Subcritical switching dynamics and humidity effects in nanoscale studies of domain growth in ferroelectric thin films

Ferroelectric domain switching in c-axis-oriented epitaxial Pb(Zr$_{0.2}$Ti$_{0.8}$)O$_3$ thin films was studied using biased scanning probe microscopy tips. While linear and logarithmic dependence of domain size on tip bias and writing time, respectively, are well known, we report an additional linear dependence on relative humidity in the 28-65% range. We map out the switched domain size as a function of both the tip bias and the applied pulse time and describe a growth-limited regime for very short pulses and a nucleation-limited regime for very low tip bias. Using "interrupted-switching" measurements, we probe the nucleation regime with subcritical pulses and identify a surprisingly long relaxation time on the order of 100 ms, which we relate to ionic redistribution both on the surface and within the thin film itself.