Theoretical analysis of the transverse Hall effect in thin monocrystalline films
TL;DR: The transverse Hall coefficient of thin monocrystalline films was derived from the recently presented bidimensional conduction model by introducing a term in the Boltzmann equation representing the effective mean free path as discussed by the authors.
Abstract: The transverse Hall coefficient of thin monocrystalline filmsRHF is derived from the recently presented bidimensional conduction model by introducing a term in the Boltzmann equation representing the effective mean free path. Numerical evaluations ofRHF show that the size effect inRHF is less marked than that in resistivity and is much more sensitive to grain-boundary scattering than it is to external-surface scattering. Good agreement with the results from the previous experiments of several authors is found.
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TL;DR: In this paper, the authors reviewed the advances that have been made during the last five years in the field of theoretical description of electronic scattering at grain boundaries and derived analytical expressions for the transport parameters of columnar, monocrystalline and polycrystalline films.
Abstract: Thin metal films can be deposited in a number of different ways. As a result several types of defects or impurities are frozen in the film. In most practical cases films exhibit grain boundaries which play a decisive role in transport properties. This paper reviews the advances that have been made during the last five years in the field of theoretical description of electronic scattering at grain boundaries. Analytical expressions for the transport parameters (such as resistivity, temperature coefficient of resistivity and thermopower) of columnar, monocrystalline and polycrystalline films are derived. Care has been taken to give linearized equations for the transport phenomena. Methods for extracting grain parameters are outlined. Special attention is focused on correlated size effects. Imperfection or impurity effects on the film resistivity and thermopower are considered. Methods for determining the energetic parametersU andV and the componentS
1 of the thermopower associated with imperfections are proposed. Special emphasis is placed on procedures for identifying imperfections by simultaneous study of the restructuration processes induced by thermal ageing and of the changes in transport parameters on ageing.
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TL;DR: Etude theorique de l'influence de la dimension des joints de grains sur la conductivite electrique as discussed by the authors is presented in Section 2.2.1.
Abstract: Etude theorique de l'influence de la dimension des joints de grains sur la conductivite electrique. Calcul
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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
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
TL;DR: In this article, the authors studied the thickness dependence of the resistivity, the Hall coefficient, and the transverse magneto-resistance, by gradually varying the thickness of a single film which was kept under high vacuum during the entire experiment.
Abstract: Bismuth films (200-1400 \AA{}) were grown epitaxially on freshly cleaved mica substrates. These films consisted of a mosaic of equally oriented crystallites averaging several microns in diameter. The plane of the films coincided with the trigonal plane of Bi. We have studied the thickness dependence of the resistivity, the Hall coefficient, and the transverse magneto-resistance, by gradually varying the thickness of a single film which was kept under high vacuum during the entire experiment. The resistivity at 360 and 77 \ifmmode^\circ\else\textdegree\fi{}K is a smooth monotonic function of the thickness. At 12 \ifmmode^\circ\else\textdegree\fi{}K, we observed small oscillations in the resistivity and in the magnetoresistance. These oscillations are regarded as probable manifestations of the quantum size effect (QSE). The thickness dependence of the Hall coefficient is in striking disagreement with the predictions of the infinite-potential-well model. Better agreement between the theory and experimental results is obtained when we assume a less rigid boundary condition. Also for several films we have investigated the temperature dependence of these three transport coefficients and found it to be quite different from that of bulk bismuth. We have attempted to explain these results in terms of the behavior of the carrier concentration and of the different scattering mechanisms that can come into play in these films.
165 citations
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