BaTiO₃ (BTO) is a ferroelectric material well suited for non-volatile information storage thanks to its switchable polarization, low-voltage operation and high endurance. When doped with electrons, BTO can also become conducting, which enables the coexistence of ferroelectricity and metallicity in a single material. This situation is rare and raises fundamental questions about how polarization, strain, carrier density and screening interact at the nanoscale. It also offers a promising route to reduce interface defects in ferroelectric field-effect transistors (FeFETs) by integrating a conducting channel directly within the ferroelectric layer. The internship will focus on the growth of epitaxial BTO thin films by hybrid molecular beam epitaxy (MBE), combined with SrRuO₃ electrodes. The student will characterize structural and ferroelectric properties and generate ultrathin conducting layers either by controlled doping or by forming a 2DEG. These layers will then be used as active channels in FeFET-like devices. The work combines advanced thin-film growth, functional characterization and device physics, with the possibility to continue as a PhD.