Estimating Damping in Microresonators by Measuring Thermomechanical Noise Using Laser Doppler Vibrometry

The fluctuation-dissipation theorem establishes the fundamental links between thermomechanical noise and damping. In this paper, we bridge the gap between theory and practice by developing protocols for estimating dissipation in low-loss microresonators by measuring thermomechanical noise using laser Doppler vibrometry. The measurement does not require external actuation of the device and damping can be estimated without relying upon knowledge of material properties, device dimensions, or structural stiffness. The power spectral density of velocity and displacement noise is computed using a direct method that avoids segmenting the measurements in the time domain, thereby avoiding any bias in the estimation of the quality factor. We demonstrate the implementation of the protocol by measuring damping at room temperature and low pressure in four silicon-based microcantilever resonators with natural frequencies ranging from 17.6 to 26.7 kHz and quality factors ranging from 2×10
⁴
to 2×10
⁵
. The accuracy of noise-based estimates is evaluated by comparison with values of the log decrement measured under free decay.