Evaluation of Temperature Variation in the Debye-Waller Factor for Single Crystalline Bulk Silicon Germanium by XAFS
Authors: Yoshioka Kazutoshi , Hanafusa Shusei , Nishi Yukihito , Arai Yasutomo , Hirosawa Ichiro , Watanabe Takeshi , Yokogawa Ryo , Ogura Atsushi 
Published: November 2022

1. Background and purpose

Silicon germanium (SiGe) is expected as a next-generation electronic and thermoelectric device materials because of its higher carrier mobility than Si and lower thermal conductivity than Si and Ge. Therefore, it is important to understand the carrier scattering and phonon transport properties in order to apply SiGe as a device. We have reported that the atomic vibration in Si-rich SiGe thin films on Si substrates may be suppressed by the lattice strain, based on X-ray absorption fine structure (XAFS) measurements [1]. In this study, we demonstrated XAFS spectra of strain-free single crystalline bulk SiGe and estimated the Einstein temperature (T
E) which characterizes phonons, to investigate the influence of Ge fraction and lattice strain in SiGe at nanoscale.

2. Experimental method

Strain-free single crystalline bulk SiGe were grown by the traveling liquidus zone method with Ge fractions of 32 and 45 % [2]. We measured the XAFS spectra of the Ge-K absorption edge for the bulk SiGe in the transmission mode at BL14B2 in the SPring-8 synchrotron facility. We also measured a single crystalline bulk Ge as a reference sample. The sample temperature was controlled between 10 - 600 K using a refrigerator or a heating cell during measurements. Then, we extracted the EXAFS oscillations from the obtained XAFS spectra in order to investigate the temperature variation of the Debye-Waller factor.

3. Results and discussion

Figure 1 shows the temperature dependence of the change in the Debye-Waller factor with reference to 10 K (Δσ
2) for Ge, SiGe thin films, and bulk SiGe. From Fig. 1, the change in Δσ
2 with temperature is slower for SiGe than for Ge. The effect of Ge fraction on the change in Δσ
2 is negligible. Further, the changes in Δσ
2 with temperature for SiGe were similar regardless of the lattice strain. Therefore, it is confirmed that the Ge fraction and the lattice strain in SiGe have little effect on the atomic vibration.
Here, since σ
2 is expressed by Eq. (1) [3], Δσ
2 can be expressed as Eq. (2), where T is the absolute temperature, σ
s
2 is the static Debye-Waller factor, A is a constant, and T
E is the Einstein temperature.

σ
2(T) = σ
s
2 + Acoth(T
E / 2T), (1)
Δσ
2(T) = A[coth(T
E / 2T) – coth{T
E / (2 × 10)}], (2)
The relationship between T
E and the Ge fraction obtained from Eq. (2) is shown in Fig. 2. Figure. 2 indicates that T
E decreases with increasing Ge fraction in Si-rich SiGe, suggesting that phonons are easily excited in SiGe with a high Ge fraction. Thus, it is considered that the effect of Ge fraction on atomic vibration in SiGe is much larger than their inner strains.

4. Acknowledgment

The XAFS measurements were performed at BL14B2 in SPring-8, approved by JASRI, under proposal numbers 2019A1773, 2019B1802, and 2021A1661.

References

[1] Yoshioka et al.,
ECS Trans.
98, 473 (2020).
[2] Kinoshita, et al., Jpn. J. Appl. Phys. 54, 04DH03 (2015).
[3] Purans, et
al., Phys. Rev. Lett. 100, 055901 (2008).

Figure 1