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Refractive Index Variation of Magnetron-Sputtered a-Si_{1−x}Ge_{x} by “One-Sample Concept” Combinatory

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## Abstract

**:**

_{1−x}Ge

_{x}layers have been deposited by ”one-sample concept” combinatorial direct current (DC) magnetron sputtering onto one-inch-long Si slabs. Characterizations by electron microscopy, ion beam analysis and ellipsometry show that the layers are amorphous with a uniform thickness, small roughness and compositions from $x=0$ to $x=1$ changing linearly with the lateral position. By focused-beam mapping ellipsometry, we show that the optical constants also vary linearly with the lateral position, implying that the optical constants are linear functions of the composition. Both the refractive index and the extinction coefficient can be varied in a broad range for a large spectral region. The precise control and the knowledge of layer properties as a function of composition is of primary importance in many applications from solar cells to sensors.

## 1. Introduction

_{1−x}Ge

_{x}films over the entire range of $0\le x\le 1$ [10].

_{1−x}Ge

_{x}films is possible over the entire range of $0\le x\le 1$ using magnetron sputtering over a length of 2 cm, but the composition, and even more importantly the refractive index (n) and extinction coefficient (k) all show a linear dependence on the position in most of the wavelength range. Using optical measurements by ellipsometry, we demonstrate that our combinatorial setup is suitable for a comprehensive optical characterization of a-Si

_{1−x}Ge

_{x}films with accurate spatial and compositional control at a high resolution.

## 2. ’One-Sample’ Combinatory

_{1−x}Ge

_{x}samples with gradient composition ranging in $0\le x\le 1$ were deposited onto 25 × 10 mm

^{2}size Si slabs by DC magnetron sputtering. We followed the “one sample concept” combinatory in order to cover the entire composition range of a binary film within a single specimen. This is implemented by means of a scaled-up device originally constructed for the preparation of 3-mm diameter micro-combinatorial TEM samples [20]. The present arrangement (Figure 1) moves a shutter with a 2 × 10 mm

^{2}slot in fine steps above the substrate while the power of the two magnetron sources is regulated in sync with the position of the slot.

^{−6}Pa. The substrate was mounted in the combinatorial device and it was load-locked into the chamber. Ar sputtering gas of partial pressure of 2.5 × 10

^{−1}Pa was introduced. The Si and Ge targets were cleaned, behind closed shutters, for five minutes applying 340 W and 100 W magnetron power, respectively. These values were selected by preliminary measurements as maximum (100%) of the regulated power of the individual sources, that provided, equally, 0.45 nm/s deposition rates. Subsequently, the slot’s movement of the combinatorial device was started, the shutter of the Si source was opened and Si was deposited at 100% power through the moving slot onto the substrate. This provided the Si section of the combinatorial track. In due time, the power of the Ge source was set to zero and its shutter was opened. It was followed by the gradual increase of the power of the Ge source, simultaneously, with the decrease of the power of the Si source, so the binary, gradient section of the combinatorial sample was deposited. As the power of the Si source arrived to zero and, simultaneously, that of the Ge arrived to its maximum, the Si source was switched off and, finally, the Ge section of the sample was deposited at 100% power of the Ge source.

## 3. Distribution of Si and Ge Atomic Fractions

^{4}He

^{+}analyzing ion beam was collimated with two sets of four-sector slits to the spot size of 0.5 mm × 0.5 mm, while the beam divergence was kept below 0.06°. The beam current was measured by a transmission Faraday cup [23]. Backscattered He

^{+}ions were detected using an ORTEC surface barrier detector (ORTEC, Illinois, USA). The energy resolution of the detection system was 20 keV. Spectra were recorded in Cornell geometry at scattering angle of $\Theta $ = 165° for two different sample tilt angles of 7° and 60°. For quantitative compositional analysis, both axial and planar channeling of the He

^{+}projectiles in the single-crystalline Si substrate were avoided. The measured data were evaluated with the spectrum simulation code named RBX [24].

## 4. Distribution of the Optical Properties

_{1−x}Ge

_{x}films, an optical model was constructed to calculate the ellipsometric angles from the model, and to fit the parameters of the model to obtain a good match between the measured and fitted ellipsometry spectra. Since the a-Si

_{1−x}Ge

_{x}film was deposited on a silicon wafer, the model uses a Si substrate assuming a vertically uniform structure, in which only a surface nanoroughness was taken into account by the usual model of mixing 50% layer material with 50% void. The dispersion of the layer was modeled using the Tauc–Lorentz (TL) approach [25]. In this parameterization, the dielectric function is described as a combination of a Lorentz oscillator with the three usual parameters (the broadening, the amplitude and the peak energy position) and an additional Tauc gap parameter. This approach allows that the total number of fitted parameters is kept at a reasonable value (thicknesses of the roughness layer and the film, and the TL parameters. The spectra measured at each position (each composition) have been fitted independently, by changing the above parameters to find the best match between the measured and calculated ellipsometry spectra. The spectra have been recorded at three angles of incidence providing six measured values at each wavelength, and a total of about 2000 measured values for each scanned position. Consequently, the fit was robust, avoiding local minima in the process, resulting in a smooth map of the optical spectra, as shown by Figure 4. Note the smooth changes of the spectra in Figure 4 in spite of the independent fit procedures at each position, which show the reliability of the fit procedure.

_{1−x}Ge

_{x}composition. It is also important to emphasize that this behavior holds for a broad range of wavelengths. Note that the refractive index can also be modified by hydrogenation, which will be the target of our next study. In this work, we deal with non-hydrogenated amorphous Si and Ge (see also Ref. [26]).

## 5. Conclusions

_{1−x}Ge

_{x}DC magnetron combinatory, the refractive index and the extinction coefficient can be varied, on purpose, in a broad range at each wavelength.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Atomic fraction as a function of position along the center line of the combinatorial sample measured by Rutherford backscattering spectrometry. The black dotted line shows the distribution of the atomic fraction based on the calibration using energy dispersive spectrometry (EDS) in a scanning electron microscope.

**Figure 3.**High resolution TEM image of a 10 nm thick self supporting combinatorial SiGe sample taken for the composition of $x=0.5$.

**Figure 4.**Spectra of the refractive index (n, color map on the middle graph) and the extinction coefficient (k, color map of the bottom graph) as a function of position along the center line of the wafer, calculated using the Tauc–Lorentz (TL) parameterization, as described in the text. The n and k spectra fitted by the TL model individually can be identified along the vertical axis of the bottom and middle maps, the values of which are color coded at the right hand side of the graphs. The composition of a-Si

_{1−x}Ge

_{x}changes from $x=0$ to $x=1$ over the lateral positions from −1 to 1, as shown in the horizontal axis at the top. The zero position corresponds to the composition of $x=0.5$. The top graph shows n and k at the wavelength of 849.7 nm.

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**MDPI and ACS Style**

Lohner, T.; Kalas, B.; Petrik, P.; Zolnai, Z.; Serényi, M.; Sáfrán, G.
Refractive Index Variation of Magnetron-Sputtered a-Si_{1−x}Ge_{x} by “One-Sample Concept” Combinatory. *Appl. Sci.* **2018**, *8*, 826.
https://doi.org/10.3390/app8050826

**AMA Style**

Lohner T, Kalas B, Petrik P, Zolnai Z, Serényi M, Sáfrán G.
Refractive Index Variation of Magnetron-Sputtered a-Si_{1−x}Ge_{x} by “One-Sample Concept” Combinatory. *Applied Sciences*. 2018; 8(5):826.
https://doi.org/10.3390/app8050826

**Chicago/Turabian Style**

Lohner, Tivadar, Benjamin Kalas, Peter Petrik, Zsolt Zolnai, Miklós Serényi, and György Sáfrán.
2018. "Refractive Index Variation of Magnetron-Sputtered a-Si_{1−x}Ge_{x} by “One-Sample Concept” Combinatory" *Applied Sciences* 8, no. 5: 826.
https://doi.org/10.3390/app8050826