Polarization retention in ultra-thin barium titanate films on Ge(001)

We investigate polarization retention in 10 to 19 nm thick ferroelectric BaTiO₃ (BTO) grown on Ge(001) by molecular beam epitaxy. The out-of-plane direction and reversibility of electric polarization were confirmed using piezoresponse force microscopy. After reverse-poling selected regions of the BTO films to a value P with a biased atomic-force microscope tip, we monitored relaxation of their net polarization for as long as several weeks using optical second-harmonic generation microscopy. All films retained reversed polarization throughout the observation period. 10 nm-thick BTO films relaxed monotonically to a saturation value of 0.9 P after 27 days and 19 nm films to 0.75 P after 24 h. Polarization dynamics are discussed in the context of a 1D polarization relaxation/kinetics model.