Model dielectric constants of Si and Ge

A method is described for calculation of the real (${\epsilon }_1$) and imaginary parts (${\epsilon }_2$) 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 $E_0$, $E_0$+${\Delta }_0$ [three-dimensional (3D) $M_0$], $E_1$, $E_1$+${\Delta }_1$ (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 ${\epsilon }_2$ 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.