Time-dependent polarization relaxation behaviors induced by a depolarization field E d were investigated on high-quality ultrathin SrRuO3/BaTiO3/SrRuO3 capacitors. The E d values were determined experimentally from an applied external field to stop the net polarization relaxation. These values agree with those from the electrostatic calculations, demonstrating that a large E d inside the ultrathin ferroelectric layer could cause severe polarization relaxation. For numerous ferroelectric devices of capacitor configuration, this effect will set a stricter size limit than the critical thickness issue.PACS numbers: 77.22. Ej, 77.22.Gm, 77.80.Dj, 77.55.+f With recent breakthroughs in fabricating high-quality oxide films [1,2,3], ultrathin ferroelectric (FE) films have attracted much attention from the scientific as well as application points of view. As the FE film thickness d approaches tens of unit cell length, the FE films often show significantly different physical properties from those of bulk FE materials. Some extrinsic effects, especially coming from FE film surfaces and/or interfaces with other materials, could be very important [4]. For some other cases, intrinsic physical quantities could play vital roles in determining the unique properties of ultrathin films.Many FE-based electronic devices have the capacitor configuration, where a FE layer is inserted between two conducting electrodes. Then, polarization bound charges will be induced at the surfaces of the FE layer, but compensated by free charge carriers in the conducting electrodes. In real conducting electrodes, however, the compensating charges will be induced with a finite extent, called the screening length λ. This will result in an incomplete compensation of the polarization charges. Such an incomplete charge compensation should induce a depolarization field E d inside the FE layer, with a direction opposite to that of the FE polarization P [5]. Therefore, E d will appear in every FE capacitor, and its effects will becomes larger with the decrease of d [5]. (For a FE film without electrodes, there is no compensation for the polarization bound charge, so the value of E d will become even larger than that of the FE capacitor case.) E d has been known to be important in determining the critical thickness [6] and domain structure of ultrathin FE films [7,8,9], and reliability problems of numerous FE devices [10,11].Recently, using a first principles calculation, Junquera and Ghosez investigated the critical thickness of BaTiO 3 (BTO) layers in SrRuO 3 (SRO)/BTO/SRO capacitor [6]. For calculations, they assumed that all of the BTO and SRO layers were fully strained with the SrTiO 3 substrate. By taking the real SRO/BTO interfaces into account properly, they showed that E d could make the ferroelectricity vanish for the BTO films thinner than 6 unit cells, i.e. 2.4 nm [6]. More recently, using pulsed laser deposition with a reflection high energy electron diffraction monitoring system, we fabricated high-quality fully-strained SRO/BTO/SRO capacitors...

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To investigate the critical thickness of ferroelectric BaTiO3 (BTO) films, we fabricated fully strained SrRuO3∕BTO∕SrRuO3 heterostructures on SrTiO3 substrates by pulsed laser deposition with in situ reflection high-energy electron diffraction. We varied the BTO layer thickness from 3to30nm. By fabricating 10×10μm2 capacitors, we could observe polarization versus electric-field hysteresis loops, which demonstrate the existence of ferroelectricity in BTO layers thicker than 5nm. This observation provides an experimental upper bound of 5nm for the critical thickness. The BTO thickness-dependent scaling of the remanent polarization agrees with the predictions of recent first-principle simulations [J. Junquera and P. Ghosez, Nature 422, 506 (2003)].

Thickness-dependence of coercive field (E C ) was investigated in ultrathin BaTiO 3 capacitors with thicknesses (d) between 30 and 5 nm. The E C appears nearly independent of d below 15 nm, and decreases slowly as d increases above 15 nm. This behavior cannot be explained by extrinsic effects, such as interfacial passive layers or strain relaxation, nor by homogeneous domain models. Based on domain nuclei formation model, the observed E C behavior is explainable via a quantitative level. A crossover of domain shape from a half-prolate spheroid to a cylinder is also suggested at d~ 15 nm, exhibiting good agreement with experimental results.

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