Possible absence of critical thickness and size effect in ultrathin perovskite ferroelectric films

Although the size effect in ferroelectric thin films has been known for long time, the underlying mechanism is not yet fully understood and whether or not there is a critical thickness below which the ferroelectricity vanishes is still under debate. Here, we directly measure the thickness-dependent polarization in ultrathin PbZr_0.2Ti_0.8O₃ films via quantitative annular bright field imaging. We find that the polarization is significantly suppressed for films <10-unit cells thick (∼4 nm). However, approximately the polarization never vanishes. The residual polarization is ∼16 μCcm^-2 (∼17%) at 1.5-unit cells (∼0.6 nm) thick film on bare SrTiO₃ and ∼22 μCcm^-2 at 2-unit cells thick film on SrTiO₃ with SrRuO₃ electrode. The residual polarization in these ultrathin films is mainly attributed to the robust covalent Pb-O bond. Our atomic study provides new insights into mechanistic understanding of nanoscale ferroelectricity and the size effects.