Abstract
This paper presents an energy trapped resonator with degenerate modal properties for application in mass sensing. Actuation and detection of the resonant modes of circular fused quartz disc is performed electromagnetically. The highly localised displacement field of the energy trapped modes makes them attractive due to their low support loss. In addition, the displacement of some of the energy trapped modes is shown to be dominated by in-plane motion at the surface of the plate and therefore radiative energy loss into any surrounding fluid will be considerably reduced. This feature, when used in conjunction with the differential sensing made possible with a degenerate mode pair, is highly attractive for biosensing applications. A thorough theoretical and experimental characterisation of the modal properties of the fused quartz plate is presented. Fused quartz is elastically isotropic and as a result the natural frequencies and normal modeshape are determined by the device geometry and material properties. For crystalline materials the elastic anisotropy can disrupt the modal properties. A numerical analysis of the modal properties of the device fabricated in single crystalline material is presented. It is shown that specific degenerate modeshapes in a silicon (111) orientated plate remain unperturbed due to its anisotropy.
Highlights
Mass sensing in a liquid environment presents a significant challenge to many conventional mechanical resonators since outof-plane displacement causes severe damping in liquid, rendering resonant based mass detection impossible [1]
The resonator geometry is configured to support vibrations which are highly dominated by shear horizontal (SH) modes and in this regard the concept is similar to the conventional Quartz Crystal Microbalance (QCM) which has been widely used in gas sensing [2]
The resonator geometry is configured such that the degenerate vibrations used for mass sensing are energy trapped, thereby increasing the resonant Q-factor and isolating the device from support loss mechanisms prevalent in conventional MEMS designs [14]
Summary
Mass sensing in a liquid environment presents a significant challenge to many conventional mechanical resonators since outof-plane displacement causes severe damping in liquid, rendering resonant based mass detection impossible [1]. Measuring the frequency split between the otherwise degenerate mode pair, [15], due to added mass provides a sensing strategy which removes common mode effects [16,17,18] This means that the sensor will be robust against temperature changes which severely compromises the QCM. Fused quartz is electrically insulating, electromagnetic actuation can be efficiently performed through Lorentz interaction of deposited metal tracking alongside a permanent magnetic field acting normal to the plane of the substrate [23,24] This excitation approach permits the tracking to be placed at a location where the forcing of the desired mode pair is maximised and, improve the signal to noise performance of the device. To perform the excitation via an eddy current approach, as described in previous work [22,25], results in a force that is distributed both radially and circumferentially, which is less effective at putting energy into the mode of interest
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