
Aim is to advance the knowledge gained in MEMS Design in both the mechanical and electrical domains. Typically this includes deepening knowledge in electronic interfacing, impedance analysis, noise (electrical and thermomechanical), axial stresses and stress gradients in beams, advanced transducer science, finite element methods (using COMSOL Multiphysics); all with the aim to design a MEMS based device / system on a more detailed level and closer to specifications. See detailed learning aims below.
Resonators and impedance
 Students can write the differential equation for the damped harmonic oscillator and understand the solutions, both for free and forced oscillations.
 Students understand the concept of quality factor, the relation with damping and the regimes overdamped, critically damped and underdamped.
 Students can compose the two equations relating the F, U, x and q for the gap closing actuator including the effect of mass and damping.
 Students understand the assumptions made to finally come to the impedance / admittance equation.
 Students are able to find the expressions for the effective component values in the equivalent electrical circuit representation of the damped electromechanical resonator.
 Students understand the two LC resonant modes/frequencies (series and parallel) in the basic equivalent circuit representation.
Mechanics
 Students can recognize the expression for the stiffness of circular elastic plates loaded by a uniform pressure difference, understand which parameters are relevant and can indicate the limit of the linear elastic regime.
 Students understand and can estimate when the non‐linearity in the transverse stiffness of clamped‐clamped beam becomes relevant.
 Students understand and can estimate the extra transverse stiffness of a beam loaded by a constant stretching force.
 Students are able to derive the internal bending moment generated by a stressed layer for given position of the neutral plane.
 Students can calculate the position of the neutral plane for a composite bimorph beam.
 Students understand the concept of composite bending stiffness.
 Students can calculate the curvature of the bimorph beam for given composite bending stiffness.
Transducers, energy minimization
 Students understand the meaning of generalized forces or “efforts” as well as generalized displacements or “quantities” in the context of lumped multi‐domain system theory.
 Students are able to construct the correct system potential energy function, and are able to perform equilibrium and stability analysis typically for a two port transducer based on minimization of this energy function.
Interfacing and electronics
 Students understand both capacitive and resistive readout circuitry and how to apply these circuits to different types of MEMS devices.
 Students understand how to reduce non‐ideal effects like offset, drift and noise using electronics.
 Students are able to use laboratory equipment to assemble, troubleshoot and characterize MEMS devices on a basic level.
Noise and damping
 Students understand the relation between the temperature of dissipative components (damping, resistance) and thermal noise in both electrical and mechanical domain.
 Students can distinguish the dominant noise source in a MEMS device and estimate the order of magnitude.
Finite element modeling
 Students are able to use the interface of a modern software package for finite element modelling and simulations.
 Students are able to design 1D, 2D, pseudo‐3D (e.g. axisymmetric) and 3D structures.
 Students are able to apply physical relations and boundary conditions to the structures to obtain a valid simulation in the electrostatic domain, mechanical domain and combined electrostatic‐mechanical domain.
 Students are able to perform postprocessing of the simulation results to obtain quantitative answers to engineering and scientific questions for different types of MEMS devices.
Students are able to critically validate the simulation results with analytical estimations.



Advanced MEMS Design is a 5EC addon on MEMS Design (191211300). In 2A a start will be made in introducing theory and operation of COMSOL Multiphysics (FEM simulation software) and instruction will be based on solving some predefined problems (1.5 EC). In 2B lectures on advanced topics such as axial stresses and stress gradients in beams, noise in (interfaced) MEMS, electronic interfacing and electromechanical impedance analysis will be provided and problems will be solved in connected tutorials (2 EC). Comsol is applied to optimize the design made in M2B as part of the basic MEMS Design course (1.5 EC).
Study load in 2A: 1.5 EC
Study load in 2B: 3.5 EC
In this way, study load of MEMS Design + Advanced MEMS Design is approximately 5 EC in 2A and 5 EC in 2B.
Assessment
Written exam, weight 60%
Comsol report, weight 40%



 Assumed previous knowledgeMandatory: A finished Bachelor's programme in one of the Technical Sciences. The course is optimized for students with a background in EE, however a background in ME, APh, AT, or similar should be fine as well. 
Master Electrical Engineering 
  Required materialsHandouts 
 Recommended materialsBookM. Elwenspoek, R. Wiegerink, Mechanical Microsensors, Springer 2001, ISBN 9783642087066. 

 Instructional modesLecture
 Project supervised
 Self study without assistance
 Tutorial

 TestsWritten exam, Comsol report


 