366.102 Nanoelectromechanical Systems
Diese Lehrveranstaltung ist in allen zugeordneten Curricula Teil der STEOP.
Diese Lehrveranstaltung ist in mindestens einem zugeordneten Curriculum Teil der STEOP.

2020S, VU, 2.0h, 3.0EC
Diese Lehrveranstaltung wird nach dem neuen Modus evaluiert. Mehr erfahren



  • Semesterwochenstunden: 2.0
  • ECTS: 3.0
  • Typ: VU Vorlesung mit Übung


Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage zu:

  • 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.

Inhalt der Lehrveranstaltung

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 book:

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

The course  content is:

  • 366.102-1: Euler-Bernoulli beam theory (book chapter 1)
  • 366.102-2: Rayleigh's method applied to strings & effective parameters (book chapter 1)
  • 366.102-3: Lumped-element model resonator (book chapter 1)
  • 366.102-4: Nonlinear & coupled resonators (book chapter 1)
  • 366.102-5: Energy loss to the environment (book chapter 2)
  • 366.102-6: Damping dilution (book chapter 2)
  • 366.102-7: Intrinsic damping (book chapter 2)
  • 366.102-8: Mass responsivity (book chapter 3)
  • 366.102-9: Force responsivity & responsivity of effective spring constant (book chapter 3)
  • 366.102-10: Electrodynamic & electrostatic transduction (book chapter 4)
  • 366.102-11: Piezoresistive, piezoelectric, thermoplastic, & optomechanic transduction (book chapter 4)
  • 366.102-12: Amplitude noise (book chapter 5)
  • 366.102-13: Frequency noise & oscillator circuits (book chapter 5)


1h lecture followed by 1h exercise in class guided by a tutor. NEW THIS YEAR: The learned theory will be demonstrated on a real world experiment based on a macroscopic string resonator!





LVA Termine

Mo.13:15 - 15:0002.03.2020 - 15.06.2020 Vorlesung
Nanoelectromechanical Systems - Einzeltermine
Mo.02.03.202013:15 - 15:00 Vorlesung
Mo.09.03.202013:15 - 15:00 Vorlesung
Mo.16.03.202013:15 - 15:00 Vorlesung
Mo.23.03.202013:15 - 15:00 Vorlesung
Mo.30.03.202013:15 - 15:00 Vorlesung
Mo.20.04.202013:15 - 15:00 Vorlesung
Mo.27.04.202013:15 - 15:00 Vorlesung
Mo.04.05.202013:15 - 15:00 Vorlesung
Mo.11.05.202013:15 - 15:00 Vorlesung
Mo.18.05.202013:15 - 15:00 Vorlesung
Mo.25.05.202013:15 - 15:00 Vorlesung
Mo.08.06.202013:15 - 15:00 Vorlesung
Mo.15.06.202013:15 - 15:00 Vorlesung


Hand in of at least 8 home assignments.


Von Bis Abmeldung bis
07.01.2020 22:00 02.03.2020 12:00 02.03.2020 12:00



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


Bachelor in any technical education.