Dynamics of ferroelectric domain formation in an atomic force microscope

The dynamics of ferroelectric domain formation in a non-homogeneous electric field of an atomic force microscope (AFM) tip are considered. Contributions of the apex and the conical part of the tip into the field are taken into account. It is supposed that this process passes through the same stages as the corresponding process in homogeneous external fields. However, the character of these stages may differ significantly. We consider all the stages of this process: formation of a nucleus, its growth, and the equilibrium domain parameters. Quantitative analysis is carried out for barium titanate. It is shown that the activation energy of nucleation strongly decreases with the applied voltage, and it is too small to limit the rate of the process even under low voltages. Dynamic equations for the time dependence of the domain length and radius are constructed and solved. Comparison of the calculated domain sizes with those observed in experiment is carried out. Calculated results obtained using different models for the field of the tip are compared.