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few to 10 Å, which leads to negligible diffraction effects) and larger depth of focus compared with optical
lithography. The ability to fabricate microstructures and microdevices in the centimeter range is partic-
ularly important in the actuators and drives applications since the specifications are imposed on the rated
force and torque developed by the microdevices, and due to the limited force and torque densities, the
designer faces the need to increase the actuator dimensions.

14.4 MEMS Electromagnetic Fundamentals and Modeling

The MEMS classifier, structural synthesis, and optimization were reported in Section 14.2. The classifica-
tion and optimization are based on the consideration and synthesis of the electromagnetic system, analysis
of the magnetomotive force, design of the MEMS geometry and topology, and optimization of other
quantities. Different rotational (radial and axial) and translational motion microdevices are classified
using endless (closed), open-ended (open), and integrated electromagnetic systems.
Our goal is to approach and solve a wide range of practical problems encountered in nonlinear design,
modeling, analysis, control, and optimization of motion microstructures and microdevices with driving/
sensing circuitry controlled by ICs for high-performance MEMS. Studying MEMS, the emphases are
placed on:
• design of high-performance MEMS through devising innovative motion microdevices with radi-
ating energy microdevices, microscale driving/sensing circuitry, and controlling/signal processing
ICs,
• optimization and analysis of rotational and translation motion microdevices,
• development of high-performance signal processing and controlling ICs for microdevices devised,
• development of mathematical models with minimum level of simplifications and assumptions in
the time domain,
• design of optimal robust control algorithms,
• design of intelligent systems through self-adaptation, self-organization, evolutionary learning, deci-
sion-making, and intelligence,
• development of advanced software and hardware to attain the highest degree of intelligence,
integration, efficiency, and performance.

In this section, our goal is to perform nonlinear modeling, analysis, and simulation. To attain these
objectives, we apply the MEMS synthesis paradigm, develop nonlinear mathematical models to model
complex electromagnetic-mechanical dynamics, perform optimization, design closed-loop control sys-
tems, and perform data-intensive analysis in the time domain.
To model electromagnetic motion microdevices, using the magnetic vector and electric scalar potentials
A and V, respectively, one usually solves the partial differential equations

2
∂ A
∂A
2
– ∇ A + µσ ------- + µe--------- = – µσ∇V
∂t ∂t 2
using finite element analysis. Here, µ, σ, and ε are the permeability, conductivity, and permittivity.
However, to design electromagnetic MEMS as well as to perform electromagnetic–mechanical analysis
and optimization, differential equations must be solved in the time domain. In fact, basic phenomena
cannot be comprehensively modeled, analyzed, and assessed applying traditional finite element analysis,
which gives the steady-state solutions and models. There is a critical need to develop the modeling tools
that will allow one to augment nonlinear electromagnetics and mechanics in a single electromagnetic–
mechanical modeling core to attain high-fidelity analysis with performance assessment and outcome
prediction.
Operating principles of MEMS are based upon electromagnetic principles. A complete electromagnetic
model is derived in terms of five electromagnetic field vectors. In particular, three electric field vectors

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