Evaluation of spring constant in plates with straight suspensions

The mechanical spring constant is one of the most important characteristics of micromechanical structures, providing a key tool for accurate behavioural modelling of the devices. It is also one of the main controllable parameters allowing maximum flexibility for the designer. A study of the spring constant of elastically suspended plates, common to MEMS tunable capacitors and RF switches, is carried out in this paper. A model for the spring constant of the plate suspended by four cantilevers incorporating residual stress is presented. The model also accounts for nonideal anchors. The model was extracted from FEM simulation data and validated experimentally. Correlation to within 3% was achieved. The model can be used for design, analysis and optimisation of tunable capacitors and radio frequency switches or other structures based on elastically suspended plates. The presented model also predicts that significant errors may result in predicting the spring constant when combined effects of residual stress, nonideal anchors and nonrigidity of the plate are neglected or underestimated.