▎ 摘　　要

The origin and influence of finite-size effects on the nonlinear dynamics of space charge stored by multilayer graphene on a ferroelectric and resistivity of graphene channel were analyzed. Here, we develop a self-consistent approach combining the solution of electrostatic problems with the nonlinear Landau-Khalatnikov equations for a ferroelectric. The size-dependent behaviors are governed by the relations between the thicknesses of multilayer graphene, ferroelectric film, and the dielectric layer. The appearance of charge and electroresistance hysteresis loops and their versatility stem from the interplay of polarization reversal dynamics and its incomplete screening in an alternating electric field. These features are mostly determined by the dielectric layer thickness. The derived analytical expressions for electric fields and space-charge-density distribution in a multilayer system enable knowledge-driven design of graphene-on-ferroelectric heterostructures with advanced performance. We further investigate the effects of spatially nonuniform ferroelectric domain structures on the graphene layers' conductivity and predict its dramatic increase under the transition from multi-to single-domain state in a ferroelectric. This intriguing effect can open possibilities for the graphene-based sensors and explore the underlying physical mechanisms in the operation of graphene field-effect transistor with ferroelectric gating.