# Hall effect in thin films of gold-silver alloys

01 Sep 1976-International Journal of Electronics (Taylor & Francis Group)-Vol. 41, Iss: 3, pp 285-292

TL;DR: In this article, an effective relaxation time is deduced from the variation of the Hall coefficient with the concentration which is found to be proportional to the mean free path of the electrons.

Abstract: Measurements on Hall constant and magnetoresistance of thin films (350 A-800 A) of Ag-Au alloys with concentrations up to 20% gold have been made. An effective relaxation time is deduced from the variation of the Hall coefficient with the concentration which is found to be proportional to the mean free path of the electrons. The mean free path of the film decreases by about a factor of 3 from the bulk value for silver on the addition of gold to silver. The results are consistent with those of other workers who have used different methods and also indicate that the relaxation time is anisotropic in thin films of alloy. Size effects have also been discussed.

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TL;DR: It was found that topologically disordered 3D nanoporosity leads to extremely low magnetoresistance and anomalous temperature dependence as the characteristic length of nanoporous gold is tuned to be approximately 14 nm.

Abstract: We report the electric conductivity of three-dimensional (3D) nanoporous gold at low temperatures and in strong magnetic fields. It was found that topologically disordered 3D nanoporosity leads to extremely low magnetoresistance and anomalous temperature dependence as the characteristic length of nanoporous gold is tuned to be approximately 14 nm. This study underscores the importance of 3D topology of a nanostructure on electronic transport properties and has implications in manipulating electron transport by tailoring 3D nanostructures.

70 citations

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TL;DR: In this paper, the Boltzmann transport equation was used to define an effective relaxation time for thin metallic films subjected to a transverse magnetic field, and analytical expressions were derived for the Hall coefficient and conductivity in the case of nearly specular scattering on external surfaces.

Abstract: Defining an effective relaxation time and then using the Boltzmann transport equation, analytical expressions have been derived, in the case of nearly specular scattering on external surfaces (p>or=0.5), for the Hall coefficient and conductivity in thin metallic films subjected to a transverse magnetic field. The results for moderately high magnetic field agree well with previous theoretical works; at low magnetic field the Hall coefficient in thin films is greater than the bulk value RH0 and becomes identical with RH0 in strong magnetic field. The theoretical predictions agree well with experimental data on copper and potassium thin films.

21 citations

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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.

13 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: 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.

12 citations

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TL;DR: In this paper, the optical constants for the noble metals (copper, silver, and gold) from reflection and transmission measurements on vacuum-evaporated thin films at room temperature, in the spectral range 0.5-6.5 eV.

Abstract: The optical constants $n$ and $k$ were obtained for the noble metals (copper, silver, and gold) from reflection and transmission measurements on vacuum-evaporated thin films at room temperature, in the spectral range 0.5-6.5 eV. The film-thickness range was 185-500 \AA{}. Three optical measurements were inverted to obtain the film thickness $d$ as well as $n$ and $k$. The estimated error in $d$ was \ifmmode\pm\else\textpm\fi{} 2 \AA{}, and that in $n$, $k$ was less than 0.02 over most of the spectral range. The results in the film-thickness range 250-500 \AA{} were independent of thickness, and were unchanged after vacuum annealing or aging in air. The free-electron optical effective masses and relaxation times derived from the results in the near infrared agree satisfactorily with previous values. The interband contribution to the imaginary part of the dielectric constant was obtained by subtracting the free-electron contribution. Some recent theoretical calculations are compared with the results for copper and gold. In addition, some other recent experiments are critically compared with our results.

15,901 citations

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General Electric

^{1}TL;DR: In this paper, experimental data for the optical constants of Ag and Cu extending to 25 eV are discussed in terms of three fundamental physical processes: (1) free-electron effects, (2) interband transitions, and (3) collective oscillations.

Abstract: Experimental data for the optical constants of Ag and Cu extending to 25 eV are discussed in terms of three fundamental physical processes: (1) free-electron effects, (2) interband transitions, and (3) collective oscillations. Dispersion theory is used to obtain an accurate estimate of the average optical mass characterizing the free-electron behavior over the entire energy range below the onset of interband transitions. The values are ${m}_{a}=1.03\ifmmode\pm\else\textpm\fi{}0.06$ for Ag and 1.42\ifmmode\pm\else\textpm\fi{}0.05 for Cu. The interband transitions to 11 eV are identified tentatively using Segall's band calculations. Plasma resonances involving both the conduction band and $d$ electrons are identified and described physically.

898 citations

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TL;DR: In this article, the shape of the Fermi surface is made to depend on a single parameter which can be interpreted as the pseudo-potential of the {111} atomic planes acting on an orthogonalized plane wave, giving rise to an energy gap of 5-10 ev at the zone boundaries.

Abstract: The Fermi Surfaces in Cu, Ag and Au are now known to be greatly distorted, with thick ‘necks’ passing through the zone boundaries. In this paper we enquire whether such an electronic structure is quantitatively consistent with the observed transport coefficients. The mathematical model is quite simple; the shape of the Fermi surface is made to depend on a single parameter which can be interpreted as the pseudo-potential of the {111} atomic planes acting on an orthogonalized plane wave, giving rise to an energy gap of 5–10 ev at the zone boundaries. Various integrals over the Fermi surface can then be evaluated by elementary methods, and compared with the corresponding experimental quantities. The electronic specific heat and optical mass in the pure metals are consistent with the model. The galvanomagnetic effects are shown to depend a great deal on the anisotropy of the electron relaxation time, whose variation with energy is also probably the electron relaxation time, whose variation with energ...

165 citations

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TL;DR: In this paper, the optical constants of thin Ag films are determined from measurements of both their transmittance and reflectance, in terms of intra and interband transitions, in relation with the film crystallographic structure.

Abstract: The optical constants of thin Ag films are determined from measurements of both their transmittance and reflectance. The complex dielectric constant is discussed in terms of intra and interband transitions, in relation with the film crystallographic structure. The optical mass of the conduction electrons is found to be very low, 0·87; their optical relaxation time to depend strongly on the film structure and to be smaller than their electrical relaxation time. The absorption due to interband transitions is considered. A supplementary absorption band related to film imperfections is observed in some cases. Plasma oscillations are also studied in relation with the film quality.

74 citations