We investigated the dependence of the maximum figure of merit of SiGe alloy on the material parameter B. We used Si_xGe_1-x samples with N- and P-type conductivity and different component compositions. For comparison, we calculated (ZT)_max ̶ B dependences for SiGe, as well as for materials containing them according to the data available in the literature. For both types Si_xGe_1-x the dependence (ZT)_max ̶ B forms a regular network together with the data for thermoelectrics containing SiGe and separately for Si or Ge. It is similar to the dependence (ZT)_max – B* (generalized parameter) of thermoelectric materials. The temperature dependence of the electronic quality factor is also considered, which provides information on the presence of additional effects. For p- and n-Si_xGe_1-x, these dependencies initially indicate the presence of additional scattering, and then band convergence and the bipolar effect are added.

Introduction

In this work, we used the dependence of the maximum figure of merit (ZT=σS²T/k; σ—specific electrical conductivity; S—Seebeck coefficient; T—absolute temperature; and k—total thermal conductivity) of SiGe alloy on the material parameter B=B_ET/k_L (B_E= σS²/B_S is electronic quality factor, B_S ≅ is the scaled power factor, S_r≅1.16∙10⁴ is the reduced Seebeck coefficient), and k_L is the lattice component of thermal conductivity. We used Si_xGe_1-x samples with p- and n-type conductivity and different component compositions. For comparison, we calculated (ZT)_max ̶ B dependences for SiGe, as well as for materials containing them according to the data available in the literature [1,2].

Method

We used Si_xGe_1-x samples with different component compositions (x = 0.7, 0.72, 0.76, 0.8, and 0.83). Boron was used as a dopant to obtain p-type conductivity, and phosphorus was used for n-type conductivity. The initial charge carrier concentration was 3.2∙10²⁶ m⁻³. It was determined by measuring the Hall constant at room temperature. The studies were conducted at temperatures of 30–1150 °C: the upper limit was limited by the melting point of the alloy. The measurement error for S was ~3%, and for resistivity ρ (=σ⁻¹), ~5%. Thermal conductivity was also measured with an error of no more than ~7%. The methodology for sample preparation is described in previous works [3,4].

Results

In addition to our samples, parameter B was also calculated for Ge_0.9Bi_0.1Te, nano-SiGe, Si+2%P, Si_0.88P_0.02, Si₈₀Ge₂₀+2%P, Si_0.58Ge_0.42, GeTe+1%Sb, GeTe+3%Sb, nanocrystalline Si, Ge_0.98In_0.02Te, SiGe+3%SrTiO₃, (Si_0.8Ge_0.2)_0.98P_0.02(SiC)_0.03, Cu₂₆Cr₂Ge₆S₃₂, (Si_0.8Ge_0.2)_0.98P_0.02(SiC)_0.015, Cu₂₆CrWGe₆S₃₂, (MnSi_1.7/Ge)₆, SiGe+5%Mg₂Si, GeTe, Ge_0.98Ta_0.02Te, Ge_0.92Ta_0.02Sb_0.06Te, SiGe, Si₉₅Ge₅P₂, Bi_0.06In_0.01Cd_0.02Te, Ge_0.888Sb_0.1In_0.012Te, Si_0.99P_0.01, GeTe+0.1%C₆₀, Ge_0.89Sb_0.1In_0.01Te, GeTe+5%Bi, Ge_0.995W_0.005Te, Ge_0.893Sb_0.1In_0.007Te, Ge_0.93In_0.01Bi_0.06Te, Ge_0.91Sb_0.09Te, Ge_0.92Sb_0.08Te, GeTe+0.2%C₆₀, nanostructured Si₈₀Ge₂₀, WSi₂+Si_xGe_1-x, and others.

For both types of Si_xGe_1-x, the dependence (ZT)_max ̶ B forms a regular network together with the data for thermoelectrics containing SiGe and separately for Si or Ge. This dependence is similar to the dependence (ZT)_max – B* (generalized parameter [5]) of thermoelectric materials.

We note that the issue of maximizing the figure of merit for Si_xGe_1-x was also considered by us in previous work [6]. There, the following empirical formulas were obtained: (ZT)_max≅3.2B+0.05, (ZT)_max≅0.39x+0.28 and lg(ZT)_max≅-0.4lgσ'+6.2, where σ' is the universal electrical conductivity (σ'=(q/k_B)²σ/B_E=(q/k_B)²B_S/S²). The dependence (ZT)_max – B differs from the dependence obtained in this work, since only our samples were considered there.

Conclusion

We investigated the dependence of the maximum figure of merit of SiGe alloy on the material parameter B. We used Si_xGe_1-x samples with p- and n-type conductivity and different component compositions. For comparison, we calculated (ZT)_max ̶ B dependences for SiGe, as well as for materials containing them according to the data available in the literature. For both types of Si_xGe_1-x, the dependence (ZT)_max ̶ B forms a regular network together with the data for thermoelectrics containing SiGe and separately for Si or Ge. For p- and n-Si_xGe_1-x, the temperature dependences of the electron quality factor initially indicate the presence of additional scattering, and then band convergence and the bipolar effect are added.

References

1. Wang J., YinY., Che Ch., Cui M. Energies, 2025, 18, 2122.
2. Sun F.-H., Li H., Tan J. et al. Materiomics, 2024, 218-233.
3. Bokuchava G., Barbakadze K, Nakhutsrishvili I. Material Sci. & Engin., 2023, 7, 54-57.
4. Bokuchava G., Barbakadze K., Nakhutsrishvili I. Bull. Georg. Acad. Sci., 2023, 17, 33-37.
5. Liu W., Han Z., Ji J. et al. Materials Today Phys., 2022, 31, 100989.
6. Nakhutsrishvili I., Adamia , Kakhniashvili G. Materials Sci. Res. and Rev., 2023, 6, 918-922.