The electronic structure of scandium nitride is determined by combining results from optical and electronic transport measurements with first-principles calculations. Hybrid functional (HSE06) calculations indicate a 0.92 eV indirect Γ-to-X band gap and direct transition energies of 2.02 and 3.75 eV at Γ-and X-points, respectively, while G o W o and GW o methods suggest 0.44-0.74 eV higher gap values. Epitaxial ScN(001) layers deposited on MgO(001) substrates by reactive sputtering exhibit degenerate n-type semiconductor properties with a temperature-independent electron density that is varied from N = 1.12-12.8×10 20 cm -3 using F impurity doping. The direct optical gap increases linearly with N from 2.18 to 2.70 eV, due to a Burstein-Moss effect. This strong dependence on N is likely the cause for the large range (2.03-3.2 eV) of previously reported gap values. However, here extrapolation to N = 0 yields 2.07±0.05 eV for the direct X-point transition of intrinsic ScN. A reflection peak at 3.80±0.02 eV is independent of N and in perfect agreement with the HSE06-predicted peak at 3.79 eV, associated with a high joint-density of states near the Γ-point. The electron mobility at 4 K is 100±30 cm 2 /Vs and decreases with temperature due to scattering at polar optical phonons with characteristic frequencies that decrease from 620 to 440±30 cm -1 with increasing N, due to free carrier screening. The transport and density-of-states electron effective mass, determined from measured intra and inter band transitions, respectively, are 0.40±0.02 m o and 0.33±0.02 m o , in good agreement with the firstprinciples predictions of m tr = 0.33±0.05 m o and m DOS = 0.43±0.05 m o . The ScN refractive index increases with increasing hν = 1.0-2.0 eV from 2.6-3.1 based on optical measurements and from 2.8-3.2 based on the calculated dielectric function. An overall comparison of experiment and simulation indicates (i) an overestimation of band gaps by GW methods but (ii) excellent agreement with a deviation of ≤0.05 eV for the hybrid functional and (iii) a value for the fundamental indirect gap of ScN of 0.92±0.05 eV.

The resistivity of 9.3-nm-thick epitaxial and polycrystalline Cu is reduced by 11%-13% when coated with 0.75 nm Ni. Sequential in situ and ex situ transport measurements show that this is due to electron surface scattering which exhibits a specularity p ¼ 0.7 for the Cu-vacuum interface that transitions to completely diffuse (p ¼ 0) when exposed to air. In contrast, Ni-coated surfaces exhibit partial specularity with p ¼ 0.3 in vacuum and p ¼ 0.15 in air, as Cu 2 O formation is suppressed, leading to a smaller surface potential perturbation and a lower density of localized surface states, yielding less diffuse electron scattering. V

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 resistivity of nanoscale metallic conductors is orientation dependent, even if the bulk resistivity is isotropic and electron scattering cross-sections are independent of momentum, surface orientation, and transport direction. This is demonstrated using a combination of electron transport measurements on epitaxial tungsten layers in combination with transport simulations based on the ab initio predicted electronic structure, showing that the primary reason for the anisotropic size effect is the non-spherical Fermi surface. Electron surface scattering causes the resistivity of epitaxial W(110) and W(001) layers measured at 295 and 77 K to increase as the layer thickness decreases from 320 to 4.5 nm. However, the resistivity is larger for W(001) than W(110) which, if describing the data with the classical Fuchs-Sondheimer model, yields an effective electron mean free path k* for bulk electron-phonon scattering that is nearly a factor of two smaller for the 110 vs the 001-oriented layers, with k à ð011Þ ¼ 18.8 6 0.3 nm vs k à ð001Þ ¼ 33 6 0.4 nm at 295 K. Boltzmann transport simulations are done by integration over real and reciprocal space of the thin film and the Brillouin zone, respectively, describing electron-phonon scattering by momentum-independent constant relaxation-time or mean-free-path approximations, and electron-surface scattering as a boundary condition which is independent of electron momentum and surface orientation. The simulations quantify the resistivity increase at the reduced film thickness and predict a smaller resistivity for W(110) than W(001) layers with a simulated ratio k à ð011Þ /k à ð001Þ ¼ 0.59 6 0.01, in excellent agreement with 0.57 6 0.01 from the experiment. This agreement suggests that the resistivity anisotropy in thin films of metals with isotropic bulk electron transport is fully explained by the non-spherical Fermi surface and velocity distribution, while electron scattering at phonons and surfaces can be kept isotropic and independent of the surface orientation. The simulations correctly predict the anisotropy of the resistivity size effect, but underestimate its absolute magnitude. Quantitative analyses suggest that this may be due to (i) a twofold increase in the electron-phonon scattering crosssection as the layer thickness is reduced to 5 nm or (ii) a variable wave-vector dependent relaxation time for electron-phonon scattering. Published by AIP Publishing.