Understanding Ferroelectricity in Hafnia Through Modeling and Simulations*

Ferroelectric hafnium and zirconium oxides have undergone rapid scientific development over the past decade, bringing them to the forefront of very low-power electronic systems. Simulations are playing an increasingly important role in understanding and guiding experimental work to maximize the potential application of these materials in low-power devices and sensors, and to address technical limitations that still hinder their use.

Numerous first-principles simulation studies have investigated the structural properties and free energy of the polar orthorhombic Pca21 phase (standard ferroelectric phase) and the possible appearance of competing polar phases, which are reviewed here. However, the functional properties need to be simulated in larger and transient systems than the unit cells, but at the same high accuracy level. This is possible through the development of machine-learned potentials, in which considerable progress has been made, and the results of which are presented here. Simulations at the grain size scale allow the study of size effects in polycrystalline hafnium and zirconium oxide materials and of real piezoelectric and pyroelectric effects. Furthermore, they allow the exploration of the energy landscape as a function of temperature, size effect, and electric field. The simulated results compare well with the experiment. Other simulations describing larger spatial and temporal scales are kinetic Monte Carlo simulations of correlated electron and charged defect motions in the ferroelectric capacitor, based on calculated diffusion coefficients and defect levels. This approach allows us to address the existing reliability problems in the devices.

R. Ganser, S. Bongarz, A. von Mach, L. Azevedo Antunes, A. Kersch, Phys. Rev. Applied 18, 054066 (2022) https://doi.org/10.1103/PhysRevApplied.18.054066

P. D. Lomenzo, L. Collins, R. Ganser, B. Xu, R. Guido, A. Gruverman, A. Kersch, T. Mikolajick, U. Schroeder, Advanced Functional Materials, 2303636 (2023), https://doi.org/10.1002/adfm.202303636