Granular Metal Films Research Articles

Onset of superconductivity in ultrathin granular metal films.

The evolution of superconductivity in ultrathin films of Sn, Pb, Ga, Al, and In has been examined as a function of thickness and temperature. The films were grown in increments by condensation from the vapor onto substrates held at temperatures below 18 K. For each metal, global superconductivity or zero electrical resistance was found when the normal-state sheet resistance ${R}_{N}$ fell below a value close to h/4${e}^{2}$, or 6.45 k\ensuremath{\Omega}/\ensuremath{\square}, an observation uncorrelated with either structural or material parameters such as thickness or transition temperature. Prior evidence of superconductivity with nonzero resistance, local superconductivity, was found at earlier stages of film growth. All evidences of superconducting behavior were observed at temperatures close to the bulk transition temperature beginning in the range of thicknesses for which normal-state resistivities were greater than 200 \ensuremath{\mu}\ensuremath{\Omega}-cm and were rapidly changing with thickness. This implies that the films consisted of fully superconducting grains connected by tunneling junctions. The strong disorder represented by a broad distribution of junction parameters can be renormalized into weak disorder. Thus theoretical calculations based on regular arrays of superconducting sites coupled by (Josephson) junctions appear to be relevant. The extreme thinness of the films implies very small junction capacitances leading to large quantum fluctuations of the phase differences of their superconducting order parameters. Two classes of theories explaining a nearly universal resistance threshold for superconductivity have emerged. Both classes involve the quenching of these quantum fluctuations. In the limit of very small junction capacitances the threshold occurs at resistance values near h/4${e}^{2}$, and is essentially independent of the capacitance and the energy gap, in good agreement with the experimental data. Not contained in any of the models is an explanation of the observed regular variation of the low-temperature resistances of the films with the normal-state sheet resistance for values just above the resistance threshold.

The crystalline structure of ultrathin gold granular films

Researchers generally imagine a granular metal film as being constituted by a single type of stable spherical shaped particles with a mean diameter d . Indeed, even the most homogeneous films are made up by particles of various diameters d with different shapes and with stable or unstable crystalline structure. Recently, it has been shown that gold particles of diameter of 2 nm are in a “quasi-solid” state. In this paper the authors show the experimental results we obtained by selected area electron diffraction (SAED) from ultrathin ( d<3 nm ) gold films. The authors show that with gold particles of mean diameter less than 3 nm and electrons of 250keV, the dynamic effects can be neglected and the kinematic theory can be used in the data analysis. The authors conclude that, for films with d > 1.5 nm , SAED data can be well interpreted by means of a simple phenomenological model of the particles taking into account the effect on the diffraction patterns due to the particle size distribution. On the contrary, SAED data obtained from films of d<1.5 nm are in disagreement with the same model suggesting the occurrence in these films of “quasi-solid” particles.

Large scale inhomogeneities in granular metals

We present direct evidence for large-scale inhomogeneities in granular metal films. Using Rutherford backscattering data and measurements of the superconducting critical fields, we show that granular materials (Al:Al 2Te 3 and Al:Al 2O 3) are deposited in layers. Each film contains 3–5 layers approximately 400 Å thick. The layer thicknesses are significantly less than the film thicknesses and are of the order of the coherence length. This layering has significant consequences when using such films to investigate dimensionally dependent theories.

Optical behavior of granular metal films: single-image versus multiple-image approaches in the treatment of substrate effects

Differences between the point-dipole approximation and a more rigorous theory for studying the optical behavior of a granular metal film are discussed.

The scattering of electrons on grain boundaries: Electrical conductivity

The electrical conductivity of granular metal films was calculated, the boundaries of grains being treated as potential barriers. It was shown that the electrical conductivity decreases with the width and height of the potential barrier. For an electron energy higher than potential barrier height, the electrical conductivity oscillates and its mean value is smaller than that of metal without grain boundaries.

Granular metal films as recording media

High-density recording media require materials with a high magnetization and high coercivity as well as chemical stability, wear, and corrosion resistance. We explore the potential of granular metal films for recording media. Films of Fe granules about 150 Å in size embedded in an amorphous SiO2 matrix exhibit coercivities as high as 3 kOe at low temperatures and 1.1 kOe at room temperature, and magnetizations of about 150 emu/g. The methods with which these materials are fabricated, the essential microstructure characterization, and magnetic measurements are described.

Conductivity variations induced by water vapor adsorption in granular metal films

The resistance variations induced by relative humidity (RH) changes were measured on Pd/Al2O3 and Au/(C2F4)n granular films in the RH range 0%–97% at room temperature. It was verified that the contact-film interface has no influence on the observed phenomena. A maximum ΔR/R0=26% was detected for the Au/(C2F4)n system.

Some transport properties of granular metal films with rough surfaces

The electrical conductivity, thermoelectric power and the temperature coefficient of resistivity of metal films are developed. The analysis is based upon Soffer's angularity dependent surface scattering theory and upon Mayadas-Shatzkes size effect theory with the grain-boundary scattering model. Considerable influence of the roughness and grain-boundary scattering on the transport properties in very thin films is observed.

Electrochemical studies of granular metal films and their application for stabilizing semiconductor photoelectrodes

The oxygen and hydrogen evolution reactions on granular metal (GM) electrodes in aqueous electrolytes have been examined. The catalytic activity of Pt/SiO 2 GM film for hydrogen evolution is as active as that of a Pt electrode at moderate current densities. The exchange current density for oxygen evolution on GM electrodes is about one fifth of that on Pt electrode, which is roughly corresponding to the ratio of their surface fractions of Pt. Coating of GM films on n-Si has been utilized to stabilize the photoanode for the photoassisted electrolysis of water. The overpotential for oxygen evolution on the optimally stabilized Si photoanode has been reduced by about 0.4 V compared with a Pt electrode. The potential gain has been attributed to the Fermi-level lowering due to injection of photogenerated holes into metal particles in the GM film, although some contribution of photopotential due to band-bending within the inner semiconductor has been suggestive. The best results have been obtained when a thin insulator layer is thermally grown on Si substrates before the GM film is deposited. This procedure is likely to be effective to avoid intimate contact between Si and metal particles.

Percolation effects in the optical properties of Ni-MgO composites.

We prepared Ni-MgO granular metal composites by coprecipitation of NiO-MgO solid solutions and their preferential reduction in a hydrogen atmosphere. These composites have a different topology from that of the granular metal system prepared by cosputtering or coevaporation. The percolation threshold ${f}_{c}$ of these Ni-Mgo composites was estimated as 0.32\ifmmode\pm\else\textpm\fi{}0.02, which is in good agreement with the prediction of the effective-medium theory (EMT) but much lower than ${f}_{c}$\ensuremath{\approxeq}0.5 of conventional granular metal films. For each composite with a metal-volume fraction between 0 and 0.4, the reflection spectrum was measured between 20 and 36 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at room temperature. The detailed comparison of these spectra with the Maxwell-Garnett theory (MGT) and the EMT showed that the Ni-MgO composites were better described by the EMT than by the MGT. The conductivities and the dielectric constants of the composites were derived by a Kramers-Kronig transformation, and they showed a qualitative agreement with the EMT. In the low-frequency region, especially in the far-infrared region, the percolation transition was observed in the reflection spectrum, and also seen in the derived conductivity and the dielectric constant.

Granular Fe metal films

Granular Fe metal films consisting of ultrafine Fe granules imbedded in a SiO 2 matrix have been fabricated. The granular microstructure has been revealed by transmission electron microscopy (TEM). Electron diffraction indicates that the Fe granules are bcc α-Fe and the SiO 2 matrix is amorphous. 57Fe Mössbauer spectroscopy indicates that there are no measurable traces of Fe oxides. The magnetic properties of the granular Fe films deviate from those of bulk Fe due to single domain effects.

Pre-exponential factor in the conductivity of liquid and amorphous semiconductors

It is suggested that the pre-exponential factor σ in the conductivity of non-crystalline systems should be 0.03 e 2 h ̵ L i , where L i is the inelastic diffusion length. Applications are suggested to hydrogenated amorphous silicon, to materials where small polarons are formed, to liquid semiconductors and to granular metal films. In cases where all collisions are inelastic, σ o will approach the author's σ min ( 0.03 e 2 h ̵ a ) .

Schottky-barrier heights at granular-metal/Si interface

Diode characteristics of granular-metal (GM)/n-Si interfaces were investigated. The granular metal film (Pd or Pt/SiO2) was deposited by the ion-beam sputtering technique. The diode characteristics were found to be influenced not only by the metal fraction in GM but also by the GM film thickness. Saturation current density Js of the diodes under reverse bias condition showed a notable peak at the metal fraction in the range between 0.1 and 0.25, the maximum value being several orders of magnitude greater than Js of a Pd-Si Schottky barrier. Assuming that the increase in Js is fully caused by the barrier-height lowering at the GM/Si interfaces, the amounts of barrier-height lowerings were found to be 0.18 eV for 150-Å-thick GM films and 0.22 eV for 600-Å-thick GM films. Possible mechanisms for the barrier-height lowering as well as the reason that the barrier height depends upon the GM films’s thickness were considered.

Multiple scattering renormalized T matrix theory for the dielectric constant of non-homogeneous thin films

A multiple scattering theory to obtain the effective dielectric constant for a granular metal film is developed considering correlation effects. A renormalization procedure is applied to obtain a field equation within a renormalized first smoothing approximation (RFSA), using T matrix formalism. From the field equation a dispersion relation is obtained that is expressed in terms of the dielectric constant of the metal corrected for size effects, the relative concentration of the constituents, the radius of the inclusions and a correlation length. Using the Maxwell Garnett model for the dielectric constant of the uncorrelated medium, the multiple scattering theory shows that correlation effects move the resonance in the imaginary part of the index of refraction predicted by the Maxwell Garnett model towards lower frequencies and broaden it. Comparison of the RFSA with experiments shows a better fit than do previous theories.

Determination of the frequency-dependent resistivity of ultrathin metallic films on Si(111).

Inelastic electron scattering is used to determine the frequency-dependent resistivity of ultrathin metallic films on Si(111). The experimental data are analyzed in the single-scattering regime using dipole scattering theory. An unusual frequency dependence of the resistivity is found for low coverages of Pd on Si(111) and analyzed using the Bruggeman effective-medium theory. This analysis together with hydrogen-titration studies indicates the presence of metallic clusters embedded in the surface. We also show that electron tunneling via surface states gives an important contribution to the dc conductivity of these ultrathin granular metal films on Si(111).

Electric conduction in metallic Ag particles—Cs2O semiconductor thin films

Granular metal films were discussed and reviewed by Abeles et al. Here we discuss the electric conduction in thin films of silver particles dispersed in a matrix of Cs2O. It is a typical system of metallic particles dispersed in a semiconductor. A thin film of Cs2O several hundred Å thick was prepared on a glass substrate with silver electrodes on both sides in a vacuum tube. An amount of silver was deposited onto the film, then its photoemission was monitored during heat treatment to obtain thin film of silver particles dispersed in Cs2O. These procedures were repeated about ten times. Curves of log 1/R vs 1/T were plotted from measurements after each heat treatment. A preliminary explanation is presented in this paper.

High-field conduction in off-stoichiometric SiO2 films

The temperature dependence of the high-field conductivity of SiO2 films with a small atomic excess of Si content is interpreted in terms of a model previously proposed for granular metal films. We have found an excellent quantitative agreement between experimental data and the theory. This agreement clarifies the conduction mechanism in this material and strongly suggests that the Si particles have metallic characteristics. With this interpretation, we are able to determine the volume fraction of the excess Si x, the diameter of the Si grains d, and the interparticle distance s. In the case of samples with an excess of Si atoms of 1% to 3%, we found that x≂0.017, d≂9.5 Å, and s≂20.5 Å.

Enhanced electron injection into SiO2 layers using granular metal films

The enhancement of electron injection into silicon dioxide layers using a metal-granular metal film-SiO2-silicon structure is reported for Al, Ni, and Mo-SiO2 cermets. This enhancement was found to be stronger for higher metal to oxide ratios. The I-V characteristic curves for these structures follow the Fowler-Nordheim tunneling mechanism behavior, indicating that the dominant effect is an enhancement of the electric field near the granular film-SiO2 interface.

The Hall effect in granular metal films near the percolation threshold

We have measured the Hall effect in the granular metals Au-SiO 2 and W-Al 2O 3 near their percolation thresholds. Our results indicate that when conduction is by electronic tunneling between isolated grains, the Hall coefficient is negative for both cermets. In the bulk, Au has a negative coefficient and W a positive one.

Hall effect in the dielectric regime of granular metal films

The Hall effect is considered in the dielectric regime of granular metal films, where the charge-transport mechanism is quantum-mechanical tunneling between isolated metallic grains. The dominant temperature dependence of the Hall mobility is found to be ${\ensuremath{\mu}}_{H}\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}{(\frac{T}{{T}_{0H}})}^{\frac{1}{2}}]$, where ${T}_{0H}&lt;&lt;{T}_{0}$, the characteristic temperature in the exponent of the electrical conductivity. The sign of the Hall effect is found to alternate with the orbital-quantum number of the highest occupied level at the grain Fermi energy, giving rise to cancellation effects which reduce the magnitude of ${\ensuremath{\mu}}_{H}$ by a temperature-dependent prefactor. These arise from finite temperature effects and the inherent spread in grain diameters.