Band structure critical point energy in germanium–tin alloys with high tin contents

The dielectric functions of germanium–tin alloy thin-films, deposited by molecular beam epitaxy on bulk Ge substrates, with relatively high Sn contents from 15 to 27 at. %, were measured by variable angle spectroscopic ellipsometry over the wavelength range from 0.190 to 6 μm, using a combination of ultraviolet-visible and infrared ellipsometers. The band structure critical point energies, specifically the E1 and E1 + Δ1 optical transitions, were extracted from the measurements by a method of parametric oscillator modeling and second derivative analysis. With increasing Sn content, the transitions shifted to lower energies, and for alloys with less than 20% Sn, the numerical values agreed reasonably with predictions based on deformation potential theory that accounted for film strain. For the higher Sn alloys, the critical point energies from measurements agreed less well with deformation potential theory. These results provide information on the band structure of GeSn alloys with high Sn contents, which are increasingly important for long-wave infrared devices and applications.