Depolarization Field and Properties of Thin Ferroelectric Films with Inclusion of the Electrode Effect

The influence of metallic electrodes on the properties of thin ferroelectric films is considered in the framework of the Ginzburg-Landau phenomenological theory. The contribution of the electrodes with different screening lengths l s of carriers in the electrode material is included in the free-energy functional. The critical temperature T cl , the critical thickness of the film, and the critical screening length of the electrode at which the ferroelectric phase transforms into the paraelectric phase are calculated. The Euler-Lagrange equation for the polarization P is solved by the direct variational method. The results demonstrate that the film properties can be calculated by minimizing the free energy, which has a standard form but involves the coefficient of the term P 2. This coefficient depends not only on the temperature but also on the film thickness, the surface and correlation effects, and the electrode characteristics. The calculations of the polarization, the dielectric susceptibility, the pyroelectric coefficient, and the depolarization field show that the ferroelectric state of the film can be destroyed using electrodes from a material whose screening length exceeds a critical value. This means that the electrodes being in operation can induce a transition from the ferroelectric phase to the paraelectric phase. The quantitative criteria obtained indicate that the phase state and properties of thin ferroelectric films can be controlled by choosing the appropriate electrode material.