Theory of Ferroelectricity and Size Effects in Thin Films

Abstract

Ferroelectrics form an important class of materials with giant electromechanical and dielectric response properties, which are crucial in technologies ranging from micro-electromechanical systems (MEMS) to computer memory devices. Ferroelectrics exhibit a spontaneous electric polarization (electric dipole moment per unit volume) that can be switched with large enough external fields to its symmetry equivalent states, in particular to the one with reversed direction. Fundamentally, the strong coupling of spontaneous polarization with external stress and electric fields is linked with a structural (or ferroelectric) phase transition exhibited by ferroelectrics as a function of temperature, which depends sensitively on applied stress and electric fields. The coupling between the polarization and stress facilitates their use as sensors and actuators, and the dielectric coupling and switchability of polarization facilitate their use in memory devices. With a constant trend of miniaturization of devices, it is essential to understand how these properties of bulk ferroelectrics evolve to the ones at nano-scale. Measurement of properties of a nano-structure of a material and its potential use in a device depend very much on its chemical, electrical and mechanical environment. Fundamentally, this is because (a) a sizeable fraction of atoms in a nano-structure belongs to its surface or interface with environment, and (b) the length-scale(s) associated with its interface depend on the nature of its environment. This becomes even more important in the context of a ferroelectric due to intrinsically strong coupling of its polarization with strain, electric field and chemistry. For example, shape of a nano-structure and the metallic versus insulating nature of its surrounding material determine the electro-static boundary conditions. The lattice mismatch between a ferroelectric nano-structure and its surrounding material determine the mechanical boundary conditions, and chemical bonding or charge transfer between them determine the changes in the local dipole moments arising from local chemistry. Thus, an accurate description of properties of a ferroelectric at nano-scale requires realistic treatment of the electrostatic, mechanical and chemical boundary conditions.