Effects of growth orientations and epitaxial strains on phase stability of HfO2 thin films

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