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Ag + ions of 200 keV were implanted into single crystal SiO2 at room temperature to five different doses: 5×1015, 2.3×1016, 4.5×1016, 5.6×1016, and 6.7×1016/cm2. With increasing dose, the implanted Ag distributions change from usual Gaussian-type profiles to abnormal bimodal profiles with narrow full width at half maximum, which are associated with Ag nanoparticles forming during high dose implantation. The implanted Ag depth profile evolution with dose can be clearly observed during Rutherford backscattering spectroscopy analysis. The nanoparticles form dual-layer structures at high doses: as far as the dose of 6.7×1016/cm2 is concerned, transmission electron microscopy proves that the shallower implanted layer contains noninteracting small Ag nanoparticles with the diameters of about 7 nm; the deeper layer contains a high density of interacting large nanoparticles with the diameters of about 25 nm. High resolution electron microscopy identifies that the nanoparticles are perfect single crystals. Although plasmon resonance frequency of the Ag nanoparticles formed at relatively low dose agrees well with the Mie’s theoretical prediction, great redshift due to multipole interactions between high density nanoparticles occurs for high doses, moreover, the magnitude of redshift increases with implanted dose.

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Nontrivial solutions exist only if the determinant of matrix C equals zero. Complex solutions of the determinant matrix are the wave numbers of the Lamb wave propagating along the plate.