A key functionality of ferroelectrics is the ability to switch their polarization between two stable orientations by application and reversal of an electrical field. As the size shrinks, polarization might become unstable, non-switchable or extremely low due to the absence or to the asymmetry in screening surface charges and asymmetry in their redistribution upon switching. Recently, it was shown that the ferroelectric polarization can be switched in epitaxial BaTiO3 films as thin as 1.6 nm (4 unit cells) on silicon. In this project, we address the ferroelectricity of nanostructures on a semiconductor, with not only ultrathin thickness but also sub-micrometer lateral dimensions. New aspects of ferroelectricity at the nanoscale will be therefore investigated with perspectives of integrating ferroelectrics on semiconductors for nanoelectronics and electro-optics. We will take up several technological challenges related to the fabrication of complex oxide nanostructures on planar semiconductor Si. Atomic layer deposition, reactive ion etching and helium ion beam milling will be used to prepare cylindrical nanostructures of various shapes and size (2-100 nm in thickness and 50-800 nm in lateral dimensions). We will address several questions at the frontier of the current knowledge regarding ferroelectricity on semiconductors. Since the surface contribution to various physical quantities becomes as large or even larger than the bulk one in nanostructures, the chemical screening in lowering the depolarization energy will compete with domain formation; these key aspects for the control of the polarization will be addressed. Piezoresponse force microscopy/spectroscopy will be used to image domains and explore the intricate contributions from electrochemical and ferroelectric states which may result even in a ferro-ionic mixed state. Raman spectroscopy and geometrical phase analysis of aberration-corrected TEM images will be used in comparison with X-ray diffraction to study the strain in the nanostructures. We will also develop advanced TEM methodologies in order to map at the nanoscale the polarization direction and amplitude. Such mapping will be used to unravel the effects of different boundary conditions and nanostructure shapes on the distribution of the polarization (flux closure, vortex...). Finally, we will aim at elucidating the ultimate switching time of the polarization of ferroelectric nanostructures by femtosecond pump probe spectroscopies and ultrafast X-ray diffraction experiments using a laboratory plasma X-ray source as well as synchrotron radiation at BESSY II. In addition, domain formation and switching will be studied in situ under an applied electric field in the dedicated I2TEM microscope. The in situ characterization by TEM of ferroelectric domains (nucleation, propagation...) under an applied electrical field is at the frontier of the current technical development and has never been demonstrated for ferroelectrics on semiconductors. Combining in situ TEM and ultrafast diffraction experiments will give unique insight into the dynamics of BaTiO3 films and nanostructures. To conclude, within FEAT, we will address fundamental questions at the frontier of the current knowledge in the ferroelectricity at the nanoscale on silicon, with expected breakthrough discoveries. Moreover, the nanostructures investigated in FEAT constitute elementary bricks with numerous potential applications in nanoelectronics and electro-optics.