Evaluation of Phonon Dispersion Relation for Bulk Silicon Germanium by Inelastic X-ray Scattering

Abstract

1. Introduction Silicon germanium (SiGe) is one of the promising candidates as a next-generation material for thermoelectric devices as an ambient energy harvesting technique because it has low thermal conductivity. For a SiGe thermoelectric device, it is important to reveal the phonon scattering mechanism for the alloy material and the thermal transport in miniaturization to the nanoscale. However, the origin of the low thermal conductivity of the SiGe alloy has not been investigated in a sufficiently rigorous manner yet. In addition, the correlation among the thermal conductivity, the phonon dispersion curve, and the lifetime remains mostly unclear.From the above, we focused on direct phonon properties evaluation by inelastic X-ray scattering (IXS) with synchrotron radiation. IXS is a powerful technique that reveals the phonon dispersion curves in contrast to Raman spectroscopy, which can only give optical phonon modes at the Brillouin zone center (the Γ point). In this study, we evaluated the phonon dispersion curve of bulk SiGe by IXS. 2. Experimental method The single-crystalline SiGe samples for IXS were prepared by two different growth methods: the Czochralski (Cz) [1] and traveling liquidus zone (TLZ) methods [2]. The sample information is summarized in Table 1. Prior to the IXS measurements, the crystal orientation and Ge fraction were confirmed by X-ray diffraction (XRD) and electron backscattering pattern (EBSP) measurements, respectively.The IXS measurements were performed at the BL35XU beamline of the SPring-8 synchrotron facility. The measurements were conducted at room temperature using a reflection geometry. The incident X-ray energy was set to 17.795 keV, which corresponds to Si (9 9 9) reflection, and the overall energy resolution was around 3 meV. The incident X-ray beam size was approximately 60 x 75 μm2. The measurements were conducted along the Γ-X ([00q]) direction. 3. Results and Discussion As an example of phonon dispersion of bulk Si1-x Ge x , we show the IXS results of x = 0.45 in Fig. 1 obtained by peak positions of IXS spectra. As a result, all optical and acoustic phonon modes for bulk SiGe were observed as shown in Fig. 1. In addition, the energy of the optical phonon modes (Si-Si, Si-Ge, and Ge-Ge modes) obtained by IXS at the zone center (Γ point) was good agreement with results of Raman spectroscopy (λ = 532 nm). Both Raman and IXS indicate that, at around Γ point, the phonon energies of Si-Si and Ge-Ge modes tend to be lower than that of pure Si and Ge, respectively. These behaviors can be considered to be caused by random distribution of Si and Ge atoms in the alloy. On the other hand, it was revealed that the acoustic phonon (LA and TA modes) energies are located between those of pure Si [3] and Ge [4]. Based on the above, the origin of the dramatic thermal conductivity reduction of the SiGe alloy, which has been reported in previous study [5], may not be derived from the reduction of group velocity, but the low phonon lifetime reduction. Acknowledgements The IXS measurements were performed at SPring-8 with the approval of JASRI (Proposal Nos. 2016A1496, 2017B1630, 2019A1678, and 2019B1750). The authors thank Dr. Koji Usuda (KIOXIA Corp.) for his great support with analyzing the IXS results throughout the work.