Nanosecond Carrier Lifetime of Hexagonal Ge

Hexagonal Si_1-<i>x</i> Ge _<i>x</i> with suitable alloy composition promises to become a new silicon compatible direct bandgap family of semiconductors. Theoretical calculations, however, predict that the binary end point of this family, the bulk hex-Ge crystal, is only weakly dipole active. This is in contrast to hex-Si_1-<i>x</i> Ge _<i>x</i> , where translation symmetry is broken by alloy disorder, permitting efficient light emission. Surprisingly, we observe equally strong radiative recombination in hex-Ge as in hex-Si_1-<i>x</i> Ge _<i>x</i> nanowires, but scrutinizing experiments on the radiative lifetime and the optical transition matrix element of hex-Ge remain hitherto unexplored. Here, we report an advanced spectral line shape analysis exploiting the Lasher-Stern-Würfel (LSW) model on an excitation density series of hex-Ge nanowire photoluminescence spectra covering 3 orders of magnitude. The analysis was performed at low temperature where radiative recombination is dominant. We analyze the amount of photoinduced bandfilling to obtain direct access to the excited carrier density, which allows to extract a radiative lifetime of (2.1 ± 0.3) ns by equating the carrier generation and recombination rates. In addition, we leveraged the LSW model to independently extract a high oscillator strength of 10.5 ± 0.9, comparable to the oscillator strength of III/V semiconductors like GaAs or GaN, showing that the optical properties of hex-Ge nanostructures are perfectly suited for a wide range of optoelectronic device applications.