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2023S, VU, 2.0h, 3.0EC

## Properties

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The course is based on the yet unpublished 2nd edition of the following book: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

Room: CD0112

The learned theory will be demonstrated on a real world experiment based on a macroscopic string resonator!

## Mode of examination

Oral

The course starts on 2023-03-08

## Course dates

DayTimeDateLocationDescription
Wed13:00 - 17:0008.03.2023 - 28.06.2023Seminarraum 366 Vorlesung und Übung
Wed13:00 - 17:0026.04.2023 ISAS Meetingroom CD0112Vorlesung und Übung
Nanoelectromechanical Systems - Single appointments
DayDateTimeLocationDescription
Wed08.03.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed15.03.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed22.03.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed29.03.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed19.04.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed26.04.202313:00 - 17:00 ISAS Meetingroom CD0112Vorlesung und Übung
Wed03.05.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed10.05.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed17.05.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed24.05.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed31.05.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed07.06.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed14.06.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed21.06.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung
Wed28.06.202313:00 - 17:00Seminarraum 366 Vorlesung und Übung

## Examination modalities

Hand in of at least 8 home assignments.

## Course registration

Begin End Deregistration end
31.01.2023 08:00 09.03.2023 23:59 09.03.2023 23:59

## Curricula

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

## Literature

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.

English