Increasing the thermoelectric figure of merit for bismuth and bismuth-antimony

Bismuth and bismuth-antimony alloys have proved to be excellent low-temperature thermoelectric materials but their small or negative energy gap has not allowed their use in Peltier or Seebeck devices at ordinary temperatures. Other authors have shown that the energy gap may become large enough for practical purposes if the materials are prepared in low-dimensional form. However, we have demonstrated that the Seebeck coefficient of such materials can be substantially increased by the introduction of ionised-impurity scattering and that this may lead to a dimensionless figure of merit, zT, approaching unity, even if the lattice thermal conductivity is as high as it is in pure bismuth. Our calculations make use of a simple model in which the reciprocals of the relaxation times for lattice and impurity scattering of the charge carriers are supposed to be additive. Furthermore, if the lattice conductivity can be reduced to a value well below that for bulk bismuth, then zT in excess of unity should be obtained. It is possible that this may be achieved for nanostructured samples in which the dimensions are not yet small enough for the band structure to be modified. However, if a positive energy gap can be reached through the formation of a nanostructure this is even better. We conclude that, in some form or other, bismuth and bismuth-antimony must be regarded as most promising materials for nanostructure studies.