The influence of depolarization field on dielectric and pyroelectric properties of ferroelectric films

Calculations of the spontaneous polarization (Ps), dielectric susceptibility (c) and pyroelectric coefficient (P) of the ferroelectric films have been performed in the thermodynamic phenomenological theory framework. The Euler-Lagrange equation determining polarization dependence on the film parameters and the external electric field was solved analytically under the boundary conditions with different extrapolation lengths at two surfaces, respectively. The depolarization field contribution was taken into account in the model of short-circuited mono-domain ferroelectric film, treated as perfect insulator. The detailed analysis of the aforementioned quantities, space distribution and their average values in two cases with and without depolarization field was carried out. It was shown that the depolarization field shifts critical temperature to smaller values and the critical thickness to bigger value in comparison to those obtained without accounting the depolarization field. Meanwhile average values of Ps, c and P dependences on the film parameters and temperature are similar to the corresponding dependences obtained without accounting the depolarization field. The depolarization field was shown to flatten Ps, c and P space distributions, which have the peculiarities otherwise (e.g. small maxima in c and P coordinate profiles near the film surfaces). It was shown that depolarization field influence in short-circuited film could be neglected when the film thickness or the extrapolation lengths in the boundary conditions are larger than the correlation length value