Dynamical dielectric susceptibility of ferroelectric thin films and multilayers

Abstract

The thickness dependence of the real and imaginary parts of the dynamical dielectric susceptibility is investigated phenomenologically for a multilayer structure consisting of alternating ferroelectric and paraelectric layers. It is shown that the frequency dependence of the linear dielectric response can be closely approximated by that of a damped harmonic oscillator, with the static susceptibility, relaxation time, and soft-mode frequency depending on the layer thickness and temperature. When the layer thickness and temperature are equal to their critical values corresponding to the onset of a size-driven ferroelectric phase transition, the static susceptibility and the relaxation time become anomalously large and then decrease with further increasing layer thickness. A spectrum of natural polarization oscillations is predicted to exist with thickness-dependent frequencies. This spectrum includes a soft-mode frequency which vanishes at the critical thickness and at the critical temperature. The frequency spectrum lies below the soft-mode frequency of a thick film (in which the gradient of polarization is negligible). The calculations are compared with experimentally measured dispersion of the dielectric response of a PbTiO3-Pb0.72La0.28TiO3 multilayer structure. The agreement between the theory and experiment is found to be good.