Depolarization corrections to the coercive field in thin-film ferroelectrics

Empirically, the coercive field needed to reverse the polarization in a ferroelectric increases with decreasing film thickness. For ferroelectric films of 100 µm to 100 nm in thickness the coercive field has been successfully described by a semi-empirical scaling law. Accounting for depolarization corrections, we show that this scaling behaviour is consistent with field measurements of ultrathin ferroelectric capacitors down to one nanometre in film thickness. Our results also indicate that the minimum film thickness, determined by a polarization instability, can be tuned by the choice of electrodes, and recommendations for next-generation ferroelectric devices are discussed.