  The application of imaging techniques based on ensembles of nitrogen-vacancy
(NV) sensors in diamond to characterise electrical devices has been proposed,
but the compatibility of NV sensing with operational gated devices remains
largely unexplored. Here we fabricate graphene field-effect transistors (GFETs)
directly on the diamond surface and characterise them via NV microscopy. The
current density within the gated graphene is reconstructed from NV magnetometry
under both mostly p- and n-type doping, but the exact doping level is found to
be affected by the measurements. Additionally, we observe a surprisingly large
modulation of the electric field at the diamond surface under an applied gate
potential, seen in NV photoluminescence and NV electrometry measurements,
suggesting a complex electrostatic response of the oxide-graphene-diamond
structure. Possible solutions to mitigate these effects are discussed.
