Direct observation of the thermal noise spectrum of a silicon flexure membrane

We present a direct measurement of the displacement noise spectrum of a macroscopic silicon flexure at room temperature. A cantilever attached to the 100 μm thick flexure holds a mirror which forms part of an optical cavity to enhance the displacement sensitivity to thermal noise. We predict the displacement noise spectrum using a simple model that assumes the dominant source of frequency-dependent loss is thermo-elastic damping and find good agreement with the experimental data. The measurement is consistent with a frequency-independent loss of ϕ0,fi=1.6×10−5 combined with frequency-dependent thermo-elastic damping as the dominant losses. A crossover between the two that occurs well above the flexure resonant frequency allows a broadband measurement of the thermal noise of the silicon flexure. The flexure material, geometry, and measurement band are similar to those of planned future gravitational wave detectors.