Retention of intermediate polarization states in ferroelectric materials enabling memories for multi-bit data storage

A homogeneous ferroelectric single crystal exhibits only two remanent polarization states that are stable over time, whereas intermediate, or unsaturated, polarization states are thermodynamically instable. Commonly used ferroelectric materials however, are inhomogeneous polycrystalline thin films or ceramics. To investigate the stability of intermediate polarization states, formed upon incomplete, or partial, switching, we have systematically studied their retention in capacitors comprising two classic ferroelectric materials, viz. random copolymer of vinylidene fluoride with trifluoroethylene, P(VDF-TrFE), and Pb(Zr,Ti)O3. Each experiment started from a discharged and electrically depolarized ferroelectric capacitor. Voltage pulses were applied to set the given polarization states. The retention was measured as a function of time at various temperatures. The intermediate polarization states are stable over time, up to the Curie temperature. We argue that the remarkable stability originates from the coexistence of effectively independent domains, with different values of polarization and coercive field. A domain growth model is derived quantitatively describing deterministic switching between the intermediate polarization states. We show that by using well-defined voltage pulses, the polarization can be set to any arbitrary value, allowing arithmetic programming. The feasibility of arithmetic programming along with the inherent stability of intermediate polarization states makes ferroelectric materials ideal candidates for multibit data storage