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The compositional dependence of the lowest direct and indirect band gaps in$\text{Ge}_{1-y}\text{Sn}_{y}$ has been determined from room-temperaturephotoluminescence measurements. This technique is particularly attractive for acomparison of the two transitions because distinct features in the spectra canbe associated with the direct and indirect gaps. However, detailed modeling ofthese room temperature spectra is required to extract the band gap values withthe high accuracy required to determine the Sn concentration $y_{c}$ at whichthe alloy becomes a direct gap semiconductor. For the direct gap, this isaccomplished using a microscopic model that allows the determination of directgap energies with meV accuracy. For the indirect gap, it is shown that currenttheoretical models are inadequate to describe the emission properties ofsystems with close indirect and direct transitions. Accordingly, an ad hocprocedure is used to extract the indirect gap energies from the data. For $y$ <0.1 the resulting direct gap compositional dependence is given by $\Delta E_{0}= -(3.57 \pm 0.06)y$ (in eV). For the indirect gap, the correspondingexpression is $\Delta E_{\text{ind}} = -(1.64\pm 0.10)y$ (in eV). If aquadratic function of composition is used to express the two transitionenergies over the entire compositional range $0 \leq y \leq 1$, the quadratic(bowing) coefficients are found to be $b_{0} = 2.46 \pm 0.06$ eV (for $E_{0}$)and $b_{\text{ind}} = 0.99 \pm 0.11$ eV (for $E_{\text{ind}}$). These resultsimply a crossover concentration $y_{c} = 0.073_{-0.006}^{+0.007}$, much lowerthan early theoretical predictions based on the virtual crystal approximation,but in better agreement with predictions based on large atomic supercells.

Compositional dependence of the direct and indirect band gaps in $\text{Ge}_{1-y}\text{Sn}_{y}$ alloys from room temperature photoluminescence