Piezo- and Pyroelectricity in Zirconia: A Study with Machine-Learned Force Fields

Abstract

The discovery of very large piezo- and pyroelectric effects in ${\mathrm{Zr}\mathrm{O}}_{2}$ and ${\mathrm{Hf}\mathrm{O}}_{2}$-based thin films opens up opportunities to develop silicon-compatible sensor and actor devices. The effects are amplified close to the polar-orthorhombic to tetragonal phase-transition temperature. Molecular dynamics is the preferred technique to simulate such effects, though its application has to solve the dilemma between sufficient accuracy and sufficient efficiency of the interatomic force field. Here we present a deep neural-network-based interatomic force field of ${\mathrm{Zr}\mathrm{O}}_{2}$ learned from ab initio data using a systematic learning procedure in the deep potential framework. The model potential is verified to predict a variety of structural and dynamic properties with an accuracy comparable to density-functional-theory calculations. Then the deep potential model is used to reproduce the different thermal expansion and piezo- and pyroelectric phenomena in ${\mathrm{Zr}\mathrm{O}}_{2}$ with molecular dynamics calculations. At low temperature simulating the direct effect we find negative values for the piezo- and pyroelectric coefficients matching the ab initio calculations. Approaching the phase-transition temperature these values remain negative and become large. Simulating the field-induced effect above the phase-transition temperature we find positive, giant piezoelectric coefficients matching the observations. The model is able to explain the large values and the sign of the experimental observations in relation to the polar-orthorhombic to tetragonal phase transition. The model furthermore explains the recently observed giant dielectric constant in a similar system.