Lumped-Parameter Modeling

Due to high fabrication costs, the microfabrication industry is extremely sensitive to design failures. An iterative design scenario requires working with mathematical and computational models of the device. Numerical simulation tools for MEMS devices that use finite element models have matured over time and have become standard to verify device performance against design specifications. Such tools are now an integral part of the design flow of MEMS devices. Given a list of specifications, computational models for the device are prepared that are simulated to confirm the behavior of the device with respect to the design specifications. The design problem can become difficult to solve when the design space increases with the multiple degrees of freedom, while the design objective also increases in its dimensionality. In such cases, an optimization script is necessary to iterate over the design space and find the best design, while the models need to be as computationally efficient as possible. Accurate and computationally efficient models of the popular MEMS devices are important for developing and improving MEMS CAD modules. Where analytical solutions are possible, they are preferred over numerical FEA solutions due to their computational efficiency and algorithmic and mathematical structure. Structured closed-form analytical solutions enable deep insight into model dynamics that helps to develop more powerful analysis techniques. Efficient solutions to analytical models of the tapered beam structure are hard to derive, as their direct solutions are expressed in terms of special functions such as Meijer G and hypergeometric functions.