Depolarization corrections to the coercive field in thin-film ferroelectrics

Abstract

Empirically the coercive field needed to reverse the polarization in a ferroelectric increases with decreasing film thickness. For ferroelectric films of 100 microns to 100 nanometers in thickness the coercive field has been successfully described by a semi-empirical scaling law. Accounting for depolarization corrections, we show that this scaling behavior is consistent with field measurements of ultrathin ferroelectric capacitors down to one nanometer 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.

Ferroelectricity in ultrathin perovskite films

“…Nevertheless, the stronger field compared to that in the Pt/PbTiO 3 /Pt structures also confirms the weaker screening effect of SrRuO 3 compared to Pt and other transition metals. 14 We note further that allowing the internal coordinates of the SrRuO 3 electrodes, especially those in the boundary layers, to relax together with the PbTiO 3 ions is crucial. When the SrRuO 3 ions are fixed in their ideal positions, we find only paraelectric structures for either of the PbTiO 3 terminations.…”

“…To address this question, we turn now to look at the depolarizing field and screening effects in these systems. The depolarizing field was previously addressed in phenomenological studies, 5,14,23 and is shown to scale with the spontaneous polarization of the ferroelectrics, the screening length of the electrodes and the inverse ferroelectric film thickness. Hence the depolarizing field would be expected to be negligible only in very thick films.…”

“…Also, a recent first-principles calculation revealed that BaTiO 3 films with SrRuO 3 electrodes lose ferroelectricity below ∼24Å (6 unit cells), 13 thus suggesting that a minimum thickness limit exists for useful ferroelectric films. While indeed a minimum film thickness must be influenced by the polarization of the ferroelectrics and the screening length of the electrodes, 14 it is not yet clear whether the depolarizing field can ever be completely removed by realistic electrodes on ultrathin films, nor how monodomain thin film ferroelectricity is affected by the choice of electrodes and by the interactions at the metal/oxide interface.…”

Size effects in ultrathin epitaxial ferroelectric heterostructures

“…[1][2][3][4][5][6][7][8][9][10][11][12] As the dimensions (both lateral and vertical direction) of the perovskite layer decreases, the fundamental question of size dependence becomes crucial. From a theoretical point of view, two models have been traditionally used to describe size effects, namely an "intrinsic" effect 9,10,13 and a "depoling field" effect.…”

“…10,17,18 Additionally a systematic increase in the coercive field is observed as the thickness is scaled down to 15 nm, in agreement with previous reports. 1,2,19 However for sub-10-nm-thick films the hysteresis loops were leaky, and not credible. Therefore we measured the polarization under pulsed probing conditions using an AFM based test setup.…”