Galvanomagnetic Effects and the Band Structure of Antimony

Abstract

The energy band structure of antimony is deduced from room temperature galvanomagnetic measurements and their interpretation in terms of a theoretical model. A systematic series of experiments is performed on oriented single crystals to measure all the 12 components of the isothermal resistivity tensor through second order in the magnetic field. The calculated galvanomagnetic effects assuming simple, independent three-valleyed bands for both the valence and conduction bands and isotropic relaxation times for both holes and electrons, are shown to fit the data by only one set of values for the 9 adjustable parameters in the theory. These parameters are: a set of three principal mobilities ${\mu }_i$ and ${\nu }_i$, for electrons and holes, respectively; angles of tilt ${\psi }_1$ and ${\psi }_2$ of one of the principal axes of the electron and hole energy ellipsoids out of the base plane; and the carrier density $N$, the same for both carriers. The best fit is determined by exploring systematically a large number of possible solutions with the aid of an IBM 650 computer. If the "1" directions refer to binary symmetry axes and the "3" directions to those making angles $\psi$ with the trigonal symmetry axis, the parameters have the values ${\mu }_1={0.15}_4\times {10}^3$, ${\mu }_2={4.0}_5\times {10}^3$, ${\mu }_3={1.1}_8\times {10}^3$, ${\nu }_1={3.5}_6\times {10}^3$, ${\nu }_2={3.3}_0\times {10}^3$, ${\nu }_3={0.13}_8\times {10}^3$ (all in ${\mathrm{cm}}^2$/volt-sec); ${\psi }_1={30}_{.7}°$, ${\psi }_2={63}_{.2}°$; $N={3.7}_4\times {10}^{19} \mathrm{carriers}/{\mathrm{cm}}^3={1.0}_5\times {10}^{-3\mathrm{}} \mathrm{carriers}/\mathrm{atom}$. The results agree well with Shoenberg's de Haas-van Alphen data if the carriers responsible for the observed susceptibility oscillations are holes.