Electrostatic BEM for MEMS with thin beams

Micro-electro-mechanical (MEM) and nano-electro-mechanical (NEM) systems sometimes use beam- or plate-shaped conductors that can be very thin—with h/L≈(10−2–10−3) (in terms of the thickness h and length L of a beam or the side of a square pate). Conventional boundary element method (BEM) analysis of the electric field in a region exterior to such thin conductors can become difficult to carry out accurately and efficiently—especially since MEMS analysis requires computation of charge densities (and then surface tractions) separately on the top and bottom surfaces of such objects. A new boundary integral equation (BIE) is derived in this work that, when used together with the standard BIE with logarithmically singular kernels, results in a powerful technique for the BEM analysis of such problems with thin beams. This new approach, in fact, works best for very thin beams. This thin beam BEM is derived and discussed in this work. Copyright © 2005 John Wiley & Sons, Ltd.

[1]  S. Mukherjee,et al.  Evaluation of nearly singular integrals in boundary element contour and node methods for three-dimensional linear elasticity , 2000 .

[2]  Srinivas Telukunta,et al.  An extended boundary node method for modeling normal derivative discontinuities in potential theory across edges and corners , 2004 .

[3]  Palghat S. Ramesh,et al.  DYNAMIC ANALYSIS OF MICRO‐ELECTRO‐MECHANICAL SYSTEMS , 1996 .

[4]  S. Mukherjee.  CPV and HFP integrals and their applications in the boundary element method , 2000 .

[5]  Jacob K. White,et al.  An efficient numerical technique for electrochemical simulation of complicated microelectromechanical structures , 1997 .

[6]  Yijun Liu,et al.  Thermal analysis of carbon-nanotube composites using a rigid-line inclusion model by the boundary integral equation method , 2004 .

[7]  Palghat S. Ramesh,et al.  On the application of 2D potential theory to electrostatic simulation , 1995 .

[8]  J. Telles.  A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals , 1987 .

[9]  Subrata Mukherjee,et al.  Electrostatic BEM for MEMS with thin conducting plates and shells , 2004 .

[10]  J. Telles,et al.  Third degree polynomial transformation for boundary element integrals: Further improvements , 1994 .

[11]  S. Mukherjee,et al.  The boundary contour method for two-dimensional linear elasticity with quadratic boundary elements , 1997 .

[12]  Yijun Liu.  ANALYSIS OF SHELL-LIKE STRUCTURES BY THE BOUNDARY ELEMENT METHOD BASED ON 3-D ELASTICITY: FORMULATION AND VERIFICATION , 1998 .

[13]  Subrata Mukherjee,et al.  Simulation methods for micro-electro-mechanical structures (MEMS) with application to a microtweezer , 1995 .

[14]  S. Mukherjee.  Finite parts of singular and hypersingular integrals with irregular boundary source points , 2000 .

[15]  S. Mukherjee.  On Boundary Integral Equations for Cracked and for thin Bodies , 2001 .

[16]  Jacob K. White,et al.  FastCap: a multipole accelerated 3-D capacitance extraction program , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[17]  Jacob K. White,et al.  A computer-aided design system for microelectromechanical systems (MEMCAD) , 1992 .