Thickness dependence of intrinsic dielectric response and apparent interfacial capacitance in ferroelectric thin films

We studied theoretically the influence of the progressive strain relaxation and the depolarizing-field effect on the thickness dependence of the out-of-plane dielectric response of epitaxial ferroelectric thin films sandwiched between extended metal electrodes. The calculations show that the inverse of the measured capacitance varies with the film thickness almost linearly in the most part of the thickness range at the majority of temperatures. Extrapolation of this linear dependence to zero thickness usually gives considerable nonzero intercept even in the absence of nonferroelectric interfacial layers. Remarkably, such apparent “interfacial capacitance” in a certain temperature range becomes negative. The physical meaning of the effective dielectric constant, which can be extracted from the slope of the reciprocal capacitance thickness dependence, is also analyzed. The theoretical predictions are compared with the experimental data obtained for single-crystalline ${\text{SrRuO}}_3∕{\text{Ba}}_{0.7}{\text{Sr}}_{0.3}{\text{TiO}}_3∕{\text{SrRuO}}_3$ and $\text{Pt}∕{\text{Ba}}_{0.7}{\text{Sr}}_{0.3}{\text{TiO}}_3∕{\text{SrRuO}}_3$ thin-film capacitors.