Theoretical model of SPM-tip electrostatic field accounting for dead layer and domain wall

A new theoretical approach for the determination of the electric field distribution in the ferroelectric/dielectric system with the presence of the SPM tip is presented. For the analytical solution of the problem some simplifications are introduced (initial model statement has only a numerical solution). Namely, the smallness of the domain wall thickness in the comparison with a domain size and high value of the ferroelectric dielectric permittivity are used. The developed approach allows us to obtain explicit formulas for the polarization and electric field intensity. The calculation and analysis of the tip capacitance as a function of the distance from the ferroelectric interface demonstrate that the presence of charges at the domain wall results in the difference in obtained values of 30% in comparison with the widely used dielectric model [1].