Calculation of the Optical Constants of PbTe from Augmented-Plane-Wave k. p Energy Bands

The augmented-plane-wave method has been used to calculate the energies and wave functions of eleven levels at the origin of the Brillouin zone (BZ) of PbTe. From the wave functions, momentum matrix elements have been calculated and these have been used in a k·p expansion of the energy bands. The k·p secular equation has been solved throughout the BZ and the results have been used to calculate the inter-band contribution to the optical constants in the random-phase approximation. The calculated value of ${\epsilon }_1(\omega =0)$ (40.0) compares favorably to the measured value (${\epsilon }_{\infty }=31.8\mathrm{}$), and the calculated reflectivity agrees with experiment to within 10% in the frequency range $0<\mathrm{}\hslash \omega <3\mathrm{}$ eV.