Microelectromechanical Systems II: Design Principles

Explore MEMS modeling with simplified, dominant-behavior models instead of full multi-physics solutions, reducing distributed microstructures and focusing on scale-dominant effects like electrostatic forces to transduce motion for electronic integration.

Use lumped element models, especially the mass–spring–damper system, to capture inertia, elasticity, and energy loss in MEMS. Replace complex structures with masses, springs, and dampers to design and tune devices.

Static and dynamic mems regimes map how displacement follows the balance of forces against stiffness, with area moment of inertia defining stiffness; dynamic regimes reveal resonance and transient response.

Investigate mems frequency response and resonance, noting that near the natural frequency small forces yield large displacements, while damping, effective mass, and stiffness shape resonance in resonators and gyroscopes.

Explore capacitive sensing in MEMS, showing how capacitance changes with plate overlap and gap, the role of permittivity, and how differential capacitors enhance sensitivity and noise rejection.

Explore capacitive sensitivity and linearity in mems, showing how gap, area, and electrostatic force shape pull-in limits and equilibrium with mechanical restoring forces.

Explore noise sources in capacitive microelectromechanical systems, focusing on Brownian thermal noise governed by Boltzmann constant, and how temperature, mass, natural frequency, and quality factor shape displacement and capacitance noise.

Explore resonance structures and mode shapes in MEMS, focusing on the fundamental mode's natural frequency via stiffness and mass, then validate with multiphysics simulations to observe motion.

Vibrate lateral resonators in a plane parallel to the substrate, driven electrostatically and sensed capacitively with differential electrodes. Provide CMOS-compatible timing references, filters, and frequency-selective sensors on chip.

Explore the Q factor, damping, and energy loss in MEMS resonators, explaining high and low Q behavior, sharp frequency selectivity, and damping mechanisms like squeeze-film, viscous, anchor, and internal losses.

Analyze how frequency stability preserves resonant frequency amid noise, and how drift degrades timing accuracy in MEMS resonators used as reference clocks.

Explore the operating principles of inertial MEMS accelerometers, derive their governing equations, and show how the suspended proof mass displacement causes capacitance changes that enable the static sensitivity relation.

Explore mechanical design trade-offs in MEMS accelerometers, linking mass, stiffness, natural frequency, bandwidth, and sensitivity to performance, noise, and survivability.

Explore how microelectromechanical systems gyroscopes use the Coriolis effect to sense angular rotation with capacitive sensing and a two-degree-of-freedom mass, highlighting resonance, q factor, and design trade-offs.

Analyze how bias errors from stiffness asymmetry and residual stress influence MEMS sensors, and how temperature and thermal mechanical noise affect stiffness, resonance, and sensitivity drift, guiding calibration.

design the springs for the MAPS accelerometer using the given mass, natural frequency, and folded-beam geometry, then compute the device capacitance from sixty comb pairs.

Explore thermal MEMS devices and the heat equation, including heat generation via joule heating, heat storage, and conduction, with a focus on steady-state analysis for microheaters and thermal sensors.

Apply dual heating as a design tool in MEMS devices by using Joule heating equations to predict temperature rise from electrical power, considering resistance, material properties, and thermal resistance.

Balance coefficient of thermal expansion, Young's modulus, and temperature change to manage thermo-mechanical stress, guiding material selection from tables for MEMS devices, including polysilicon and glassy carbon.

Examine common microelectromechanical systems failure modes and design pitfalls, including buckling under compressive thermal stress and fatigue from thermal cycles, guided by radius of gyration, boundary conditions, and material selection.

Finish the MEMS II course by mastering accelerometer design, springs, and capacitance. Explore the governing equations for mechanical, electrical, and thermo phenomena and preview MEMS manufacturing in the next course.