Frequency splitting of the main mode in a microelectromechanical resonator due to coupling with an anchor resonance
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(a) Structure of the square-plate resonator. The 28-μm-thick, single-crystalline silicon resonator plate is attached to the substrate at the plate corners with 4-μm-wide meander anchors. A 350-nm-thick piezoelectric AlN layer is deposited on top of the plate. A 300-nm Mo layer on top of the AlN layer acts as a top electrode, and the Si resonator plate itself acts as a bottom electrode. (b) Photograph of the L = 209 μm resonator sample and the rectangular scan areas I (scan step 1.54 μm), II (0.44 μm), and III (0.44 μm) used for laser probe measurements. To enable in-plane laser probe measurements, the top-electrode Mo layer is patterned with a 5-μm grid of circular 2.5-μm-diameter holes. The electrical equivalent circuit model of the resonator is shown at the bottom-right corner.
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(Color) The electrical characterization and laser probing results. The electrically characterized resonance frequencies (black “+”) are plotted as a function of the plate side length L. Only the resonances corresponding to the two frequency branches closest to the pure SE mode frequency curve (black line) predicted by the single spring-mass model (shown in inset A) are presented. The red curves represent the least squares fit of the coupled resonator model (shown in inset B) to the electrical data. The measured OP (colormap) and IP amplitude data (black arrows on the OP data) of selected plate sizes are shown as insets. To visualize the vibration fields, each OP data figure has a separate logarithmic scaling normalized to its maximum OP amplitude, and also the lengths of the arrows indicating the IP fields have a separate linear scaling for each data figure. Insets C and D: The IP phase data of the top-right anchor of the L = 209 μm resonator. The instantaneous movement directions of the anchor and the resonator plate are depicted with red and yellow arrows. Inset E: Frequency sweep of the IP vibration amplitude of a selected resonance within the 20-22 MHz range, in which increased anchor activity is observed (measured from the top-right anchor).
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