Carbon-nanotube-based nanoelectromechanics

Doctoral thesis, 2007

Carbon nanotubes, a novel material with extraordinary mechanical and electrical properties, are good candidates for designing nanoelectromechanical systems. The typical length scale of these systems is nanometers and an important characteristic is a coupling between electrical and mechanical degrees of freedom. In this thesis I present theoretical investigations of two different systems, where the mechanically active component is a carbon nanotube. The first is a nanometer sized version of an electromechanical relay. Electrical control of the mechanical degree of freedom changes the electrical properties of the system. The dynamics of the device is analyzed and phononic excitations in the drain contact are shown to make switching times of a few nanoseconds possible. The influence of surface forces is investigated. They are of the same order of magnitude as the elastic and electrical forces, and play an important role for the device characteristics. In some cases the forces may induce stiction, \emph{i.e.} the surface forces overcome the elastic forces, making the tube stick to the surface of the drain electrode. To circumvent this problem a new non-contact design is proposed. The high frequency response of the relay is investigated and clear signatures of a tunable non-linear resonance are observed. The response observed can be related to the well-known Duffing oscillator. The second system studied in this thesis is a suspended carbon nanotube which is probed using a scanning tunneling microscope. If dissipation is sufficiently weak, the position of the nanotube is unstable and a new steady state is reached, which is characterized by finite amplitude periodic vibrations. This instability is analogous to the so called shuttle instability, and the suspended carbon nanotube is a promising setup for detecting such an instability on the nanometer length scale. The importance of higher order mechanical modes is investigated and is shown to be minor if the electromechanical coupling is weak. In the steady state, a single mode is excited leading to finite amplitude vibrations, although several modes are, in principle, unstable. In the strong coupling limit, other modes are important and modes are not independent. Optimal conditions for the instability to occur are found when tunneling rates are symmetric. This is important for designing an experiment to observe the effect.