Resistivity of thin gold films on mica induced by electron-surface scattering from a self-affine fractal surface

Abstract

We present a rigorous comparison between resistivity data and theoretical predictions involving the theory of Palasantzas [G. Palasantzas and J. Barnas, Phys. Rev. B 56, 7726 (1997)], and the modified Sheng, Xing, and Wang-fractal theory [R. C. Munoz et al., Phys. Rev. B 66, 205401 (2002)], regarding the resistivity arising from electron scattering by a self-affine fractal surface on gold films using no adjustable parameters. We find that both theories lead to an approximate description of the temperature dependence of the resistivity data. However, the description of charge transport based upon fractal scaling seems oversimplified, and the predicted increase in resistivity arising from electron-surface scattering seems at variance with other experimental results. If the samples are made up of grains such that the mean grain diameter D > ℓ0(300), the electronic mean free path in the bulk at 300 K, then the predicted increase in resistivity at 4 K is of the order of a few percent. This contradicts published measurements of magnetomorphic effects arising from size effects where electron-surface scattering is the dominant electron scattering mechanism at 4 K. On the contrary, if the samples are made out of grains such that D < ℓ0(300), then the dominant electron scattering mechanism controlling the resistivity is not electron-surface scattering but rather electron-grain boundary scattering, and the latter electron scattering mechanism is not included in either theory.

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

“…The effect of surfaces on electron transport in thin films has attracted great interest over many decades, for both its technological importance and the underlying physics of mesoscopic systems. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The Fuchs-Sondheimer (FS) model, 1 first proposed in 1938 and extended by various researchers, [20][21][22][23][24][25][26][27][28] is still the best known and most widely used analytical approach to describe the resistivity due to electron surface scattering. It is a classical model based on the Boltzmann transport equation, incorporating surface scattering as a boundary condition, and employing a phenomenological scattering specularity parameter p which represents the probability for specular (rather than diffuse) electron reflection from a surface.…”

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

“…26 Applying quantum models to the measured resistivity and surface roughness of gold films 32 results in considerable deviations between the different models while their analytic solutions also deviate by 7-15% from the measured resistivity. 33 It is common to attempt to describe the surface scattering specularity p in terms of the surface roughness. 4,15,[34][35][36] However, some authors suggest that there is no direct correlation between p and the surface roughness.…”

Quantum size effect and the two types of interference between bulk and boundary scattering in ultrathin films

“…Even for thicker films, away from QSE, it is not always clear what to use as the "bulk" collision time τ b . 7 This leaves us with measuring σ (L).…”

“…Here ρ b is the resistivity in unrestricted bulk and ρ w is the resistivity under the conditions when the bulk mean free path is much larger than the film thickness L (we do not want to dwell here on uncertainty in ascribing the bulk parameters to the films). 7 The real resistivity ρ often differs significantly from the Mathiessen's value ρ M , Eq.…”

“…The presence of grain boundaries is not important when one produces films in which the size of the grains is larger than both the bulk mean free path and the film thickness (see, i.e., Ref. 7).…”