Building A Better Resonator

The resonant frequency of a beam depends on the mass and stiffness of the beam.

Resonance has always been important in the design of musical instruments and amplification systems, as well as the design of bridges and buildings. With the advent of MEMS fabrication techniques, though, came the ability to create very small beams, in the micron or nanometer size range, with resonant frequencies sensitive to very small changes in mass or stiffness. Changes of the same order of magnitude as a toxic gas molecule, a red blood cell, or a DNA molecule, for instance. Suddenly, nanoresonators are being considered for a wide range of potential applications in molecular-scale detection, filtering, and transport.

There is a caveat, though. If the resonant frequency is the ultimate source of a detection signal, it needs to be extremely stable. Nanoresonators that have been tested to date mostly are not that stable.

As Marc Sansa and colleagues at CEA-LETI explained in a recent issue of Nature Nanotechnology, theoretical analyses of nanoresonators have held that frequency stability is maximized when random noise-driven motion — such as thermal vibrations can be resolved. However, this is only true if fluctuations in the resonant frequency itself are small enough to ignore.

Unfortunately for theory, the CEA-LETI group reviewed 25 different studies, covering many different resonator designs and 15 orders of magnitude of mass. Across the board, the experimentally measured frequency stability was typically 2.1 orders of magnitude worse than the thermomechanical noise limit.

To investigate potential noise sources further, the group used SOI wafers used to make silicon nanoresonators, with gauges typically 1 micron long by 100nm wide. The exceptional quality and purity of electronics-grade silicon minimized such potential sources of frequency fluctuations as composition variations and lattice defects. The experimental setup was straightforward.

Nonetheless, theory failed to describe the stability of these resonators. While performance was as predicted by the Allan Deviation for short integration times and low amplitudes, substantial deviation from the expected behavior occurred at higher amplitudes and longer times. The ultimate detection limit for these devices was two orders of magnitude worse than expected.

So where is the noise coming from?

It isn’t white noise, the researchers concluded, because white noise is uncorrelated across frequencies. Rather, the results indicate a shift in the whole frequency response of the resonator. The group also considered and rejected several other plausible noise sources. For example, measurements on out-of-resonance control devices exonerated the measurement system. Temperature shifts, molecular absorption/desorption, and other causes were likewise insufficient to explain such a large discrepancy.

Instead, the CEA-LETI group was forced to conclude that frequency fluctuations of unknown origin are a substantial performance limiter for nanoresonators. Having eliminated the impossible, what remains must be the answer, but just what that might be isn’t clear.