Characterization of bending in single crystal Si beams and resonators

Optical interferometry has been applied to determine the displacement of p⁺⁺ Si beams. Clamped-clamped Si beams and cantilevered beams were fabricated with short and long B diffusion processes and characterized. Measurements of beam bending for released Si structures with length varying from 50 to 1000 μm, width varying from 5 to 15 μm, and thickness varying from 6 to 37 μm were obtained. By taking advantage of an etch-diffusion process, thicker beams can be fabricated which have less bending due to stress gradients. A 6.0-μm-thick cantilevered beam had a deflection of 11.2 μμm due to stress gradients, while a 36.7-μm-thick beam had a deflection of only 0.3 μm. Beams fabricated using a dissolved wafer process with a 12 h B diffusion were found to bend the same amount as those fabricated with a 4 h diffusion. This indicates that bending in doped Si beams not only depends on the gradients in the B concentrations, it could also be related to the distribution of dislocations. Using the deep-etch shallow-diffusion process, resonating elements that are 20 μm long, 4 μμm wide, and 28 μm thick were found to be perfectly flat without any bending.