Development of ion-beam sputtered silicon nitride thin films for low-noise mirror coatings of gravitational-wave detectors

Brownian thermal noise of thin-film coatings is a fundamental limit for high-precision experiments based on optical resonators such as gravitational-wave interferometers. Here we present the results of a research activity aiming to develop lower-noise ion-beam sputtered silicon nitride thin films compliant with the very stringent requirements on optical loss of gravitational-wave interferometers. In order to test the hypothesis of a correlation between the synthesis conditions of the films and their elemental composition and optical and mechanical properties, we varied the voltage, current intensity and composition of the sputtering ion beam, and we performed a broad campaign of characterizations. While the refractive index was found to monotonically depend on the beam voltage and linearly vary with the N/Si ratio, the optical absorption appeared to be strongly sensitive to other factors, as yet unidentified. However, by systematically varying the deposition parameters, an optimal working point was found. Thus we show that the loss angle and extinction coefficient of our thin films can be as low as $(1.0 \pm 0.1) \times 10^{-4}$ rad at $\sim$2.8 kHz and $(6.4 \pm 0.2) \times 10^{-6}$ at 1064 nm, respectively, after thermal treatment at 900 $^{\circ}$C. To the best of our knowledge, such loss angle value is the lowest ever measured on this class of thin films. We then used our silicon nitride thin films to design and produce a multi-material mirror coating showing a thermal noise amplitude of $(10.3 \pm 0.2) \times 10^{-18}$ m Hz$^{-1/2}$ at 100 Hz, which is 25\% lower than in current mirror coatings of the Advanced LIGO and Advanced Virgo interferometers, and an optical absorption as low as $(1.6 \pm 0.5)$ parts per million at 1064 nm.