  Transient negative capacitance effects in epitaxial ferroelectric
Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ capacitors are investigated with a focus on the
dynamical switching behavior governed by domain nucleation and growth. Voltage
pulses are applied to a series connection of the ferroelectric capacitor and a
resistor to directly measure the ferroelectric negative capacitance during
switching. A time-dependent Ginzburg-Landau approach is used to investigate the
underlying domain dynamics. The transient negative capacitance is shown to
originate from reverse domain nucleation and unrestricted domain growth.
However, with the onset of domain coalescence, the capacitance becomes positive
again. The persistence of the negative capacitance state is therefore limited
by the speed of domain wall motion. By changing the applied electric field,
capacitor area or external resistance, this domain wall velocity can be varied
predictably over several orders of magnitude. Additionally, detailed insights
into the intrinsic material properties of the ferroelectric are obtainable
through these measurements. A new method for reliable extraction of the average
negative capacitance of the ferroelectric is presented. Furthermore, a simple
analytical model is developed, which accurately describes the negative
capacitance transient time as a function of the material properties and the
experimental boundary conditions.
