材料科学

热电材料PbTe能带带隙温度相关性的第一性原理计算

  • 甘露 ,
  • 杨炯 ,
  • 奚晋扬
展开
  • 上海大学 材料基因组工程研究院, 上海 200444

收稿日期: 2025-07-03

  网络出版日期: 2026-03-16

基金资助

国家重点研发计划资助项目(2024YFF0505900);国家自然科学基金资助项目(52172216,92163212)

Temperature-dependent band gap of thermoelectric PbTe from first-principles calculations

  • GAN Lu ,
  • YANG Jiong ,
  • XI Jinyang
Expand
  • Materials Genome Institute, Shanghai University, Shanghai 200444, China

Received date: 2025-07-03

  Online published: 2026-03-16

摘要

能带带隙是半导体材料重要性质之一,已有研究表明温度诱导的结构振动对材料带隙具有显著影响.采用第一性原理计算了热电材料PbTe在有限温度下的能带,考察了电声耦合重整化(electron-phonon renormalization,EPR)和自旋轨道耦合(spin-orbit coupling,SOC)效应对带隙温度依赖性的影响.研究结果表明:EPR效应导致PbTe带隙随温度升高而变化;SOC的引入使得带隙变化趋势发生反转(未考虑SOC,温度从0 K升至750 K,带隙减小88 meV;考虑SOC,带隙则增大144 meV);零点振动对带隙变化的贡献较小.因此,EPR效应和SOC效应对PbTe带隙有重要影响,不可忽略.该成果为理解PbTe带隙温度依赖性提供了理论依据,对其热电性能优化具有指导意义.

本文引用格式

甘露 , 杨炯 , 奚晋扬 . 热电材料PbTe能带带隙温度相关性的第一性原理计算[J]. 上海大学学报(自然科学版), 2026 , 32(1) : 33 -43 . DOI: 10.12066/j.issn.1007-2861.2700

Abstract

The band gap is one of the most fundamental properties of semiconductors. Manystudies have demonstrated that temperature-induced vibrations have a significant impact on the band gap. In this paper, the band structure of the thermoelectric compound PbTe at finite temperature is investigated using first-principles calculations, focusing on the effects of electron-phonon renormalization (EPR) and spin-orbit coupling (SOC) on the temperature-dependentband gap. The results reveal that EPR leads to temperature- dependent variations in the band gap of PbTe, while the inclusion of SOC reverses the trend of band gap change (without SOC, the band gap decreases by 88 meV as the temperature rises from 0 K to 750 K, while the band gap increases by 144 meV with SOC). Furthermore, the zero-point renormalization contributes minimally to the band gap change. Therefore, both EPR and SOC effects have a significant influence on the band gap of PbTe and must be taken into account. This paper provides theoretical insight into the temperature dependence of PbTe’s band gap and ofiers guidance for optimizing its thermoelectric performance.

参考文献

[1] Biswas K, He J, Blum I D, et al. High-performance bulk thermoelectrics with all-scale hierarchical architectures [J]. Nature, 2012, 489(7416): 414-418.
[2] Jia B H, Huang Y, Wang Y, et al. Realizing high thermoelectric performance in nonnanostructured n-type PbTe [J]. Energy & Environmental Science, 2022, 15(5): 1920-1929.
[3] Varshni Y P. Temperature dependence of the energy gap in semiconductors [J]. Physica, 1967, 34(1): 149-154.
[4] Gobel A, Ruf T, Cardona M, et al. Efiects of the isotopic composition on the fundamental gap of CuCl [J]. Physical Review B, 1998, 57(24): 15183-15190.
[5] D’innocenzo V, Grancini G, Alcocer M J P, et al. Excitons versus free charges in organolead tri-halide perovskites [J]. Nature Communications, 2014, 5(1): 3586.
[6] Giustino F, Louie S G, Cohen M L. Electron-phonon renormalization of the direct band gap of diamond [J]. Physical Review Letters, 2010, 105(26): 265501.
[7] Ponce S, Antonius G, Gillet Y, et al. Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation [J]. Physical Review B, 2014, 90(21): 214304.
[8] Ponce S, Gillet Y, Laflamme J J, et al. Temperature dependence of the electronic structure of semiconductors and insulators [J]. The Journal of Chemical Physics, 2015, 143(10): 102813.
[9] Giustino F. Electron-phonon interactions from first principles [J]. Reviews of Modern Physics, 2017, 89(1): 015003.
[10] Saidi W A, Ponce S, Monserrat B. Temperature dependence of the energy levels of methylammonium lead iodide perovskite from first-principles [J]. The Journal of Physical Chemistry Letters, 2016, 7(24): 5247-5252.
[11] Antonius G, Ponce S, Lantagne-Hurtubise E, et al. Dynamical and anharmonic effects on the electron-phonon coupling and the zero-point renormalization of the electronic structure [J]. Physical Review B, 2015, 92(8): 085137.
[12] Quarti C, Mosconi E, Ball J M, et al. Structural and optical properties of methylammonium lead iodide across the tetragonal to cubic phase transition: implications for perovskite solar cells [J]. Energy & Environmental Science, 2016, 9(1): 155-163.
[13] Zhang Y, Ke X, Kent P R C, et al. Anomalous lattice dynamics near the ferroelectric instability in PbTe [J]. Physical Review Letters, 2011, 107(17): 175503.
[14] Zacharias M, Giustino F. One-shot calculation of temperature-dependent optical spectra and phonon-induced band-gap renormalization [J]. Physical Review B, 2016, 94(7): 075125.
[15] Zhang Y M, Wang Z Y, Xi J Y, et al. Temperature-dependent band gaps in several semiconductors: from the role of electron{phonon renormalization [J]. Journal of Physics: Condensed Matter, 2020, 32(47): 475503.
[16] Pei Y Z, Shi X Y, Lalonde A, et al. Convergence of electronic bands for high performance bulk thermoelectrics [J]. Nature, 2011, 473: 66-69.
[17] An J M, Franceschetti A, Zunger A. Electron and hole addition energies in PbSe quantum dots [J]. Physical Review B, 2007, 76(4): 045401.
[18] Mahan G D. Figure of merit for thermoelectrics [J]. Journal of Applied Physics, 1989, 65(4): 1578-1583.
[19] Hook J R, Hall H E. Solid state physics [M]. New York: John Wiley & Sons, 2013.
[20] Wang Z Y, Xi J, Ning J, et al. Temperature-dependent band renormalization in CoSb3 skutterudites due to Sb-ring-related vibrations [J]. Chemistry of Materials, 2021, 33(3): 1046-1052.
[21] Ning J, Zheng L, Lei W, et al. Temperature-dependence of the band gap in the all-inorganic perovskite CsPbI3 from room to high temperatures [J]. Physical Chemistry Chemical Physics, 2022, 24(26): 16003-16010.
[22] Zhao Y H, Li Y X, Xi J Y, et al. Signiflcant temperature tunability of the band gap in two-dimensional materials [J]. Computational Materials Today, 2025, 5: 100019.
[23] Hohenberg P, Kohn W. Inhomogeneous electron gas [J]. Physical Review B, 1964, 136(3): 864-871.
[24] Kresse G, Furthmuller J. E-cient iterative schemes for ab initio total-energy calculations using a plane-wave basis set [J]. Physical Review B, 1996, 54(16): 11169.
[25] Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method [J]. Physical Review B, 1999, 59(3): 1758.
[26] Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals [J]. Physical Review B, 1993, 47(1): 558-561.
[27] Blochl P E. Projector augmented-wave method [J]. Physical Review B, 1994, 50(24): 17953.
[28] Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple [J]. Physical Review Letters, 1996, 77(18): 3865.
[29] Togo A, Tanaka I. First principles phonon calculations in materials science [J]. Scripta Materialia, 2015, 108: 1-5.
[30] Monkhorst H J, Pack J D. Special points for brillouin-zone integrations [J]. Physical Review B, 1976, 13(12): 5188-5192.
[31] Medeiros P V C, Stafstrom S, Bj ork J. Efiects of extrinsic and intrinsic perturbations on the electronic structure of graphene: retaining an effective primitive cell band structure by band unfolding [J]. Physical Review B, 2014, 89(4): 041407.
[32] Medeiros P V C, Tsirkin S S, Stafstrom S, et al. Unfolding spinor wave functions and expectation values of general operators: introducing the unfolding-density operator [J]. Physical Review B, 2015, 91(4): 041116.
[33] Kumar J, Tanwar P, Paliwal U, et al. Ab initio study of elastic, electronic, and vibrational properties of SnTe and PbTe [J]. Journal of Molecular Modeling, 2023, 29(11): 335.
[34] Albanesi E A, Okoye C M I, Rodriguez C O, et al. Electronic structure, structural properties, and dielectric functions of Ⅳ-Ⅵ semiconductors: PbSe and PbTe [J]. Physical Review B, 2000, 61(24): 16589-16595.
[35] Gibbs Z M, Kim H, Wang H, et al. Temperature dependent band gap in PbX (X=S, Se, Te) [J]. Applied Physics Letters, 2013, 103: 262109.
[36] Lu L, Sun Y Y. Temperature dependence of spin-orbit coupling effect in solids [J]. Physical Review B, 2025, 111(8): 085129.
[37] Querales-Flores J D, Aguado-Puente P, Dangic D, et al. Towards temperature-induced topological phase transition in SnTe: a first- principles study [J]. Physical Review B, 2020, 101(23): 235206.
文章导航

/