“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.

A critical review of recent progress on negative capacitance field-effect transistors

“…A differential voltage amplification on DE capacitor by the FE capacitor was observed 25 . Once again, the result can be explained either by single domain or multi-domain switching model 22 .…”

Modeling of Negative Capacitance in Ferroelectric Thin Films

“…b) Experimental data from Kim et al and the fitted results from two different models; the transient NC model (blue dotted line) and the KAI model (red solid line). c) Simulated result of the transient negative slope by Miller–Saha model . The voltage applied to the ferroelectric capacitor (black dotted line) is always increasing.…”

“…Saha et al also offered an alternative explanation for the V ‐drop effect by treating the ferroelectric capacitor as a sum of a nonlinear positive capacitor and a nonlinear resistor . The idea that an FE capacitor can be modeled as a nonlinear positive capacitor was originally suggested by Miller et al, using a hyperbolic tangent function to model the polarization ( P s )–electric field ( E f ) hysteresis curve of the FE film.…”

“…While this was a purely mathematical approach to describe the apparent P − V curves, Saha et al showed that the V ‐drop effect can be explained by a voltage overshoot mechanism even with this simple model without invoking the concept of the intrinsic energy barrier. For the interpretation of such behavior, they noted that the ferroelectric switching inherently involves a damped response with a finite time constant defined as τ, which is incorporated into the so‐called Miller–Saha (M–S) model . An equivalent circuit of the M–S model is comprised of an intrinsic resistor R FE serially connected to the nonlinear capacitor C FE and a parallel linear capacitor C 0 representing both the parasitic capacitance of the measurement setup and the linear capacitance from the background dielectric constant of the FE film.…”

Stepwise internal potential jumps caused by multiple-domain polarization flips in metal/ferroelectric/metal/paraelectric/metal stack

“…However, physical understanding of NC effects is still under intensive debate [25][26][27][28][29][30][31][32][33][34][35][36] . Experimentally observed NC effects are different from each other, and also from the concepts initially proposed.…”