Electric-Susceptibility Hole Mass of Lead Telluride

Abstract

Experimental values of the electric-susceptibility hole mass ${m}_{s}$ of PbTe are given for temperatures ranging from 24 to 300\ifmmode^\circ\else\textdegree\fi{}K and carrier concentrations from 3.5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ to 4.8\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The masses are deduced from measurements of infrared reflectivity using the method of Spitzer and Fan. The mass increases monotonically with increasing temperature and carrier concentration in a way which indicates strong nonparabolicity of the valence band. The carrier-concentration dependence at 30\ifmmode^\circ\else\textdegree\fi{}K is explained in terms of a single-band, non-parabolic multivalley model and the band-edge parameters reported by Cuff, Ellett, Kuglin, and Williams. The constant-energy surfaces involved are $〈111〉$ prolate surfaces of revolution located at the zone boundaries. The temperature dependence of ${m}_{s}$ for a carrier concentration of 3.5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ can also be explained in terms of this single-band model. The agreement depends upon the assumption that the interaction gap varies linearly with temperature in the same way as the optical gap, the coefficient being 4.9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV/\ifmmode^\circ\else\textdegree\fi{}K. For a carrier concentration of 4.8\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, the single-band model does not yield results which are consistent with the observed values of ${m}_{s}$ as a function of temperature, except at the lowest temperature of 30\ifmmode^\circ\else\textdegree\fi{}K. Differences between calculation and experiment at higher temperatures suggest that a second band becomes appreciably populated.