  This work explores a nontrivial temperature behavior of the carriers
concentration, which governs graphene channel conductance in the nano-structure
"graphene channel on ferroelectric substrate" that is a basic element for FETs
in non-volatile memory units of new generation. We revealed the transition from
a single to double antiferroelectric-like hysteresis loop of the concentration
voltage dependence that happens with the temperature increase and then exist in
a wide temperature range (from 350 to 500 K). Unexpectedly we revealed the
double loops of polarization and concentration can have irregular shape that
remains irregular as long as the computation takes place, and the voltage
position of the different features (jumps, secondary maxima, etc.) changes from
one period to another, leading to the impression of quasi-chaotic behavior. It
appeared that these effects originate from the nonlinear screening of
ferroelectric polarization by graphene carriers, as well as it is conditioned
by the temperature evolution of the domain structure kinetics in ferroelectric
substrate. The nonlinearity rules the voltage behavior of polarization
screening by graphene 2D-layer and at the same time induces the motion of
separated domain walls accompanied by the motion of p-n junction along the
graphene channel (2D-analog of Hann effect). Since the domain walls structure,
period and kinetics can be controlled by varying the temperature, we concluded
that the considered nano-structures based on graphene-on-ferroelectric are
promising for the fabrication of new generation of modulators based on the
graphene p-n junctions.
