Optimal Synthesis Methods for MEMS

The field of "microelectromechanical systems," or "MEMS," has gradually evolved from a "discipline" populated by a small group of researchers to an "enabling technology" supporting a variety of products in such diverse areas as mechanical and inertial sensors, optical projection displays, telecommunications equipment, and biology and medicine. Critical to the success of these products is the ability to design them, and this invariably involves detailed modeling of proposed designs. Over the past twenty years, such modeling has become increasingly sophisticated, with full suites of MEMS-oriented computer-aided-design tools now available worldwide. But there is another equally important side to the design process ­ In my own book, Microsystem figuring out what to build in the first place. Design, I chose to emphasize the modeling aspect of design. The task of figuring out what to build was defined by a vague step called "creative thinking." I used practical product examples to illustrate the many subtle characteristics of successful designs, but I made no attempt to systematize the generation ofdesign proposals or optimized designs. That systemization is called "synthesis," which is the subjectofthis book.

1 Introduction.- 1. Design of Microelectromechanical Systems.- 2. Synthesis vs. Analysis.- 2.1 An example: mode shape synthesis of a bar.- 3. Optimization as a synthesis tool.- 3.1 Components of an optimal synthesis procedure.- 4. Contents of the chapters.- 5. Closure.- 2 Synthesis for Mechanical Behavior.- 1. Introduction.- 2. Synthesis of beam-like structures.- 3. Topology Synthesis.- 3.1 Flexibility-stiffness formulation.- 3.1.1 An accelerometer with a built-in displacement amplifier.- 3.1.2 A micromechanical AND logic gate.- 3.1.3 Synthesized solutions as design aids.- 3.2 Flexibility-strength formulation.- 3.2.1 Modeling stress constraints.- 3.2.2 Sensitivity analysis for stress constraints.- 3.2.3 An example.- 4. Synthesis for dynamic attributes.- 4.1 Synthesis for desired natural frequencies.- 4.2 Synthesis for desired normal mode shapes.- 4.2.1 Mode shape synthesis for beams.- 5. Conclusions.- 3 Synthesis of Electrostatically Actuated Mems.- 1. Introduction.- 2. Governing Equations.- 3. Shape Synthesis of Electrostatically Driven Actuators.- 3.1 Simulation of the driving force.- 3.2 Sensitivity analysis.- 3.3 Optimization.- 4. An Example: Variable Comb-drive Actuators.- 4.1 2-D Designs.- 4.1.1 Driving force.- 4.1.2 Sensitivity analysis.- 4.1.3 The inverse problem.- 4.2 3-D Design.- 4.2.1 Driving force.- 4.2.2 Sensitivity analysis.- 4.2.3 The inverse problem.- 4.3 Fabrication of a shaped motor — a demonstration.- 4.3.1 SCREAM I process.- 4.3.2 Test results.- 5. Closure.- 4 Synthesis Methods for Electrothermal Actuation.- 1. Introduction.- 2. Generalization of the BasiC electro-thermal actuator.- 2.1 Changing dimensions.- 2.2 Changing material properties.- 2.3 Changing thermal boundary conditions.- 2.4 Changing electrical boundary conditions.- 2.5 Electro-thermal-compliant designs.- 3. Modeling.- 3.1 Electrical analysis.- 3.2 Thermal analysis.- 3.3 Elastic analysis.- 4. Synthesis.- 4.1 Design parameterization.- 4.2 Problem statement.- 4.3 Solution procedure.- 5. Numerical examples.- 6. Alternative implementation using “line elements”.- 6.1 Line elements.- 6.2 Finite element modeling with line elements.- 6.3 Problem formulation.- 6.4 Sensitivity analysis and solution procedure.- 6.5 Numerical examples with line elements.- 7. Advanced example.- 8. MicroFabrication.- 8.1 PennSOIL.- 8.2 Excimer laser micromachining.- 8.3 Electro-plating combined with photolithography.- 9. Closure.- 5 Synthesis with Piezoelectric Actuation.- 1. Introduction.- 2. Background Theory for Piezoelectricity.- 3. FEM Applied to Piezoelectricity.- 4. Flextensional Actuator Design.- 4.1 Mean Transduction.- 4.2 Material Model.- 4.3 Formulation of Optimization Problem.- 4.4 Sensitivity Analysis.- 4.5 Examples.- 4.5.1 A Multilayer Actuator.- 4.5.2 A Flextensional Gripper.- 4.6 Manufactured Prototypes.- 5. Conclusion.- 6 Synthesis of Piezocomposites.- 1. Piezocomposite Design.- 1.1 Performance Characteristics of Piezocomposite Materials.- 1.1.1 Low-Frequency Applications.- 1.1.2 High-Frequency Applications.- 2. Homogenization Method.- 3. Piezocomposite Design Problem.- 3.1 Formulation of Optimization Problem.- 4. Examples.- 4.1 Piezocomposite Manufacturing.- 4.1.1 Microfabrication by Coextrusion Technique.- 4.1.2 Stereolithography Technique.- 4.2 Experimental Results.- 5. Conclusions.- 7 Synthesis of Periodic Micro Mechanisms.- 1. Introduction.- 2. Numerical homogenization, FE modeling, and sensitivity analysis.- 3. Formulation of the problem.- 4. Numerical implementation.- 5. Examples.- 5.1 Shearing materials.- 5.2 Negative Poisson’s ratio matrials.- 5.3 Extremal thermal expansion coefficient.- 5.4 Piezoelectric transducers.- 6. Wave propagation.- 6.1 Modeling of wave propagation.- 7. Concluding remarks.- 8 Process Synthesis.- 1. Introduction.- 2. State-space representation.- 3. Planar device representation.- 4. Basic synthesis method.- 5. Cardinality of design space.- 6. Granularity control through condensation.- 7. Other miscellaneous graph-theoretical results.- 8. Process flow construction.- 9. Determination of selective operators.- 10. Process flow parameters.- 11. Software implementation.- 12. Compiler testing.- 13. Summary.- 9 Mask Synthesis.- 1. Introduction.- 1.1 Terminology.- 2. Related work.- 2.1 Mask synthesis for bulk micromachining.- 2.2 Mask synthesis for surface micromachining.- 3. Mathematical framework.- 4. Synthesis.- 4.1 Deposits.- 4.2 Etches.- 4.3 Doping.- 4.4 Generating potential mask openings.- 4.5 Subdivision of mask openings.- 4.6 Validating Mask Openings.- 5. Examples.- 6. Conclusions.- 10 System-Level Synthesis.- 1. MEMS Design representations.- 2. Synthesis Methodology.- 2.1 Design Variables.- 2.2 Constraints.- 2.2.1 Geometric Constraints.- 2.2.2 Functional Constraints.- 2.3 Synthesis Formulation.- 2.4 Layout Generation.- 3. Performance Models.- 4. Synthesis Results.- 4.1 Synthesis with In-plane Mode Separation Constraints.- 4.2 Synthesis with Out-of-plane Mode Separation Constraints.- 5. Summary.