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We describe the measurement and modeling of amplitude noise and phase noisein ultra-high Q nanomechanical resonators made from stoichiometric siliconnitride. With quality factors exceeding 2 million, the resonators' noiseperformance is studied with high precision. We find that the amplitude noisecan be well described by the thermomechanical model, however, the resonatorsexhibit sizable extra phase noise due to their intrinsic frequencyfluctuations. We develop a method to extract the resonator frequencyfluctuation of a driven resonator and obtain a noise spectrum with dependence,which could be attributed to defect motion with broadly distributed relaxationtimes.

Frequency and phase noise of ultra-high Q silicon nitride nanomechanical resonators