FEM versus BEM - Efficaciously modeling exterior electrostatic problems with singularity for electron devices

Abstract

For the performance of electron devices, an accurate electrostatic analysis is essential, and the boundary element method (BEM) has become a better method than the domain-type finite element method (FEM) because BEM can provide a complete solution in terms of boundary values only with substantial savings in modeling effort for the variable design stage. But, for exterior problems with singularity arising from the degenerate boundary (e.g., the edge of parallel-plate capacitor), the dual BEM becomes one of the most efficacious and robust tools for simulating the fringing field near the edge of electron devices because no laborious artificial boundary technique was needed like conventional BEM. After the fringing field is known well, the charge and capacitance of electron devices can be accurately calculated, and we can also understand the minimum allowable data of dielectric strength for keeping off dielectric breakdown. Electrostatics, as used here, involves charges in motion as well as at rest. Generally, there are five fundamental quantities (voltage, charge, current, capacitance, and resistance) in electrostatics that are involved in almost all applications. For most electrical engineers, voltage, or electromotive force (EMF) is the most important one. Electrostatic problems generally play a very important role in improving the performance and reliability of electron devices in the design stage (Cheng, 1989). Although we all understand that the beginning of electrostatic theory is believed to have occurred several centuries before, the first meaningful application, the commercially electrostatic precipitator, was just installed by Cottrell in 1907. Besides two major present technologies from 1907 to now, electrostatic precipitation and electrostatic coating, Castle also suggested that there would be several new industrial applications to come from developments in the fields of micro electromechanical systems (MEMS), biotechnology, ultrafine particles, nanotechnology, and space for the future applications of electrostatics. Because electrostatics still affects the performance of MEMS and electron devices critically nowadays, how to accurately obtain the electric potential V and electric field intensity E becomes especially important for engineers. We all know that scientists and engineers usually use several techniques in solving continuum or field problems. Loosely speaking, these techniques can be classified as experimental, theoretical (or analytical), or numerical.