Optimal Synthesis Methods for MEMS

Design consists of two distinct components, viz. analysis and synthesis. Extensive research on analysis of Microelectromechanical Systems (MEMS) in the last decade has led to commercially available software tools. In contrast, synthesis has received less attention. On the one hand, the integrated and the multi-disciplinary nature of MEMS creates a necessity for time-saving systematic synthesis tools, and on the other, restrictions related to microfabrication provide new opportunities to make synthesis techniques practically viable. This book is a collection of synthesis efforts that cover many, but not all, aspects of MEMS. Since synthesis has many different connotations, a simple example is presented to explain how it is viewed in this book. Optimization is used as the primary tool for synthesis in this book. The essential steps in the optimal synthesis procedure are described in this chapter. Finally, the contents of each chapter are briefly noted.

The mechanical elements of most of the MEMS devices are based on compliant designs such as the ones found in beams, plates, and other types of elastic structures. The advantages of single-piece, assembly-free compliant designs are well known. The extruded planar geometry of MEMS devices and almost unrestricted possibilities for shapes in the plane parallel to the substrate make it possible to develop systematic synthesis methods. This chapter describes such methods for desired mechanical attributes including stiffness, flexibility, motion, strength, natural frequencies, and normal mode shapes. Topology optimization is the main focus of the chapter but some other methods are also briefly presented. Some applications are included.

This chapter presents a synthesis methodology for electrostatically driven microelectromechanical systems. It addresses issues of simulation, sensitivity analysis and optimization. As an application of the general methodology, design of variable gap comb drives (shape motors) is presented. Direct simulation of the electrostatic field is carried out by the exterior, indirect boundary element method and shape sensitivities are obtained by the direct differentiation approach. The inverse problem determines the shapes of fingers of a comb drive such that the driving force is a desired function of its travel distance. Commercially available optimization codes are used to solve the synthesis problems. Numerical results are presented for shape motors that produce linear, quadratic or cubic force profiles. Based on the design, a cubic motor was fabricated using the SCREAM process. The driving forces were measured and the results were compared with the theoretical predictions.

Synthesis methods, such as topology optimization method, have been widely applied to design mechanical structures. Therefore, it is natural that they can also be applied to design smart materials and MEMS structures whose current development has been based on the use of simple analytical models, test of prototypes, and analysis using the finite element method (FEM), usually limiting the problem to a parametric optimization. In contrast to those approaches, this chapter presents systematic synthesis methods for MEMS actuated by piezoelectric materials by using topology optimization combined with homogenization technique. In this method, the topology of a flexible structure coupled to a piezoceramic (flextensional actuator) is designed to maximize the output displacement (or force) in some specified direction. Beginning with a brief introduction to the piezoelectric constitutive equations and the FEM theory applied to the piezoelectricity, the chapter provides a self-contained description of the synthesis method for piezoelectrically actuated MEMS. The examples presented show that the synthesis method is indeed a promising tool to design smart materials and structures.

Piezocomposite materials are largely applied to acoustical devices such as sonars and ultrasonic transducers. Their development has also been based on the use of simple analytical models, test of prototypes, and analysis using the finite element method (FEM). Thus, following the idea of applying synthesis methods to design smart materials and MEMS structures, this chapter presents systematic synthesis methods for piezocomposite materials by using the topology optimization combined with the homogenization technique. In this method, a piezocomposite material with improved electromechanical efficiency is obtained by designing its unit cell topology. Beginning with a brief introduction to piezocomposite materials, its performance measurement, the concept of the homogenization method, and its manufacturing technique, the chapter provides a self-contained description of the synthesis method for these materials. The examples presented show that the synthesis method is indeed a promising tool to design these smart materials.

Extremal materials may exhibit mechanism like behaviours. Examples are negative Poisson’s ratio materials that expand transversely when pulled horizontally. Such materials are often composed of periodic arrays of simple microscopic mechanisms and may therefore be called Periodic Micro Mechanisms (PMMs). This chapter describes how PMMs can be systematically synthesized using the topology optimization method. A number of examples including design of negative Poisson’s ratio, negative thermal expansion coefficient and band gap PMMs are given.

This chapter describes a systematic method for the automatic generation of fabrication processes of thin film devices. The method uses a partially ordered set (poset) representation of the device topology describing the order between its various components in the form of a directed acyclic graph. The component fabrication sequence is determined from the poset exensions. The component sequence is then expanded into a corresponding process flow. The graph-theoretic synthesis method is powerful enough to establish existence and multiplicity of flows thus creating a design space D suitable for optimization. The cardinality ∥D∥ for a device with N components is large with a worst case ∥D∥ ≤ (N — 1)! yielding in general a combinatorial explosion of solutions. The number of solutions is controlled through a priori estimates of ∥D∥ and condensation of the device graph. Algorithms to construct process flows from schematics of thin film devices have been developed and implemented in the computer program MISTIC (Michigan Synthesis Tools for Integrated Circuits) which calculates specific process parameters using an internal database of process modules and materials. Currently MISTIC includes process modules for deposition, lithography, etching, ion implantation, coupled simultaneous diffusions, and reactive growth.

Photolithography masks provide the link between the design of a MEMS device and its microfabrication. Numerous techniques and computer software tools are available for creating a geometric model from the masks by geometrically emulating the microfabrication process. This is the analysis or the forward problem. The opposite of this, i.e., the synthesis or the inverse problem, entails direct generation of masks from a 3-D or 2-D model of a device. There are only a few techniques available for this important aspect of MEMS design and fabrication. After noting the current practice adopted by MEMS designers of today, approaches to mask synthesis of devices fabricated with bulk micromachining and surface micromachining are presented in this chapter. The latter kind is described in detail. A mathematical framework for geometric modeling, which was developed to streamline the mask synthesis problem, is also presented. It is shown, illustrated with examples, how this framework reduces the geometric problem of mask synthesis of surface micromachined devices to an over constrained linear system of equations that can be solved using singular value decomposition..

Microelectromechanical Systems such as resonators, accelerometers, gyroscopes, IR sensors, RF filters, electrothermal converters and force sensors can be composed out of beam springs, plate masses, dampers, and electromechanical comb sensors and actuators. MEMS design involves iteratively designing each of these submodules and the entire transducer including the electronics, to meet given design specifications. System-level synthesis helps automate much of this design problem for a fixed MEMS transducer topology. First, geometric layout design variables are identified to describe the topology. Next, functional constraints that map these variables to engineering performance specifications are obtained by static and dynamic mechanical as well as electrostatic analysis. Then, the variables and constraints are used to formulate a mixed-integer non-linear optimization problem, which is solved to synthesize the transducer layout from high-level engineering specifications. A variety of objective functions can be used to automate the exploration of the entire design space given specific user-specified engineering constraints, allowing the designer to understand the complex design trade-offs inherent to the design problem.