Abstract
Clamping loss in micromechanical resonators can strongly depend on the boundary conditions far away from the actual vibrating structure because the acoustic wavelength greatly exceeds the device dimensions. We demonstrate a scheme for post-fabrication tuning of the clamping loss in flexural-mode and bulk-mode resonators by modifying the boundary conditions of the chip with the frame. The measured quality factor increases by more than an order-of-magnitude for the microcantilevers and more than a factor of three for the bulk-mode resonators when frame contact is minimized via suspension of the chip by wirebonds. We propose a two-degree-of-freedom fluctuation-dissipation model to describe the thermomechanical noise and forced response in the presence of this tunable anchor damping. By studying the thermomechanical displacement spectrum with tunable clamping loss, we show that variable clamping loss tunes the mechanical quality factor, modifying both the resonator transfer function and thermomechanical noise force. We delineate the dependence of the tunable clamping loss mechanism on microcantilever beam length and ambient temperature from 300 K down to 40 K, and observe potential temperature dependence to clamping loss with reducing temperature. [2021-0141]
Highlights
M ICRO- and nanoelectromechanical (MEM/NEM) resonators are widely used in sensors [1] and oscillators [2]
These mechanisms are linked to the mechanical quality factor of the resonator, and their tuning modifies both the transfer function and thermomechanical noise force acting on the resonator
In this Article, we demonstrate tunable clamping loss in encapsulated micromechanical resonators, by adjusting the boundary conditions of the chip with the frame
Summary
M ICRO- and nanoelectromechanical (MEM/NEM) resonators are widely used in sensors [1] and oscillators [2]. A variety of dissipation mechanisms contribute to determining the Q in MEM/NEM resonators, such as clamping loss (Qclamp), thermoelastic dissipation (QT E D), surface loss (Qsur f ), gas damping (Qgas), and phonon loss (Q phon) These mechanisms are linked to the mechanical quality factor of the resonator, and their tuning modifies both the transfer function and thermomechanical noise force acting on the resonator. The advantage of modifying the chip mounting conditions over the phononic crystal or engineered tether methods is that it enables post-fabrication tuning of clamping loss [58] This is useful for increasing the post-fabrication mechanical quality factor of doubly-clamped beams [20], thermal-piezoresistive oscillators [6], [59]–[63], and other resonator geometries that require multiple attachment points via rigid anchor tethers.
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