Valence Disproportionation of GeS in the PbS Matrix Forms Pb₅Ge₅S₁₂Inclusions with Conduction Band Alignment Leading to High n-Type Thermoelectric Performance

Converting waste heat into useful electricity using solid-state thermoelectrics has a potential for enormous global energy savings. Lead chalcogenides are among the most prominent thermoelectric materials, whose performance decreases with an increase in chalcogen amounts (e.g., PbTe > PbSe > PbS). Herein, we demonstrate the simultaneous optimization of the electrical and thermal transport properties of PbS-based compounds by alloying with GeS. The addition of GeS triggers a complex cascade of beneficial events as follows: Ge²⁺substitution in Pb²⁺and discordant off-center behavior; formation of Pb₅Ge₅S₁₂as stable second-phase inclusions through valence disproportionation of Ge²⁺to Ge⁰and Ge⁴⁺. PbS and Pb₅Ge₅S₁₂exhibit good conduction band energy alignment that preserves the high electron mobility; the formation of Pb₅Ge₅S₁₂increases the electron carrier concentration by introducing S vacancies. Sb doping as the electron donor produces a large power factor and low lattice thermal conductivity (κ_lat) of ∼0.61 W m^-1K^-1. The highest performance was obtained for the 14% GeS-alloyed samples, which exhibited an increased room-temperature electron mobility of ∼121 cm²V^-1s^-1for 3 × 10¹⁹cm^-3carrier density and a ZT of 1.32 at 923 K. This is ∼55% greater than the corresponding Sb-doped PbS sample and is one of the highest reported for the n-type PbS system. Moreover, the average ZT (ZT_avg) of ∼0.76 from 400 to 923 K is the highest for PbS-based systems.