Multi-domain Phase-field Modeling of Polycrystalline Hafnia-based (Anti-)ferroelectrics Capable of Representing Defects, Wake-up and Fatigue

In this paper, for the first time, a multi-domain phase-field device-level framework for polycrystalline hafnia-based ferroelectric (FE) and anti-ferroelectric (AFE) thin films is developed to describe (i) pristine states with different dominant phases, (ii) wake-up driven by either depolarization or tetragonal (t-) to orthorhombic (o-) phase transition, (iii) fatigue induced by o- to monoclinic (m-) phase transition, and (iv) imprint resulting from defect accumulation at phase boundaries during electric field cycling. The model shows excellent agreements with a wide range of electrical polarization-voltage (P-V) measurements in both pristine and after field cycling while being consistent to density functional theory (DFT) calculations, the phase analysis from x-ray diffraction (XRD), and the observations reported in literature; therefore, this work not only provides a fundamental theoretical platform for device-level simulations with polycrystalline hafnia thin films, but also opens new opportunities for device designs using the mixture of phases in hafnium oxide.