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

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

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.

Figures/Tables 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

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