  We theoretically study the nuclear spin induced decoherence of a quantum dot
in Si that is confined at a SiGe interface. We calculate decoherence time
dependence on $^{73}$Ge in the barrier layer to evaluate the importance of Ge
as well as Si enrichment for long decoherence times. We use atomistic
tight-binding modeling for an accurate account of the electron wavefunction
which is particularly important for determining the contact hyperfine
interactions with the Ge nuclear spins. We find decoherence times due to Ge
spins at natural concentrations to be milliseconds. This suggests SiGe/Si
quantum dot devices employing enriched Si will require enriched Ge as well in
order to benefit from long coherence times. We provide a comparison of $T_2$
times for various fractions of nonzero spin isotopes of Si and Ge.
