Competition between intrinsic and extrinsic size effects in ferroelectric thin films with dead layers and charged point defects

We analyze the effect of charged point defects on the electrical domains, phase transition characteristics and electrical properties of ferroelectric thin films with thin dead layers using a non-linear thermodynamic model. The numerical analysis takes into account various electrostatic boundary conditions, presence of thickness-wise asymmetrically distributed charged point defects as well as the elastic energy associated with the film-substrate misfit and various polarization configurations. We demonstrate that these charged defects, even when having an effective charge density less than an electron per unitcell and positioned wide apart, can pin and couple to electrical domains in films with ferroelectrically passive, so-called dead layers. Such an outcome alters the hystereses and especially the phase transition characteristics. In films that are a few nanometers thick, the spatial charge effects compete with the depolarizing field, and could lead to highly stable 180o domains accompanied by spatial pinning of polarization depending on the sign of the charge associated with the defect. It has not been clear until recently whether strong spatial variations of polarization due to charged defects could, in the absence of free charges, trigger domain formation. We find that domains do form but only when dead layers are present and not due to strong variations of polarization around defects due to their spatial fields. While relatively thick films (>14 nm in this work) with no defects could have single domain state energy close to multidomain state even when thin dead layers (~ 0.4 nm) are present, we show that charged defects locally enhance polarization, with the reservation that it might be pinned, and could enforce 180o domain formation. For films with thick dead layers (> 0.8 nm in this work), depolarizing effects dominate and the transition from the paraelectric state is into the multidomain ferroelectric state during cooling. Charged defects, on the other hand, might also override the intrinsic limit set by the dead layers in ultrathin films through their long range fields and lead to multidomains with weak, induced polarization. Ultrathin films with asymmetrically distributed charged defects have a strongly smeared ferroelectricparaelectric transition while this effect is weaker in thicker films. The competition between defect induced extrinsic effects and the dead layer related limit is discussed.