  We have measured the inverse spin Hall effect (ISHE) in \textit{n}-Ge at room
temperature. The spin current in germanium was generated by spin pumping from a
CoFeB/MgO magnetic tunnel junction in order to prevent the impedance mismatch
issue. A clear electromotive force was measured in Ge at the ferromagnetic
resonance of CoFeB. The same study was then carried out on several test
samples, in particular we have investigated the influence of the MgO tunnel
barrier and sample annealing on the ISHE signal. First, the reference CoFeB/MgO
bilayer grown on SiO$_{2}$ exhibits a clear electromotive force due to
anisotropic magnetoresistance and anomalous Hall effect which is dominated by
an asymmetric contribution with respect to the resonance field. We also found
that the MgO tunnel barrier is essential to observe ISHE in Ge and that sample
annealing systematically lead to an increase of the signal. We propose a
theoretical model based on the presence of localized states at the interface
between the MgO tunnel barrier and Ge to account for these observations.
Finally, all of our results are fully consistent with the observation of ISHE
in heavily doped $n$-Ge and we could estimate the spin Hall angle at room
temperature to be $\approx$0.001.
