Understanding Anti-ferroelectric Behavior and Wake-up in La Doped HZO Metal-FerroelectricMetal Capacitors Using Nucleation Limited Switching Model

Anti-ferroelectricity (AFE) and wake-up in La doped HZO films is modeled using nucleation limited switching (NLS) model. We show that the pinched polarization versus electric field (P-E) loop can be modeled by two groups of independent ferroelectric domains with asymmetric switching barrier caused by built-in electric field. The wake-up of the film is modeled by adapting the built-in electric field experienced by both group of domains as a function of the fatigue cycling time using a sigmoid function. Further investigation of the electric field dependence of wake-up reveals that wake-up at lower electric field $(\lt 3 M V / c m)$ is dominated by merging of ferroelectric current peaks. Beyond $3 M V / \mathrm{cm}$, an additional phase conversion between paraelectric, ferroelectric and antiferroelectric phases cannot be ruled out. This points to a threshold electric field above and below which different wakeup mechanisms may dominate.