Negative Capacitance Behavior in a Leaky Ferroelectric

We present a simulation study of the negative capacitance effect incorporating leakage through the ferroelectric (FE) negative capacitor. The dynamics of the FE is modeled using the Landau-Khalatnikov equation. When an FE and a dielectric are simply connected in series without a metal contact between them, the stabilization of negative capacitance remains unchanged irrespective of leakage. However, when a metal is used, any finite leakage through the FE makes it impossible to stabilize negative capacitance at the steady state. Nonetheless, when a voltage is applied, the series configuration enters the negative capacitance state and as long as the gate voltage is cycled faster than the time needed by the leakage current to discharge all the capacitors, the transistor shows improved subthreshold swing. These results are expected to provide insight into understanding and analyzing recent experimental results on negative capacitance.