Direct Observation of Polarization vs. Thickness Relation in Ultra-Thin Ferroelectric Films

A reduction of polarization in ultra-thin ferroelectric films appears to be fundamental to ferroelectricity at the nanoscale. For the model system PbTiO3 on SrTiO3, we report observation of the polarization vs. thickness relation. Distinct periodicity changes of ferroelectric domains obtained from x-ray diffraction and total energy calculations reveal a linear lowering of the polarization below a critical thickness of ~12 nm. Independent polarization and tetragonality measurements provide insight into the fundamental relation between polarization and tetragonality in nanoscale ferroelectrics.