366.102 Nanoelectromechanical Systems
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2024S, VU, 2.0h, 3.0EC


  • Semester hours: 2.0
  • Credits: 3.0
  • Type: VU Lecture and Exercise
  • Format: Presence

Learning outcomes

After successful completion of the course, students are able to 

  • Compare different fundamental continuum mechanical resonator types,
  • Conduct an eigenfrequency analysis of standard continuum nanomechanical resonators,
  • Understand and apply the dynamic mechanics of damped linear resonators,
  • Analyse the dynamic mechanical behavior of a continuum mechanical resonator in terms of a lumped-element model,
  • Explain the fundamental behavior of damped non-linear and coupled linear resonators,
  • Know different definitions of the quality factor,
  • Compare different loss mechanisms (medium, clamping, and intrinsic),
  • Explain damping dilution,
  • Predict the quality factor of a specific nanomechanical resonator,
  • Understand and discuss responsivity and sensitivity of a nanomechanical resonator,
  • Derive point mass responsivity, and compare strings to beams,
  • Derive distributed mass responsivity,
  • Compare static vs resonant force responsivity,
  • Discuss force gradient and softening effects,
  • Discuss temperature responsivity,
  • Discuss and compare various transduction schemes, such as electrodynamic, electrostatic, thermoelastic, piezoresistive, piezoelectric, and optic,
  • Discuss thermomechanical amplitude noise,
  • Explain electronic noise sources (shot noise, Johnson noise),
  • Derive frequency noise based on thermomechanical amplitude noise,
  • Discuss oscillator circuits such as PLL and closed-loop,
  • Discuss Allan deviation.

Subject of course

Nanoelectromechanical systems (NEMS) have been developed for a bit more than two decades now. NEMS are the continuation of Microelectromechanical Systems (MEMS), which have become omnipresent helpers in smart phones, cars, watches, etc. The two driving forces for NEMS research have been improved sensor technology and fundamental research.

This course introduces the latest models and skills required to design and optimise nano electromechanical resonators, taking a top-down approach that uses macroscopic formulas to model the devices. The course covers the electrical and mechanical aspects of NEMS devices. The introduced mechanical models are also key to the understanding and optimisation of nanomechanical resonators used e.g. in optomechanics.

The course is based on the yet unpublished 2nd edition of the following book:

S. Schmid, L. Villanueva, M. Roukes: 
"Fundamentals of Nanomechanical Resonators"; 
Springer International Publishing, Switzerland, 2023, 2nd Edition;

A PDF of the book is available on TUWEL.

The course  content is:

  • 366.102-01: Damped linear resonators (book chapter 1)
  • 366.102-02: Coupled linear resonators, damped nonlinear resonators, parametric amplification (book chapter 1)
  • 366.102-03: Rayleigh-Ritz method, Euler-Bernoulli beam theory (book chapter 2)
  • 366.102-04: Effective parameters, geometric nonlinearities (book chapter 2)
  • 366.102-05: Medium interaction losses, clamping losses, friction (book chapter 3)
  • 366.102-06: Fundamental losses, dissipation dilution (book chapter 3)
  • 366.102-07: Electrodynamic & electrostatic transduction (book chapter 4)
  • 366.102-08: Piezoresistive, piezoelectric, thermoplastic, & optomechanic transduction (book chapter 4)
  • 366.102-09: Amplitude noise (book chapter 5)
  • 366.102-10: Frequency noise (book chapter 5)
  • 366.102-11: Response to change of mass (book chapter 6)
  • 366.102-12: Response to change of effective spring constant (book chapter 6)

Teaching methods

Lecture including an exercise guided by a tutor.
Time: Wednesdays 13:00 - 16:00 (In the first lecture we will discuss and find a time that suits all students.)
The learned theory will be demonstrated on a real world experiment based on a macroscopic string resonator!

Mode of examination


Additional information

The course starts on 2024-03-13



Course dates

Tue14:00 - 16:0012.03.2024 - 25.06.2024Seminarraum 366 Vorlesung und Übung
Nanoelectromechanical Systems - Single appointments
Tue12.03.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue19.03.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue09.04.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue16.04.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue23.04.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue30.04.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue07.05.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue14.05.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue28.05.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue04.06.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue11.06.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue18.06.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung
Tue25.06.202414:00 - 16:00Seminarraum 366 Vorlesung und Übung

Examination modalities

Hand in of at least 8 home assignments.

Course registration

Begin End Deregistration end
30.01.2024 08:00 07.03.2024 23:59 07.03.2024 23:59


Study CodeObligationSemesterPrecon.Info
066 504 Master programme Embedded Systems Mandatory elective
066 508 Microelectronics and Photonics Mandatory elective
066 646 Computational Science and Engineering Not specified


S. Schmid, L. Villanueva, M. Roukes: 
"Fundamentals of Nanomechanical Resonators"; 
Springer International Publishing, Switzerland, 2016, ISBN: 978-3-319-28689-1;

Previous knowledge

Bachelor in any technical education.