Negative Capacitance in a Ferroelectric Capacitor

The Boltzmann distribution of electrons poses a fundamental barrier to lowering energy dissipation in conventional electronics, often termed as Boltzmann Tyranny$^{\mathrm{1}}$. Negative capacitance in ferroelectric materials, which stems from the stored energy of phase transition, could provide a solution, but a direct measurement of negative capacitance has so far been elusive. Here we demonstrate the negative differential capacitance in an epitaxial ferroelectric film, by constructing a simple R-C network and monitoring the voltage dynamics across the ferroelectric capacitor$^{\mathrm{2}}$. When a voltage pulse is applied, the voltage across the ferroelectric capacitor is found to be decreasing with time--in exactly the opposite direction to which voltage for a regular capacitor should change. The results are analyzed on the basis of the Landau-Khalatnikov equation, which shows that as the ferroelectric polarization switches its direction, it passes through the unstable negative capacitance region. Analysis of this behavior from a capacitor presents an unprecedented insight into the intrinsic energy profile of the ferroelectric material. \newline 1. Salahuddin et al. Nano Lett.~8, 405 (2008). 2. Khan et al. Nature Mater. 14, 182 (2015).