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Dependence of the energies of the various band extrema on composition x in Bi100−xSbx alloys at T = 0 K (compiled from Refs. 10–13). At the L-points of the Brillouin zone, the symmetric and antisymmetric bands are inverted between elemental Bi and Sb, leading to a Dirac point near x = 5 at. % fraction. The T-point valence band is the upper valence band of the semimetal Bi, but in elemental Sb, the holes are inside the Brillouin zone in three distorted ellipsoidal pockets near the H-points. This band becomes the upper valence band for x > 18. As in most solids, temperature can make band extrema shift by 100 meV between liquid nitrogen and room temperatures, an effect that is secondary in wide-gap semiconductors, but has a very important relative influence on the present diagram.
Comparison of thermoelectric properties of single crystal Bi81.05Sb18.2Sn0.75 sample between in the trigonal plane and along the trigonal axis directions. (a) Thermal conductivity κ, (b) thermopower S, (c) electrical resistivity ρ, and (d) figure of merit zT as functions of temperature. Points are experimental data and lines are added to guide the eye.
Thermoelectric properties of single crystal Bi100−xSbxSn0.75 samples for x = 11.6, 18.2, 19.5, 22.9, 26.5, 30, and 37 from 2 K to 400 K. All properties were measured with the heat flux and current in the trigonal plane. (a) Thermal conductivity κ, (b) electrical resistivity ρ, and (c) thermopower S as functions of temperature. The insert shows the figure of merit zT as a function of temperature. Points are experimental data and lines are added to guide the eye.
(a) Pisarenko’s plot of thermopower versus hole concentration at T = 80 K for all measured samples in this study. Solid line and dashed line are calculated for the valence bands at the H-points and the valence band at the T-point, respectively. Points are experimental data. Carrier density of each sample was obtained from Hall measurement assuming a Hall prefactor of unity. (b)-(d) Schematic band diagrams for the three different Sb concentration regimes shown. Relative position of each band and the position of Fermi energies (EF ) are not to scale.
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