Some Effects of Sample Size on Electrical Transport in Bismuth

The effects of sample size on the electrical conductivity and Hall constant of single crystals of bismuth have been measured between 2 and 10°K. In addition, both components of the conductivity tensor and the Hall tensor component ${\rho }_{23,1}$, with magnetic field $\parallel$ to the trigonal axis, have been measured between 2 and 77°K in samples which are among the purest reported in the literature. This work was done to determine the proportion of specular reflection of carriers from the electropolished sample surface. The nature of the experimental results, however, has made it impossible to fit observation to any sort of theory with mean free path as the internal parameter. Analysis of these data, however, has shown the following: The scattering is, indeed, partially specular; the scattering time of electrons is highly anisotropic, being of the order of ten times longer in the bisectrix direction than in the binary direction; and both electron and hole mobilities have been shown to have an approximate $T^{-2\mathrm{}}$ dependence down to 4.2°K.