Degeneracy Breaking, Modal Symmetry and MEMS Biosensors

This work is concerned with degenerate modes of vibration in problems involving rotational symmetries of finite order. In the case of infinite order symmetry of the material and the geometry, two degenerate mode pairs exist for each natural number, corresponding to the cyclic periodicity of the solution. Degenerate sensors have been developed in MEMS over the past 20 years that exploit weak couplings introduced between the modes by an environmental effect of interest. In the presence of breaking of the cyclic symmetry of the problem – either in the geometry or in the substrate the degeneracy between the modes may be broken, leading to performance degradation. Thus motivated, we investigate the effects of material and geometric symmetry breaking using COMSOL Multiphysics ® and analytical techniques. The possibility of significant degeneracy breaking is demonstrated, and techniques to mitigate the problem are discussed from a systems design perspective.