Internal friction measurements of ion beam sputtered amorphous silica

The ability to minimize low-temperature acoustic loss in amorphous materials would have implications in fields as wide-ranging as gravitational wave detection and quantum computing. In this paper, we measure the internal friction between $300\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$ and room temperature of several thin silica films deposited by ion beam sputtering onto ultra-high-$Q$ silicon resonators. The measurements reveal internal configurations of as-deposited films that are markedly different from that of bulk silica. Over a broad temperature range, the films' internal frictions differ from one another by a factor of two; by contrast, a review shows that sub-MHz internal friction measurements of bulk silica fall within a 35% band with a pronounced main absorption peak between $20\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and $40\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. This peak is absent in the films presented here, except for one film that had been annealed at $900\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\circ}}\mathrm{C}$. Annealing at $500\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\circ}}\mathrm{C}$ erased the thermal histories of the other thin films to create internal friction values that are consistent from film-to-film but yet still markedly different from those of the bulk below $100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, while creating the steep bulk-like drop-off above $100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ that the as-deposited films lacked. In the context of theoretical structural modeling, our results suggest that exposure to temperatures of at least $900\phantom{\rule{0.16em}{0ex}}{}^{\ensuremath{\circ}}\mathrm{C}$ is needed to form the network of tetrahedra considered characteristic of amorphous silica. The present measurements, especially when compared alongside previous work, appear to show that these structures are suppressed in many thin film preparations. These measurements also show, for as-deposited films, an excess of excitations in the 0.15--$0.3\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ range which can be annealed away to bring about the ${Q}^{\ensuremath{-}1}$ drop-off above the main absorption peak. The shear moduli of all the films are qualitatively similar to bulk silica, with a positive temperature coefficient above a minimum near $60\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and a negative temperature coefficient below.