Fabrication and Modification of Metal Nanocluster Composites Using Ion and Laser Beams
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Mat. Res. Soc. Symp. Proc. Vol. 354 01995 Materials Research Society
THE ROLE OF QUANTUM-DOT SIZE IN NONLINEAR OPTICAL RESPONSE The local structure of a nanocomposite material is shown schematically in Figure 1. The metal
quantum dots are assumed to be separated sufficiently that there are no interactions between dots.
Under these conditions, the electrons in a metal quantum dot embedded in an insulating matrix can be treated as a system of n independent electrons confined to a spherical box, with an electronic structure consisting11of distinct, though perhaps overlap......
ping, energy levels.
Optical transitions in the quantum
dots may be described using density matrix formalism for a two-level system in contact with a reservoir of unexcited material. Despite the simplicity of this model, "theresults it produces give zeroth-order clues to the Smaterials parameters which can reasonably be measured via third-order non-linear optics. Three distinct optical transitions are allowed in metal quantum dots: (1) hot-electron transitions, in which electrons near the Fermi level absorb energy from inci..dent light; (2) interband transitions between the localized diagram of a metal dorbitals of the metal valence bands and empty conducSchematic 1. Figure quanure Sembeddd oa tion band states; and (3)near intraband transitions filled quantum dot dot embeddeddina in a dieletri. dielectric, conduction-band states the Fermi edgefrom to empty states higher in the conduction band. The latter two are shown schematically in Figure 2. The nonlinear optical response of electrons in a metal quantum-dot material is most strongly affected by two confinement effects: one a classical effect due to electric-field enhancement, the other a quantum-mechanical effect due to the spatial constriction of the electronic wave functions. The classical confinement effect produces a local field enhancement associated with interband transitions; it is also the cause of the surface plasmon resonance. Interband effects can be greatly enhanced by embedding metal quantum dots in a Conduction Bands nonlinear dielectric.' 2 The quantum confinement effect, on the other hand, is especially pronounced for the intraband transitions where both the initial and final states experience the confinement due to the shortened mean free path between electron collisions with the
hard boundary separating metal and dielectric. The quantum-confined electronic susceptibility is proportional to the inverse cube of the dot radius, and rapidly increases in magnitude below particle diameters of approximately 10 nm, as we have dem-
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SF
rand
onstrated for Cu dots in fused silica.13 This makes small average quantum-dot diameter especially desirable for enhanced third-order susceptibility
the nonlinear effect associated with nonlinear refraction and optical switching. Size effects have different origins in metal and Figure2. Schematic diagram of semiconductor quantum dots. When the radii of optical transitions in a nobleunwanted excitonic states are larger than the partimet
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