Electron spin coherence of shallow donors in germanium

The presence of magnetic nuclei is one major source of electron and nuclear spin decoherence in semiconductors. Germanium is one of the few semiconductor materials that can be isotopically enriched to have no magnetic nuclear isotopes, making it a promising material for quantum computing applications. In this talk we report T$_{1}$ and T$_{2}$ relaxation times for $^{75}$As and $^{31}$P donors in natural Ge and isotopically enriched $^{74}$Ge for temperatures down to 350 mK. We find that T$_{1}$ is limited by a direct phonon process at these temperatures, in agreement with previous reports. Above 2K, the coherence time for donor spins is limited by T$_{1}$, while below 2K it is limited by spectral diffusion from $^{73}$Ge nuclear spins. In isotopically-enriched $^{74}$Ge (3.8{\%} residual $^{73}$Ge) we find a T$_{2}$ of 110 us for $^{75}$As donors. Electron Spin Echo Envelope Modulation (ESEEM) data will be presented identifying the hyperfine coupling of the donor electron to several $^{73}$Ge lattice sites with couplings ranging from 200 kHz to 1 MHz.