Microscope picture of the single-crystal paddle oscillator. The dimensions are , , , and . Each perforation on the paddle plate measures .
Microscopic scanning picture of the first five out-of-plane resonance modes of a single-crystal paddle oscillator measured by scanning laser Doppler vibrometer. The normal components of the surface velocity for the five modes are presented. The gray scale bar represents surface velocity or displacement from . The negative dB means 180° out of phase with the positive.
Quality factor vs resonant frequency of the first five out-of-plane modes before anneal and six months after anneal at for .
Time dependence of quality factor or internal friction for the 1-1 mode after an anneal at for : (a) The quality factor after annealing, , is shown as solid squares. The open square is after an anneal at for . The dashed line is a guide to the eye only. (b) The time-dependent part of the internal friction, , is shown as solid squares. The dashed line is a guide to the eye only.
Quality factor vs oscillator size, either thickness or width, whichever is smaller, for single-crystal silicon oscillators measured at room temperature from this work and literature. The dashed line is a guide to the eye.
The measured resonance frequencies , the eigenfrequencies from the FEM, the difference from the prediction , the measured before annealing, the participation factor , and the thermoelastic limit of the first five out-of-plane resonance modes.
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