Comprehensive spring constant modelling of tethered micromechanical plates

A study of the spring constant of elastically suspended plates, commonly used in MEMS tunable capacitors and RF switches, is carried out in this paper. Formulae for calculating the spring constant of a plate suspended by four straight tethers incorporating residual stress and non-ideal anchor compliance are presented. The model was extracted from FEM simulation data and is validated experimentally. A measurement/modelling correlation of 13% was achieved. It is also shown that significant errors (over 100%) may result in predicting the spring constant when the combined effects of residual stress, non-ideal anchors and non-rigidity of the plate are neglected or underestimated. The model presented in this paper can be used for the design, analysis and optimization of MEMS structures based on elastically suspended plates.