The effect of the surface roughness on the electrical resistivity of metallic thin films is described by electron reflection at discrete step edges. A Landauer formalism for incoherent scattering leads to a parameter-free expression for the resistivity contribution from surface mound-valley undulations that is additive to the resistivity associated with bulk and surface scattering. In the classical limit where the electron reflection probability matches the ratio of the step height h divided by the film thickness d, the additional resistivity Dq ¼ ffiffiffiffiffiffiffi ffi 3=2 p /(g 0 d) Â x/n, where g 0 is the specific ballistic conductance and x/n is the ratio of the root-mean-square surface roughness divided by the lateral correlation length of the surface morphology. First-principles non-equilibrium Green's function density functional theory transport simulations on 1-nm-thick Cu(001) layers validate the model, confirming that the electron reflection probability is equal to h/d and that the incoherent formalism matches the coherent scattering simulations for surface step separations !2 nm. Experimental confirmation is done using 4.5-52 nm thick epitaxial W(001) layers, where x ¼ 0.25-1.07 nm and n ¼ 10.5-21.9 nm are varied by in situ annealing. Electron transport measurements at 77 and 295 K indicate a linear relationship between Dq and x/(nd), confirming the model predictions. The model suggests a stronger resistivity size effect than predictions of existing models by Fuchs [Math. ]. It provides a quantitative explanation for the empirical parameters in these models and may explain the recently reported deviations of experimental resistivity values from these models. Published by AIP Publishing. https://doi.

The effect of electron surface scattering on the thickness-dependent electrical resistivity ρ of thin metal layers is investigated using non-equilibrium Green's function density functional transport simulations. Cu(001) thin films with thickness d = 1-2 nm are used as a model system, employing a random one-monolayer-high surface roughness and frozen phonons to cause surface and bulk scattering, respectively. The zero-temperature resistivity increases from 9.7±1.0 μΩ•cm at d = 1.99 nm to 18.7±2.6 μΩ•cm at d = 0.90 nm, contradicting the asymptotic T = 0 prediction from the classical Fuchs-Sondheimer model. At T = 900 K, ρ = 5.8±0.1 μΩ•cm for bulk Cu and ρ = 13.4±1.1 and 22.5±2.4 μΩ•cm for layers with d = 0.90 and 1.99 nm, respectively, indicating an approximately additive phonon contribution which, however, is smaller than for bulk Cu or atomically smooth layers. The overall data indicates that the resistivity contribution from surface scattering is temperature-independent and proportional to 1/d, suggesting that it can be described using a surface scattering mean free path λ s for 2D transport which is channel-independent and proportional to d. Data fitting indicates λ s = 4×d for the particular simulated Cu(001) surfaces with a one-monolayer-high surface roughness. The 1/d dependence deviates considerably from previous 1/d 2 predictions from quantum models, indicating that the small-roughnessapproximation in these models is not applicable to very thin (< 2 nm) layers, where the surface roughness is a considerable fraction of d.

Electron transport in metal conductors with ~5-30 nm width is dominated by surface scattering. In situ transport measurements as a function of surface chemistry demonstrate that the primary parameter determining the surface scattering specularity is the localized surface density of states at the Fermi level N(E f). In particular, the measured sheet resistance of epitaxial Cu(001) layers with thickness d Cu = 9-25 nm increases when coated with d Ti = 0.1-4.0 monolayers (ML) of Ti, but decreases again during exposure to 37 Pa of O 2. These resistivity changes are a function of d Cu and d Ti and are due to a transition from partially specular electron scattering at the Cu surface to completely diffuse scattering at the Cu-Ti interface, and the recovery of surface specularity as the Ti is oxidized. X-ray reflectivity and photoelectron spectroscopy indicate the formation of a 0.47±0.03 nm thick Cu 2 O surface layer on top of the TiO 2-Cu 2 O during air exposure, while density functional calculations of TiO x cap layers as a function of x = 0-2 and d Ti = 0.25-1.0 ML show a reduction of N(E f) by up to a factor of four. This reduction is proposed to be the key cause for the recovery of surface specularity and results in electron confinement and channeling in the Cu layer upon Ti oxidation. Transport measurements at 293 and 77 K confirm the channeling and demonstrate the potential for highconductivity metal nanowires by quantifying the surface specularity parameter p = 0.67±0.05, 0.00±0.05, and 0.35±0.05 at the Cu-vacuum, Cu-Ti, and Cu-TiO 2 interfaces.

The resistivity q of epitaxial W(001) layers grown on MgO(001) at 900 C increases from 5.63 6 0.05 to 27.6 6 0.6 lX-cm with decreasing thickness d ¼ 390 to 4.5 nm. This increase is due to electron-surface scattering but is less pronounced after in situ annealing at 1050 C, leading to a 7%-13% lower q for d < 20 nm. The q(d) data from in situ and ex situ transport measurements at 295 and 77 K cannot be satisfactorily described using the existing Fuchs-Sondheimer (FS) model for surface scattering, as q for d < 9 nm is larger than the FS prediction and the annealing effects are inconsistent with a change in either the bulk mean free path or the surface scattering specularity. In contrast, introducing an additive resistivity term q mound which accounts for surface roughness resolves both shortcomings. The new term is due to electron reflection at surface mounds and is, therefore, proportional to the ballistic resistance times the average surface roughness slope, divided by the layer thickness. This is confirmed by a measured linear relationship between q mound and r/(Ld), where the root-mean-square roughness r and the lateral correlation length L of the surfaces are directly measured using atomic force microscopy and X-ray reflectivity. Published by AIP Publishing. [http://dx.

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We present an ab initio evaluation of electron scattering mechanisms in Al interconnects from a back-end-of-line (BEOL) perspective. We consider the ballistic conductance as a function of nanowire size, as well as the impact of surface oxidation on electron transport. We also consider several representative twin grain boundaries and calculate the specific resistivity and reflection coefficients for each case. Lastly, we calculate the vertical resistance across the Al/Ta(N)/Al and Cu/Ta(N)/Cu interfaces, which are representative of typical vertical interconnect structures with diffusion barriers. Despite a high ballistic conductance, the calculated specific resistivities at grain boundaries are 70-100% higher in Al than in Cu, and the vertical resistance across Ta(N) diffusion barriers are 60-100% larger for Al than for Cu. These results suggest that in addition to the well-known electromigration limitations in Al interconnects, electron scattering represents a major problem in achieving low interconnect line resistance at fine dimensions.

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