Abstract
Third-order nonlinear elastic coefficients of silicon have been assumed to be the dominant factor in describing the nonlinear behavior of silicon-based resonators in literature. In this article, it is postulated that in spite of the common belief, third-order elastic coefficients may not be adequate to explain the nonlinear elastic behavior of silicon micro-resonators at high n-type doping concentrations. The nonlinear behavior observed in degenerately n-type-doped bulk-extensional mode resonators aligned to $\langle {100}\rangle $ orientation is carefully studied in which a spring-hardening effect is observed at large vibration amplitudes. It is shown that the existing analytical/numerical calculations and a proposed finite element model that are based on the utilization of third-order elastic (TOE) coefficients will all predict spring-softening in such resonators, thus suggesting insufficiency of the nonlinear model.
Accepted Version
Published Version
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