Semiconductor Effects in Ferroelectrics

In this textbook ferroelectrics have so far been dealt with as insulators. External electric fields can and will induce polarization in any insulating material. This is dielectricity. On top of this, pyroelectrics exhibit a temperature dependent spontaneous electric polarization, namely a crystallographic phase transition which is polar. It disappears above the Curie-point. Below the Curie point, external electric fields can rotate or alter the direction of this spontaneous polarization. If this becomes a remanent state, the material is ferroelectric and exhibits electric hysteresis. Another aspect in these materials is the fact that electrical insulation is a stretchable term. While metals are well defined and offer conductivity down to very low temperatures, already semi-metals will turn partly insulating at low temperature. Semiconductors are typically insulating in a certain low temperature range (energetically \(\lesssim 1/10 kT\)) above which thermal excitation of charge carriers into the conduction band will induce a finite conductivity. The energetic band gap determines this barrier and the exponential tail of the Fermi-Dirac distribution determines the number of charge carriers in the conduction band as well as the missing electrons (termed holes) in the valence band. Typical ferroelectrics exhibit band gaps that turn the material insulating at room temperature. This is the case for most oxides. Ferroelectric sulfides typically display much lower band gaps and turn conducting at or even below room temperature already. Another aspect enters when one considers that external electroding is always necessary to drive a ferroelectric capacitor. In the context of a semiconductor picture we deal with a classical Schottky barrier. Grain boundaries play another particular role in polycrystalline materials. This may even lead to positive temperature coefficient resistor (PTCR) characteristics. In this lecture we will draw the connection between a ferroelectric, its semiconductor character, point defects, and their overall interactions. Particularly the inner and outer boundaries of crystallites become subject to band bending, 2D-conducting planes, space charge regions, and diverse other effects. Also optical effects as well as fatigue depend on the semiconductor and defect induced properties. We intend to give the newcomer access to this complex field which has seen a peak in understanding in the late 70\(\text {ies}\) of the 20\(\text {th}\) century experiencing a certain revival recently due to a number of exciting findings associated with domain walls. Furthermore, magnetoelectric composites have recently been found to display peculiar electrical effects related to their semiconductor character rather than the magnetic part of their properties.