Strain dependence of the band structure and critical points of pseudomorphic Ge$_{1-y}$Sn$_{y\, }$alloys on Ge

The energy band structure of Ge is a strong function of strain, and a transition from an indirect to a direct band gap has been observed for y \textasciitilde 6-10{\%} for Ge$_{1-y}$Sn$_{y}$ indicating the possibility of widespread applications of Ge-based photonic devices. Hence it is important to study the composition and strain dependence of the Ge$_{1-y}$Sn$_{y}$ alloy band structure through measurements of the optical properties. The complex pseudodielectric functions of pseudomorphic Ge$_{1-y}$Sn$_{y}$ alloys grown on Ge by MBE were measured using spectroscopic ellipsometry and FTIR ellipsometry in the 0.1-6.6 eV energy range for Sn contents up to 10{\%}, to investigate the compositional dependence of the direct band gap E$_{0}$, E$_{1}$~and E$_{1}+\Delta _{1}$~critical point (CP) energies. CP energies and related parameters were obtained by analyzing the second-derivative of the dielectric function. Our experimental results are in good agreement with the theoretically predicted~CP energies of Ge$_{1-y}$Sn$_{y}$ on Ge based on deformation potential theory. We will present the nature of the band gap of pseudomorphic Ge$_{1-y}$Sn$_{y}$ on Ge and the effects of strain that control the indirect to direct band gap transition.