The surface effect from surface stress and surface elasticity on the elastic behavior of nanowires in static bending is incorporated into Euler-Bernoulli beam theory via the Young-Laplace equation. Explicit solutions are presented to study the dependence of the surface effect on the overall Young's modulus of nanowires for three different boundary conditions: cantilever, simply supported, and fixed-fixed. The solutions indicate that the cantilever nanowires behave as softer materials when deflected while the other structures behave like stiffer materials as the nanowire cross-sectional size decreases for positive surface stresses. These solutions agree with size dependent nanowire overall Young's moduli observed from static bending tests by other researchers. This study also discusses possible reasons for variations of nanowire overall Young's moduli observed.
The influence of surface stress on the resonance frequencies of bending nanowires was studied by incorporating the generalized Young–Laplace equation into Euler–Bernoulli beam theory. Theoretical solutions are presented for three different boundary conditions. The overall Young’s modulus was used to study the surface stress influenced mechanical behavior of bending nanowires and a comparison was made for the overall Young’s modulus calculated from nanowires in resonance and static bending. It was found that the overall Young’s modulus can be simply related to a nondimensional surface effect factor via empirical formulae.
Copper nanowires were patterned with e-beam lithography and fabricated with a copper film deposited by e-beam evaporation. Various electrical properties of these nanowires (including resistivity, temperature coefficient of resistance, and failure current density) were characterized. It was experimentally found that surface and size have apparent effects on the electrical properties. Smaller values for the temperature coefficient of resistance and higher failure current density were found for Cu nanowires with decreasing wire width. The experimental finding of width dependent failure current density also agrees with finding for theoretical heat transfer of the nanowire and substrate system as calculated with the finite element method.
Electromigration in copper (Cu) nanowires deposited by electron beam evaporation has been investigated using both resistance measurement and the in situ scanning electron microscopy technique. During electromigration, voids formed at the cathode end while hillocks (or extrusions) grew close to the anode end. The failure lifetimes were measured for various applied current densities and the mean temperature in the wire was estimated. Electromigration activation energies of 1.06 eV and 0.94 eV were found for the wire widths of 90 nm and 141 nm, respectively. These results suggest that the mass transport of Cu during electromigration mainly occurs along the wire surfaces. Further investigations of the Auger electron spectrum show that both Cu atoms and the surface contaminants of carbon and oxygen migrate from cathode to anode under the electrical stressing.
Fundamental questions as to the nature of electron surface scattering in nanoscale materials remain unanswered. In order to isolate the effects of surface scattering from grain boundary scattering, single crystalline trapezoidal silver (Ag) nanowires were self-assembled on vicinal silicon substrate. The well established kinetic theory to model electron surface scattering effects on the electrical resistivity of nanowires was extended to include trapezoidal geometries. The experimentally measured electrical resistivity for Ag nanowires was found to fit the theoretical resistivity for the case of electrons diffusely scattering from the nanowire surface.
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