There's Plenty of Room in Higher Dimensions - Nonlinear Dynamics of Nanoelectromechanical Systems

Doctoral thesis, 2017

Mathematical modeling can be used to understand different dynamical phenomena in nature. The dynamical response of a system can be drastically altered even for tiny changes of the system parameters due to so called nonlinearities. The general framework of nonlinear dynamics is widely applicable for instance in predator-prey dynamics in biology, reaction of substances in chemistry, collective behavior in social media and interacting neurons in the brain.

This thesis uses analytical methods from nonlinear dynamics in order to understand the response of nanoelectromechanical systems (NEMS). These systems are typically made of tiny suspended beams or membranes which are about one nanometer thick, a 100'000 times smaller than a human hair. NEMS can be utilized for instance for sensor applications and nanoelectronics.

In NEMS, researchers take advantage of the interaction between mechanical motion of the suspended structure and the flow of electrons. The suspended structure can be forced to vibrate by pulling electrons in and out of the structure by means of electric fields. These vibrations are similar to the vibrations of a guitar string or a drum. There are several ways to actuate mechanical oscillations. One option is direct resonance which is what we utilize when we push a child on a swing.

In the research presented in this thesis, we investigated how NEMS can be mechanically actuated by nonresonant techniques. In particular, actuation can be achieved if the electric field is so fast that there is a pronounced delay in the electron response. We also studied how heat can be converted to mechanical energy by utilizing the interaction between electrons, and how mechanical actuation can be used to generate super­conducting currents.

Furthermore, exotic nonlinear response can be observed in NEMS if they are properly tuned. Different kinds of vibrations (modes) will then be strongly coupled and combinations of modes can be selectively addressed thanks to the extraordinary parameters of the systems. Especially when two or more modes are coupled, the complexity of the dynamics drastically increases because of the increased dimensionality of the corresponding mathematical equations. One aim of nonlinear nanomechanics is to understand and utilize this complex dynamical response.

An important conclusion of this thesis is that interesting dynamical regions might not be observed by standard experiments. However, nonlinear modeling can provide maps which reveal ''hidden'' regions. Such maps can guide researchers to experimentally find the hidden regions.

The famous physicist Richard Feynman stated that ''There's plenty of room at the bottom'' referring to the forthcoming field of nanoscience. From the advances in coupled nanoresonators, it can be concluded that there's also plenty of room in higher dimensions.