1. Introduction

The binary material system of GeO₂:SiO₂ has been well studied in the past, primarily due to the advent of optical fiber communications in the early 1970s. As germanium is in the same group as silicon in the periodic table, they are chemically compatible substitutes for each other. The refractive index (RI) of pure SiO₂ is ~1.46 and that of GeO₂ is ~1.61 have allowed the respective binary system to be well-suited for numerous applications in optical communications. According to the Lorentz-Lorenz equation, the RI depends upon the polarizability of the atomic species. Germanium having a higher electron count and hence a larger atomic size understandably possess a higher polarizability, thus a higher RI, than Si. When mixed, the binary oxide has been observed to exhibit linear relationships with compositions for many physical properties like RI, density which enable the material to be used with facile. Besides being chemically stable comparing to other oxides, recent studies have found the GeO₂:SiO₂ system interesting due to such properties as photosensitivity, an efficient host for optically active dopants, nonlinearity upon UV radiation [1–5].

The versatility of spectroscopic ellipsometer (SE) in characterization of material properties of semiconductor and dielectric films has been evident through the abundance of work in the literature [6, 7]. By using SE, the optical function of the thin film can be determined to a fair degree of accuracy (~10^-4). For an accurate determination of the optical function, the noise associated with SE measurements can be further reduced by performing a multi-sample analysis. Alternatively, by employing multiple incident-angles measurements, enabled by commercial variable-angle SEs, the number of samples used in optical function determination can, thus, be reduced. Such information provides details of the material dispersion that can be useful in applications such as dispersion management devices, linear and nonlinear optical applications. An accurate determination of the optical function of dense GeO₂:SiO₂ material also enables accurate ellipsometric porosimetry in applications as employed in Ref. [8]. GeO₂:SiO₂ is also finding applications in the microelectronics in the form of insulation for SiGe transistors [9] and interlayer dielectric in ULSI [10]. The knowledge of how the optical function of (x)GeO₂:(1-x)SiO₂ changes with the molar fraction of GeO₂, x, will facilitate the characterization of such dielectric oxide films. Also, the anticipated expansion of the telecommunication window to wavelengths of 1.2–1.7 µm warrants a reliable and fast method to determine the spectral RI of ceramic films at different compositions for different photonics devices.

GeO₂:SiO₂ films have been studied using many deposition techniques such as flame hydrolysis deposition, plasma assisted CVD, RF sputtering and sol-gel process. The latter presents itself as a commercially attractive fabrication technique which is capable of yielding stoichiometric multi-component dielectric films at low costs. The study presented here deals with thin films of GeO₂:SiO₂ prepared by the sol-gel/spin-coating process and material characterization of (x)GeO₂:(1-x)SiO₂ thin films. However, reports [4, 11–13], to-date, have not provided spectral RI for germanosilicate at different compositions. With the use of spectroscopic ellipsometer, the authors are able to determine spectral optical properties of (x)GeO₂:(1-x)SiO₂ glass over a substantial wavelength range. A simple and robust scheme based on the Sellmeier dispersion is demonstrated to predict any refractive index, for x≤0.4, between the wavelength of 210 and 1700 nm inclusively. The difference in the dispersion characteristics with varying concentration x will be discussed.

2. Experiments

The sol-gel solutions were prepared according to procedures similar to Ref. [14]. Briefly, the silicon precursor, TEOS (Aldrich, 99.999%) was pre-hydrolyzed by diluted HCl in de-ionized water before mixing with pre-dissolved germanium precursor (Germanium Isopropoxide, 99.99% Chemat Technology Inc.) in anhydrous isopropanol. The sols were kept at pH 3 to reduce the likelihood of GeO₂ crystallization [15]. The mixed sols containing both Si and Ge precursors were aged for at least 3 hours before spin coating. The spinnable sol was then spin-coated at 1000 rpm under ~25°C in flowing N₂. The substrates were resistive (12–16 Ω-cm) p-doped (Boron) Si <100> wafers. Conventional electric furnaces were used to heat treat the samples in air for 15 minutes. Two samples were made for each composition, one being ~100 nm and the other at ~300 nm thick. The thicker samples are made by multiple coating with 1 to 3 minutes of intermediate heating at the densifying temperature of 1000°C and 1100°C. The sol recipes were designed to yield films with atomically smooth surface, thickness uniformity and striation-free films.

A Spectroscopic Ellipsometer (VASE, J.A. Woollam Co.) was used to measure the ellipsometric values at incident angles of 60° and 75° for a spectral range of 210 to 1700 nm. The errors on the ellipsometric angles, Ψ and Δ, were less than 0.30° and 1.50°, respectively. The data acquisition and analysis software application used was WVASE32^™ by J.A. Woollam Co. It uses a Levenberg-Marquardt algorithm to search for optimized model parameters. Due to the complexity and the large volume of data involved to derive the dispersion spectra, the details of the data analysis are beyond the scope of this report. FTIR (Perkin-Elmer Spectrum 2000 spectrometer) transmission spectra were measured with a resolution of 4 cm^-1. UV-VIS transmission spectra were taken by HP 8453 spectrophotometer. Raman scattering was measured by a micro-Raman Spectroscopy system (Renishaw Ramascope) using a 514.5 nm Argon Ion laser with an average output of 25 mW. Raman shifts in the range of 100 cm^-1 to 1200 cm^-1 were monitored. Glancing-angle XRD (Siemens D5005 using a CuKα source) was used to scan 2θ angles from 0 to 65°. Surface roughness of the films was measured by a Scanning Probe Microscope (SPM, Digital Instruments Dimension 3000 with a Nanoscope IIIa control module). Scan range was 1 µm×1 µm and 256 lines/µm. From the measured data of mircro-Raman, XRD and SPM, our films were found to be free of crystalline phases and surface roughness (RMS roughness < 1 nm). Cross-sectional TEM was performed with Philps/FEI CM200 FEG. Rutherford Backscattering (RBS) was carried out with 2 MeV He²⁺ (Errors on thickness values are ≤5% and on composition are ≤2%).

3. Results and discussions

FTIR measurements revealed all tested samples, up to x=0.400, to be dense with the prominent peaks representing Si-O-Si (1080–1200 cm^-1), Si-O-Ge (960–1020 cm^-1) and Ge-O-Ge (900–980 cm^-1) bonds and indiscernible OH related absorption between 2700 to 3800 cm^-1. UV-VIS transmission spectra were taken for similar films deposited on quartz substrates. The oxygen-deficient defects in GeO₂:SiO₂ films with an absorption peak at ca. 240 nm [4] are absent from all of the spectra. Hence, we conclude that our films are dense and stoichiometric in composition. Furthermore, XRD and micro-Raman measurements reveal that all the signature peaks of crystalline GeO₂ are absent in all samples. These results demonstrate that our samples are indeed free of crystalline phases of GeO₂ at a high temperature of 1000°C. With such a priori information, a physical model representing the film structure was constructed for analyzing the spectroscopic ellipsometer (SE) data.

As revealed by the UV-VIS spectra, the optical bandgap of the homogeneous GeO₂:SiO₂ films (x≤0.4) is less than 200 nm. The Sellmeier model (the material absorption is assumed to be negligible) is, thus, appropriate for the determination of the optical constants from 210 to 1700 nm. Using the Sellmeier model, the dispersion in RI is expressed as [7]

where ε_offset, a, b, c are the adjustable characteristic Sellmeier parameters. With the spectral dependence on optical constants now implicitly represented in n, λ refers to the wavelength in microns. The term, cλ ², accounts for the IR absorption tail of oxide materials. Another advantage of using the Sellmeier expression is that its simplicity warrants facile fitting of the SE data and it is easily differentiable to yield material dispersion coefficients.

The modeled physical structure of the sample used is shown in Fig. 1(a). A surface layer was omitted for the following reasons: i) adding such a surface layer does not improve fitting and ii) AFM measurements reveal sub-nanometer roughness for all our films. The TEM micrograph in Fig. 1(b) shows that a thermal SiO₂ layer (in the lighter hue) is much thicker than ~2 nm (i.e. the thickness of an ambient-grown native SiO₂). We suspect that during annealing in air, thermal oxidation occurs on the Si substrate. The multi-sample, multi-angle SE scans effectively lifted the correlation between the fitting parameters (due to their relatively similar RIs): the thickness of GeO₂:SiO₂, ε_offset, a and the thickness of the interlayer thermal SiO₂. The thickness of thermal SiO₂ was determined by the reduction of the SE data to within 2.5 nm of the thickness values derived from RBS. The RBS measurements also served to verify that the actual composition (x) is within 0.008 of the nominal composition. The interface SiO₂ layer (~1 nm) has been well characterized (see Ref. [7] and references therein) to be a transition layer between the Si substrate and the thermal oxide with an RI higher than the thermal oxide. The optical functions for the thermal SiO₂ and interface SiO₂ layers and the Si substrate layer were adopted from Herzinger et al. [7].

 

Fig. 1. (a) Film structure model for ellipsometer analysis. (b) TEM micrograph showing a 40 mol% Ge film after annealing of 1000°C for 15 mins.

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Table 1. Sellmeier dispersion parameters for films of varying Ge content. (* taken from thermal oxide in Ref. [7])

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The Sellmeier model satisfactorily represents the GeO₂:SiO₂ films yielding a mean-squared error (see Ref. [7]) of less than 3. Table 1 summarizes the final best fit parameters corresponding to the Sellmeier dispersion in Eqn. (1) for all test samples. The variation in Sellmeier parameters, as shown in Table 1, suggests a change in the curvature of the dispersion. By correlating the respective material dispersion, modeled by the Sellmeier expression, with composition, x, the RI-composition contour map is shown in Fig. 2(a). As seen in Table 1, the Sellmeier parameter values do not seem to vary in a simple relationship with composition; hence, extending the Sellmeier model to any arbitrary composition, 0≤x≤0.4, by parametrizing the Sellmeier model to the Ge content become difficult. However, by performing a linear interpolation, we have tested our RI-composition contour map in Fig. 2(a) by measuring the RI of a 16 mol% Ge (x=0.160) film annealed under 1000°C for 1 hour by using the prism-coupling technique. The estimated and measured RIs are respectively 1.4645 and 1.4650±0.0003 (1550 nm).

 

Fig. 2. (a) The RI-composition contour map showing the Sellmeier dispersion interpolated for a Ge content 0≤x≤0.4. (b) Linearity of RIs with variation in composition. The dash line represents the linear regression of the n(He-Ne) data from this work.

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In general, the RI of mixed oxides may not vary linearly with composition [16]. However, like other mixed oxides formed by network forming constituents, our results, as shown in Fig. 2(b), confirm previous findings that for germanosilicate systems, the RI-composition relationship is linear. In comparison with the RIs of Huang et al. at 598.3 nm [13], Chen et al. at 632.8 nm [12] and Bellman et al. at 1550 nm [11], our results very much agree with their reported values. Such agreement also verifies that the density of our films is comparable with glasses made by CVD and heat treated at over 1230°C and from a similar sol-gel method using dip-coating. It is worthwhile to note that the slopes of the linear relationships are not constant for different wavelengths (see the inset of Fig. 2(b)). This indicates that the dispersion curves change shape with composition. Hence, empirically determined linear parameterizations based on RI at a certain wavelength as formulated by Ref. [17, 18] are not necessarily applicable for all wavelengths. In the study of optical properties of glasses [16], the dispersion parameter, D_FC=n_F-n_C (where n_F and n_C refer to the RIs measured at the blue F-line [486.13 nm], and the red C-line [656.28 nm], of excited hydrogen atom respectively), is often used to quantify and to compare the material dispersion. However, modern optical equipments are usually equipped with laser sources at 632.8 nm and 1550 nm. Therefore, we introduce here an additional dispersion parameter, D_NIR=n_He-Ne-n_NIR, with n_He-Ne and n_NIR denoting RI measured respectively at 632.8 nm and 1550 nm. In Fig. 3(a), D_FC exhibits a linear compositional dependence till x ~0.3 and thereafter the increment seems to deviate from linearity. This behaviour is quite common in other multi-component silicate glasses [16], whereby D_FC increases linearly only in part of the x regime. On the other hand, D_NIR decreases, then increases again at higher values of x. This trend is likely due to the shift of the Si-O-Si to Ge-O-Ge dominant IR absorption region ca. 1000 cm^-1 (10 µm).

In optical communications, the material dispersion coefficient, D_MAT, is expressed as

where c refers to the speed of light in vacuum. We have substituted the Sellmeier dispersion expression of Eqn. (1) into (2) to calculate D_MAT for each composition (x) using the respective parameter values in Table 1. The wavelength dependence of D_MAT is plotted in Fig. 3(b). The variations in D_FC, D_NIR and D_MAT with x reiterate the above observation of changing dispersion shape as seen from the Sellmeier parameters. Furthermore, in the inset of Fig. 3(b), the zero-dispersion wavelengths of the various compositions are plotted. The zero-dispersion wavelength increases with x. We then conclude that the material dispersion is sensitive to Ge content within the optical communication window and the zero-dispersion wavelength can be tailored by selecting a specific x. Leveraging on the flexibility of the sol-gel process, devices with different material compositions can be realized with ease and cost-effectiveness.

 

Fig. 3. (a) Change in dispersion parameters versus Ge content. The solid line represents an extrapolated linear fit of the D_FC values without the data point at x=0.4. (b) Spectral material dispersion coefficient, D_MAT, and the zero-dispersion wavelengths (inset) are shown for the different compositions.

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4. Conclusions

From the non-destructive, multi-sample and multi-angle SE analysis, an accurate 3-dimensional relationship of RI, wavelength (210–1700 nm) for (x)GeO₂:(1-x)SiO₂ films, 0≤x≤0.4 is presented. By linear interpolation on the Sellmeier-based dispersion relations, the RI at any given wavelength and Ge content can be predicted. In addition, refractive indices were found to be linear with composition in the whole wavelength range with diminishing change at longer wavelengths due to the compositional-dependent change in dispersion characteristics. Dispersion parameters, D_FC, D_NIR and D_MAT are reported to facilitate a quantitative comparison of the change in the dispersion. The zero-dispersion wavelength was found to increase with GeO₂ content. With continual developments in telecommunications and optical metrology in the field of microelectronics and photonics, the method demonstrated herein and results found in this work can be versatile in characterization and diagnosis of materials and processes.