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Effects of annealing and temperature on acoustic dissipation in a micromechanical silicon oscillator
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Image of FIG. 1.
FIG. 1.

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.

Image of FIG. 2.
FIG. 2.

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.

Image of FIG. 3.
FIG. 3.

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.

Image of FIG. 4.
FIG. 4.

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.


Generic image for table
Table I.

Experimentally measured resonance frequencies at before annealing , after , and the fractional change, for five resonant modes.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effects of annealing and temperature on acoustic dissipation in a micromechanical silicon oscillator