Thickness dependent ferroelectric properties of BaTiO3 ultra-thin films

For decades, ferroelectricity in ultra-thin ferroelectric films has attracted much attention because of high-density nonvolatile memory application. Recently, first-principle calculation on the thickness limit of ferroelectricity in BaTiO$_{3}$(BTO) thin films was reported [1]. Experimental evidence of thickness limit and macroscopic polarization behaviors in the ultra-thin ferroelectric films were rarely studied. In this work, we investigated thickness dependence of polarization retention properties and coercive field in BTO films. SrRuO$_{3}$/BTO/SrRuO$_{3}$ capacitors were prepared with BTO layer thickness from 30 nm to 5 nm. From the electrical measurements, we observed that the upper limit of the critical thickness should be less than 5 nm. All the capacitors showed rapid relaxation of polarization in 1 s, and coercive field is independent of thickness. We would discuss these thickness-dependent polarization relaxation and coercive field in connection with depolarization field, which plays an important role in ultra-thin ferroelectric capacitor [2]. [1] J. Junquera and P. Ghosez, Nature (London) \textbf{422}, 506 (2003). [2] A. M. Bratkovsky and A. P. Levanyuk, Phys. Rev. Lett. \textbf{84}, 3177 (2000).