Optical Dispersion of Lead Sulfide in the Infrared

Measurements of the reflectivity of $n$-type PbS have been made as a function of wavelength, temperature, and carrier density. The reflectivity at wavelengths ranging from 5 to 200 μ is accounted for in terms of the combined effects of classical free-carrier and lattice dispersion. The contributions of free carriers and lattice vibrations to the real part of the dielectric constant from 5 to 25 μ are separated and analyzed to obtain values of the carrier effective mass and optical dielectric constant. The optical dielectric constant ${\epsilon }_{\infty }$ is shown to increase with decreasing temperature and carrier density. The relationship between these variations in ${\epsilon }_{\infty }$ and the absorption spectrum associated with bound electrons is presented. The susceptibility effective mass of free electrons decreases with decreasing temperature and carrier density. The ratio of the mass at 300°K to that at 85°K is found to be equal to the ratio of the corresponding optical energy gaps at these temperatures. Calculations based on the band parameters given by Cuff, Ellett, and Kuglin show that nonparabolicity of the conduction band accounts for a large part of the observed change of effective mass with carrier by a single classical lattice oscillator having values of the longitudinal and transverse optical-mode frequencies in agreement with those obtained by other workers.