Study of the noise of micromechanical oscillators under quality factor

Abstract

The performance of devices based on micro- and nanomechanical oscillators depends critically on the quality factor (Q). The quality factor can be externally increased about two orders of magnitude by coherent amplification of the oscillation at resonance with a fast feedback amplifier. Here, theory and experiments performed with microcantilevers are presented to study the oscillation noise under external Q enhancement and how it differs from the noise when the Q is naturally enhanced by decreasing the mechanical energy loss. The application of the feedback amplifier produces a significant increase of the thermal noise and the noise that arises from the cantilever-displacement sensor. The main consequence is that the signal-to-noise ratio (S/N) remains constant and independent of the Q enhancement when measuring the amplitude and phase of the oscillation in the slope detection technique. This behavior is opposite to the enhancement of the S/N when the Q naturally increases, which is proportional to Q1/2, ignoring instrumental sources of noise. More important, by taking into account the maximum driving force provided by the actuator, it is concluded that external Q enhancement does not enhance the sensitivity of devices based on micro- and nanomechanical oscillators, using the slope detection technique. The lack of sensitivity enhancement is attributed to the fact that thermal forces are not altered by the increase of the quality factor via the fast feedback amplifier. Finally, it is proposed to use the fast feedback amplifier in a different measurement mode to obtain high sensitivity. This consists in the self-excitation of the cantilever without application of a reference driving force, and the measurement of the frequency of the oscillation. Self-excitation of the cantilever produces amplification of the noise and its squeezing around the resonant frequency, hence the oscillation resembles Brownian motion of the cantilever with a superior quality factor.