Quantum confinement in germanium nanocrystals

The electronic structure of Ge nanocrystals is studied using a ${\mathrm{sp}}^3$ tight binding description. Analytical laws for the confinement energies, valid over the whole range of sizes, are derived. We validate our results with ab initio calculations in the local density approximation for smaller clusters. Comparing to experimental data, we conclude that, similar to the case of silicon: (a) the blue-green photoluminescence (PL) of Ge nanocrystals comes from defects in the oxide and (b) the size dependent PL in the near infrared probably involves a deep trap in the gap of the nanocrystals. We predict that the radiative lifetimes remain long in spite of the small difference (0.14 eV) between direct and indirect gaps of bulk Ge.