Intrinsic Defect Limit to the Growth of Orthorhombic HfO₂ and (Hf,Zr)O₂ with Strong Ferroelectricity: First-Principles Insights

It is believed that promoting the fraction of ferroelectric orthorhombic phase (o-phase) through O-poor growth conditions can increase the spontaneous polarization of HfO₂ and (Hf,Zr)O₂ thin films. However, the first-principles calculations show that the growth may be limited by the easy formation of point defects in the orthorhombic and tetragonal phases of HfO₂, ZrO₂, and (Hf,Zr)O₂. Their dominant defects, O interstitial (O_i) under O-rich conditions and O vacancy (V_O) under O-poor condition, have low formation energies and quite high density (10¹⁶–10¹⁹ cm⁻³ for 800–1400 K growth temperature). Especially, O_i has negative formation energy in tetragonal HfO₂ under O-rich condition, causing non-stoichiometry and limiting the crystalline-seed formation during o-phase growth. High-density defects can cause disordering of dipole moments and increase leakage current, both diminishing the polarization. These results explain the experimental puzzle that the measured polarization is much lower than the ideal value even in O-poor thin films and highlight that controlling defects is as important as promoting the o-phase fraction for enhancing ferroelectricity. The O-intermediate condition (average of O-rich and O-poor conditions) and low growth temperature are proposed for fabricating HfO₂ and (Hf,Zr)O₂ with fewer defects, lower leakage current, and stronger ferroelectricity, which challenges the belief that O-poor condition is optimal.