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

Abstract

We study the effect of full and partial depletion on the dielectric response characteristics of ferroelectric thin films with impurities via a computational approach. Using a thermodynamic approach along with the fundamental equations for semiconductors, we show that films with partial depletion display unique features and an enhanced dielectric response compared with those fully depleted. We find that the capacitance peak at switching can be significantly suppressed in the case of high impurity densities (>1025 m−3) with relatively low ionization energy, of the order of 0.5 eV. For conserved number of species in films, electromigration of ionized impurities at room temperature is negligible and has nearly no effect on the dielectric response. 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 (<1024 m−3). We demonstrate that partially depleted films should be expected to exhibit peculiar capacitance–voltage characteristics at low and high bias and that the thickness effect probed in experiments in ferroelectric thin films could be entirely inverted in thin films with depletion charges where a higher dielectric response can be measured in thicker films. Therefore, depletion charge densities in ferroelectric thin films should be estimated before size-effect-related studies. Finally, we noted that these findings are in good qualitative agreement with dielectric measurements carried out on PbZrxTi1−xO3.