Electronic structure and transport properties of doped PbSe

Understanding the electronic structure and transport properties of doped PbSe for its thermoelectric applications is an urgent need. Using a first-principles approach, we first explore the band structures of PbSe doped with a series of impurities, including cation-site substitutional impurities (Na, K, Rb; Mg, Ca, Sr; Cu, Ag, Au; Zn, Cd, Hg; Ga, In, Tl; Ge, Sn; As, Sb, Bi) and anion-site substitutional impurities (P, As, Sb; O, S, Te). Then we calculate the density of states (DOS) difference between the doped samples and pure host sample, which is a useful quantity to recognize the possibility of improving transport properties. The exhibited chemical trends and the nature of the impurity states are well explained with a simplified linear combination of atomic orbitals (LCAO) picture. Finally, we calculate the transport properties of these doped systems within the framework of Boltzmann theory and constant relaxation time approximation. Typical competing behavior between the electrical conductivity and Seebeck coefficient is exhibited, and a significant enhancement of thermoelectric power factor is found in the cation-site Au-doped $p$-type samples, and cation-site As-doped $n$-type samples.