Using empirical pseudopotential theory, the direct (Γ) and indirect bandgaps (L and X) of unstrained crystalline SixGe1-x-ySny have been calculated over the entire xy composition range. The results are presented as energy-contour maps on ternary diagrams along with a ternary plot of the predicted lattice parameters. A group of 0.2 to 0.6 eV direct-gap SiGeSn materials is found for a variety of mid-infrared photonic applications. A set of “slightly indirect” SiGeSn alloys having a direct gap at 0.8 eV (but with a smaller L-Γ separation than in Ge) have been identified. These materials will function like Ge in various telecom photonic devices. Hetero-layered SiGeSn structures are described for infrared light emitters, amplifiers, photodetectors, and modulators (free carrier or Franz-Keldysh). We have examined in detail the optimized design space for mid-infrared SiGeSn-based multiple-quantum-well laser diodes, amplifiers, photodetectors, and quantum-confined Stark effect modulators.