Evaluating the Relationship between Phonon and Thermal Properties of Group IV Alloys Using Molecular Dynamics Simulation
Authors: Tomita Motohiro , Ogasawara Masataka , Terada Takuya , Watanabe Takanobu 
Published: February 2020

Introduction

Group IV alloy semiconductor material is anticipated to be used for the miniaturized thermoelectric (TE) energy harvester, because it has high TE properties, which is called ZT (= S
2
σTκ
-1), is related to the Seebeck coefficient S, the electrical conductivity σ, the thermal conductivity κ, and the temperature T. In the previous study, it was indicated the drastically low thermal conductivity in group IV alloy is mainly caused by the mass disorder scattering of phonon [1]. The low thermal conductivity of group IV alloy was reproduced by our molecular dynamics (MD) simulations [2]. In classical MD simulation, it was considered the difference of the atomic mass and the interatomic potentials. Both mass and potential disorder scattering of phonon is deeply linked with the decreasing thermal conductivity.

In this study, we quantitatively investigated which disorder is more affected to thermal conductivity in the group IV alloys whose atomic mass and interatomic potentials were varied independently by MD simulations to clarify.

Simulation Procedure

The models in MD simulation were 28Si
x

73Si(1−x), 28Si
x

119Si(1−x), 28Si
x

28Ge(1−x), 28Si
x

28Sn(1−x), 28Si
x

73Ge(1−x), and 28Si
x

119Sn(1−x) wire with periodic boundary condition. The initial model length and the one side width of square were 30ai
and 4ai
Å, respectively. The employed interatomic potential is the Stillinger-Weber (SW) potential, which is defined by the sum of two- and three-body potential energy terms that depend on local geometric positions. This potential was optimized to reproduce the lattice constant and the phonon frequencies in the group IV alloy [2]. The thermal conductivity was calculated by equilibrium MD method. The phonon related properties were conducted from the Fourier analysis.

Results and Discussion

Fig. 1 shows 28Si concentration dependences of thermal conductivities. Red lines represent results of 28Si
x

73Si(1−x) and 28Si
x

119Si(1−x) alloys, purple lines represent results of 28Si
x

28Ge(1−x) and 28Si
x

28Sn(1−x) alloys, blue lines represent results of 28Si
x

73Ge(1−x), and orange lines represent calculation results from the research of Khatami et al. [1]. Fig. 2 shows the phonon dispersion of 28Si0.5
73Si0.5, 28Si0.5
28Ge0.5, and 28Si0.5
73Ge0.5 alloys. The changing of the thermal conductivities and the phonon dispersion is caused by mass and potential disorders. The amount of the changing by potential disorder is smaller than that of mass disorder.

Fig. 3 shows frequency spectra of vibration density of states (VDOS) and phonon lifetimes in 28Si0.5
73Si0.5, 28Si0.5
28Ge0.5, and 28Si0.5
73Ge0.5 alloys. The VDOS D(ω) is closely related to the phonon lifetime due to alloying τalloy, which is defined as τalloy
-1(ω) = (π/6)V
0Γalloy
D(ω)ω
2, where V
0 is volume per atom, Γalloy is scattering strength due to the mass and potential disorders, and ω is phonon frequencies. The phonon lifetime in 28Si0.5
28Ge0.5 is almost ten times than that of 28Si0.5
73Si0.5 and 28Si0.5
73Ge0.5.

The thermal conductivity is defined as κ(ω) = (1/3)C(ω)v
2(ω)τall(ω), and the phonon lifetime is defined as τall
-1(ω) = τpure
-1(ω) + τalloy
-1(ω) = τpure
-1(ω) + τmass
-1(ω) + τforce
-1(ω), where C is heat capacity, v is phonon velocity, τpure is phonon lifetime in pure crystal, τmass is mass disorder phonon lifetime, and τforce is potential disorder phonon lifetime [1].

When we assumed Cv
2 = 100, τpure = 1, τmass = 1/100, and τforce = 1/10, the thermal conductivity scattered by only potential disorder is 9.09, that scattered by only mass disorder is 0.99, and that scattered by both mass and potential disorder is 0.90. This tendency is agree to the results of MD calculation. The mass disorder is dominant factor for the changing of the thermal and phonon properties. Moreover, the potential disorder is ignorable in phonon and thermal calculation by MD method.

Acknowledgements

This study was partially supported by the Japan Science and Technology Agency’s (JST) CREST program (JPMJCR15Q7) and the Japan Society for the Promotion of Science (JSAP) through a Grant-in-Aid for JSPS Fellows (15J07583).

References

[1] S. N. Khatami et al., Phys. Rev. Appl. 6, 014015 (2016). [2] M. Tomita et al., Jpn. J. Appl. Phys. 57, 04FB04 (2018).

Figure 1