D. R. Southworth

Stress-based vapor sensing using resonant microbridges

We demonstrate that silicon-polymer composite microbridges provide a robust means of water vapor detection at ambient pressure. Volumetric changes in the reactive polymer alter the tension in a doubly clamped structure leading to large and rapid changes in the resonance frequency. We demonstrate stress-based sensing of water vapor in ambient pressure nitrogen using doubly clamped buckled beams coated with a hygroscopic polymer. We show stress sensitivity of around 20 kPa (∼170 ppb of water vapor) and subsecond response time for coated microbridges.

High-Q nanomechanics via destructive interference of elastic waves.

Mechanical dissipation poses a ubiquitous challenge to the performance of nanomechanical devices. Here we analyze the support-induced dissipation of high-stress nanomechanical resonators. We develop a model for this loss mechanism and test it on Si(3)N(4) membranes with circular and square geometries. The measured Q values of different harmonics present a nonmonotonic behavior which is successfully explained. For azimuthal harmonics of the circular geometry we predict that destructive interference of the radiated waves leads to an exponential suppression of the clamping loss in the harmonic index. Our model can also be applied to graphene drums under high tension.

Pressure dependent resonant frequency of micromechanical drumhead resonators

We examine the relationship between squeeze film effects and resonance frequency in drum-type resonators. We find that the resonance frequency increases linearly with pressure as a result of the additional restoring force contribution from compression of gas within the drum cavity. We demonstrate trapping of the gas by squeeze film effects and geometry. The pressure sensitivity is shown to scale inversely with cavity height and sound radiation is found to be the predominant loss mechanism near and above atmospheric pressure. Drum resonators exhibit linearity and sensitivity suitable to barometry from below 10 Torr up to several atmospheres.

Evaluation of Mode Dependent Fluid Damping in a High Frequency Drumhead Microresonator

Design of high quality factor (Q) micromechanical resonators depends critically on our understanding of energy losses in their oscillations. The Q of such structures depends on process induced prestress in the structural geometry, interaction with the external environment, and the encapsulation method. We study the dominant fluid interaction related losses, namely, the squeeze film damping and acoustic radiation losses in a drumhead microresonator subjected to different prestress levels, operated in air, to predict its Q in various modes of oscillation. We present a detailed research of the acoustic radiation losses, associated with the 15 transverse vibration modes of the resonator using a hybrid analytical-computational approach. The prestressed squeeze film computation is based on the standard established numerical procedure. Our technique of computing acoustic damping based quality factor Qac includes calculation of the exact prestressed modes. We find that acoustic losses result in a non-monotonic variation of Qac in lower unstressed modes. Such non-monotonic variation disappears with the increase in the prestress levels. Although squeeze film damping dominates the net Q at lower frequencies, acoustic radiation losses dominate at higher frequencies. The combined computed losses correctly predict the experimentally measured Q of the resonator over a large range of resonant frequencies.

Real-time synchronous imaging of electromechanical resonator mode and equilibrium profiles.

The single-shot interferometric imaging of normal mode dynamics in MEMS resonators, oscillating in the radio frequency (rf) regime, is demonstrated by synchronous imaging with a pulsed nanosecond laser. Profiles of mechanical modes in suspended silicon and graphene thin-film structures, and their extracted equilibrium profiles, are measured through nondestructive all-optical Fabry-Perot reflectance fits to the temporal traces. As a proof of principle, the modal patterns of a microdrum silicon resonator is analyzed, and its extracted vibration modes and equilibrium profile show good agreement with other characterization and numerical estimations.

Synchronizing a single-electron shuttle to an external drive

The nanomechanical single-electron shuttle is a resonant system in which a suspended metallic island oscillates between and impacts at two electrodes. This setup holds promise for one-by-one electron transport and the establishment of an absolute current standard. While the charge transported per oscillation by the nanoscale island will be quantized in the Coulomb blockade regime, the frequency of such a shuttle depends sensitively on many parameters, leading to drift and noise. Instead of considering the nonlinearities introduced by the impact events as a nuisance, here we propose to exploit the resulting nonlinear dynamics to realize a highly precise oscillation frequency via synchronization of the shuttle self-oscillations to an external signal. We link the established phenomenological description of synchronization based on the ADLER equation to the microscopic nonlinear dynamics of the electron shuttle by calculating the effective ADLER constant analytically in terms of the microscopic parameters.