# Hall coefficient of thin polycrystalline metallic films in a three-dimensional scattering model

TL;DR: In this article, a three-dimensional grain boundary model is used to calculate the transport properties of fine-grained films where background and grain boundaries scattering processes occur simultaneously, and analytical expressions are easily derived for the Hall coefficient and conductivity in polycrystalline films subjected to a transverse magnetic field.

Abstract: A three-dimensional grain boundary model can be used to calculate the transport properties of fine-grained films where background and grain boundaries scattering processes occur simultaneously. In the absence of a magnetic field a total relaxation time which is related to the grain size D and to the transmission coefficient t of electrons through grain boundaries is defined. Using the Boltzmann transport equation analytical expressions are easily derived for the Hall coefficient and conductivity in polycrystalline films subjected to a transverse magnetic field. The Hall coefficient is independent of both the grain parameters and the strength of the magnetic field whereas the film resistivity depends markedly on the grain size D and the transmission coefficient t. Some experimental data on polycrystalline films can be interpreted on the basis of these theoretical predictions.

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TL;DR: In this article, the authors derived analytical equations to describe the grain-boundary and thickness dependence of fine-grained films, and showed that the analytical equations so derived are convenient tools to describe both, the grain boundary and the thickness dependence.

Abstract: The temperature coefficient of the total film resistivity of thin polycrystalline films is calculated from the three-dimensional model of grain-boundaries. This study reveals that the analytical equations so derived are convenient tools to describe both, the grain-boundary and the thickness dependence of the t.c.r. of fine-grained films. The fit of the data obtained for polycrystalline zinc films is successful; values of the transmission coefficient t and specularity parameter p determined from measurements on annealed zinc films are reasonable.
Der Temperaturkoeffizient des Gesamtschichtwiderstands dunner polykristalliner Schichten wird mit dem dreidimensionalen Modell der Korngrenzen berechnet. Die Untersuchung zeigt, das die so abgeleiteten analytischen Gleichungen geeignete Mittel sind, um sowohl die Korngrenze als auch die Dickenabhaangigkeit der t.c.r. von feingekornten Schichten zu beschreiben. Die An- passung der fur polykristalline Zinkschichten erhaltenen Werte ist erfolgreich; die Werte fur den Transmissionskoeffizienten t und des Reemissionsparameters p, die aus Messungen an getemperten Zinkschichten bestimmt werden, sind vernunftig.

17 citations

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TL;DR: In this paper, the authors derived analytical equations for the conductivity and the Hall coefficient of thin metallic films subjected to a longitudinal electric field and a transverse magnetic field from previously proposed general expressions.

Abstract: New analytical equations for the conductivity and the Hall coefficient of thin metallic films subjected to a longitudinal electric field and a transverse magnetic field are derived from previously proposed general expressions. Effects of electronic scattering at external surfaces and due to the magnetic field can be expressed separately. Conclusions are derived about the slight size effect in the Hall coefficient and its temperature dependence, which agree with previous experiments. A correlation between the size effects in the Hall coefficient and the product of the resistivity and the temperature coefficient of resistivity is proposed.

13 citations

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TL;DR: In this article, a new unique general expression for the resistivity, the temperature coefficient of resistivity and the Hall coefficient of monocrystalline, polycrstalline and columnar films was proposed.

Abstract: Starting from the multidimensional statistical model of grain boundaries a new unique general expression is proposed for the resistivity, the temperature coefficient of resistivity and the Hall coefficient of monocrystalline, polycrstalline and columnar films. The ranges of validity of linearized equations are determined. Experiments of other workers related to columnar films are interpreted satisfactorily in this way.

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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

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TL;DR: In this paper, the influence of a transverse magnetic field on the conduction properties of thin metallic films, of thickness comparable with the free path of conduction electrons, is investigated.

Abstract: The influence of a transverse magnetic field on the conduction properties of thin metallic films, of thickness comparable with the free path of the conduction electrons, is investigated. It is shown that, owing to scattering of electrons at the boundaries of the film, the Hall coefficient is increased, and the electrical resistance oscillates with the strength of the applied magnetic field.

264 citations

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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.

89 citations

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TL;DR: In this paper, a model is proposed to express the resistivity of metal films in which two electron scattering mechanisms operate simultaneously: an isotropic background scattering and a scattering caused by three distributions of planar potentials which represent the grain boundaries.

Abstract: In this work a model is proposed to express the resistivity of metal films in which two electron scattering mechanisms operate simultaneously: an isotropic background scattering and a scattering caused by three distributions of planar potentials which represent the grain boundaries. In order to describe the average properties of grain boundaries a transmission coefficient t is introduced. An interpretation of published fine-grained film data in terms of the three-dimensional model yields reasonable values of t .

78 citations