Silicon nitride and silica quarter-wave stacks for low-thermal-noise mirror coatings

This study investigates a multilayer high reflector with new coating materials for next-generation laser interferometer gravitational wave detectors operated at cryogenic temperatures. We use the plasma-enhanced chemical vapor deposition method to deposit amorphous silicon nitride and silica quarter-wave high-reflector stacks and studied the properties pertinent to the coating thermal noise. Room- and cryogenic-temperature mechanical loss angles of the silicon nitride and silica quarter-wave bilayers are measured using the cantilever ring-down method. We show, for the first time, that the bulk and shear loss angles of the coatings can be obtained from the cantilever ring-down measurement, and we use the bulk and shear losses to calculate the coating thermal noise of silicon nitride and silica high-reflector coatings. The mechanical loss angle of the silicon nitride and silica bilayer is dispersive with a linear weakly positive frequency dependence, and, hence, the coating thermal noise of the high reflectors show a weakly positive frequency dependence in addition to the normal $1/\sqrt{f}$ dependence. The coating thermal noise of the silicon nitride and silica high-reflector stack is compared to the lower limit of the coating thermal noise of the end test mirrors of ET-LF, KAGRA, LIGO Voyager, and the directly measured coating thermal noise of the current coatings of Advanced LIGO. The optical absorption of the silicon nitride and silica high reflector at 1550 nm is 45.9 ppm. Using a multimaterial system composed of seven pairs of ion-beam-sputter deposited $\mathrm{Ti}:{\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$ and silica and nine pairs of silicon nitride and silica on a silicon substrate, the optical absorption can be reduced to 2 ppm, which meets the specification of LIGO Voyager.