Point Defects and Grain Boundaries Effects on Electrical Transports of PbTe Using the Non-equilibrium Green’s Function

doi:10.1007/s40195-025-01834-0

金属学报英文版 ›› 2025, Vol. 38 ›› Issue (5): 811-822.DOI: 10.1007/s40195-025-01834-0

收稿日期:2024-11-25 修回日期:2024-12-13 接受日期:2024-12-27 出版日期:2025-05-10 发布日期:2025-03-20

Point Defects and Grain Boundaries Effects on Electrical Transports of PbTe Using the Non-equilibrium Green’s Function

Mi Qin¹^,², Bingqing Cao¹^,², Pan Zhang³, Xuemei Zhang⁴^,⁵, Ziqi Han⁶, Xiaohong Zheng⁷, Xianlong Wang¹, Xin Chen⁸(), Yongsheng Zhang⁸()

¹Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China
²Science Island Branch of Graduate School, University of Science and Technology of China, Hefei 230026, China
³School of Physics, Hubei University, Wuhan 430062, China
⁴School of Physics and Electronic Information Engineering, Ningxia Normal University, Guyuan 756000, China
⁵Engineering Technology Research Centre for Nano-Structures and Functional Materials, Ningxia Normal University, Guyuan 756000, China
⁶Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
⁷College of Information Science and Technology, Nanjing Forestry University, Nanjing 210037, China
⁸Advanced Research Institute of Multidisciplinary Sciences, Qufu Normal University, Qufu 273165, China

Received:2024-11-25 Revised:2024-12-13 Accepted:2024-12-27 Online:2025-05-10 Published:2025-03-20
Contact: Xin Chen,chenxin@qfnu.edu.cn;Yongsheng Zhang,yshzhang@qfnu.edu.cn

摘要/Abstract

Abstract:

Defect engineering is a commonly methodology used to enhance the thermoelectric performance of thermoelectric PbTe by improving its electronic transport properties. At the nanoscale, defects can induce quantum tunneling effects that significantly impact the electrical properties of materials. To understand the specific mechanisms underlying the quantum transport properties of PbTe, we employ the non-equilibrium Green's function (NEGF) method to investigate the effects of intrinsic defects (point defects and grain boundaries) on the electronic transport properties of PbTe-based nanodevices from a quantum mechanical perspective. Our results show that the Pb vacancy (V_Pb) has the highest conduction. The conduction depends on the defect type, chemical potential and bias voltage. The presence of intrinsic point defects introduces impurity levels, facilitating the electron tunneling and leading to an increase in the transmission coefficient, thereby enhancing the electronic transport properties. For PbTe containing grain boundaries, these boundaries suppress the electronic transport properties. The Te occupied twin boundary (Te-TB) exerts a stronger inhibitory effect than the Pb occupied twin boundary (Pb-TB). Nevertheless, the combined effect between twin boundaries and point defects can enhance the electrical properties. Therefore, in order to obtain highly conductive of PbTe materials, a Te-rich synthesis environment should be used to promote the effective formation of Pb vacancy. Our work offers a comprehensive understanding of the impact of defects on electron scattering in thermoelectric materials.

Key words: Thermoelectric material, PbTe, Non-equilibrium Green’s function, Transmission, Defects

. [J]. 金属学报英文版, 2025, 38(5): 811-822.

Mi Qin, Bingqing Cao, Pan Zhang, Xuemei Zhang, Ziqi Han, Xiaohong Zheng, Xianlong Wang, Xin Chen, Yongsheng Zhang. Point Defects and Grain Boundaries Effects on Electrical Transports of PbTe Using the Non-equilibrium Green’s Function[J]. Acta Metallurgica Sinica (English Letters), 2025, 38(5): 811-822.

图/表 8

Fig. 1 Schematic diagram of a two-probe systems: a PbTe with intrinsic point defects. b PbTe with Pb and Te occupying the grain boundary. The red dashed lines indicate the positions of the twin boundaries. The blue dashed box indicates the location of the intrinsic point defects. The minimum twin spacing (U) is 1.14 nm in this nanotwin unit. The purple and blue spheres represent lead and tellurium atoms, respectively

Fig. 2 a Transmission function under zero bias voltage for the device with bulk PbTe and intrinsic point defects in PbTe. b Conductances of bulk PbTe and intrinsic point defects in PbTe at zero bias voltage. c The I-V curves for bulk PbTe and intrinsic point defects in PbTe with bias voltage

Fig. 3 EBS spectrum for the six different intrinsic point defected PbTe configurations: a Pb vacancy, b Te vacancy, c Pb interstitials, d Te interstitials, e PbTe anti-site and f TePb anti-site. The Fermi energy level is indicated by the horizontal white dashed line. The color bar represents the magnitude of the spectral weight, which characterizes the probability of the primitive cell eigenstates contributing to a particular supercell eigenstate of the same energy

Fig. 4 Averaged local density of states distribution over the x-y plane of the central scattering regions (Fig. 1a) as a function of electron energy and transport direction coordinate z for bulk PbTe and intrinsic point defects in PbTe: a Pb vacancy, b Te vacancy, c Pb interstitials, d Te interstitials, e PbTe anti-site and f TePb anti-site. The horizontal black dashed lines indicate the Fermi energy level. The black dashed box represents the location of the intrinsic point defects in PbTe. The color-coding values are given by the vertical bar

Fig. 5 a Transmission function under zero bias voltage for the device with bulk PbTe and PbTe nanotwin structures with Pb and Te occupying the twin boundary. b Conductances of bulk PbTe and PbTe nanotwin structures with Pb and Te occupying the twin boundary at zero bias voltage. c The I-V curves for bulk PbTe and PbTe nanotwin structures with Pb and Te occupying the twin boundary with bias voltage

Fig. 6 Averaged local density of states distribution over the xy plane of the central scattering regions (Fig. 1b) as a function of electron energy E and transport direction coordinate z for PbTe nanotwin structure with a Pb, b Te at the twin boundary, respectively. The horizontal black dashed lines indicate the Fermi energy level. The black dashed box represents the location of the twin boundary. The color-coding values are given by the vertical bar

Fig. 7 Transport properties of bulk PbTe, Pb vacancy in PbTe, Te vacancy in PbTe, PbTe twin boundaries, Te vacancy at Te-TB and Pb vacancy at Pb-TB: a transmission function under zero bias voltage, b zero bias conductance, c I-V curves, respectively,

Fig. 8 Averaged local density of states distribution over the x-y plane of the central scattering regions (Fig. 1) as a function of electron energy and transport direction coordinate z for a Pb vacancy in PbTe, b Te vacancy in PbTe, c Pb vacancy at Pb-TB, d Te vacancy at the Te-TB, respectively. The horizontal black dashed lines indicate the Fermi energy level. The black dashed box represents the location of point defects in the bulk PbTe and twin boundary. The color-coding values are given by the vertical bar

参考文献 33

[1]	L.E. Bell, Science 321,1457 (2008) DOI PMID
[2]	G.J. Snyder, E.S. Toberer, Nat. Mater. 7, 105 (2008)
[3]	K. Biswas, J. He, I.D. Blum, C.I. Wu, T.P. Hogan, D.N. Seidman, V.P. Dravid, M.G. Kanatzidis, Nature 489, 414 (2012)
[4]	X. Guan, Z. Liu, N. Ma, Z. Li, J. Liu, H. Zhang, H. Li, Q. Ba, J. Ma, C. Jin, A. Xia, Acta Metall. Sin.-Engl. Lett. (2024). https://doi.org/10.1007/s40195-024-01794-x
[5]	P. Chen, H. Xie, L. Zhao, Acta Metall. Sin.-Engl. Lett. (2024). https://doi.org/10.1007/s40195-024-01798-7
[6]	Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, G.J. Snyder, Nature 473, 66 (2011)
[7]	S. Lin, S. Wang, Y. Li, Z. Lai, X. Yang, X. Lu, M. Jin, Acta Metall. Sin.-Engl. Lett. (2024). https://doi.org/10.1007/s40195-024-01790-1
[8]	Y. Fan, C. Xie, J. Li, X. Meng, J. Sun, J. Wu, X. Tang, G. Tan, Energy Environ. Sci. 7, e12535 (2024)
[9]	J.P. Heremans, V. Jovovic, E.S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, G.J. Snyder, Science 321, 554 (2008) DOI PMID
[10]	G. Tan, C.C. Stoumpos, S. Wang, T.P. Bailey, L.D. Zhao, C. Uher, M.G. Kanatzidis, Adv. Energy Mater. 7, 1700099 (2017)
[11]	C. Wood, Rep. Prog. Phys. 51, 459 (1988)
[12]	C. Zhang, K. Jin, H. Dong, W. Xu, P. Xu, Z. Yan, W. Zhao, B. Xu, L. Fu, Nano Energy 126, 109615 (2024)
[13]	W. Qiu, H. He, Z. Wang, Q. Hu, X. Cui, Z. Wang, Y. Zhang, L. Gu, L. Yang, Y. Sun, L. Zhao, L. Chen, H. Deng, J. Tang, Nano Today 39, 101176 (2021)
[14]	Y. Wu, P. Nan, Z. Chen, Z. Zeng, R. Liu, H. Dong, L. Xie, Y. Xiao, Z. Chen, H. Gu, W. Li, Y. Chen, B. Ge, Y. Pei, Adv. Sci. 7, 1902628 (2020)
[15]	X. Zhang, M.Y. Toriyama, J.P. Male, Z. Feng, S. Guo, T. Jia, Z. Ti, G.J. Snyder, Y. Zhang, Mater. Today Phys. 19, 100415 (2021)
[16]	M. Qin, X. Zhang, J. Zhu, Y. Yang, Z. Ti, Y. Shen, X. Wang, X. Liu, Y. Zhang, J. Mater. Chem. A 11, 10612 (2023)
[17]	A. Goyal, P. Gorai, E.S. Toberer, V. Stevanović, N.P.J. Comput. Mater. 3, 42 (2017)
[18]	D. An, J. Wang, J. Zhang, X. Zhai, Z. Kang, W. Fan, J. Yan, Y. Liu, L. Lu, C.L. Jia, M. Wuttig, O.C. Miredin, S. Chen, W. Wang, G.J. Snyder, Y. Yuan, Energy Environ. Sci. 14, 5469 (2021)
[19]	Y. Zhou, J.Y. Yang, L. Cheng, M. Hu, Phys. Rev. B 97, 085304 (2018)
[20]	M. Fiorentini, N. Bonini, Phys. Rev. B 94, 085204 (2016)
[21]	P.E. Blochl, Phys. Rev. B 50, 17953 (1994)
[22]	J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996) DOI PMID
[23]	H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13, 5188 (1976)
[24]	J. Maassen, M. Harb, V. Michaud-Rioux, Y. Zhu, H. Guo, Proc. IEEE 101, 518 (2013)
[25]	S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, 2005)
[26]	S. Ahmad, S. Mahanti, K. Hoang, M. Kanatzidis, Phys. Rev. B 74, 155205 (2006)
[27]	M. Büttiker, Y. Imry, R. Landauer, S. Pinhas, Phys. Rev. B 31, 6207 (1985) PMID
[28]	P. Bauer Pereira, I. Sergueev, S. Gorsse, J. Dadda, E. Müller, R.P. Hermann, Phys. Status Solidi B 250, 1300 (2013)
[29]	Y.B. Xue, Y.T. Zhou, D. Chen, X.L. Ma, J. Alloys Compd. 582, 181 (2014)
[30]	M. Lannoo,Point Defects in Semiconductors I: Theoretical Aspects, vol. 22 (Springer, New York, 2012)
[31]	P. Brommer, D. Quigley, J. Phys. Condens. Matter 26, 485501 (2014)
[32]	K. Kushnir, K. Chen, L. Zhou, B. Giri, R.L. Grimm, P.M. Rao, L.V. Titova, J. Phys. Chem. C 122, 11682 (2018)
[33]	H. Hattori, J. Cryst. Growth 66, 205 (1984)

Point Defects and Grain Boundaries Effects on Electrical Transports of PbTe Using the Non-equilibrium Green’s Function

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