Effect of electrodes on the properties of a thin ferroelectric film

The effect of various metal electrodes on the properties of thin ferroelectric films is considered using the phenomenological Ginzburg-Landau theory. The electric field produced by charges on electrodes is taken into account (with allowance for the screening of the charges in the metals) in the free energy functional and in the Euler-Lagrange equation for the film polarization. This equation is solved using the variational method, and the free energy functional is reduced to the conventional free energy with a renormalized coefficient of P ². This coefficient is dependent on the properties and thickness of the film and the properties of the electrode. Therefore, the physical characteristics of the size effect can be found by merely substituting the renormalized coefficient into the usual formulas from phenomenological theory. The calculations are shown to be in good agreement with the experimental data for Pt, Ir, IrO₂, and SrRuO₃.