  Charge noise can be detrimental to the operation of quantum dot (QD) based
semiconductor qubits. We study the low-frequency charge noise by charge offset
drift measurements for Si-MOS devices with intentionally implanted donors near
the QDs. We show that the MOS system exhibits non-equilibrium drift
characteristics in the form of transients and discrete jumps that are not
dependent on the properties of the donor implants. The equilibrium charge noise
indicates a $1/f$ noise dependence, and a noise strength as low as
$1~\mathrm{\mu eV/\sqrt{Hz}}$, comparable to that reported in more model GaAs
and Si/SiGe systems (which have also not been implanted). We demonstrate that
implanted qubits, therefore, can be fabricated without detrimental effects on
long-term drift or $1/f$ noise.
