Size Effects in Vibrating Silicon Crystal Microbeams

The vibrations of ultrathin silicon cantilever microbeams are studied using consistent couple-stress theory to investigate size-dependent effects. The corresponding Euler-Bernoulli beam theory is used to estimate the couple-stress length scale parameter of single crystal silicon, based on measured experimental data for the resonant frequency of cantilever microbeams. The present work demonstrates that conventional use of classical beam theories, along with rigidly clamped cantilever boundary conditions, can lead to misinterpretation of experimental data, necessitating the introduction of nonphysical size-dependent effective material properties, such as an effective Young's modulus. Alternatively, proper modeling of the cantilever boundary conditions combined with use of couple-stress theory can account for the observed mechanical scale dependence in silicon micro- and nanostructures from fundamental principles of continuum mechanics. Moreover, the modeling approach presented here can be generalized to other micro- and nanoscale structures and materials. As such, the developed approach may be useful for the rational design of additional novel applications of such structures, ranging from optomechanical transducers to ultrasensitive biochemical sensors.