effective n and k coefficients, the fits for transmission coefficients by comparing the data from ellipsometry and spectrophotometry are not perfect. The differences observed between the transmission coefficient curves obtained by ellipsometry calculations and direct spectrophotometry measurements in Figure 6. for ITO, TiO 2 or Bi 2 O 3 /Au/Bi 2 O 3 are coherent with the differences observed between the thickness values measured directly by profilometry and those calculated from ellipsometry and indicate the limits the optical models. However, once an analytical method is established, it becomes possible to perform high-precision characterization using spectroscopic ellipsometry. From this study, it can be considered that a good optical model can be established when the calculated curves of transmission coefficient obtained by ellipsometry coincides with the experimental values obtained by spectrophotometry and not only when good fits between experimental data and calculated values are obtained for the angles  and  angles, or effective n and k coefficients. The parameter which is most critically subject of errors, in the case of ellipsometry models calculations, is the films thickness, especially in the case of very thin films.
The dispersion curves of n and k of single layer oxides were extracted from these models and depicted in Figure 8.
The obtained values are in good agreement with the data obtained by other authors for ITO [56], AZO [57], TiO 2 [58] and Bi 2 O 3 [59].
The absorption coefficient was calculated using the formula [3]: The plot of (h α) n versus photon energy gives information about energy of the indirect (n = 1/2) or direct transitions (n = 2), respectively. By using the Eq. For the direct allowed transition, (h α) 2 versus photon energy, hν was plotted for ITO and AZO (Figure 9a and 9b). The intercept on the abscissa gives the value of the direct band gap [3]. The optical band gap values obtained (eV) are very close to the values quoted in literature [3,9].
The values for indirect band transitions for TiO 2 [60] and Bi 2 O 3 [61] were determined from the linear extrapolation of (h α) 1/2 = f(hν) curves towards the intersection with the x-axis (Figure 9c and  9d).
The values of the optical band gaps determined from spectrophotometry data and ellipsometry calculations are given in Table 8. Good correlations between the calculations by the two methods were obtained. Single oxide layers films are high resistive due to the size effect as a consequence of their low thickness. The oxide/Au/oxide films have a good electrical conductivity due to the Au interlayer film. The electrical resistivity is of 8 × 10 −4 ·cm for ITO/Au/ITO, 2 × 10 −3 ·cm for AZO/Au/AZO, 7 × 10 −3 ·cm for TiO 2 /Au/TiO 2 , 3 × 10 −2 ·cm for Bi 2 O 3 /Au/Bi 2 O 3 .
The total (sheet) resistance of the multi-layer is a combination of the resistances of three consecutive layers [62]: Hence: If we note p = R m /R ox According to Drude's theory in metals the plasma frequency is given by [63]: where n is the carriers concentration, * is the effective mass of charge carriers,   and  0 represent the dielectric constants of medium and free space. On the other hand the electrical conductivity is given by: where 〈 〉 is the mean value of the relaxation time, hence from the Eq. (18) and Eq. (19) it results that: ω 4πσ ε ε 〈τ〉 (20) Figure 10 presents the values of obtained from the ellipsometric models (see Table 6) in function of the measured electrical conductivity in direction parallel to the substrate for the oxide/metal/oxide samples. We remark a linear dependence in agreement with Eq. (20). The resistance of single oxide layer of TiO 2 and Bi 2 O 3 is higher than the resistance of individual ITO an AZO layers . In conclusion, the condition R ox >> R m is better verified for TiO 2 /Au/TiO 2 and Bi 2 O 3 /Au/Bi 2 O 3 which is coherent with the fact that for these samples the points   (Table 6) in function of the measured electrical conductivity in direction parallel to the substrate for the oxide/metal/oxide samples.

Conclusions
A complete study of the optical and electrical properties of single oxide layer and oxide/metal/oxide (Oxide = ITO, AZO, TiO 2 and Bi 2 O 3 , Metal = Au) three layers was done by spectrophotometry, ellipsometry and four probe electrical measurements. At our best knowledge, the multi-layer structure Bi 2 O 3 /Au/Bi 2 O 3 was studied for the first time. Oxide films were deposited by reactive sputtering and all are amorphous and have a transmission coefficient higher than 80%. The improvement of the developed optical models was done by refining the fittings, not only, between the measured and the calculated values for the  and  angles, but also by comparing the calculated values of the transmission coefficient from ellipsometric models with the experimental values of the transmission coefficient determined from spectrophotometry, and also by other correlations of specific parameters measured by other methods. This procedure allows to better establish the validity of the different optical models in function of the correlations obtained for different thin films characteristics such as the films thickness, transmission coefficient, optical band gap and electrical resistivity obtained by different techniques. The best dispersion models for n() and k() were hence established by the correlations of data obtained by spectrophotometry and ellipsometry. The global and individual refractive index and global and individual extinction coefficients were calculated. This approach also shows how the ellipsometric modelling can be improved, with maybe the possibility, in the future to predict, by ellipsometric simulations, the suitable device architecture in function of the desired optical and electrical properties.