The building blocks of MEMS design through closed-form solutions
Microelectromechanical Systems, or MEMS, is the technology of very small systems; it is found in everything from inkjet printers and cars to cell phones, digital cameras, and medical equipment. This book describes the principles of MEMS via a unified approach and closed-form solutions to micromechanical problems, which have been recently developed by the author and go beyond what is available in other texts. The closed-form solutions allow the reader to easily understand the linear and nonlinear behaviors of MEMS and their design applications.
Beginning with an overview of MEMS, the opening chapter also presents dimensional analysis that provides basic dimensionless parameters existing in large- and small-scale worlds. The book then explains microfabrication, which presents knowledge on the common fabrication process to design realistic MEMS. From there, coverage includes:
Statics/force and moment acting on mechanical structures in static equilibrium
Static behaviors of structures consisting of mechanical elements
Dynamic responses of the mechanical structures by the solving of linear as well as nonlinear governing equations
Fluid flow in MEMS and the evaluation of damping force acting on the moving structures
Basic equations of electromagnetics that govern the electrical behavior of MEMS
Combining the MEMS building blocks to form actuators and sensors for a specific purpose
All chapters from first to last use a unified approach in which equations in previous chapters are used in the derivations of closed-form solutions in later chapters. This helps readers to easily understand the problems to be solved and the derived solutions. In addition, theoretical models for the elements and systems in the later chapters are provided, and solutions for the static and dynamic responses are obtained in closed-forms.
This book is designed for senior or graduate students in electrical and mechanical engineering, researchers in MEMS, and engineers from industry. It is ideal for radio frequency/electronics/sensor specialists who, for design purposes, would like to forego numerical nonlinear mechanical simulations. The closed-form solution approach will also appeal to device designers interested in performing large-scale parametric analysis.
1.1 Microelectromechanical Systems.
1.2 Coupled Systems.
1.3 Knowledge Required.
1.4 Dimensional Analysis.
2.1 Bulk and Surface Micromachining.
2.3 Layer Deposition.
2.4 Layer Etching.
2.5 Fabrication Process Design.
3.1 Static Equilibrium.
3.2 Stress–Strain Relationship.
3.3 Thermal Stress.
3.4 Beam Behavior Subjected to a Torsional Moment.
3.5 Moment–Curvature Relationship.
3.6 Beam Equation.
3.7 Galerkin's Method.
3.8 Energy Method.
3.9 Energy Method for Beam Problems.
4 STATIC BEHAVIOR OF MICROSTRUCTURES.
4.1 Elements of Microstructures.
4.2 Stiffness of Commonly Used Beams.
4.4 Stiffness Transformation.
4.5 Static Behavior of Planar Structures.
4.6 Residual Stress.
4.7 Cubic Force of Structures.
4.8 Potential Energy.
4.9 Analogy Between Potential Energies.
5.1 Cubic Equation.
5.2 Description of Motion.
5.3 Governing Equations of Dynamics.
5.4 Energy Conversion Between Potential and Kinetic Energy.
5.5 Free Vibration of Undamped Systems.
5.6 Vibration of Damped Systems.
5.7 Multidegree-of-freedom systems.
5.8 Continuous Systems.
5.9 Effective Mass, Damping, and Stiffness.
5.10 Systems with Repeated Structures.
5.11 Duffi ng's Equation.
6 FLUID DYNAMICS.
6.1 Viscous Flow.
6.2 Continuity Equation.
6.3 Navier–Stokes Equation.
6.4 Reynolds Equation.
6.5 Couette Flow.
6.6 Oscillating Plate in a Fluid.
6.7 Creeping Flow.
6.8 Squeeze Film.
7.1 Basic Elements of Electric Circuits.
7.2 Kirchhoff’s Circuit Laws.
7.4 Force and Moment Due to an Electric Field.
7.5 Electrostatic Forces and Moments Acting
on Various Objects / 395
7.6 Electromagnetic Force / 410
7.7 Force Acting on a Moving Charge in Electric and
Magnetic Fields / 418
8 PIEZOELECTRIC AND THERMAL ACTUATORS.
8.1 Composite Beams.
8.2 Piezoelectric Actuators.
8.3 Thermal Actuators.
9 ELECTROSTATIC AND ELECTROMAGNETIC ACTUATORS.
9.1 Electrostatic Actuators.
9.2 Comb Drive Actuator.
9.3 Parallel-Plate Actuator.
9.4 Torsional Actuator.
9.5 Fixed–Fixed Beam Actuator.
9.6 Cantilever Beam Actuator.
9.7 Dynamic Response of Gap-Closing Actuators.
9.8 Approximation of Gap-Closing Actuators.
9.9 Electromagnetic Actuators.
10.1 Force and Pressure Sensors.
10.3 Electrostatic Accelerometers.
10.4 Vibratory Gyroscopes.
10.5 Other Issues.