Measuring and Modeling the Optical Constants of Germanium Near the Band Gap

The standard theory of indirect gap optical absorption in semiconductors predicts an unphysical divergence when the photon energy reaches the direct band gap. Current theoretical efforts to eliminate this divergence require experimental validation with measurements covering a spectral region that exceeds the direct band gap. For transmittance and reflectance measurements needed in examining the absorption in a material like Ge, the needed film thicknesses are too small for the samples to be mechanically stable. On the other hand, very thin films can be grown epitaxially on silicon. This thesis focuses on testing a novel technique for examining absorption in these thin films. Spectrophotometry was used to measure the reflection and transmission over a spectral range of 0.54 eV to 1.38 eV for various epitaxial thin film Ge on Si samples. The resultant data was then renormalized and used in a custom spline fitting procedure to extract the dielectric/optical constants over the established spectral range. Analysis of the extracted dielectric function spectra indicates an apparent bias towards thinner films (less than 1000 nm) in producing spectra having good agreement with new theoretical models. Dielectric function spectra from thick samples (over 2000 nm) show well matched general behavior but fail to accurately predict regions of absorption around the band gap.