Stable Subloop Behavior in Ferroelectric Si-Doped HfO₂

The recent demand for analogue devices for neuromorphic applications requires modulation of multiple nonvolatile states. Ferroelectricity with multiple polarization states enables neuromorphic applications with various architectures. However, deterministic control of ferroelectric polarization states with conventional ferroelectric materials has been met with accessibility issues. Here, we report unprecedented stable accessibility with robust stability of multiple polarization states in ferroelectric HfO₂. Through the combination of conventional voltage measurements, hysteresis temperature dependence analysis, piezoelectric force microscopy, first-principles calculations, and Monte Carlo simulations, we suggest that the unprecedented stability of intermediate states in ferroelectric HfO₂ is due to the small critical volume size for nucleation and the large activation energy for ferroelectric dipole flipping. This work demonstrates the potential of ferroelectric HfO₂ for analogue device applications enabling neuromorphic computing.