Towards Direct Gap Emission in GeSn and GeC: a Hybrid Functional DFT Analysis

We use density functional theory including Heyd Scuseria Ernzerhof (HSE) hybrid functionals to investigate the electronic structure of $\text{Ge}_{1-\mathrm{x}}\text{Sn}_{\mathrm{x}}$ and $\text{Ge}_{1-\mathrm{y}}\mathrm{C}_{\mathrm{y}}$ supercells. The calculations confirm that a direct gap semiconductor can be obtained in the supercell calculations for low tin $(\mathrm{x}-6\%)$ and carbon (y $(\mathrm{y}\sim 1\%)$ ) also has significant indirect character.