Effect of Stress and Temperature on the Optical Properties of Silicon Nitride Membranes at 1,550 nm

Future gravitational-wave detectors operated at cryogenic temperatures are expected to be limited by thermal noise of the highly reflective mirror coatings. Silicon nitride is an interesting material for such coatings as it shows very low mechanical loss, a property related to low thermal noise, which is known to further decrease under stress. Low optical absorption is also required to maintain the low mirror temperature. Here, we investigate the effect of stress on the optical properties at 1,550 nm of silicon nitride membranes attached to a silicon frame. Our approach includes the measurement of the thermal expansion coefficient and the thermal conductivity of the membranes. The membrane and frame temperatures are varied, and translated into a change in stress using finite element modeling. The resulting product of the optical absorption and thermo-optic coefficient (dn/dT) is measured using photothermal common-path interferometry.