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

摘要

MEMS devices such as comb drives and rotary drives are geometrically simple in that each of the components may be represented as a 'sweep' of a 2-D cross-section through a given height. This simplicity leads to simpler CAD requirements, geometric robustness, faster visualization, etc. Further, 3-D electrostatic simulation may be simplified to a 2-D problem over the cross-section if one neglects 3-D fringing. Such 2-D simulations provide a quick feedback to the designer on various parameters such as capacitance and electrostatic forces. However, as is well known, 3-D simulations cannot be avoided if fringing is significant, or when these devices need to be fully optimized. Such 3-D simulations unfortunately involve constructing the full 3-D geometry, volume/surface mesh, etc. 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.