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    Size effects on the resistivity of metallic thin films: A combined analysis of temperature and thickness dependences

    Victor Haspot1,2,3, Yunlin Zheng1, Denis Guimard3, Hervé Montigaud2, and Rémi Lazzari1,*

    • *Contact author: remi.lazzari@insp.jussieu.fr

    Phys. Rev. Materials 10, 055001 – Published 7 May, 2026

    DOI: https://doi.org/10.1103/2d7r-cdxz

    Abstract

    The question of the size effects in metal film resistivity is revisited through a systematic analysis of its temperature dependence ρf(T) (4–300 K) for increasing layer thickness (4.1–216 nm). Ag-based model thermal-control coatings involving symmetric ZnO/Ag/ZnO interfaces are used as test beds for the Mayadas-Shatzkes model [Phys. Rev. B 1, 1382 (1970)]. All contributions to electron scattering, i.e., intragrain, grain boundaries (GBs) and interfaces, are considered while taking into account the actual film microstructure as determined from x-ray scattering. Encapsulated Ag films are studied as-deposited but also after a recrystallization annealing. The electron reflection coefficient R at GBs and the interface scattering parameter p are deduced from ρf(T) fits. They are found to vary with film thickness and microstructure. The grain disorientation seems to drive R, which remains below ∼0.1 as expected for a perturbation parameter in the M-S model. In parallel to grain coarsening, the observed increase in R upon annealing is assigned to the most disoriented and healing-resilient GBs. The metal interfaces are found strongly scattering for electrons in as-deposited samples (p≃0) but become nearly perfect reflectors after annealing (p≃1). But no cleat-cut correlation of p with interface roughness can be evidenced. A tentative explanation based on the electronic structure of the interfaces is proposed. Inconsistent results are obtained with the widespread procedure of thickness dependent resistivity fits, which implicitly assumes constant R and p values. Beside an increased role of intragrain contribution for the thicker films having the larger grains, it is shown that no single scattering mechanism dominates the film resistivity as expected from the implicit breakdown of the Matthiessen rule as derived from the M-S equation.

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