Determining both adhesion energy and residual stress by measuring the stiction shape of a microbeam

The competition between the adhesive force and the beam restoring force determines the stiction shape of a microbeam. The presence of residual stress changes the beam stiffness and thus leads to the change of the beam restoring force. This study presents a model of incorporating the residual stress effect for the beam stiction. The previous models of arc-shape and S-shape correspond to the zero residual stress case, which also prescribes the stiction shape. When the residual stress becomes large, arc-shape and S-shape significantly deviate from the actual stiction shape of a slender beam. With the assumed stiction shape of arc-shape and S-shape, suspension length is the only parameter needed to characterize the stiction shape and suspension length can also be used to uniquely determine the adhesion energy. However, there are infinite combinations of residual stress and adhesion energy which can result in the same suspension length. Besides suspension length, the beam rise above the substrate can also be used as a parameter to characterize the stiction shape. This study presents a method of using these two parameters to uniquely determine the residual stress and adhesion energy as an inverse problem. A computation technique of using the stiction shape symmetry to significantly reduce the computation is also demonstrated.