# Electron transport properties of thin copper films. I.

01 Jun 1975-Journal of Applied Physics (American Institute of Physics)-Vol. 46, Iss: 6, pp 2574-2582

TL;DR: In this paper, a critical analysis of the observed size effects in all cases depart markedly from the predictions of the Fuchs-Sondheimer theory (and also that of the Mayadas-Shatzkes theory which takes into account the grain boundary surface scattering).

Abstract: The thickness dependence at 300 and 80 K of the electrical resistivity and its temperature coefficient, Hall coefficient, mobility, and thermoelectric power of as‐deposited and annealed thin (< 1000 A) evaporated polycrystalline copper films and films deposited at elevated temperatures have been studied. All transport parameters in carefully prepared and well‐characterized films exhibit monotonically increasing size effects with decreasing film thickness. Both annealing and deposition at elevated temperatures cause considerable reduction of the ’’apparent’’ size effects in all the transport parameters of the room‐temperature deposited films. A critical analysis of the observed size effects shows that the data in all cases depart markedly from the predictions of the Fuchs‐Sondheimer theory (and also that of the Mayadas‐Shatzkes theory which takes into account the grain boundary surface scattering). The departure from theory is different for each transport parameter. The annealing studies show that the enhanced size effects are due to the presence of a large concentration of structural defects in the films. The observed behavior may be understood by assuming the large concentration of point and/or line defects to decrease with film thickness and with annealing as well as deposition of films at elevated temperatures. The thermopower data suggest strongly that the large concentration of defects causes distortion of the Fermi surface and thereby a strong energy dependence of the mfp or relaxation time at the Fermi surface.

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TL;DR: In this article, Namba's model that uses the measured surface roughness provides the best description of the resistivity-thickness behavior in sub-40-nm thick Cu films.

213 citations

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TL;DR: In this article, an expression for the temperature coefficients of resistance of thin metal films is derived, wherein size effects, thermal strain and difference in the thermal expansion coefficients between film and its substrate are taken into account.

Abstract: An expression for the temperature coefficients of resistance of thin metal films is derived wherein size effects, thermal strain and difference in the thermal expansion coefficients between film and its substrate are taken into account.

59 citations

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TL;DR: In this paper, the effects of the film thickness, average grain size, impurities, and morphological defect on the resistivity increase of Cu films in addition to the surface scattering of the Fuch-Sondheimer model and the grain boundary scattering in the Mayadas-Shatzkes model were evaluated.

Abstract: Cu films deposited by ion beam deposition with or without a negative substrate bias voltage were found to have different states of dependence of electrical resistivity on film thickness. We have attempted to evaluate the effects of the film thickness, average grain size, impurities, and morphological defect on the resistivity increase of Cu films in addition to the surface scattering of the Fuch-Sondheimer model and the grain boundary scattering of the Mayadas-Shatzkes model. When the theoretical model was fit to the experimental data, the Cu films deposited at a substrate bias voltage of −50V showed that the electrical resistivity was in good agreement with the theoretical curve under the condition that the film thickness was 2.3 times larger than the average grain size and when p=0 and R=0.24. For the Cu films deposited without a substrate bias voltage, however, there was a slight deviation between the theoretical curve and the measured resistivity below a 100nm thickness, even at the condition of the f...

59 citations

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01 Jan 2017TL;DR: In this article, a review of the semi-classical approach that leads to the concepts of drift velocity, mobility and conductivity, from which Matthiessen's Rule is derived, is presented.

Abstract: Electrical transport through materials is a large and complex field, and in this chapter we cover only a few aspects that are relevant to practical applications. We start with a review of the semi-classical approach that leads to the concepts of drift velocity, mobility and conductivity, from which Matthiessen’s Rule is derived. A more general approach based on the Boltzmann transport equation is also discussed. We review the conductivity of metals and include a useful collection of experimental data. The conductivity of nonuniform materials such as alloys, polycrystalline materials, composites and thin films is discussed in the context of Nordheim’s rule for alloys, effective medium theories for inhomogeneous materials, and theories of scattering for thin films. We also discuss some interesting aspects of conduction in the presence of a magnetic field (the Hall effect). We present a simplified analysis of charge transport in semiconductors in a high electric field, including a modern avalanche theory (the theory of lucky drift). The properties of low-dimensional systems are briefly reviewed, including the quantum Hall effect.

57 citations

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TL;DR: The thickness dependence of the temperature coefficient of resistivity of polycrystalline metal films is given by approximate Mayadas-Shatzkes expressions using the grain intrinsic mean free path of the conduction electrons as mentioned in this paper.

47 citations

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Royal Society

^{1}TL;DR: The mean free path of electrons in metals has been studied in this paper, where the authors show that electrons follow a straight line along the path of the electron in the metal atom.

Abstract: (2001). The mean free path of electrons in metals. Advances in Physics: Vol. 50, No. 6, pp. 499-537.

2,273 citations

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IBM

^{1}TL;DR: In this paper, the total resistivity of a thin metal film is calculated from a model in which three types of electron scattering mechanisms are simultaneously operative: an isotropic background scattering (due to the combined effects of phonons and point defects), scattering due to a distribution of planar potentials (grain boundaries), and scattering by the external surfaces.

Abstract: In this paper, the total resistivity of a thin metal film is calculated from a model in which three types of electron scattering mechanisms are simultaneously operative: an isotropic background scattering (due to the combined effects of phonons and point defects), scattering due to a distribution of planar potentials (grain boundaries), and scattering due to the external surfaces. The intrinsic or bulk resistivity is obtained by solving a Boltzmann equation in which both grain-boundary and background scattering are accounted for. The total resistivity is obtained by imposing boundary conditions due to the external surfaces (as in the Fuchs theory) on this Boltzmann equation. Interpretation of published data on grain-boundary scattering in bulk materials in terms of the calculated intrinsic resistivity, and of thin-film data in terms of the calculated total resistivity suggests that (i) the grain-boundary reflection coefficient in Al is \ensuremath{\approx} 0.15, while it is somewhat higher in Cu; (ii) the observed thickness dependence of the resistivity in thin films is due to grain-boundary scattering as well as to the Fuchs size effect; and (iii) the common observation that single-crystal films possess lower resistivities than polycrystalline films may be accounted for by grain-boundary effects rather than by differences in the nature of surface scattering.

1,842 citations