Stabilizing metastable tetragonal HfO(2) using a non-hydrolytic solution-phase route: ligand exchange as a means of controlling particle size

There has been intense interest in stabilizing the tetragonal phase of HfO(2) since it is predicted to outperform the thermodynamically stable lower-symmetry monoclinic phase for almost every application where HfO(2) has found use by dint of its higher dielectric constant, bandgap, and hardness. However, the monoclinic phase is much more thermodynamically stable and the tetragonal phase of HfO(2) is generally accessible only at temperatures above 1720 °C. Classical models comparing the competing influences of bulk free energy and specific surface energy predict that the tetragonal phase of HfO(2) ought to be stable at ultra-small dimensions below 4 nm; however, these size regimes have been difficult to access in the absence of synthetic methods that yield well-defined and monodisperse nanocrystals with precise control over size. In this work, we have developed a modified non-hydrolytic condensation method to precisely control the size of HfO(2) nanocrystals with low concentrations of dopants by suppressing the kinetics of particle growth by cross-condensation with less-reactive precursors. This synthetic method enables us to stabilize tetragonal HfO(2) while evaluating ideas for critical size at which surface energy considerations surpass the bulk free energy stabilization. The phase assignment has been verified by atomic resolution high angle annular dark field images acquired for individual nanocrystals.