One of the exciting features of graphene is a possibility to affect
its electrical, optical, and chemical properties by gating, that is,
by application of an electric field. This requires reasonably large
fields (at the level of 1 V/nm necessary to induce relevant electron
density changes) applied over a gating dielectric material. At these
fields, most dielectrics show some conduction, which leads to an important
question: what is the best dielectric to gate graphene? Here, we show
that this question is imprecise as a dielectric material produced
by different fabrication methods can exhibit dramatically different
gating properties. Namely, we show that two oxide dielectrics (hafnia
and alumina) result in positive hysteresis of graphene gating characteristics
being fabricated by atomic layer deposition and negative hysteresis
being fabricated by electron beam evaporation. We attribute this behavior
to the stoichiometry of the samples and oxygen ion migration. It implies
that oxide dielectrics should be avoided in graphene gated devices
working at room temperatures.