Comprehensive interpretations of thermodynamic and kinetic effects on the phase fractions in Hf1-xZrxO2 by first principle calculations

Phase control in Hf1-xZrxO2 (HZO) is crucial for optimizing its electrical properties, such as ferroelectricity and high dielectricity. However, phase optimization in HZO has remained challenging due to limited theoretical understanding. This work devised an atomistic methodology based on density functional theory calculations to predict the phase fractions in HZO. The detailed phase evolution and phase fractions during the sequential processes of crystallization, annealing, and cooling were predicted by calculating the nucleation barrier from amorphous, the transition barrier between polymorphs, and Boltzmann fractions, considering the combined effects of composition (x), grain size (dT), and annealing temperature (Tannealing). The findings revealed that the polar orthorhombic (PO) phase exhibited the highest fraction at Tannealing = 770 K in Hf0.5Zr0.5O2, resulting in maximum ferroelectricity. Meanwhile, the fractions of PO and tetragonal phases are similar at dT = 7 nm in Hf0.4Zr0.6O2 and dT = 11 nm in Hf0.3Zr0.7O2, both at Tannealing = 770 K, leading to the highest dielectricity. These results are highly consistent with the experimental results. This work demonstrates that the comprehensive interpretations of both thermodynamic and kinetic effects are essential for quantitatively predicting the phase fraction and their corresponding electrical functionality.