Modeling ferroelectric film properties and size effects from tetragonal interlayer in Hf1–xZrxO2 grains

Abstract

Size effects from surface or interface energy play a pivotal role in stabilizing the ferroelectric phase in recently discovered thin film Zirconia-Hafnia. However, sufficient quantitative understanding has been lacking due to the interference with the stabilizing effect from dopants. For the important class of undoped Hf_1–xZr_xO₂, a phase stability model based on free energy from Density functional theory (DFT) and surface energy values adapted to the sparse experimental and theoretical data has been successful to describe key properties of the available thin film data. Since surfaces and interfaces are prone to interference, the predictive capability of the model is surprising and directs to a hitherto undetected, underlying reason. New experimental data hint on the existence of an interlayer on the grain surface fixed in the tetragonal phase possibly shielding from external influence. To explore the consequences of such a mechanism, we develop an interface free energy model to include the fixed interlayer, generalize the grain model to include a grain radius distribution, calculate average polarization and permittivity, and compare the model with available experimental data. Since values for interface energies are sparse or uncertain, we obtain its values from minimizing the least square difference between predicted key parameters to experimental data in a global optimization. Since the detailed values for DFT energies depend on the chosen method, we repeat the search for different computed data sets and come out with quantitatively different but qualitatively consistent values for interface energies. The resulting values are physically very reasonable and the model is able to give qualitative prediction. On the other hand, the optimization reveals that the model is not able to fully capture the experimental data. We discuss possible physical effects and directions of research to possibly close this gap.