Exciton Radiative Lifetimes in Hexagonal Diamond Ge and SixGe1-x Alloys

Recent reports of strong room-temperature photoluminescence in hexagonal diamond (2H) germanium stand in marked contrast to theoretical predictions of very weak band-edge optical transitions. Here, we address radiative emission in 2H-Ge and related materials through a comprehensive investigation of their excitonic properties and radiative lifetimes, performing Bethe–Salpeter calculations on pristine and uniaxially strained 2H-Ge, 2H- (Formula presented.) (Formula presented.) alloys with (Formula presented.), and wurtzite GaN as a reference. Pristine 2H-Ge features sizable exciton binding energies ((Formula presented.)) but extremely small dipole moments, yielding radiative lifetimes above (Formula presented.). Alloying with Si reduces the lifetime by nearly two orders of magnitude, whereas a 2% uniaxial strain along the (Formula presented.) axis induces a band crossover that strongly enhances the in-plane dipole moment of the lowest-energy exciton and drives the lifetime down to the nanosecond scale. Although strained 2H-Ge approaches the radiative efficiency of GaN, its much lower exciton energy prevents a full match. These results provide the missing excitonic description of 2H-Ge and 2H- (Formula presented.) (Formula presented.), demonstrating that, even when excitonic effects are fully accounted for, the strong photoluminescence reported experimentally cannot originate from the ideal crystal.