The learning objectives of this course are that the students will be able to:

• Calculate the eigenmodes and their respective eigenfrequencies of the most common continuum mechanical structures used as nanomechanical resonators;
• Analyse a continuum mechanical resonator as equivalent lumped element model;
• Estimate the expected quality factor of a particular nanomechanical resonator;
• Calculate the mass, force and temperature responsivity of a particular nanomechanical resonator and the resulting mass, force and temperature sensitivities;
• Evaluate the appropriate combination of mechanical structure and transduction mechanisms for a particular application;
• Understand amplitude and frequency noise

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  content is:

• 1-D bending (beams vs strings) and bulk vibrations
• 2-D bending and torsion + Rayleigh's method
• Damped linear resonator +  Effective parameters
• Coupled and nonlinear resonators
• Medium and clamping loss
• Intrinsic loss
• Damping dilution
• Mass responsivity
• Force and temperature responsivity
• Transduction (electrodynamic, electrostatic)
• Transduction (piezoresistive, piezoelectric)
• Transduction (thermoelastic, optic) + optomechanics
• Amplitude noise + amplitude calibration
• Frequency noise + PLL, closed loop, Allan Deviation

The exercises are integrated in the weekly 2 hours.

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