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 μ m, width varying from 5 to 15 μ m, and thickness varying from 6 to 37 μ m 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- μ m-thick cantilevered beam had a deflection of 11.2 μ m due to stress gradients, while a 36.7- μ m-thick beam had a deflection of only 0.3 μ m. 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 μ m long, 4 μ m wide, and 28 μ m thick were found to be perfectly flat without any bending.