“Negative capacitance” in resistor-ferroelectric and ferroelectric-dielectric networks: Apparent or intrinsic?

Abstract

In this paper, we describe and analytically substantiate an alternate explanation for the negative capacitance (NC) effect in ferroelectrics (FE). We claim that the NC effect previously demonstrated in resistance-ferroelectric (R-FE) networks does not necessarily validate the existence of “S” shaped relation between polarization and voltage (according to Landau theory). In fact, the NC effect can be explained without invoking the “S”-shaped behavior of FE. We employ an analytical model for FE (Miller model) in which the steady state polarization strictly increases with the voltage across the FE and show that despite the inherent positive FE capacitance, reduction in FE voltage with the increase in its charge is possible in a R-FE network as well as in a ferroelectric-dielectric (FE-DE) stack. This can be attributed to a large increase in FE capacitance near the coercive voltage coupled with the polarization lag with respect to the electric field. Under certain conditions, these two factors yield transient NC effect. We analytically derive conditions for NC effect in R-FE and FE-DE networks. We couple our analysis with extensive simulations to explain the evolution of NC effect. We also compare the trends predicted by the aforementioned Miller model with Landau-Khalatnikov (L-K) model (static negative capacitance due to “S”-shape behaviour) and highlight the differences between the two approaches. First, with an increase in external resistance in the R-FE network, NC effect shows a non-monotonic behavior according to Miller model but increases according to L-K model. Second, with the increase in ramp-rate of applied voltage in the FE-DE stack, NC effect increases according to Miller model but decreases according to L-K model. These results unveil a possible way to experimentally validate the actual reason of NC effect in FE.