Optimal Carrier Concentration for High Thermoelectric Performance of Lead Substituted Bismuth Telluride in p-Type Doping

Abstract

Bi\(_{2}\)Te\(_{3}\) and its alloys are the well-known state-of-the-art thermoelectric materials operating at around room temperature. With lead substituted, the newly formed quasi-binary compound PbBi\(_{4}\)Te\(_{7}\), shows relatively high electrical conductivity and Seebeck coefficient. In this report, we employed the solution of the Boltzmann Transport Equation in a constant relaxation-time approximation within a first-principles density-functional-theory calculation to explore the role of the electronic thermal conductivity, \(\kappa _{e}\), on the thermoelectric performance of the compound with p-type doping. Results show that \(\kappa _{e}\) increases drastically with the increases of both temperature and carrier concentration. Even the power factor has been found to be markedly improved with the increase of the carrier concentration, a rapid increase of \(\kappa _{e}\) emerges as a big hindrance to improve the dimensionless figure of merit, ZT, of the compound. This is responsible for the limit of ZT. The larger ZT is found in low temperatures and carrier concentrations. The highest ZT of about 0.48 occurs at 223 K and at the carrier concentration of \(6\times 10^{17}\)cm\(^{ - 3}\). At room temperature the maximum ZT is slightly smaller. We demonstrated that at a particular temperature to maximize the thermoelectric performance of the compound, the carrier concentration must be optimized. Results show that the compound with p-type doping is a promising thermoelectric materials operating at around room temperature.