Role of Local Cation Environment on the Formation Energy of Oxygen Vacancies in Ferroelectric Hf1−xZrxO2

Abstract

Oxygen vacancies play a critical role in stabilising the ferroelectric phase of hafnia–zirconia thin films, yet their interplay with zirconium doping is less well understood. In this work, we employ Den- sity Functional Theory to uncover how local cation environments caused by zirconium doping, and charge states (q = −2 to +2), shape the oxygen vacancy landscape in ferroelectric hafnia-zirconia (Hf1−xZrxO2; x = 0.25, 0.50, 0.75). We reveal the crucial role of the local cation environment in facilitating the formation of oxygen vacancies in ferroelectric hafnia-zirconia compared to hafnia, extending the analysis to nine unique environments. The environment comprised of four zirconium cations was found to have the lowest formation energy out of the set of local cation environments for neutral oxygen vacancy formation. The charge transition to positively charged vacancies (q = +2) dramatically increases the number of available sites, suggesting that electric-field-induced charge transitions can facilitate vacancy diffusion. We find that the concentration of zirconium doping surprisingly did not impact the formation energies of oxygen vacancies, instead acting as a lever controlling the population of available sites for oxygen vacancy formation. Bonding analysis re- veals that zirconium content weakens the cation–oxygen bond by introducing occupied anti-bonding states, further stabilising defect formation. These findings reveal how doping and charge state modulate the defect landscape, offering a blueprint for tuning oxygen vacancy behaviour and, by extension, the performance of next-generation ferroelectric devices.