Correlation between coercive tip bias and domain wall width evolution, and tunable mechanism transition in ferroelectric films

Based on a modified Kittel's law, a theoretical approach was developed to study the relaxation-driven ferroelectric domain wall width evolution in an inhomogeneous SPM-tip electric field and its dependence on coercive bias. The proposed approach, which is in agreement with both the existing experimental observations and theories, was also employed to investigate the famous phenomenon of ferroelectric domain breakdown (FDB). It has been shown that the domain wall width, which varied slightly in the initial stage but changed drastically subsequently, can influence coercive bias through the linear increase region, unstable region, and nonlinear reducing region. It has also been illustrated that there are possibly three tunable FDB mechanisms in BaTiO₃ films, i.e., absence mode, activation mode, and nonactivation mode. Finally, two possible methods for the realization of the proposed mode-tuning process were suggested.