Low-frequency two-dimensional resonators for vibrational micro energy harvesting

The fabrication, characterization and theoretical analysis of a novel two-dimensional silicon resonator with threefold rotational symmetry are described. The resonator consists of a 4 mm wide disk-shaped seismic mass having the full-wafer thickness of 525 µm and suspended by a system of concentric circular springs. The device is structured using two-sided deep reactive-ion etching of silicon. With its current spring thickness and height, the device has two closely spaced resonance frequencies at 370.5 and 373.9 Hz and a quality factor of 1800 at ambient pressure. The spring height and thus the resonance frequency of the device are easily tuned by simple adjustment of a single etch duration in the entire fabrication process. The dynamic response of the structure is modeled under the two assumptions that silicon is elastically (i) isotropic and (ii) anisotropic. In comparison with the isotropic model, the elastic anisotropy leads to a predicted mode splitting by 6.2 Hz, with oscillation directions aligned with the cubic crystal axes. Even small geometrical imperfections are found to significantly rotate the eigenmodes and to further modulate their frequency splitting. Experimental and numerical results corroborate these conclusions. Overall the present resonator design has the potential for a higher energy harvesting efficiency than a combination of two separate one-dimensional oscillators.