Negative Capacitance transients 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 [1,2]. 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 a thin, single crystalline ferroelectric film, by constructing a simple R-C network and monitoring the voltage dynamics across the ferroelectric capacitor6. 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 resulting in the characteristic ``negative capacitance transients.'' Analysis of this ``inductance''-like behavior from a capacitor allows us to calculate the value of the negative capacitance directly and presents an unprecedented insight into the intrinsic energy profile of the ferroelectric material.\\[4pt] [1] Salahuddin et al.~Nano Lett.~8, 40 (2008).\\[0pt] [2] Zhirnov et al. ~Nature Nanotechnology~3, 77 (2008).\\[0pt] [3] Khan et al. Nature Materials (in press).