Modelling of Molecular-Scale Nanoelectromechanical Systems

Abstract: Nanoelectromechanical systems (NEMS) couple electronic and mechanical degrees of freedom in a nanoscopic structure. The small size introduces many atomistic and quantum mechanical features which on the one hand open up for interesting new features and possibilities but on the other hand make it very difficult to formulate quantitative predictions. In this work a wide range of tools has been applied to determine NEMS characteristics; from the quantum mechanical {it ab initio} method density functional theory (DFT), through the density-functional tight-binding (DFTB) method and molecular mechanics, to the continuum approach used in elasticity theory. The main topic of this thesis concerns the electromechanical shuttle, which in its simplest description comprises a double junction and a mobile central island. In the first part, DFT is used to calculate forces and transition rates for a single atom central island. The parameters are implemented in a macroscopic dynamics module, which computes the motion and electron transport for the system. In the second part, simplifications based on the physical insights from the first part are applied to an atomic as well as a small cluster central island in order to obtain the system IV-characteristics. The systems exhibit almost ubiquitous electronic shuttling, which for certain bias voltage intervals is very stable. The study also shows a strong and non-trivial dependence on the detailed properties of the electronic structure. The work on the shuttle is concluded with a brief microscopic study of C$_{60}$ scattering from a gold surface using time-dependent DFTB. This study probes the non-adiabatic properties of a free molecular shuttle in the strong coupling regime. In the final part of this work, an elastic model for the mechanical properties of a graphene sheet is introduced. The parameters of the model have been determined using molecular mechanics. The computationally much simpler continuum approach is shown to be in good agreement with the atomistic model for the structural degrees of freedom.