Thickness dependence of the dielectric function of ferroelectric thin films

Abstract

A Green's function technique for a modified Ising model in a transverse field is applied, which allows to calculate the real and the imaginary parts of the dielectric function Eðk; EÞ for ferroelectric thin films. Compared to bulk materials the frequency of the soft-mode in thin film is reduced whereas the damping is enhanced. The dependence of Eðk; EÞ on temperature and film thickness is obtained for k ¼ 0 numerically. It is demonstrated, that the maximum of the dielectric function decreases with decreasing film thickness. The temperature, where the dielectric function offers a maximum, can decrease or increase depending on the strength of the surface transverse field and the exchange interaction parameter. Due to stronger damping effects in thin films the peak in the dielectric function becomes more diffuse when the film thickness decreases. The results are in reasonable qualitative agreement with experimental data for different ferroelctrics.

Dielectric function of antiferroelectric thin films

“…The obtained results are in good agreement with the behaviour of the dielectric function in AFE PbZrO 3 nanoparticles obtained by Chattopadhyay et al [9] and by Jiwei et al [11] for PNZST thin films. The behaviour of the dielectric constant for this case is similar to the dielectric behaviour of FE PbTiO 3 and BaTiO 3 thin films obtained experimentally [4 -6] or theoretically [14]: With a decrease in the film thickness or the particle size, c T decreases, max e decreases, and the peaks become increasingly broader. Figure 2 shows the temperature dependence of the dielectric constant for the other case s b J J > .…”

“…The behaviour of the dielectric constant of the AFE thin film for this case is similar to the dielectric behaviour of KDP-typ FE thin films [8,14]. Therefore it could explain the results of the analogous to KDP-typ AFE compounds, for example NH 4 H 2 PO 4 .…”

“…1) which undergo displacive phase transition, and from the analogy of the results shown in Fig. 2 for an AFE film and a FE KDP thin film [14] (KDP undergoes an order-disorder phase transition), we can conclude, that the second case …”

“…First attempts to find out the implications of the finite size or the film thickness on the temperature dependence of the dielectric constant for FE's in the paraelectric or ferroelectric phase are elucidated by Zhang et al [13] and by Wesselinowa and Trimper [14], respectively. In this paper, the film thickness dependence of the dielectric function of AFE thin films described by the transverse Ising model is investigated and compared with the experimental results.…”

Extinction efficiencies of coated absorbing aerosols measured by cavity ring down aerosol spectrometry

“…While we are not dealing with microwave wavelengths in this study, the bonds between a thin film and a substrate have been theorized to cause damping in a number of other situations as well, e.g. : friction in the flow of electrons in conducting and semi-conducting thin films (Lazarev et al, 2003), damping of the alignment of dipoles in ferroelectric and anti-ferroelectric thin films (Wesselinowa, 2005;Wesselinowa and Trimper, 2004), damping of molecular vibrations in thin films at infrared wavelengths (Chu, 1993), and damping of dipole vibration near the surface of a waveguide (LaFortune and Hall, 2002). For lack of specific data on damping in our system, we chose a reduction in the dielectric constant of our coating of similar relative magnitude to that used in Friedman (1998) (k=10 8 cm −1 , ε min =1.05).…”