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 Ls in the Ge substrate. We experimentally observe that Ls > 20 μm for lightly doped samples and, by taking into account the electron diffusion coefficient, we estimate electron spin lifetime values τs larger than 50 ns. In contrast, for heavily doped Ge substrates, the spin diffusion length decreases to a few micrometers, corresponding to τs ≈ 20 ns. These results can be exploited to refine spin transport models in germanium and reduce the experimental uncertainties associated with the evaluation of Ls from other spin injection/detection techniques.