Network Topology of Hafnia-Based Amorphous Optical Coatings by Grazing-Incidence X-ray Total Scattering and Atomic Modeling

Abstract

Amorphous hafnia-based films are promising optical-coating materials for cryogenic GW detectors, but their performance depends on how doping and annealing modify the atomic network. We combine grazing-incidence X-ray total scattering measurements with experimentally constrained atomic modeling to study the as-deposited HfO$_2$ and 27% SiO$_2$-doped HfO$_2$ films annealed at 150$^\circ$C and 400$^\circ$C. Pure amorphous HfO$_2$ is a dense, high-coordination network of Hf-centered polyhedra with substantial edge- and face-sharing connectivity. Incorporating SiO$_2$ introduces stable SiO$_4$ tetrahedra, lowers the Hf and O coordination, and replaces highly connected Hf-rich oxygen environments with mixed Si--O--Hf bridges. This produces a chemically mixed network rather than isolated SiO$_2$-rich regions, and shifts the cation topology toward corner-sharing connectivity. Annealing to 400$^\circ$C produces only modest additional structural relaxation. These results provide an atomic-scale description of how SiO$_2$ modifies the topology of amorphous HfO$_2$-based coatings and suggest structural descriptors relevant to understanding their mechanical-loss behavior.