Electron transport properties of sub-3-nm diameter copper nanowires

Abstract

Type of publicationArticle (peer-reviewed) Density functional theory and density functional tight binding are applied to model electron transport in copper nanowires of approximately 1-and 3-nm diameters with varying crystal orientation and surface termination. The copper nanowires studied are found to be metallic irrespective of diameter, crystal orientation, and/or surface termination. Electron transmission is highly dependent on crystal orientation and surface termination. Nanowires oriented along the [110] crystallographic axis consistently exhibit the highest electron transmission while surface oxidized nanowires show significantly reduced electron transmission compared to unterminated nanowires. Transmission per unit area is calculated in each case; for a given crystal orientation we find that this value decreases with diameter for unterminated nanowires but is largely unaffected by diameter in surface oxidized nanowires for the size regime considered. Transmission pathway plots show that transmission is larger at the surface of unterminated nanowires than inside the nanowire and that transmission at the nanowire surface is significantly reduced by surface oxidation. Finally, we present a simple model which explains the transport per unit area dependence on diameter based on transmission pathways results.

The electrical resistivity of rough thin films: A model based on electron reflection at discrete step edges

“…This is in direct contrast to the conventional Fuchs-Sondheimer (FS) model, 1,20 which accounts for both effects using a single phenomenological specularity parameter p, as shown in Eq. (15). In order to directly compare the FS model with our new prediction, we express the conventional specularity parameter as a sum p ¼ p s þ Dp, where p s accounts for electron scattering at a flat surface and Dp accounts for the surface roughness.…”

“…We attribute this deviation to the uncertainty in the determination of q ff , which requires values for the bulk resistivity and the bulk electron mean free path as shown in Eq. (15). In particular, a small error in the low-temperature bulk resistivity due to residual impurities leads to a systematic error in q ff that could explain the 24% difference in the slope.…”

“…The effect of surfaces on electron transport in thin films has attracted great interest over many decades, for both its technological importance and the underlying physics of mesoscopic systems. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The Fuchs-Sondheimer (FS) model, 1 first proposed in 1938 and extended by various researchers, [20][21][22][23][24][25][26][27][28] is still the best known and most widely used analytical approach to describe the resistivity due to electron surface scattering. It is a classical model based on the Boltzmann transport equation, incorporating surface scattering as a boundary condition, and employing a phenomenological scattering specularity parameter p which represents the probability for specular (rather than diffuse) electron reflection from a surface.…”

On the extraction of resistivity and area of nanoscale interconnect lines by temperature-dependent resistance measurements

“…Currently, there is no well-established tractable model for the temperature dependence of the resistivity in nanowires. Semiclassical approaches [38] still require further quantitative verification while ab initio methods have been successful to describe quantum effects in ultrasmall nanowires but are limited to low temperatures or treat finite temperatures via a heuristic mean free path [39][40][41][42]. The resistivity of thin films has typically been modeled by semiclassical models, such as the one originally derived by Mayadas and Shatzkes [9] based on the original work of Fuchs and Sondheimer [5,6] as well as quantum models for surface scattering [43][44][45].…”

Lower limits of line resistance in nanocrystalline back end of line Cu interconnects

“…The mismatch in line resistance between nanowire orientations comes from the anisotropy in the ballistic conductance between orientations that has been discussed in previous publications 12,22 . The conductance anisotropy under confinement for a prototypical metal such as Cu that has an approximately spherical bulk Fermi surface can in turn be explained by reference to the planar averaged electrostatic potential in the nanowires along the direction of confinement.…”