Hybrid BEM/FEM Coupled Electromechanics

Most commercially successful MEMS devices rely on coupling between electrostatic fields and moving mechanical parts as their principle of operation, whether for sensing, actuation, or transduction. These electrostatic fields must be simulated with extremely high accuracy in order to accurately predict derived quantities such as electrostatic force, pull-in/lift-off voltage and electrostatic spring softening. CoventorWare is widely appreciated in the MEMS industry for simulating electrostatics and coupled electro-mechanics with unparalleled accuracy and efficiency.


Caption: A cantilever beam with two electrodes, showing the required mesh in other tools vs. CoventorWare, which does not require meshing the “air” around the cantilever.

Other FEA tools pose meshing requirements that significantly compromise accuracy and speed: either a truncated air gaps around moving parts must be filled with volume elements and the mesh must be morphed or re-generated as the device moves, or the air gaps must be meshed with special electrostatic elements that neglect electrostatic fringing fields. Coventor’s hybrid BEM/FEM approach avoids these compromises.

Caption: CoventorWare couples the boundary element method (BEM) for electrostatics with the finite element method (FEM) for mechanics, fully including electrostatic fringing effects while avoiding the approximations and much larger mesh associated with a pure FEM approaches.

The much smaller mesh required by CoventorWare’s hybrid BEM/FEM approach provides significant time savings, both by simplifying model preparation and by reducing the degrees of freedom that have to be solved. More importantly, the BEM approach is a more accurate way of simulating electrostatics. It does not require truncating the electrostatic field at a finite distance from the device or neglecting fringing field effects.

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