Observation of kBT/f frequency noise in ultrahigh Q silicon nitride nanomechanical resonators

In this report, we study the noise characteristics of the high quality factor nanomechanical resonators made of tensile-stressed stoichiometric silicon nitride. Quality factors (Q) of more than 2 million are measured at liquid helium temperature. With such high Q, the resonator noise performance is studied with high precision. We observe that while the amplitude noise agrees well with the thermomechanical noise, the phase noise is significantly higher than that. Such discrepancy is found to be due to the intrinsic resonance frequency fluctuation. We develop a mathematical model to describe the observed phenomenon and derive an expression relating the phase noise and the resonance frequency noise power spectral densities. From the phase noise measurement, we calculate the resonance frequency noise spectrum of the resonators and conclude that it has a k_BT/f dependence.