Formation of Nanocluster Colloids of Tin, Gold and Copper in Magnesium Oxide by MeV Ion Implantation
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s-no +2n(1) where 6 is the dielectric constant of the material of the spheres. For spheres of conducting material E = &1 + j 62, where the real component F, is negative and the imaginary component F,2 is proportional to the conductivity which causes energy loss from a time varying electric field, such as that in visible light. Mie [1] derived the optical absorption coefficient (x of a material with a volume fraction Q occupied by metal spheres whose radii are small compared with incident light of wavelength 2, 2 187tQ2no03 62 cm'-. (2) A minimum occurs in the denominator of Equation 2 when , I (Xp) + 2n2 =0(3) and causes a maximum absorption of light at a characteristic wavelength Xp, the so called surface plasmon resonance [2-5]. Metallic colloids embedded in a dielectric transmit only part of the visible spectrum, a phenomenon used since ancient times to decorate glassware. Figure 1 shows the values of 81 and 82 for gold, silver, copper and tin derived from the electronic constants of the bulk metals [6,7]. The downward trend of 6i, linear in wavelength, together with the slow variation of 82 , leads us to expect quasi Lorentzian optical absorption peaks centered at a wavelength Xp characteristic of the index of refraction of the host and of the permittivity of the 375
Mat. Res. Soc. Symp. Proc. Vol. 504 ©1998 Materials Research Society
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600
200
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WAVELENGTH
WAVELENGTH Figure 1 The permittivity for gold, silver, copper and
Figure 2 Optical absorption spectra for (a) copper,
tin from Refs {11,12]
(b) gold and (c)tin.
metal. Using n 0=1.73 for MgO and the values of 8. from Figure 1, Equation (3) predicts wavelengths of 564, 551 and 250 nm for the surface plasmon resonance for colloidal Cu, Au and Sn in MgO, respectively. Figure 2 shows experimental optical absorption spectra for gold, tin and copper, with the observed wavelengths for maximum optical density in reasonable agreement with Equation 2. Ion implantation induces additional optical absorption in the MgO substrate that must be removed by careful heat treatment of the implanted samples. Doyle [81 has improved the Mie theory by showing that for spheres whose size is less than the mean free path of the conduction electrons the plasmon resonance is broadened not by the conductivity, represented by 82 , of the bulk material but by the radius r of the spheres. For the full width at half maximum AX of the peak determined from an optical absorption measurement, in accordance with Doyle 2
r
Vf),p
(4)
2-cA
where vf is the electron velocity corresponding to the Fermi energy of the metal. XP depends on the substrate and the element implanted in it and AX is related to the size of the nanoclusters. These changes in the optical properties of insulating materials can be made to occur following the implantation of metal using MeV ion accelerators. Small metal clusters form in the implanted layer, either spontaneously or by heat treatment, and absorb light at the surf
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