Dielectric response of fully and partially depleted ferroelectric thin films and inversion of the thickness effect

Abstract

We consider the effect of full and partial depletion on the dielectric response characteristics of ferroelectric thin films with impurities via a computational approach and show that films with partial depletion display unique features and an enhanced dielectric response compared to those fully depleted. Polarization-applied bias loops for such films are often not able to provide information on the character of the ferroelectric dipoles in films predominantly due to leakage currents rather than the depletion charge itself. Capacitance-Voltage measurements are often an alternative way to find out whether ferroelectricity exists in a sample with high densities of depletion charge and inevitably forming leakage currents. In this work, we use a thermodynamic approach in a thin film geometry along with the fundamental equations for semiconductors and scrutinize the computed dielectric response-voltage characteristics of ferroelectric films for various densities of impurities. For n-type impurities in a wide bandgap BaTiO3 ferroelectric semiconductor film with Pt electrodes, we find that the capacitance peak at switching can be significantly suppressed in the case of high impurity densities (>10^25/m3) with relatively low ionization energy, at the order of 0.5 eV. For conserved number of species in films, electromigration of defect centers at room temperature is negligible and has no effect on the charge distribution and therefore on the dielectric response. Despite the general reduction in the switching peaks at coercive bias in films with high impurity density, the dielectric response at zero bias is enhanced with respect to charge-free films or those with relatively low impurity density (<10^24 /m3). For a given thickness, the full depletion and partial depletion conditions will depend on the electrode type in addition to impurity density and we demonstrate that partially depleted films should be expected to exhibit peculiar capacitance-voltage characteristics at low and high bias. Our results imply that the thickness effect probed in experiments in ferroelectric thin films could be entirely inverted in thin films with depletion charges, meaning that thick films with depletion charges might undergo reduction or heavy smearing of transition temperatures with respect to thinner ones having the same depletion charge density, resulting in a higher dielectric response in thicker films. Therefore, depletion charge densities in ferroelectric thin films should be estimated before size-effect related studies. We finally noticed that these findings are in good qualitative agreement with dielectric measurements done on PbZrxTi1-xO3.