Optical properties of pure and ultraheavily doped germanium: Theory and experiment

We have measured by spectroellipsometry the dielectric function ε of pure and ultraheavily doped germanium from the near-infrared (ħω≃1.6 eV) to the near-ultraviolet (ħω≃5.6 eV) regions. The dependence of the $E_1$, $E_1$+${\Delta }_1$, $E_0^{\mathcal{’}}$, and $E_2$ critical energies on impurity concentration was obtained. A red shift of the different critical-point energies, together with an increase of the lifetime broadening, has been observed. Amplitudes and phase angles for the corresponding critical points were also obtained. The results are compared with full band-structure calculations of the effect of the impurities on the band structure of germanium.