  Electron-beam (e-beam) lithography is commonly used in fabricating
metal-oxide-silicon (MOS) quantum devices but creates defects at the Si/SiO$_2$
interface. Here we show that a forming gas anneal is effective at removing
shallow defects ($\leq$ 4 meV below the conduction band edge) created by an
e-beam exposure by measuring the density of shallow electron traps in two sets
of high-mobility MOS field-effect transistors (MOSFETs). One set was irradiated
with an electron-beam (10 keV, 40 $\mu$C/cm$^2$) and was subsequently annealed
in forming gas while the other set remained unexposed. Low temperature (335 mK)
transport measurements indicate that the forming gas anneal recovers the e-beam
exposed sample's peak mobility (14,000 cm$^2$/Vs) to within a factor of two of
the unexposed sample's mobility (23,000 cm$^2$/Vs). Using electron spin
resonance (ESR) to measure the density of shallow traps, we find that the two
sets of devices are nearly identical, indicating the forming gas anneal is
sufficient to anneal out shallow defects generated by the e-beam exposure.
Fitting the two sets of devices' transport data to a percolation transition
model, we extract a T=0 percolation threshold density in quantitative agreement
with our lowest temperature ESR-measured trap densities.
