Вплив пасивного шару на розподіл електричного поля в сегнетоелектричних тонких плівках

Abstract

The influence of the passive layer on the electric field distribution in ferroelectric thin films is analyzed analytically.The study was carried out for monodomain ferroelectric thin films with a nonuniform spontaneous polarization distribution along the polar direction. The polarization polar direction coincides with the film surface normal. During the study it was assumed that on the ferroelectric film surfaces there are passive layers of fixed thickness, in which there is no spontaneous polarization. Their physical origin is the inevitable contamination of the ferroelectric surface, which becomes paraelectric in order to provide maximum effective screening of bulk polarization. This corresponds to an overwhelming majority of experiments. The dielectric susceptibility of these films significantly differs from the dielectric susceptibility of ferroelectric film. The paper considers the one-dimensional case, that is, the distributions of the electric field and electric potential are considered only along the polar axis of polarization of the ferroelectric thin film. The problem statement is described in general and can be solved for different initial conditions. A system of two second-order linear differential equations for the electric potential, obtained on the basis of Maxwell's equations, was solved. To solve the equations was use interface conditions for electromagnetic fields and the zero potential on the structure surfaces. The solution of the initial differential equations is obtained for three cases. The first case is the absence of charge at the interface of the fixed thickness dielectric passive layer with the ferroelectric film. The next case is the absence of charge at the interface of the infinite thickness semiconductor passive layer with the ferroelectric film. The last case is the presence of charge at the interface of the fixed thickness dielectric passive layer with the ferroelectric film. The analytical dependence of the electric potential distribution in ferroelectric thin films on the passive layer thickness was derived separately for each of these cases. It is shown that all considered cases have the same kind of the dependence of the electric potential and electrical field distribution in feroelectric thin film on the passive layer thickness. Ref. 7, Fig. 1.