Finite-size effects of hysteretic dynamics in multilayer graphene on a ferroelectric

Abstract

The origin and influence of finite size effects on the nonlinear dynamics of space charge stored by multi-layer graphene on 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 ferroelectric. The size-dependent behaviors are governed by the relations between the thicknesses of multi-layer graphene, ferroelectric film and the dielectric layer.The appearance of charge and electro-resistance 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 multi-layer system enable knowledge-driven design of graphene-on-ferroelectric heterostructures with advanced performances.We further investigate the effects of spatially non-uniform ferroelectric domain structures on the graphene layers conductivity and predict its dramatic increase under the transition from multi-to single-domain state in ferroelectric. This intriguing effect can open new possibilities for the graphenebased sensors and explore the physical mechanisms underlying in the operation of graphene field effect transistor with ferroelectric gating.

Influence of Domain Structure in Ferroelectric Substrate on Graphene Conductance (Authors' Review)

“…normal to the graphene plane; and f 11 is the permittivity of ferroelectric along the -direction, i.e. along the channel), * is the sum of the dielectric layer thickness and the effective screening length in graphene [14,33].…”

“…The nonlinear response of a perfect ferroelectric substrate can be described using the Ginzburg-Landau-Khalatnikov relaxation equation [33,41,42] …”

“…The mean free path ( 2D ) ∼ √ 2D for the scattering at ionized centers in the substrate and in the temperature interval far from the Curie temperature [33].…”

“…The concentration 2D of 2D electrons far from the FDWs can be regarded as a constant voltage-independent value, namely, 2D ≈ | / | [17,18,33]. Then, for the most common case of electron scattering in the graphene channel at ionized impurities in the substrate, = = √ 2D , where the proportionality coefficient depends on the substrate material and graphene-ferroelectric interface chemistry.…”

Limits for the graphene on ferroelectric domain wall p-n-junction rectifier for different regimes of current

“…The electrostatic problem of the electric field distribution was solved in ref [14], several modifications have been considered earlier [15,16,17].…”