Fermi-surface parameters of $p$-type PbTe as a function of carrier density

Nine samples of $p$-type PbTe were studied. Carrier densities, as determined by the high-field Hall coefficient at 4.2 K, ranged from 4.0×${10}^{17}$ to 4.5×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The corresponding conductivity mobilities decreased from 704 000 to 12 500 ${\mathrm{cm}}^2$/V sec. Shubnikov-de Haas oscillations were measured for the magnetic field $\overrightarrow{\mathrm{H}}$ in the ($1\overline{1}0$) and (001) planes. The component frequencies were determined by Fourier analysis. The angular dependence of these frequencies was fitted by an ellipsoid of revolution model. For all carrier densities except the highest, this model was found to be adequate. In contrast to most previous work, large enough frequencies were measured to determine the anisotropy accurately. For all carrier densities up to and including 1.1×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$, $K=13\mathrm{}\pm 1$. The cyclotron effective mass $m_t$ was measured for $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[111\right]\mathrm{}$. It was found to increase from $0.035m_0$ at 2.0×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ to $0.072m_0$ at 4.5×${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Over this same range, the ratio of spin splitting to Landau level separation was about 0.60 independent of carrier density, and the corresponding $g$ value showed a modest decrease.