Free carriers, coupled modes, and the generalized dielectric function in PbTe

The reflectivity of $n$-PbTe has been measured at 300°K in the range 16-235 ${\mathrm{cm}}^{-1\mathrm{}}$ for samples with carrier concentrations between 2 × ${10}^{17}$ and 2 × ${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Both the conventional two-oscillator dielectric function and the generalized function ${\epsilon }_K$ proposed by Kukharskii were used to fit the data with equally valid results. Unlike previous low-temperature measurements there was no serious difference between the dc and optical values for the free-carrier scattering time $\tau$ except at the highest concentration where $\frac{{\tau }_{\mathrm{dc}}}{{\tau }_{\mathrm{opt}}}=3\mathrm{}$. This discrepancy may be related to screening effects. Kukharskii's extended Lyddane-Sachs-Teller relation was found to hold despite the relatively heavy damping. ${\epsilon }_K$ was used to analyze the damped plasmon-phonon modes and indicated the presence of an overdamped mode at very low frequencies. The lattice damping constant was found to be 21±5 ${\mathrm{cm}}^{-1\mathrm{}}$, a value comparable to that measured in PbSe but much larger than is typical for other semiconductors.