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Role of local cation environment on the formation energy of oxygen vacancies in ferroelectric Hf1−xZrxO2

Sunil Taper1, Bo Cai1,2, Nives Strkalj3, Bartomeu Monserrat1,*, and Giuliana Di Martino1,4,†

  • *Contact author: bm418@cam.ac.uk
  • †Contact author: giuliana.dimartino@materials.ox.ac.uk
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Phys. Rev. B 113, 134114 – Published 22 April, 2026

DOI: https://doi.org/10.1103/vz64-n5xh

Abstract

Oxygen vacancies play a critical role in stabilizing the ferroelectric phase of hafnia-zirconia thin films, yet their interplay with zirconium doping is less well understood. In this work, we employ Density 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 reveals that zirconium content weakens the cation-oxygen bond by introducing occupied antibonding states, further stabilizing defect formation. These findings reveal how doping and charge state modulate the defect landscape, offering a blueprint for tuning oxygen vacancy behavior and, by extension, the performance of next-generation ferroelectric devices.

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Phys. Rev. B 113, 134114– Published 22 April, 2026
  • Received 17 September 2025
  • Revised 12 February 2026
  • Accepted 17 March 2026
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