Ferroelectric phase transitions in thin films, ferroelectric-paraelectric superstructures and small particles: effects of the depolarizing field

The basic aspects of physics and diverse functional properties available in ferroelectrics have been established primarily through studies on bulk samples. But when it comes to utilizing these properties in modern nano-, microelectronics, thin films accumulated knowledge is turned to be very insufficient.

Here I describe in short the basic ferroelectricity concepts and unique properties of ferroelect¬ric materials and then show its transformations and limitations for so-called nano-systems: very thin (down to several monolayers) films, in superstructures consisting of equally thin layers of ferroelectric and paraelectric materials and very small particles. This lecture is focused on the principal problems in understanding of physics and properties of such systems and on key role of depolarizing field, whose importance for ferroelectrics is much larger than of the demagnetizing field for ferromagnets. Such field can be relatively easily compensated in macroscopic system but this compensation becomes difficult or impossible in very small systems. This is bad news because one of the effects of the depolarizing field is formation of domain structures while single domain states are what are needed for many applications.

I show how depolarizing field influences phase transition from paraelectric to ferroelectric state. The main aim is to answer the question what state, single or multi domain, forms at the transition in different systems and what is the situation with the competing state. The systems under consideration are:

1. thin films with real metallic electrodes, where the electric field penetrates at distances less than 1 Å, what proves sufficient to make the phase transition into multi domain state,
2. ferroelectric-paraelectric superstructures when the depolarizing field not only makes the phase transition multi domain at some conditions of the parameters of the structure but also leads to inhomogeneity of the forming domain structure along the superstructure,
3. small isolated particles or crystal regions with locally elevated phase transition temperature due to, e.g. clusters of impurities, where it is possible to avoid domain structure formation under very special conditions.