The mechanics in two nanosized systems Size effect and threshold field

Sammanfattning: This thesis investigates the mechanics in two nanosized system. Paper I investigates a size effect in a cantilever nanowire affecting its resonance frequency. Paper II reveals a threshold field for the formation of a mound by the diffusion of surface atoms on a substrate under a STM-tip.Paper I: Using a one dimensional jellium model and standard beam theory we calculate the spring constant of a vibrating nanowire cantilever. By using the asymptotic energy eigenvalues of the standing electron waves over the nanometer sized cross section area, the change in the grand canonical potential is calculated and hence the force and the spring constant. As the wire bends, more electron states fits in its cross section. This has an impact on the spring ”constant” which oscillates slightly with the bending of the wire. In this way we obtain an amplitude dependent resonance frequency of the oscillations that should be detectable.Paper II: By applying a voltage pulse to a scanning tunneling microscope tip, the surface under the tip will be modified. In this paper we have taken a closer look at the model of electric field induced surface diffusion of adatoms including the van der Waals force as a contribution in formations of a mound on a surface. The dipole moment of an adatom is the sum of the surface induced dipole moment (which is constant) and the dipole moment due to electric field polarisation which depends on the strength and polarity of the electric field. The electric field is analytically modelled by a point charge over an infinite conducting flat surface. Based on this we calculate the force that cause adatoms to migrate. The calculated force is small considering the voltage used, typical 1 pN, but due to thermal vibration adatoms are hopping about the surface and even a small net force can be significant in the drift of adatoms. In this way we obtain a novel formula for a polarity dependent thresholdvoltage for mound formation on the surface for positive tip. Knowing the voltage of the pulse, we are then able to calculate the radius of the formed mound. A threshold electric field for mound formation of about 2 V/nm is calculated. In addition, we found that van der Waals force is of importance for shorter distances and its contribution to the radial force on the adatoms has to be considered for distances smaller than 1.5 nm for commonly used voltages.