Contribution of the Morphological Grain Sizes to the Electrical Resistivity of Platinum and Gold Thin Films

Abstract

We have measured the morphological grain sizes of nanostructured platinum and gold thin films. In previous works their electrical resistivities have been measured and a theoretical approach was proposed to explain the resistivity experimental data. It will be shown that within the framework of our theoretical approach, the morphological grain sizes play an essential role in the electrical resistivity of these metallic thin films.

Surface-Induced Electrical Resistivity of Conducting Thin Films

“…(4), the determination of σ s (d) depends on measurements of the surface roughness ∆(d) and morphological grain sizes D(d). 12,16 The comparison between our predictions and the complete experimental data is persented in our papers. [10][11][12]17 A good agreement was found between experiment and theory.…”

“…[10][11][12] As can be seen from Eq. (4), the determination of σ s (d) depends on measurements of the surface roughness ∆(d) and morphological grain sizes D(d).…”

“…This function was represented by the Fourier series, 13,14 h(ρ) = n h n cos(2πρ/λ n ), where h n and λ n are the amplitudes and wavelengths, respectively, of the surface undulations created by the granular structure of the surface. [10][11][12][13][14][15][16] In this picture, 13 the wavelengths λ are given by λ ≈ D, where D is the morphological grain size. 11,12,16 So, as shown in preceding papers, 10,11 the form factor g(d) is given by:…”

“…Our induced-surface conductivity model was applied [10][11][12] to study the resistivities of Pt and Au thin films. Since for metallic films N 1, Eq.…”

“…In real films, surfaces are rough. If only one of the surfaces is rough, for example that near z = d/2, this surface z(x, y) will be written as z(x, y) = d/2 + h(x, y), with h(x, y) d. These height fluctuations h(x, y) are responsible for a perturbative potential U (x, y) that is given by [1][2][3][4][5][10][11][12][13] …”