Doping dependence of the electron spin diffusion length in germanium

We have investigated the electron spin diffusion length at room temperature in bulk n-doped germanium as a function of the doping concentration. To this purpose, we exploit a nonlocal spin injection/detection scheme where spins are optically injected at the direct gap of Ge and electrically detected by means of the inverse spin-Hall effect (ISHE). By optically generating a spin population in the conduction band of the semiconductor at different distances from the spin detector, we are able to directly determine the electron spin diffusion length L in the Ge substrate. We experimentally observe that L > 20 ?m for lightly doped samples and, by taking into account the electron diffusion coefficient, we estimate electron spin lifetime values ? larger than 50 ns. In contrast, for heavily doped Ge substrates, the spin diffusion length decreases to a few micrometers, corresponding to ? ? 20 ns. These results can be exploited to refine spin transport models in germanium and reduce the experimental uncertainties associated with the evaluation of L from other spin injection/detection techniques.