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Valley degeneracy is a key feature of the electronic structure that benefits the thermoelectric performance of a material. Despite recent studies which claim that high valley degeneracy can be achieved with inverted bands, our analysis of rock-salt IV–VI compounds using first-principles calculations and k · p perturbation theory demonstrates that mere band inversion is an insufficient condition for high valley degeneracy; rather, there is a critical degree to which the bands must be inverted to induce multiple carrier pockets. The so-called “band inversion parameter” is formalized as a chemically-tunable property, offering a design route to achieving high valley degeneracy in compounds with inverted bands. We predict that the valley degeneracy of rock-salt IV–VI compounds can be increased from N V = 4 to N V = 24, which could result in a corresponding increase in the thermoelectric figure of merit zT . 

Diamond like semiconductors (DLS) have emerged as candidates for thermoelectric energy conversion. Towards understanding and optimizing performance, we present a comprehensive investigation of the electronic properties of two DLS phases, quaternary Cu 2 HgGeTe 4 and related ordered vacancy compound Hg 2 GeTe 4 , including thermodynamic stability, defect chemistry, and transport properties. To establish the thermodynamic link between the related but distinct phases, the stability region for both is visualized in chemical potential space. In spite of their similar structure and bonding, we show that the two materials exhibit reciprocal behaviors for dopability. Cu 2 HgGeTe 4 is degenerately p-type in all environments despite its wide stability region, due to the presence of low-energy acceptor defects V Cu and Cu Hg and is resistant to extrinsic n-type doping. Meanwhile Hg 2 GeTe 4 has a narrow stability region and intrinsic behavior due to the relatively high formation energy of native defects, but presents an opportunity for bi-polar doping. While these two compounds have similar structure, bonding, and chemical constituents, the reciprocal nature of their dopability emerges from significant differences in band edge positions. A Brouwer band diagram approach is utilized to visualize the role of native defects on carrier concentrations, dopability, and transport properties. This study elucidates the doping asymmetry between two solid-solution forming DLS phases Cu 2 HgGeTe 4 and Hg 2 GeTe 4 by revealing the defect chemistry of each compound, and suggests design strategies for defect engineering of DLS phases. 

The optimization and application of new functional materials depends critically on our ability to manipulate the charge carrier density. Despite predictions of good n-type thermoelectric performance in the quaternary telluride diamond-like semiconductors ( e.g. Cu 2 HgGeTe 4 ), our prior experimental survey indicates that the materials exhibit degenerate p-type carrier densities (>10 20 h + cm −3 ) and resist extrinsic n-type doping. In this work, we apply the technique of phase boundary mapping to the Cu 2 HgGeTe 4 system. We begin by creating the quaternary phase diagram through a mixture of literature meta-analysis and experimental synthesis, discovering a new material (Hg 2 GeTe 4 ) in the process. We subsequently find that Hg 2 GeTe 4 and Cu 2 HgGeTe 4 share a full solid solution. An unusual affinity for Cu Hg and Hg Cu formation within Cu 2 HgGeTe 4 leads to a relatively complex phase diagram, rich with off-stoichiometry. Through subsequent probing of the fourteen pertinent composition-invariant points formed by the single-phase region, we achieve carrier density control ranging from degenerate (>10 21 h + cm −3 ) to non-degenerate (<10 17 h + cm −3 ) via manipulation of native defect formation. Furthermore, this work extends the concept of phase boundary mapping into the realm of solid solutions and clearly demonstrates the efficacy of the technique as a powerful experimental tool within complex systems.