Abstract
Semiconductor dopability is inherently limited by intrinsic defect chemistry. In many thermoelectric materials, narrow band gaps due to strong spin–orbit interactions make accurate atomic level predictions of intrinsic defect chemistry and self-doping computationally challenging. Here we use different levels of theory to model point defects in PbTe, and compare and contrast the results against each other and a large body of experimental data. We find that to accurately reproduce the intrinsic defect chemistry and known self-doping behavior of PbTe, it is essential to (a) go beyond the semi-local GGA approximation to density functional theory, (b) include spin–orbit coupling, and (c) utilize many-body GW theory to describe the positions of individual band edges. The hybrid HSE functional with spin–orbit coupling included, in combination with the band edge shifts from G0W0 is the only approach that accurately captures both the intrinsic conductivity type of PbTe as function of synthesis conditions as well as the measured charge carrier concentrations, without the need for experimental inputs. Our results reaffirm the critical role of the position of individual band edges in defect calculations, and demonstrate that dopability can be accurately predicted in such challenging narrow band gap materials.
Highlights
The dopability of semiconductor materials plays a decisive role in device performance
By using hybrid functionals (HSE stands for HSE0638,39) along with spin–orbit coupling to perform defect calculations and quasi-particle GW approach to describe the valence and conduction band edges, we obtain (1) a quantitatively accurate description of the defect chemistry and associated free carrier concentrations in PbTe, and (2) bipolar doping behavior, in agreement with experiments
We show that all other levels of theory (GGA, generalized gradient approximation (GGA) + Spin–orbit coupling (SOC), GGA + SOC + GW, HSE, HSE + SOC) qualitatively fail to describe the experimentally observed self-doping behavior in PbTe
Summary
The dopability of semiconductor materials plays a decisive role in device performance. Note that band gaps are further corrected based on band edge shifts computed using quasi-particle GW calculations a References 31,68 b References 42,68,69 including SOC effects and found PbTe to be intrinsically n-type under both Te-poor and Te-rich conditions, and found p-type behavior under intermediate Te-rich conditions This is in contrast to experimentally-observed p-type conductivity under Te-rich conditions and n-type under Te-poor conditions.[34,35,36,37]. By using hybrid functionals (HSE stands for HSE0638,39) along with spin–orbit coupling to perform defect calculations and quasi-particle GW approach (at G0W0 level) to describe the valence and conduction band edges, we obtain (1) a quantitatively accurate description of the defect chemistry and associated free carrier concentrations in PbTe, and (2) bipolar doping behavior, in agreement with experiments. Our findings highlight (1) the importance of accurate band edge energies in predicting dopability for systems with strong SOC and (2) that quantitatively accurate dopability predictions are achievable in such challenging material systems
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