In parallel with the development of new technologies, new device configurations, and new applications for microsensors, microactuators, and microsystems, also referred to as microelectromechanical devices and systems (MEMS), there has arisen a growing need for computer-aided engineering and design systems. There is a wide range of design problems: process simulation, solid-body geometric renderings from photomasks and process descriptions, energetically correct simulations of behavior across multiple coupled energy domains, extraction of lumped low-order models of device behavior, optimization of geometry and process sequence, and design of full systems that include MEMS devices. Because of the computational demands of the modeling required to support full computer-aided design (CAD), there is a premium on fast and memory-efficient algorithms that help the designer, both by automating, where possible, complex sets of related tasks and by providing rapid computational prototyping at critical points in the design cycle. This paper presents an overview of the present state of the art in CAD for MEMS, with particular emphasis on the role of macromodels and test structures as part of the design environment.

In this paper, two approaches to self-consistent electromechanical analysis of three-dimensional micro-electro-mechanical structures are described. Both approaches combine finite-element mechanical analysis with multipole-accelerated electrostatic analysis, the first using a relaxation algorithm and the second using a surface/Newton generalized conjugate-residual scheme. Examples are given to demonstrate the relative merits of the two approaches.

Several improvements to the multipole-accelerated 3-D capacitance extraction program previously described are presented. A new adaptive multipole algorithm is given, and a preconditioning strategy for accelerated iterative method convergence is described. Results using these algorithms to compute the capacitance of general three-dimensional structures are presented, and they demonstrate that the modified approach is nearly as accurate as the more standard direct factorization algorithm, and can be as much as two orders of magnitude faster.>

We discuss the use of the covariance method for the analysis of transients, in particular to determine the number and time constants of decaying exponentials. We propose a new technique, involving the repeated use of the covariance method with many different orders, all larger than the the actual number of terms in the transient, and a comparison the results as a good means for the estimation of the true values of the parameters of interest.