  The nuclear spin of a phosphorus atom in silicon has been used as a quantum
bit in various quantum-information experiments. It has been proposed that this
nuclear-spin qubit can be efficiently controlled by an ac electric field, when
embedded in a two electron dot-donor setup subject to intrinsic or artificial
spin-orbit interaction. Exposing the qubit to control electric fields in that
setup exposes it to electric noise as well. In this work, we describe the
effect of electric noise mechanisms, such as phonons and $1/f$ charge noise,
and estimate the corresponding decoherence time scales of the nuclear-spin
qubit. We identify a promising parameter range where the electrical
single-qubit operations are at least an order of magnitude faster then the
decoherence. In this regime, decoherence is dominated by dephasing due to $1/f$
charge noise. Our results facilitate the optimized design of nanostructures to
demonstrate electrically driven nuclear spin resonance.
