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Microscope picture of the single-crystal silicon paddle oscillator. The dimensions are: , , , and . Each perforation measures . The paddle and supports are suspended from the rectangular frame. Superposed are simulated temperature contours during laser annealing. Parameters used are a net radiative flux of , equaling 80% of the estimated annealing power, and a diameter Gaussian spot, calculated from the optical geometry. Assuming ambient temperature (on the frame) fixed at , temperature at paddle center is . The contour interval is . Material thickness is for the paddle and supports, and for the frame.
Schematic of mode shapes for 1-1, 2-0, torsion, plunging, and rocking modes. Nodal lines are shown for the 1-1 and 2-0 “plate” modes, torsion mode, and rocking mode. In the plunging mode, motion is perpendicular to the plane of the paddle.
Example of an annealing sequence showing Q of the 1-1 mode vs power in the optical fiber (which is proportional to the power incident on the sample). The line is a guide to the eye.
Dissipation or is plotted against temperature (a) before and (b) after laser annealing. Postanneal rocking mode data were of poor quality and omitted. For the 1-1 and 2-0 “plate” modes, dissipation near is reduced tenfold by the anneal. The solid curve in (b) shows the predicted thermoelastic loss for the 2-0 mode near room temperature. Dashed lines are a guide to the eye.
Experimentally measured resonance frequencies at before annealing , after , and the fractional change, for five resonant modes.
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