Essay On Micromechanical Resonators

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8 We systematically demonstrate that one-dimensional phononic crystal (1-D PnC) tethers can signif-
9 icantly reduce tether loss in micromechanical resonators to a point where the total energy loss is
10 dominated by intrinsic mechanisms, particularly phonon damping. Multiple silicon resonators are
11 designed, fabricated, and tested to provide comparisons in terms of the number of periods in the
12 PnC and the resonance frequency, as well as a comparison with conventional straight-beam tethers.
13 The product of resonance frequency and measured quality factor (f_Q) is the critical figure of
14 merit, as it is inversely related to the total energy dissipation in a resonator. For a wide range of fre-
15 quencies, devices with PnC tethers
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Phonon loss is a result of the anharmonicity of the
38 material lattice, while TED is due to the irreversible heat flow
39 across thermal gradients induced during vibration.1,2,4 Tether
40 loss8–11 is the energy lost through the tethers to the substrate
41 anchors and is the subject of the experiments presented here.
42 In general, the goal is to design the tethers to minimize the
43 amount of elastic energy that leaks through to the substrate.
44 One common approach treats the tether as a transmission line,
45 assuming that the best isolation is achieved by using quarter-
46 wavelength tethers. For specific resonator designs, the tether
47 dimensions can be optimized to provide improved Q.11,12
48 Recent research into phonon-engineered structures has led to a
49 number of designs that allow selective phonon control, from
50 phonon cavities,13–16 waveguides,17,18 and filters.19,20 The abil-
51 ity to control acoustic phonon dispersion enables the design of
52 acoustic/phononic bandgaps19,20 that can be used as tethers or
53 shields to efficiently confine energy in a phonon cavity or resonator. 54 15,21–26 In such devices, acoustic propagation is miti- gated by using multiple repeating units to create a phononic 55 crystal (PnC) that has a transmission bandgap. Several of these 56 studies have focused on improving the Q of acoustic Fabry- 57

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