Investigation of Phonon Spectral Model for Silicon-Germanium By Inelastic X-Ray Scattering and Raman Spectroscopy
Authors: Yokogawa Ryo , Ito Yuta , Maeda Yuiha , Arai Yasutomo , Yonenaga Ichiro , Ogura Atsushi 
Published: December 2024

Background and purpose

Silicon-germanium (SiGe) alloy thin films are expected to be candidates for next-generation electronic and thermoelectric device materials because they have much lower thermal conductivity than Si and Ge single crystals and high hole-mobility. It is gradually becoming important to understand the physical properties of SiGe in devices. Raman spectroscopy is widely used to evaluate strain, Ge fraction, and temperature from Raman shift. The Raman shifts are Ge fraction dependent, and asymmetric broadening of the Raman spectra occurs at the low energy side. This is because the momentum conservation is relaxed due to the random atom position, and the phonons other than the zone center (Γ point) are excited. Raman scattering of alloy materials can be explained by a spatial correlation model [1] to understand nanoscale characterization. However, Raman spectral fitting of SiGe using a spatial correlation model has not been performed because the phonon dispersion curves of SiGe are unclear. In this study, we investigated the accurate Raman spectral fitting of SiGe using a spatial correlation model based on the SiGe phonon dispersion curve observed by X-ray inelastic scattering (IXS) to understand the local ordering of atoms in SiGe alloy.

Experiments

The (001)-oriented bulk SiGe samples were prepared by two different growth methods: the Czochralski (Ge fraction: 16%) [2] and the traveling liquidus zone (Ge fraction: 32 and 45%) [3] methods. The crystal orientation and Ge fraction were confirmed by X-ray diffraction measurement.

The IXS measurements were performed at the BL35XU beamline of the SPring-8 synchrotron facility [4]. The measurements were performed at room temperature using a reflection geometry. The incident X-ray energy was 17.795 keV, which corresponds to Si (9 9 9) reflection, and the overall energy resolution is 3 meV. The measurements were performed along the Γ-X ([00q]) direction.

We obtained the Raman spectra of Si-Si, Si-Ge, and Ge-Ge vibrational modes derived from the bulk SiGe. The focal length and wavenumber resolution of the Raman spectrometer were 2,000 mm and 0.1 cm-1, respectively. The excitation light source was a green laser (wavelength: 532 nm).

Results and discussion

Figure 1 shows the phonon dispersion curves ([00q]) of the longitudinal optical (LO) mode for Si-Si vibration obtained by IXS. The phonon dispersion curves of bulk Si are shown in Ref. [5]. As the Ge fraction increases, the phonon dispersion curve shifts to the lower energy side and the curvature decreases. Figure 2 shows the results of Raman spectral fitting of the Si-Si mode for bulk SiGe (Ge fraction: 32%) using a spatial correlation model. We used the model for fitting as shown in the inset of Fig. 2, where q, L, and α are momentum, spatial correlation length, and spatial correlation weighting parameter, respectively. ω and Γ0 are Raman shift and natural width, respectively [6]. ω(q) is the phonon dispersion curve. We reproduced the spectrum based on the LO mode phonon dispersion curve of SiGe, and the Roodenko model was applied to α [7]. The fitting results showed that the asymmetric broadening in Raman spectra is reproduced by an application of the spatial correlation model based on the phonon dispersion curves by IXS. In addition, we found that the values of L for Si-Si bonds in bulk SiGe using a spatial correlation model was small as the Ge fraction increases.

In conclusion, we investigated the SiGe Raman spectral model based on the SiGe phonon dispersion curve. The proposed model provides an accurate Raman spectral fit and clarifies the nanoscale characterization of the SiGe alloy.

Acknowledgements

The IXS measurements were performed at SPring-8 with the approval of JASRI (Proposal Nos. 2019A167, 2019B1750, 2020A1463, and 2020A0662). This work was supported by JSPS KAKENHI Grant Number 21K14201, Japan.

References

[1] P. Parayanthal et al., Phys. Rev. Lett. 52, 1822 (1984).

[2] I. Yonenaga, J. Cryst. Growth 275, 91 (2005).

[3] K. Kinoshita et al., Jpn. J. Appl. Phys. 54, 04DH03 (2015).

[4] A. Q. R. Baron et al., J. Phys. Chem. Solids 61, 461 (2000).

[5] Md. N. Islam et al., J. Appl. Phys. 98, 024309 (2005).

[6] K. Nagata et al., Jpn. J. Appl. Phys. 53, 032401 (2014).

[7] K. Roodenko et al., Phys. Rev. B 82, 115210 (2010).

Figure 1