Optical Constants of Lead Sulfide in the Fundamental Absorption Edge Region

Large discrepancies exist between the results of previous measurements of the optical constants of PbS at room temperature in the absorption edge region. For this reason the absorption coefficient $\alpha$ and the index of refraction $n$ have been remeasured over the spectral range from 0.1 to 1.5 eV. These quantities were obtained from an analysis of the reflectance and transmittance of high-quality epitaxial PbS films. Our results for $\alpha$ are in approximate agreement with those of Scanlon from 0.4 to 1.0 eV and approach those of Avery at higher energies. Analysis of these data yields a value of 0.42 eV for the direct gap. Near the edge, the absorption coefficients obey the relation $\alpha =4.29\mathrm{}\times {10}^4$ ${\mathrm{}(E-0.42\mathrm{})\mathrm{}}^{\frac{1}{2}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, where $E$ is the photon energy in eV. Indices of refraction were determined from reflectance-transmittance data and also by using the more accurate interference fringe method described by Riedl and Schoolar. A sharp peak in $n$ as a function of energy is observed near the absorption edge. A Kramers-Kronig analysis using experimental $\alpha \text{'}\mathrm{s}$ yields values of $n$ in excellent agreement with experiment. This agreement substantiates the absorption measurements.