Compositional Dependence of the Bowing Parameter for the Direct and Indirect Band Gaps in Ge1-ySny Alloys

Photoluminescence spectroscopy has been used to determine the direct gap E₀ of Ge_1-ySn_y alloys over a broad compositional range from pure Ge to Sn concentrations exceeding 10%. A fit of the compositional dependence of E₀ using a standard quadratic expression is not fully satisfactory, revealing that the bowing parameter (quadratic coefficient) b₀ is compositionally dependent. Excellent agreement with the data is obtained with b₀(y) = (2.66 ± 0.09) eV − (5.4 ± 1.1)y eV. A theoretical model of the bowing is presented, which explains the strong compositional dependence of the bowing parameter and suggest a similar behavior for the indirect gap. Combining the model predictions with experimental data for samples with y ≤ 0.06, it is proposed that the bowing parameter for the indirect gap is b_ind(y) = (1.11 ± 0.07) eV − (0.78 ± 0.05)y eV. The compositional dependence of the bowing parameters shifts the crossover concentration from indirect to direct gap behavior to y_c  = 0.087, significantly higher than the value predicted earlier based on strictly quadratic fits.