Silicon-germanium (SiGe) is used for thermoelectric devices since its thermal conductivity is lower than either pure Si or Ge. Indeed, the material was used in components of the Voyager and New Horizons deep-space craft because of its superior nanoscale heat conductivity. Improving SiGe for better thermoelectric devices requires ever more precise measurements of nanoscale heat conductivity and a comprehensive study on its phonon-scattering mechanism. Especially, a relationship between Raman shift ω and temperature T (dω/dT) is required through the highly precise measurements of its temperature-dependence. Burke et al. have reported the Ge fraction dependence of dω/dT for Si-Si, Si-Ge, and Ge-Ge vibration modes of polycrystalline bulk SiGe samples with high laser power excitation [1]. However, the reported values of dω/dT may be affected by phonon scattering at grain boundaries and the local heating caused by high laser power excitation. Here, we investigated dω/dT of single-crystalline bulk SiGe and its dependence on the Ge fraction by using variable-temperature Raman spectroscopy.

Experiments

The (001)-oriented single-crystalline Si-rich SiGe bulk samples were prepared by two different growth methods; the Czochralski (Ge fraction: 16%) [2] and traveling liquidus zone (TLZ) methods (Ge fraction: 32 and 45%) [3]. All samples were confirmed to be strain-free by X-ray diffraction (XRD). We also measured Raman spectrum of single-crystalline Si as a reference. For Raman spectroscopy measurements, the wavelength of the excitation source was 532 nm, the focal length of the spectrometer was 2,000 mm, the laser power at the sample surface was kept to less than 1 mW. The sample temperatures were set between 50 and 300°C in 50°C steps, and the Raman signal was measured twice at each temperature (i.e., during heating and cooling).

Results and Discussion

Raman spectra of Si-Si mode in SiGe (Ge fraction: 16%) are shown in Fig. 1(a). With increasing temperature, the full width at half maximum (FWHM) of the Raman spectra increased and shifted toward the lower side of wavenumber. This wavenumber shift is considered to be caused by the anharmonic vibrations becoming dominant as the temperature increases, and the phonon frequency decrease due to the thermal expansion of the crystal. Figure 1(b) shows the temperature dependences of the Si-Si Raman peak shifts. We experimentally clarified the dω/dT are approximately constant in each bulk SiGe sample, as shown in Fig. 1(b). Figure 1(c) shows the Ge fraction dependence of -(dω/dT) for Si-Si mode. As a result, we found that dω/dT for Si-Si mode is independent of Ge fraction unlike the study of Burke et al. It was reported that the dω/dT depends on the coefficient of linear thermal expansion and anharmonic constants [4]. From the obtained dω/dT values in the investigated range of Ge fraction, we consider that the anharmonic constants of SiGe alloy do not change by Ge fraction. Thus, the Si-Si anharmonic vibration is supposed to be not affected by the Ge fraction in SiGe alloy. In conclusion, we determined dω/dT= -0.023 cm^-1/℃ for Si-Si mode from experiments with single-crystalline bulk SiGe samples and low laser power excitation.

Acknowledgement

This work was supported by Grant-in-Aid for Scientific Research (21K14201).

References

[1] H. H. Burke, et al., Phys. Rev. B 48, 15016 (1993).

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

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

[4] G. S. Doerk, et al., Phys. Rev. B 80, 073306 (2009).