An analytical approach for scanning probe microscope-tip electrostatic field distribution accounting for dead layer and domain wall

We have proposed a new theoretical approach for the determination of the electric field distribution in the ferroelectric/dielectric system with the presence of the SPM tip. The initial statement of the model has only a numerical solution. To find an analytical solution of the problem, some assumptions are introduced: the domain wall thickness can be considered to be much smaller than the domain size, and we use a high ferroelectric dielectric permittivity. The developed approach allows us to obtain explicit formulas for the polarization and electric field intensity. We have calculated and then analyzed the tip capacitance as a function of the distance from the ferroelectric interface. Additionally, different forms of the SPM tip are considered. It is demonstrated that in the presence of charges at the domain, the results differ from those obtained with the widely used dielectric model by 30%.