Stress analysis at singular points of micromachined silicon membranes

From 3D Finite Element simulations of square silicon micromachined membrane, we know that stress singularities are located close to the membrane median Lines. As 3D simulations do not reach a sufficient level of accuracy to describe singularity behaviour, we use an iterative method to calculate the stress field components in the immediate vicinity of the singularity with more precision. However, this implies a reliable knowledge of the stress field in the surrounding of the singularity as a Limiting condition. This was achieved through the development of a 2D axisymmetric Finite Element model (FEM) with a refined meshing around the singularity. The consistency of the results of the 3D and 2D model is discussed with regards to the description of the membrane behavior in both cases. Finally, the singular stress held is described numerically and its ability to raise up the local stress field is discussed in terms of crack initiation mechanisms. (C) 2000 Elsevier Science S.A. All rights reserved.