Frequency fluctuations in silicon nanoresonators

Abstract

Frequency stability is key to performance of nanoresonators. This stability is thought to reach a limit with the resonator’s ability to resolve thermally-induced vibrations. Although measurements and predictions of resonator stability usually disregard fluctuations in the mechanical frequency response, these fluctuations have recently attracted considerable theoretical interest. However, their existence is very difficult to demonstrate experimentally. Here, through a literature review, we show that all studies of frequency stability report values several orders of magnitude larger than the limit imposed by thermomechanical noise. We studied a monocrystalline silicon nanoresonator at room temperature, and found a similar discrepancy. We propose a new method to show this was due to the presence of frequency fluctuations, of unexpected level. The fluctuations were not due to the instrumentation system, or to any other of the known sources investigated. These results challenge our current understanding of frequency fluctuations and call for a change in practices.

Spectral effects of dispersive mode coupling in driven mesoscopic systems

“…Equations (14) and (21) reduce this averaging to solving an ordinary differential equation (20) with the coefficient that varies with time stepwise. The solution can be simplified by taking advantage of this specific time dependence.…”

“…21 for a recent review of the broadening mechanisms. The most familiar broadening mechanism is vibration decay due to energy dissipation.…”

Nonlinear frequency transduction of nanomechanical Brownian motion

“…As such, the understanding of the sources of frequency fluctuations in nano-mechanical devices becomes an essential technical topic [1,[19][20][21][22][23]. But in the first place, it is also a fundamental research goal: the measured frequency noise in actual devices is much larger than all expectations [22,[24][25][26], demonstrating even non-linear features for carbon-based systems [27,28]. Thus, attempts have been made to model noise sources [29,30], or to create model experiments experimentally demonstrating the underlying mechanisms [19,31,33,34].…”

Measurement and Noise

“…The data is taken from [34] that the application requires faster response time (smaller integration time ) and thus resolution is compromised in favor of a faster measurement. It has been shown recently that the theoretical calculation of the frequency noise is resulting in values that are roughly two order of magnitude lower than experimentally observed values [34]. However, the Allan deviation was found to correlate with the resonator's mass (see Fig.…”