Enhanced Thermoelectric Properties in Na-Doped PbTe via Pb Vacancies and Trace Eu Doping

Enhancing the thermoelectric performance of Na-doped PbTe is challenging due to the low solubility of Na, a problem that remains insufficiently explored from a theoretical perspective, particularly regarding the role of Pb vacancies. In this study, we utilize crystal orbital Hamilton population and electron localization function analyses to investigate the impact of Pb vacancies on Na solubility in PbTe. Our findings indicate that Pb vacancies strengthen Na-Te bonding and improve electron localization around Te atoms, which reduces the formation of Te vacancies and facilitates a higher dissolution of Na. Furthermore, we examine the effects of trace Eu doping in Pb