Numerical simulation of domain wall motion in a surface discharge over a ferroelectric

The article presents a simplified numerical simulation of a vacuum ferroelectric cathode operating in a low-current mode (without surface plasma formation). The field emission from the cathode was simulated for the range of applied electric field magnitudes. The polarization domain growth process during the charging of ferroelectric surface was simulated using Landau-Ginzburg-Devonshire model. Interaction of the electrons with a depolarization field of a domain wall led to an attraction of the electrons to the polarization domain boundaries. A close to the linear dependence of the equilibrium domain wall position from the applied electric field was found with the total emitted charge proportional to the domain size.