Design rules for improving dielectric constants of hafnium-based oxides

As promising dielectric alternatives to SiO₂, hafnium-based oxides show broad application prospects in integrated circuits, dielectric sensors, and optoelectronics. Nevertheless, stabilizing the T-phase with a high dielectric constant (high-κ) and further improving its κ value remain key challenges for practical applications. Using first-principles calculations, we reveal the dielectric enhancement mechanism in the T-phase HfO₂ by demonstrating that the high-κ primarily originates from the softening of phonon vibration frequencies, which can be effectively tuned by bond length and atomic mass. Furthermore, we find that doping atoms with lower electronegativity form stronger ionic interactions with O atoms, favoring the stabilization of the high-coordination T-phase. Based on these analyses, we propose a general design rule: doping atoms with remarkable size, heavy mass, and small electronegativity could effectively improve high-κ and stabilize the T-phase simultaneously. Guided by this rule, a more promising Ce-doping strategy in HfO₂ than Zr-doping is proposed, which is also supported by some experimental results. This work not only delves into the physical mechanism of the high-κ in hafnium-based oxides, but also provides practical methods to enhance their dielectric constants.