The low-temperature near-band-gap photoluminescence of ${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ is studied over the whole composition range 0≤x≤1. We identify free- and bound-exciton processes and determine the properties of momentum-conserving phonons. From our results we determine the low-temperature band gap of the alloys. Analytical expressions are derived for the X and L bands: $E_{\mathrm{gx}}^X$(x) =1.155-0.43x+0.206$x^2$ eV; $E_{\mathrm{gx}}^L$(x)=2.010-1.270x eV. The intensity and the linewidth of the various excitonic transitions are found to depend only on the statistical alloy fluctuations. No preferential clustering of Si and Ge atoms is detected.

• Received 6 March 1989

DOI:https://doi.org/10.1103/PhysRevB.40.5683