First-principles investigation of dual substitutional impurity-induced electronic structural modulation of PbTe on cationic and anionic sites

In view of recent experimental results, enhanced thermoelectric performance can be achieved in PbTe via dual doping at both cationic and anionic sites. However, little information is available for a deep understanding of how the various dual dopants tune the electronic structures of PbTe. In this work, the lattice geometry and band structures of (M, N) (M = {K, Ag, Ge, Sn, Sb, Bi}, N = {S, Se, I}) dually doped pairs are systematically clarified using first-principles calculations. The results indicate that the dual-dopant pairs tend to cluster in PbTe and impose a remarkable effect on the band structures near the band gap by the splitting of bands. The alkali K re-enlarges the nearly closed band gap in S- or Se-doped PbTe, while Ag introduces additional bands near the Fermi level in both solely and dually doped configurations. Unexpectedly, (Ag, S), (Ge, Se), (Sn, S) and (Sn, Se) co-doping produce camel's-back-like structures with multiple extrema due to abnormal bending of bands near the band gap, which are anticipated to enhance the power factor of PbTe. Similarly, the Sb- and Bi-induced bands are also bent on the bottom of the conduction band. The band gaps in (Sb, S), (Sb, Se) and (Bi, N) are closed to drive the system towards metallicity. However, a re-opened band gap is obtained in the SbI-3 doping configuration. Supplementary calculations on larger supercells for the Ag–S doping configuration indicate that the single (Ag, S) dual-dopant pair behaves in a similar way to that in the small supercells with lower local atomic relaxation, weak band splitting and reduced band gap. The formation of dual-dopant nanoclusters can widen the band gap due to the introduction of large local strain in the vicinity of clusters. The impurity cluster size exerts a prominent effect on the band-edge states of PbTe. Our calculations reveal that it is possible to intentionally modulate the band structures of PbTe by appropriate collocation of dual-doping atoms for improved thermoelectric properties