Whither Steady-State Negative Capacitance of a Ferroelectric Film?

Abstract

We theoretically explore mechanisms that can potentially give rise to steady-state negative capacitance in a uniaxial ferroelectric film stabilized by a dielectric layer. The analytical expressions for the steady-state capacitance of a single-domain state are derived within Landau-Ginzburg-Devonshire approach and used to study the state stability vs. the domain splitting as a function of dielectric layer thickness. Analytical expressions for the critical thickness of the dielectric layer, polarization amplitude, equilibrium domain period and susceptibility are obtained and corroborated by finite element modelling. In the absence of screening charges neither single-domain, nor poly-domain states can exhibit globally-detectable steady-state negative capacitance. We further explore the possible effects of nonlinear screening at the ferroelectric-dielectric interface and show that if at least one of the screening charges is very slow, the total polarization dynamics can exhibit complex time- and voltage dependent behaviors that can be interpreted as a negative capacitance. In this setting, the negative capacitance effect is accompanied by almost zero dielectric susceptibility in a wide voltage range and low frequencies. These results may help to elucidate the fundamental dispute about the possible origin of the quasi-steady-state negative capacitance in thin ferroelectric films, and identify materials systems that can give rise to this behavior.