Skin-Deep Aspect of Thermopower in Bi 2 Q 3 , PbQ, and BiCuQO (Q = Se, Te): Hidden One-Dimensional Character of Their Band Edges Leading to High Thermopower.

ConspectusThermoelectric (TE) materials have received much attention because of their ability to convert heat energy to electrical energy. At a given temperature T , the efficiency of a TE material for this energy conversion is measured by the figure of merit zT , which is related to the thermopower (or Seebeck coefficient) S , the thermal conductivity κ, and the electrical conductivity σ of the TE material as zT = ( S 2 σ T )/κ. Bi 2 Q 3 and PbQ (Q = Se, Te) are efficient TE materials with high zT , although they are not ecofriendly and their stability is poor at high temperature. In principle, a TE material can have a high zT if it has a low thermal conductivity and a high electrical conductivity, but the latter condition is hardly met in a real material because the parameters S , σ and κ have a conflicting dependence on material properties. The difficulty in searching for TE materials of high zT is even more exasperated because the relationship between the thermopower S and the carrier density n (hereafter, the S -vs- n relationship) for the well-known hole-doped samples of BiCuSeO showed that the hole carriers responsible for their thermopower are associated largely with the electronic states lying within ∼0.5 eV of its valence band maximum (VBM). Thus, the states governing the TE properties lie in the "skin-deep" region from the VBM. For electron-doped TE systems, the electron carriers responsible for their thermopower should also be associated with the electronic states lying within ∼0.5 eV of the conduction band minimum (CBM). This makes it difficult to predict TE materials of high zT . One faces a similar skin-deep phenomenon in searching for superconductors of high transition temperature because the transition from a normal metallic to a superconducting state involves the normal metallic states in the vicinity of the Fermi level E F . Other skin-deep phenomena in metallic compounds include the formation of charge density wave (CDW), which involves the electronic states in the vicinity of their Fermi levels. For magnetic materials of transition-metal ions, the preferred orientation of their spin moments is a skin-deep phenomenon because it is governed by the interaction between the highest-occupied and the lowest unoccupied d-states of these ions. In the present work we probe the issues concerning how to find the possible range of thermopower expected for a given TE material and hence how to recognize what experimental values of thermopower are expected or unusual. For these purposes, we analyze the accumulated S and n data on the three well-studied TE materials, Bi 2 Q 3 , PbQ, and BiCuQO (Q = Se, Te), as representative examples, in terms of the ideal theoretical S -vs- n relationships, which we determine for their defect-free Bi 2 Q 3 , PbQ, and BiCuQO structures using density functional theory (DFT) calculations under the rigid band approximation. We find that the general trends in the experimental S -vs- n relationships are reasonably well explained by the calculated S -vs- n relationships, and the carrier densities covering these relationships are associated with the states lying within ∼0.5 eV from their band edges confirming the skin-deep nature of their thermoelectric properties. Despite the fact that these TE materials are not one-dimensional (1D) in structure, they mostly possess sharp density-of-state peaks around their band edges because their band dispersions have a hidden 1D character so their thermopower is generally high in magnitude.