LAUSR

The discovery of ferroelectricity in both pure and doped HfO$_2$-based thin films have revitalized the interest in using ferroelectrics for nanoscale device applications. To take advantage of this silicon-compatible ferroelectric, fundamental questions such as the origin of ferroelectricity and better approach to controlled realization of ferroelectricity at the nanoscale need to be addressed. The emergence of robust polarization in HfO$_2$-based thin films is considered as the cumulative effect of various extrinsic factors such as finite-size effects and surface/interface effects of small grains, compressive stress, dopants, oxygen vacancies, and electric fields. The kinetic effects of phase transitions and their potential impacts on the emergence of ferroelectricity in HfO$_2$ at the nanoscale are not well understood. In this work, we construct the transition paths between different polymorphs of hafnia with density functional theory calculations and variable-cell nudged elastic band technique. We find that the transition barriers depend strongly on the mechanical boundary conditions and the transition from the tetragonal phase to the polar orthorhombic phase is a fast process kinetically under clamping. The effects of growth orientations and epitaxial strains on the relative stability of different phases of HfO$_2$ are investigated. The two orthorhombic phases, polar $Pca2_1$ and non-polar $Pbca$, become thermodynamically stable in (111)-oriented thin films over a wide range of epitaxial strain conditions. This work suggests a potential avenue to better stabilize the ferroelectric phase in HfO$_2$ thin films through substrate orientation engineering.