  We report the first experimental study of graphene transferred on
\b{eta}-Si3N4(0001)/Si(111). Our work provides a comprehensive quantitative
understanding of the physics of ultrathin Si3N4 as a gate dielectric for
graphene-based devices. The Si3N4 film was grown on Si(111) under ultra-high
vacuum (UHV) conditions and investigated by scanning tunneling microscopy
(STM). Subsequently, a graphene flake was deposited on top of it by a
polymer-based transfer technique, and a Hall bar device was fabricated from the
graphene flake. STM was employed again to study the graphene flake under UHV
conditions after device fabrication and showed that surface quality is
preserved. Electrical transport measurements, carried out at low temperature in
magnetic field, revealed back gate modulation of carrier type and density in
the graphene channel and showed the occurrence of weak localization. Under
these experimental conditions, no leakage current between back gate and
graphene channel was detected.
