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 fabricat ed with short and long B diffusion processes and characterized. Measurement s of beam bending for released Si structures with length varying from 50 to 1000 mu m, width varying from 5 to 15 mu m, and thickness varying from 6 t o 37 mu m were obtained. By taking advantage of an etch-diffusion process, thicker beams can be fabricated which have less bending due to stress gradi ents. A 6.0-mu m-thick cantilevered beam had a deflection of 11.2 mu m due to stress gradients, while a 36.7-mu m-thick beam had a deflection of only 0.3 mu m. Beams fabricated using a dissolved wafer process with a 12 h B di ffusion were found to bend the same amount as those fabricated with a 4 h d iffusion. 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 dis tribution of dislocations. Using the deep-etch shallow-diffusion process, r esonating elements that are 20 mu m long, 4 mu m wide, and 28 mu m thick we re found to be perfectly flat without any bending. (C) 1999 American Vacuum Society. [S0734-211X(99)00104-3].