Failure of semiclassical models to describe resistivity of nanometric, polycrystalline tungsten films

Abstract

Size effects and charge transport in metals: Quantum theory of the resistivity of nanometric metallic structures arising from electron scattering by grain boundaries and by rough surfaces Applied Physics Reviews 4, 011102 (2017);

Surface roughness dependence of the electrical resistivity of W(001) layers

“…III, the comparison of in situ and ex situ resistivity measurements indicate no resistivity change during W surface oxidation. Therefore, both the W(001)-vacuum interface and the W(001)-WO 3 surface exhibit completely diffuse scattering, which is consistent with previous reports on W. 12,62 We attribute the diffuse scattering before air exposure to atomic-level surface defects, including adatoms, vacancies, and clusters, which cause a lateral perturbation of the flat surface potential drop, resulting in a destructive interference of the electron plane waves after reflection. 17,18 An additional independent argument for p ¼ 0 is based on the fact that data fitting with p ¼ 0 leads to relatively large k values of 33.0 6 0.4 and 37.6 6 0.5 nm, approximately double the isotropic value predicted from first principles.…”

“…In addition, it is a purely additive term, as demonstrated with the temperature dependent resistivity results. The model provides a method to improve the existing FS model to account for the effect from surface roughness and may explain the reported systematic deviation from the FS prediction for small d. [12][13][14] V. CONCLUSIONS Epitaxial W(001) layers were deposited and their resistivity measured as a function of thickness d both in situ and after air exposure at both 295 and 77 K. In situ annealing causes a reduction in q for small thicknesses but no change for d ! 320 nm.…”

“…10,11 Experimental studies that include small wire diameters or thicknesses d 10 nm consistently report resistivity values that are higher than the F-S prediction. [12][13][14] This deviation may be attributed to the increasing importance of the surface roughness at small d. Correspondingly, various studies have investigated how the surface roughness affects the resistivity of Cu thin films using either transport simulations, [15][16][17] or experiments including epitaxial Cu(001) layers with thickness down to 4 nm. [18][19][20] However, when attempting to describe the experimental data using above models that describe the roughness as a geometric variation in thickness, 9,10 the extracted roughness is too large to be physical.…”

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

“…This may explain the reported discrepancy between measured thin film resistivities and the FS model prediction. 30,34,37,38 A well-known extension to the FS model which has the goal to resolve this discrepancy has been proposed by Kuan et al, 27,34 who introduced an empirical parameter S to account for surface roughness effects such that the FS prediction becomes…”

“…The surface roughness of narrow conductors contributes to the resistivity increase associated with electron scattering and may be the cause for the incorrect resistivity prediction by the FS model for narrow conductors. More specifically, the reported measured resistivity of thin films <20 nm is consistently higher than the prediction from the FS model, 30,34,[37][38][39] suggesting that a single parameter p may be insufficient to correctly describe the resistivity vs thickness dependence. As a consequence, multiple models have been developed which explicitly treat surface roughness as a contributor to the resistivity.…”