Nonlinear mechanical effects in silicon longitudinal mode beam resonators

The fundamental nonlinear mechanical effects in micromachined single-crystal silicon resonators are investigated. Longitudinal mode beam resonators are chosen for the analysis due to their simple geometry and high quality factor (Q>100000). Analytical model for the resonator is developed in terms of nonlinear engineering Young's modulus that incorporates both geometrical and material effects. For comparison with the theory, beam resonators were fabricated in two different crystalline directions. The measured nonlinearity is larger for beams in [1 1 0] direction than for beams in [1 0 0] direction in agreement with the theoretical prediction. The results provide a quantitative value for the appearance of the material-induced nonlinear effects in single-crystal silicon microresonators.