A 2-D model that accounts for 3-D fringing in MEMS devices

In this paper, we demonstrate that one can pose and solve a 2-D problem that accounts for 3-D fringing. The proposed technique does not require the construction of the 3-D CAD model or surface/volume mesh. Instead, the 3-D electrostatics problem is collapsed to 2-D via a novel dimensional reduction method. Once the 2-D problem is solved, the full 3-D field and associated charges/forces can be recovered, as a post-processing step. The simplicity and computational efficiency of the technique lends itself well to parametric study and design optimization.