Anisotropic Size Effect in Thin Aluminium Films

Sato, Hideyuki; Yonemitsu, K.

doi:10.1002/pssb.2220730242

Cited by 18 publications

(8 citation statements)

References 15 publications

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“…For example, the value of p(4.2 K) for the thickest <110> specimen suggests that the size effect due to the { 100) surface is significantly larger than that due to the { 110) surface. This is consistent with previous experiments on the anisotropic size effect in thin aluminium films [9]. If such a contribution from the side surface is negligible to the total resistivity, the FuchsSondheimer theory with a suitable value of pblb as described above will be plausible to estimate the bulk residual resistivity, p,, at 4.2 K for the specimens studied.…”

Section: Thickness Dependence Of P(42 K)supporting

confidence: 90%

Anisotropy of Electrical Resistivity in High-Purity Aluminium Single Crystals

et al. 1995

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Section: Thickness Dependence Of P(42 K)supporting

confidence: 90%

Anisotropy of Electrical Resistivity in High-Purity Aluminium Single Crystals

et al. 1995

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“…Experimentally, an anisotropic size effect has been measured for Al, using single crystal rods with different major surface orientations and in-plane transport directions. 10,11 However, the results did not match the theoretical expectations, such that it is unclear if the observed effect is related to the anisotropy in the Fermi surface, anisotropic electron scattering at different crystal facets, or impurities that change the carrier relaxation time near zone boundaries. 11 This question regarding the physical origin for the anisotropy in the size effect is the primary motivation for the study presented in this article, which tests the hypothesis that the resistivity anisotropy is primarily due to the anisotropy in the Fermi surface.…”

Section: Introductionmentioning

confidence: 89%

“…10,11 However, the results did not match the theoretical expectations, such that it is unclear if the observed effect is related to the anisotropy in the Fermi surface, anisotropic electron scattering at different crystal facets, or impurities that change the carrier relaxation time near zone boundaries. 11 This question regarding the physical origin for the anisotropy in the size effect is the primary motivation for the study presented in this article, which tests the hypothesis that the resistivity anisotropy is primarily due to the anisotropy in the Fermi surface. This is done by comparing the experimentally measured resistivity with results from a Boltzmann transport model that uses the electronic structure calculated from first-principles and therefore correctly accounts for the anisotropy in the Fermi surface and velocity.…”

Section: Introductionmentioning

confidence: 89%

“…In contrast, first-principles methods that quantitatively predict the electron scattering specularity at metal-barrier interfaces are still limited, 44 and experimentally, it has been found that electron scattering at heterogeneous interfaces between wires and metallic barrier layers is mostly diffuse. 4,11,12,81 We envision that the proposed textured nanowires that will take the advantage of the resistivity anisotropy can be achieved by engineering interface and strain energy, 82,83 local epitaxy to an under layer, 68,84 alloying, 85,86 and appropriate choice of processing parameters and method, 87 as previously demonstrated for a tungsten nanowire formed by subtractive patterning of an epitaxial W(011) film. 30 (2) The second result of this study affecting the search for a metal to replace Cu for nanoscale wires is discussed in Sec.…”

Section: Implications For Nanoscale Interconnectsmentioning

confidence: 98%

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The anisotropic size effect of the electrical resistivity of metal thin films: Tungsten

Zheng

Gall

2017

Journal of Applied Physics

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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 Ã ð011Þ ¼ 18.8 6 0.3 nm vs k Ã 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 Ã ð011Þ /k Ã 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.

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“…The essential additional ingredient is significant Fermi surface (FS) anisotropy. Early theoretical consideration of ellipsoidal Fermi surfaces 8 – 11 led to predictions of transport anisotropies, but experiments in aluminium 12 , 13 did not resolve such effects. Recent results on epitaxial tungsten thin films have detected a growth-direction dependence of the resistance when the films are thin enough to be in the ballistic limit in the direction perpendicular to the substrate 14 .…”

Section: Mainmentioning

confidence: 99%

Directional ballistic transport in the two-dimensional metal PdCoO2

et al. 2022

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In an idealized infinite crystal, the material properties are constrained by the symmetries of the unit cell. The point-group symmetry is broken by the sample shape of any finite crystal, but this is commonly unobservable in macroscopic metals. To sense the shape-induced symmetry lowering in such metals, long-lived bulk states originating from an anisotropic Fermi surface are needed. Here we show how a strongly facetted Fermi surface and the long quasiparticle mean free path present in microstructures of PdCoO2 yield an in-plane resistivity anisotropy that is forbidden by symmetry on an infinite hexagonal lattice. We fabricate bar-shaped transport devices narrower than the mean free path from single crystals using focused ion beam milling, such that the ballistic charge carriers at low temperatures frequently collide with both of the side walls that define the channel. Two symmetry-forbidden transport signatures appear: the in-plane resistivity anisotropy exceeds a factor of 2, and a transverse voltage appears in zero magnetic field. Using ballistic Monte Carlo simulations and a numerical solution of the Boltzmann equation, we identify the orientation of the narrow channel as the source of symmetry breaking.

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Anisotropic Size Effect in Thin Aluminium Films

Cited by 18 publications

References 15 publications

Anisotropy of Electrical Resistivity in High-Purity Aluminium Single Crystals

Anisotropy of Electrical Resistivity in High-Purity Aluminium Single Crystals

The anisotropic size effect of the electrical resistivity of metal thin films: Tungsten

Directional ballistic transport in the two-dimensional metal PdCoO2

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