Perimeter effect in very small ferroelectrics

We conducted impedance spectroscopy measurements on lead zirconate titanate capacitors of varying lateral size from 130×180 μm down to 1×1 μm. We discovered a peak in the impedance response with a frequency that depends on the perimeter of the capacitor with an exponential relationship. Our model for this effect is based on the idea that at low fields, nucleation occurs at stress free areas (in our case, the capacitor perimeter) and that domain-wall motion is restricted by viscous drag caused by the coupling of the domain wall to acoustic phonons. The relaxation time for the impedance peak is the time for the domain walls to propagate from the perimeter to the center. This process is somewhat different from the normal switching response; it occurs for small fields, when the capacitor has not been prepoled. The mechanism is similar to that for relaxation of an unstable polarization state. This model can also explain the logarithmic time dependence sometimes observed in those studies.