Thickness driven stabilization of saw-tooth–like domains upon phase transitions in ferroelectric thin films with depletion charges

Abstract

Ionized impurities have nearly always been neglected in discussing the limit of functionality of ferroelectric thin films. One would certainly expect that the thickness limit for functionality would be altered in the presence of ionized impurities, but how this would occur remains unclear. In this article, we analyze the domain structures as well as the phase transition temperatures in films with depletion charges for various film thicknesses. Depletion charges induce a position-dependent built-in field that leads to an inhomogeneous distribution of ferroelectric polarization. Such an inhomogeneity in the polarization results in strong depolarizing fields in films. We show that formation of saw-tooth–type domains is a way to circumvent the depolarizing fields, even in films with ideal electrodes. There is a critical film thickness above which the saw-tooth domains develop. On the other hand, the phase transition of the ultrathin structures with electrodes having a finite screening length, namely real electrodes, is always into the multidomain state during cooling from the paraelectric state, regardless of the presence of depletion charges. An important finding we have is that the transition temperature in films with real electrodes does not depend nearly at all on the depletion charge density unless it is very high (>1026 ionized impurities/m3). Relatively thick films (>8 nm in this work) with real electrodes that have very high depletion charge densities have transition temperatures very similar to those with the same charge density, but with ideal electrodes, making us conclude that thick films with high depletion charge densities will hardly feel the finite screening effects. The results are provided for (001) BaTiO3 films grown on (001) SrTiO3 substrates with pseudomorphic top and bottom metallic electrodes.