Reversible and Irreversible Polarization Contributions

To characterize ferroelectric materials usually the dependence of the polarization on the applied voltage is measured by means of a Sawyer-Tower circuit or by recording the current response to a voltage step. The / (V/)-hys(crcsis curve is used to determine the remanent polarization and coercive voltage, respectively coercive field. These two parameters are of critical importance to the design of external circuits of FeRAMs. 

The ferroelectric hysteresis originates from the existence of irreversible polarization processes by polarization reversals of a single ferroelectric lattice cell (see Section 1.4.1). However, the exact interplay between this fundamental process, domain walls, defects and the overall appearance of the ferroelectric hysteresis is still not precisely known. The separation of the total polarization into reversible and irreversible contributions might facilitate the understanding of ferroelectric polarization mechanisms. Especially, the irreversible processes would be important for ferroelectric memory devices, since the reversible processes cannot be used to store information. 

For ferroelectrics, mainly two possible mechanisms for irreversible processes exist. First, lattice defects which interact with a domain wall and hinder it from returning into its initial position after removing the electric field that initiated the domain wall motion ( pinning ) [16]. Second, the nucleation and growth of new domains which do not disappear after the field is removed again. In ferroelectric materials the matter is further complicated by defect dipoles and free charges that also contribute to the measured polarization and can also interact with domain walls [17]. Reversible contributions in ferroelectrics are due to ionic and electronic 

A further approach to separate the reversible and irreversible 90° and non-90° contributions is the investigation of the piezoelectric small and large signal response of the ferroelectric 

Analogue to the dielectric case, the reversible contribution to the strain (see Equation 1.1) can be determined by the integration of the piezoelectric small signal coefficient d j over the applied bias field. 

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