Optical properties of Ge-richGe1−xSixalloys: Compositional dependence of the lowest direct and indirect gaps

Ge-rich $\mathrm{G}{\mathrm{e}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{i}}_x$ alloys have been investigated using spectroscopic ellipsometry and photoluminescence at room temperature. Special emphasis was placed on the compositional dependence of the lowest-energy interband transitions. For $x\ensuremath{\le}0.05$, a compositional range of particular interest for modern applications, we find ${E}₀=0.799(1)+3.214(45)x+0.080(44){x}²$ (in eV) for the lowest direct gap. The compositional dependence of the indirect gap is obtained from photoluminescence as ${E}_{\mathrm{ind}}=0.659(4)+1.18(17)x$ (in eV). We find no significant discrepancies between these results and the extrapolations from measurements at higher Si concentrations. Such discrepancies had been suggested by recent work on $\mathrm{G}{\mathrm{e}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{i}}_x$ films on Si. Accurate knowledge of the interband transition energies is an important requirement for the design of devices incorporating Ge-rich $\mathrm{G}{\mathrm{e}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{i}}_x$ alloys and for the understanding of more complex systems, such as ternary $\mathrm{G}{\mathrm{e}}_{1\ensuremath{-}x\ensuremath{-}y}\mathrm{S}{\mathrm{i}}_x\mathrm{S}{\mathrm{n}}_y$ alloys, in terms of its binary constituents.