Determination of E$_{\mathrm{0}}$ band gaps of Ge-rich GeSi films using UV-Vis ellipsometry

Ge-rich Ge$_{\mathrm{1-x}}$Si$_{\mathrm{x}}$ (x$=$0.003-0.132) films were grown in a gas-source molecular epitaxy reactor on Si(100) by using new-generation group-IV gaseous reactants Ge4H10 and Si4H10. Films were around 1.5 micron thick with excellent crystallinity as shown by sharp and symmetric XRD peaks. UV-Vis ellipsometry data were taken in the range of 0.6-1.5 eV with 5 meV intervals. Dielectric functions were obtained from point-by-point fits, and two data analysis methods were employed to extract fundamental band gap E$_{\mathrm{0}}$ values. The 1st method fits the imaginary part $\varepsilon $2 with a theoretical expression consolidating all contributions to the dielectric function. The 2nd method first numerically smoothes and differentiates the experimental $\varepsilon $1 and $\varepsilon $2 to obtain second derivatives with respect to energy, which are then fitted together using an expression of a three-dimensional critical point. Effects of small residual strains were corrected to obtain band gap values for strain-free materials. Excellent agreement between these two methods has been achieved. Analysis of the compositional dependence of E$_{\mathrm{0}}$ revealed a negative bowing parameter which is greater compared to literature.