Nanosecond\nCarrier Lifetime of Hexagonal Ge

Hexagonal Si<sub>1–<i>x</i></sub>Ge<sub><i>x</i></sub> with suitable alloy composition promises\nto become\na new silicon compatible direct bandgap family of semiconductors.\nTheoretical calculations, however, predict that the binary end point\nof this family, the bulk hex-Ge crystal, is only weakly dipole active.\nThis is in contrast to hex-Si<sub>1–<i>x</i></sub>Ge<sub><i>x</i></sub>, where translation symmetry is broken\nby alloy disorder, permitting efficient light emission. Surprisingly,\nwe observe equally strong radiative recombination in hex-Ge as in\nhex-Si<sub>1–<i>x</i></sub>Ge<sub><i>x</i></sub> nanowires, but scrutinizing experiments on the radiative lifetime\nand the optical transition matrix element of hex-Ge remain hitherto\nunexplored. Here, we report an advanced spectral line shape analysis\nexploiting the Lasher–Stern–Würfel (LSW) model\non an excitation density series of hex-Ge nanowire photoluminescence\nspectra covering 3 orders of magnitude. The analysis was performed\nat low temperature where radiative recombination is dominant. We analyze\nthe amount of photoinduced bandfilling to obtain direct access to\nthe excited carrier density, which allows to extract a radiative lifetime\nof (2.1 ± 0.3) ns by equating the carrier generation and recombination\nrates. In addition, we leveraged the LSW model to independently extract\na high oscillator strength of 10.5 ± 0.9, comparable to the oscillator\nstrength of III/V semiconductors like GaAs or GaN, showing that the\noptical properties of hex-Ge nanostructures are perfectly suited for\na wide range of optoelectronic device applications.