Evidence for anisotropic dielectric properties of monoclinic hafnia using high-resolution TEM valence electron energy-loss spectroscopy and ab initio time-dependent density-functional theory

The effect of nanocrystal orientation on the energy loss spectra of monoclinic hafnia (m-HfO$_2$) is measured by high resolution transmission electron microscopy (HRTEM) and valence energy loss spectroscopy (VEELS) on high quality samples. For the same momentum-transfer directions, the dielectric properties are also calculated ab initio by time-dependent density-functional theory (TDDFT). Experiments and simulations evidence anisotropy in the dielectric properties of m-HfO$_2$, most notably with the direction-dependent oscillator strength of the main bulk plasmon. The anisotropic nature of m-HfO$_2$ may contribute to the differences among VEELS spectra reported in literature. The good agreement between the complex dielectric permittivity extracted from VEELS with nanometer spatial resolution, TDDFT modeling, and past literature demonstrates that the present HRTEM-VEELS device-oriented methodology is a possible solution to the difficult nanocharacterization challenges given in the International Technology Roadmap for Semiconductors.