  We propose a general theory for the analytical description of versatile
hysteretic phenomena in a graphene field effect transistor (GFET) allowing for
the existence of the external dipoles on graphene free surface and the
localized states at the graphene-surface interface. We demonstrated that the
absorbed dipole molecules (e.g. dissociated or highly polarized water
molecules) can cause hysteretic form of carrier concentration as a function of
gate voltage and corresponding dependence of graphene conductivity in GFET on
the substrate of different types, including the most common SiO2 and
ferroelectric ones. It was shown that the increase of the gate voltage sweeping
rate leads to the complete vanishing of hysteresis for GFET on SiO2 substrate,
as well as for GFET on ferroelectric substrate for applied electric fields E
less than the critical value Ec. For E>Ec the crossover from the hysteresis to
antihysteresis takes place. These results well correlate with the available
experimental data up to the quantitative agreement. Proposed model takes into
consideration the carriers trapping from the graphene channel by the interface
states and describes the antihysteresis in GFET on PZT substrate well enough.
Obtained results clarify the fundamental principles of GFET operation as well
as can be directly applied to describe the basic characteristics of advanced
nonvolatile ultra-fast memory devices using GFET on versatile substrates.
