10. Managing Parameter Variations in Microsystems Device Design

The information covered from the previous chapters is brought together in this chapter to explain various techniques used in the microsystems design to manage the parameter variations resulting from use of microsystems manufacturing. Design for manufacturability (DfM) of microsystems is covered followed by some general recommendations for developing microsystems designs that adhere to DfM principles for MEMS devices. A review of the design techniques to manage device parameter variations is then provided including design centering: device parameter variation reduction; device size scaling; acceptance region increase; and best practices for layout. These techniques allow the variation region to be better aligned with the acceptance region. Each of these techniques is substantiated with examples in a one-dimensional parameter space, followed by how these techniques are used in multidimensional space. The use of Monte Carlo analysis techniques for design methods is then discussed including specific methods such as the centers of gravity algorithm; correlated sampling; and the common points method. The confidence of correct yield ranking is included in this discussion. Subsequently, sensitivity analysis for manufacturing or performance function improvement is outlined in both one- and multidimensional spaces. Lastly, a method for optimization of the manufacturing cost function is given.