Model dielectric constants of Si and Ge.

A method is described for calculation of the real (${\ensuremath{\epsilon}}_{1}$) and imaginary parts (${\ensuremath{\epsilon}}_{2}$) of the dielectric function of Si and Ge at energies below and above the fundamental absorption edge, in which the model is based on the Kramers-Kronig transformation and strongly connected with the electronic energy-band structure of the medium. A complete set of the critical points (CP's) are considered in this study. This model reveals distinct structures at energies of the ${E}_{0}$, ${E}_{0}$+${\ensuremath{\Delta}}_{0}$ [three-dimensional (3D) ${M}_{0}$], ${E}_{1}$, ${E}_{1}$+${\ensuremath{\Delta}}_{1}$ (3D ${M}_{1}$ or 2D ${M}_{0}$), ${E}_{2}$ [a mixture of damped harmonic oscillator (DHO) and 2D ${M}_{2}$], ${E}_{1}^{\mathcal{'}}$, and ${E}_{0}^{\mathcal{'}}$ (triplet) CP's (DHO). The indirect-band-gap transitions also play an important part in the spectral dependence of ${\ensuremath{\epsilon}}_{2}$ of Si. Results are in satisfactory agreement with the experimental information over the entire range of photon energies. The strength and broadening parameters at energies of each CP are obtained and discussed.