Transport effects in semi-metals and narrow-gap semiconductors

Abstract

The semi-metals and narrow-gap semiconductors are characterized by high values of the electron mobility, and sometimes, of the hole mobility too. When both carriers have a high mobility in intrinsic material the bipolar transport effects become prominent. Properties that are particularly sensitive to bipolar conduction are the electronic thermal conductivity and the Nernst and Ettingshausen coefficients. When there is a very large magnetoresistance effect, as there is in some semi-metals at low temperatures, high electric fields can be applied without excessive power dissipation. This allows the observation of an enhanced phonon interaction with carriers that are drifting with the speed of sound, the effect being manifested as a kink in the current-voltage characteristic. Other non-linear effects have been observed at high current densities due to self-magnetic fields of the charge carriers. These and other effects can be influenced by diffusion phenomena associated with the relatively high carrier lifetimes. The long relaxation times of the carriers in some of the materials at very low temperatures allow one to observe oscillations in the magnetoresistance (and other properties) as well as size-dependent effects. Most of the materials have multi-valley energy bands for at least one type of charge carrier. Although the band parameters are given most directly by cyclotron resonance experiments, they can in general also be determined from galvanomagnetic measurements under less critical experimental conditions. Several of the materials belong to the crystal class R3m and have ellipsoidal (or quasi-ellipsoidal) energy surfaces in the Brillouin zone which are tilted with respect to the crystal axes. These materials provide an interesting example of the determination of band structures from the galvanomagnetic coefficients. Even for a two-band non-parabolic conductor, there are generally sufficient data to allow the band parameters for any specific model to be calculated, provided, of course, that the model is appropriate. Thermoelectric measurements, together with Nernst or magnetothermoelectric observations, can provide the data on the Fermi energy and scattering law that are needed to complete a description of the material. The high carrier concentrations in the semi-metals (and the heavily-doped semiconductors) give rise to the possibility of superconducting behaviour. In this case, however, a low mobility is an advantage, since a high mobility implies a weak interaction between the electrons and the lattice. The recent observations on the variation with voltage of the tunnelling current at a junction between a semi-metal and an insulator indicate a promising technique for band-structure studies. Applications of the semi-metals are somewhat restricted by the parameters of the presently available materials, but the possibility of thermomagnetic energy conversion should encourage comprehensive studies of the transport properties on existing and new semi-metals.