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 (= S²σTκ^-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_x⁷³Si_(1−x), ²⁸Si_x¹¹⁹Si_(1−x), ²⁸Si_x²⁸Ge_(1−x), ²⁸Si_x²⁸Sn_(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 30a_i and 4a_i 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_x⁷³Si_(1−x) and ²⁸Si_x¹¹⁹Si_(1−x) alloys, purple lines represent results of ²⁸Si_x²⁸Ge_(1−x) and ²⁸Si_x²⁸Sn_(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 ²⁸Si_0.5⁷³Si_0.5, ²⁸Si_0.5²⁸Ge_0.5, and ²⁸Si_0.5⁷³Ge_0.5 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 ²⁸Si_0.5⁷³Si_0.5, ²⁸Si_0.5²⁸Ge_0.5, and ²⁸Si_0.5⁷³Ge_0.5 alloys. The VDOS D(ω) is closely related to the phonon lifetime due to alloying τ_alloy, which is defined as τ_alloy^-1(ω) = (π/6)V₀Γ_alloyD(ω)ω², where V₀ is volume per atom, Γ_alloy is scattering strength due to the mass and potential disorders, and ω is phonon frequencies. The phonon lifetime in ²⁸Si_0.5²⁸Ge_0.5 is almost ten times than that of ²⁸Si_0.5⁷³Si_0.5 and ²⁸Si_0.5⁷³Ge_0.5.

The thermal conductivity is defined as κ(ω) = (1/3)C(ω)v²(ω)τ_all(ω), and the phonon lifetime is defined as τ_all^-1(ω) = τ_pure^-1(ω) + τ_alloy^-1(ω) = τ_pure^-1(ω) + τ_mass^-1(ω) + τ_force^-1(ω), where C is heat capacity, v is phonon velocity, τ_pure is phonon lifetime in pure crystal, τ_mass is mass disorder phonon lifetime, and τ_force is potential disorder phonon lifetime [1].

When we assumed Cv² = 100, τ_pure = 1, τ_mass = 1/100, and τ_force = 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).