Resonant microbeam strain transducers

Vacuum-enclosed resonant microbeam elements 200 or 400 mu m long and 1.8 mu m thick have been fabricated using LPCVD (low-pressure chemical vapor deposited) mechanical-grade polysilicon. The fundamental resonant frequency and overtone frequencies of the beams have been measured, with 550 kHz, 1.2, 2.2, and 5.2 MHz typical of the frequencies of the 1D bending modes for the 200 mu m length. Q-values determined using gain/phase analysis vary from less than 10 to over 25,000 for the devices tested. Closed-loop operation using piezoresistive sense and electrostatic drive has been achieved with AGC to prevent excessive drive. The 1D differential equation of motion of a doubly clamped single-span beam with an axial load can be solved analytically for lateral natural frequencies and mode shapes. These solutions have been verified by finite element methods. In addition, the finite element models were used to identify both lateral and torsional modes. The closed-form solutions are compared with the numerical results and the experimental data.<>