Abnormal breaks in the resistance-temperature (A-T) curves for granular thin films containing numerous metallic particles have been observed recently. We propose an extra contribution to the resistivity arising from the spin-Aip scattering (the Kondo effect) among the spins of conducting electrons and the local magnetic moments of metallic nanoparticles. Each metallic nanoparticle in a granular thin film behaves like a local spin S in analogy to the well localized magnetic moments in dilute alloys. We also find that a log-normal distribution of particle sizes will cause the sharp break in the R-T curve to become broad. With sufFicient fitting parameters we can explain the breaks around 120 K. I. INTRGDUCTIDNRecently, many theoretical' and experimental works have been devoted to the study of the size effect on the optical properties of small particles. Quantum confinement enlarges the energy-level splitting of electronic states as the particle size is reduced, which causes a blueshift of the absorption spectra. On account of the uncertainty principle, the momentum or the kinetic energy of electrons inside the particle increases as the size reduces. The electron-density distribution may spread outside the particle boundary, causing a decrease of the amplitudes of the electron wave functions inside the particle and reducing the dipole transition matrices. Consequently, a redshift' '" may occur for particle sizes less than 4 nm or for nonspherical surface shapes. The exotic optical behavior, depending on the particle size, has prompted many authors to study the physical properties of quantum dots.The crucial factor that determines the optical and electrical properties of small metallic particles is the filling factor f, which is defined as the volume ratio of the sum of the metallic particles to the total volume of the substrate and particles. For a proper detection of optical absorption, the filling factor is constrained to be smaller than 10 . In such a diluted concentration, the multiscattering and interaction between adjacent particles can be neglected. According to the Mies scattering, ' the absorption coefficient o. is proportional to the filling factor.Consequently, the transmitted optical intensity written as I=I~e ' is a single function of f, and the resonant absorption frequency co+ is independent of f.When the filling factor is large enough for the particles to aggregate into clusters, and at least one conducting path is connected from one side of the sample to the other, the sample begins to exhibit current conduction. The resistivity p(R, f, 2 ) will be dependent on the particle size R, the filling factor f, and the aggregation factor A which represents the extent to which the particles are connected with each other to those are discrete. Potential barriers usually occur between the boundaries of grains to grains, therefore the conduction electrons subject to grain boundary scattering. If the electron mean free path l within each grain is larger than the grain size D, the Monte Carlo simulation' by the r...
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