Efficient 3D computation of electrostatic fields and forces in microsystems

This thesis reports the development and application of BemModule, a new com¬ puter-aided design (CAD) tool for the numerical simulation of electrostatic poten¬ tial, field and force distributions in microsystems, chip interconnects and dynamic random-access memory cells. Efficient and accurate characterization of the elec¬ trostatic behavior is crucial to device development, allowing to predict and opti¬ mize the performance of capacitive sensors and electrostatic microactuators, and improve large scale integrated circuit interconnects. This thesis presents the theory and implementation of an 0(/V log N) efficient method and associated algorithms for numerical device simulation based on the boundary element method (BEM). The BEM is the method of choice for the solu¬ tion of Poisson's equation for large, complex geometries, especially when highly accurate secondary field values are required. Boundary elements simplifies the meshing of device geometries, since only surface patch elements are required. BemModule is designed for electrostatic analysis of complex twoand threedimensional geometries. Key issues addressed by this work include • Multipole acceleration. • Various classes of discontinuous high-order elements. • Various types of boundary conditions. • Element error and refinement indicators. • Automatic hp-adaptive refinement. • Efficient linear solvers and preconditioner.s. BemModule is a stand-alone simulation environment, featuring a complete set of meshing and visualization tools, and a software library to be integrated into exist¬ ing technology CAD systems. Object-oriented program design, combined with rigorous software quality assurance and testing guarantee a reliable, modular and extendable system. The power of BemModule is demonstrated by engineering applications in the areas of microactuator simulation and VLSI characterization.