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Nonlinear optical properties of metal nanoparticle composites for optical applications
Nuclear Instruments and Methods in Physics Research B 206 (2003) 620–623 www.elsevier.com/locate/nimb
Nonlinear optical properties of metal nanoparticle composites for optical applications Y. Takeda *, N. Kishimoto Nanomaterials Laboratory, National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan
Abstract Optical absorption and nonlinear optical response were investigated for nanoparticle composites in amorphous SiO2 fabricated by negative Ta ion implantation at 60 keV. X-ray photoelectron spectroscopy was used to identify Ta and the oxide formation in the matrix. Optical absorption clearly indicated a surface plasmon peak at 2.2 eV and the peak resulted from formation of nanoparticles embedded in the matrix. The measured absorption was compared with calculated ones, evaluated by Maxwell-Garnett theory. Nonlinear absorption was measured with a pump-probe method using a femtosecond laser system. The pumping laser transiently bleached the surface plasmon band and lead to the nonlinearity. The transient response recovered in several picoseconds and behaved in terms of electron dynamics in metallic nanoparticles. The Ta nanoparticle composite is one of the promising candidates for nonlinear optical materials with good thermal stability. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 42.70.Nq; 78.47.+p; 78.67.Bf Keywords: Ion implantation; Ta nanoparticle; Optical absorption; Transient absorption; Core shell nanoparticle
1. Introduction All-optical devices, which directly operate optical signals with optical gate pulses, are attractive for future ultrafast networks and circuits ahead of semiconductor devices. The metal nanoparticles are of great interests for the photonic applications due to photo-induced nonlinear optical properties [1–3]. The nanoparticle composites consist of metal nanoparticles embedded in a transparent insulator and have the large optical nonlinearity with
*
Corresponding author. Tel.: +81-298-59-5058; fax: +81298-59-5010. E-mail address: [email protected] (Y. Takeda).
picosecond response around surface plasmon resonance in the visible light region. For device applications, it is imperative to tune the resonance band for the demanded wavelengths of optical circuits. The resonance of the composites depends on both dielectric constants of a matrix and of nanoparticles. The negative ion implantation has the advantage of application to various ion species and insulating substrates, and has enabled us to form self-assembled Cu nanoparticles in SiO2 and other insulators [4]. We have reported that tuning of the surface plasmon band and transient nonlinear absorption band is possible by selecting appropriate substrates [5,6]. Flexible selection of ions, not only applying to noble metals, is also vital to
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(03)00797-3
Y. Takeda, N. Kishimoto / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 620–623
tune the optical band of nanoparticle composites. Refractory metals, such as Ta and W, with high thermal stability are of high interests in optical properties for device applications. Applicability of refractory metal ions, in a nonequilibrium manner, is a unique merit of ion implantation techniques. In this paper, we present X-ray photoelectron spectroscopy, steady-state optical absorption and nonlinear transient response of Ta-implanted silica glass. We discuss the chemical state of Ta nanoparticles and performance of the composite as a nonlinear optical material.
2. Experimental Negative Ta ions of 60 keV were produced by a Cs-assisted plasma-sputter-type ion source with a cusp magnetic field. The detailed techniques have already been described elsewhere [7]. The dose rate and total dose were 0.3 lA/cm2 and 3 1016 ions/ cm2 , respectively. Insulating substrates used were optical-grade amorphous (a-)SiO2 (KU-1: 820 ppm OH ). The projectile range predicted by the SRIM 2000 [8] is 29 nm for SiO2 . A sample was annealed at 900 °C for 1 h in an Ar gas flow after the ion implantation. X-ray photoelectron spectroscopy data were obtained with an X-ray source of 15 kV–400 W Mg Ka (hm ¼ 1253:6 eV). Steady-state optical measurements were made in a photon energy range from 0.5 to 6.5 eV using a dual beam spectrometer. The measurements were carried out from both surfaces, i.e. the implanted- and the rear surface. Absorbance of the metal nanoparticle composites was measured after rigorous evaluation of incoherent multiple reflections [9]. Optical parameters of the substrate were determined by spectroscopic ellipsometry. Transient absorption experiments were performed using the femtosecond pump-probe method [10]. We used an output pulse from an optical parametric amplifier with sum-frequency generation as a pump pulse. The wavelength of the pump pulse was tuned near the surface-plasmon resonance, 574 nm (2.16 eV). The pulse duration was a few hundreds of femtoseconds. All the optical experiments were carried out at room temperature.
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3. Results and discussion X-ray photoelectron spectrum in Fig. 1 exhibits Ta 4f signals for an annealed sample after Ta ion implantation. Overlapped peaks are observed ranging from 20 to 30 eV of the binding energy in the spectrum. The strongest and the second peaks are assigned to the binding energy of Ta5þ 4f7=2 (26.1 eV) and 4f5=2 (28.5 eV), corresponding to oxide [11,12]. The shoulders at the lower energy are identified as the binding energy of Ta0 4f7=2 (21.8 eV) and 4f5=2 (23.7 eV), associated with metal [11,12]. The XPS result shows implanted Ta ions exist as both oxide and metal in silica glass. According to a cross-sectional TEM image of annealed sample, spheres of particles of 10–40 nm in diameter are distributed near the surface. Fig. 2 shows absorbance spectra of as-implanted sample and annealed sample. The as-implanted sample shows a broad peak at 2.2 eV in absorption, corresponding to the surface plasmon resonance, and the peak structure results from the formation of nanoparticle dispersed in the matrix
Fig. 1. XPS spectrum of Ta 4f of annealed a-SiO2 in Ar at 900 °C for 1 h, after implantation with 60 keV Ta to a total fluence of 3 1016 ions/cm2 at a flux of 0.3 lA/cm2 .
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Y. Takeda, N. Kishimoto / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 620–623
Fig. 2. Steady-state absorption spectra of as-implanted a-SiO2 and annealed a-SiO2 after Ta implantation with 60 keV, where a total dose and dose rate are 3 1016 ions/cm2 and 0.3 lA/cm2 , respectively.
[13]. In the annealed sample, the plasmon peak is enhanced, corresponding to the growth of nanoparticles, and slightly shifts to blue. The absorption above the peak position bleaches due to annihilation of defects in the matrix and nanoparticles [14]. Numerical calculations of absorption spectra of various nanoparticle composites in silica glass are also shown in Fig. 3. In the calculation the effective dielectric constants of the composites are evaluated by the Maxwell-Garnett formula [9,15], where the thickness of the composites is 50 nm and the volume fraction of
Fig. 3. Numerical calculations of absorption spectra of metal Ta, TaSi2 , TaOx and Ta + TaOx nanoparticle composites, evaluated by Maxwell-Garnett theory.
nanoparticles in the composites is 0.10. Tantalum silicide and oxide nanoparticle composites have no peak around 2 eV, while metal Ta nanoparticle composites clearly shows a surface plasmon peak at 1.8 eV. A composite, which consists of independent metal and oxide nanoparticles, has the spectrum averaged with them and the peak is held at the same position. Core-shell nanoparticles have been reported as a composite including of two components [16–18]. However the oxide shell largely attenuates the absorption [16]. The sharply plasmon peak results from metallic nanoparticles in the matrix. The optical and XPS results suggest that the composite form metal Ta nanoparticles and solute Ta oxides. The free enthalpies of formation, from tantalum and oxygen to tantalum oxide, are )762 and )532 kJ at 300 and 1700 K at 1 atm for 1 mol of oxygen molecular, respectively and slightly higher than those of silicon oxide, which are )824 and )578 kJ [19]. Coexistence of tantalum oxide and silicon oxide in the matrix is reasonable because the difference of the enthalpy is relatively small. The measured plasmon peak shifts to blue in comparison with the calculated one. Dielectric constants constant of nanoparticles varies by size effects of intraband and interband transition [20,21]. The peak position is almost independent of a size effect of the intraband transition, derived from the Drude model. The size effect causes change of the peak shape, which is not shown here. The interband transition has a large peak at 2 eV and dominates the dielectric constant of metal tantalum in the range [22]. The difference of the peak position may be due to the size effect of interband transition near the Fermi level. Nonlinear optical response in picoseconds is important to apply the composites to ultrafast alloptical switching devices, working at THz. Laser irradiation excites electrons in the metal nanoparticles and finally modulates the absorbance and transmittance. Fig. 4 shows temporal change of the absorption of an annealed sample. Immediately after the laser pumping near the plasmon band, the surface plasmon band of the nanoparticle composite is bleached around the center of 2.2 eV as shown in the inset in Fig. 4. The bleaching spectrum recovers within several picoseconds. The behavior shows typical conduction electron dynamics
Y. Takeda, N. Kishimoto / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 620–623
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Acknowledgements A part of this study was financially supported by the Budget for Nuclear Research of the MEXT, based on the screening and counseling by the Atomic Energy Commission. The authors are grateful to Dr. H. Amekura, Mr. K. Kono, Dr. T. Suga, Ms. J. Lu and Mr. N. Umeda for their assistance in the experiments.
References
Fig. 4. Time resolved data of laser-excited transient absorption for Ta nanoparticles in a-SiO2 , where the probe is at surface plasmon peak. The inset shows transient absorption spectrum, right after the laser excitation at 2.16 eV.
in metal nanoparticles and also suggests the existence of metallic nanoparticles in the composite. The tantalum nanoparticles have comparable transient response to noble metal nanoparticles and are potential as a nonlinear optical material for device applications. The ion implantation technique would be applied for optical design to fabricate nanoparticles by appropriate choice of refractory metal ions and a substrate.
4. Conclusions Negative Ta ions at 60 keV have been implanted into a-SiO2 and fabricated nanoparticles. XPS spectrum indicates both metal tantalum and the oxide embedded in the matrix. The Ta-implanted a-SiO2 shows a surface plasmon peak in the absorption spectrum and the peak is enhanced after annealing. TEM images show particles of 10– 40 nm in diameter distributed near the surface. The optical and XPS results suggest that the composite form metal Ta nanoparticles and solute Ta oxides in a-SiO2 . The nonlinear transient absorption obeys electron dynamics in the metallic nanoparticles. The transient response with several picoseconds bears comparison with that of noble metal nanoparticles.
[1] R.F. Haglund Jr., L. Yang, R.H. Magruder III, C.W. White, R.A. Zuhr, L. Yang, R. Dorsinville, R.R. Alfano, Nucl. Instr. and Meth. B 91 (1994) 493. [2] R.F. Haglund Jr., Mater. Sci. Eng. A 253 (1998) 275. [3] J.-Y. Bigot, J.-C. Merle, O. Cregut, A. Daunois, Phys. Rev. Lett. 75 (1995) 4702. [4] N. Kishimoto, N. Umeda, Y. Takeda, C.G. Lee, V.T. Gritsyna, Nucl. Instr. and Meth. B 148 (1999) 1017. [5] Y. Takeda, C.G. Lee, N. Kishimoto, Nucl. Instr. and Meth. B 190 (2002) 797. [6] Y. Takeda, C.G. Lee, V.V. Bandourko, N. Kishimoto, Mater. Trans. 43 (2002) 1057. [7] N. Kishimoto, V.T. Gritsyna, Y. Takeda, C.G. Lee, J. Surf. Sci. 4 (1998) 220. [8] J.F. Zieger, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon Press, New York, 1985 (http://www.srim.org/). [9] Y. Takeda, V.T. Gritsyna, N. Umeda, C.G. Lee, N. Kishimoto, Nucl. Instr. and Meth. B 148 (1999) 1029. [10] Y. Takeda, N. Umeda, V.T. Gritsyna, N. Kishimoto, Nucl. Instr. and Meth. B 175–177 (2001) 463. [11] J.Y. Zhang, I.W. Boyd, Appl. Surf. Sci. 168 (2000) 234. [12] A.Y. Mao, K.A. Son, J.M. White, D.L. Kwong, D.A. Roberts, R.N. Vrtis, J. Vac. Sci. Technol. A 17 (1999) 954. [13] U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer-Verlag, Berlin, 1995. [14] Y. Takeda, J.P. Zhao, C.G. Lee, V.T. Gritsyna, N. Kishimoto, Nucl. Instr. and Meth. B 166–167 (2000) 877. [15] J.C. Maxwell-Garnett, Philos. R. Soc. London 205 (1906) 237. [16] C.G. Granqvist, O. Hunderi, Phys. Rev. B 16 (1977) 3513. [17] J.H. Hodak, A. Henglein, G.V. Hartland, J. Phys. Chem. B 104 (2000) 5053. [18] J. Sinzig, M. Quinten, Appl. Phys. A 58 (1994) 157. [19] R.A. Swlin, Thermodynamics of Solid, John Wiley & Sons, Inc., New York, 1962. [20] U. Kreibig, in: J. Bourdon (Ed.), Growth and Properties of Metal Cluster, Elsevier, Amsterdam, 1980, p. 371. [21] F. Hache, D. Ricard, C. Flytzanis, U. Kreibig, Appl. Phys. A 47 (1988) 347. [22] J.E. Nestell Jr., R.W. Christy, Phys. Rev. B 21 (1980) 3173.
Nonlinear optical properties of metal nanoparticle composites for optical applications Y. Takeda *, N. Kishimoto Nanomaterials Laboratory, National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan
Abstract Optical absorption and nonlinear optical response were investigated for nanoparticle composites in amorphous SiO2 fabricated by negative Ta ion implantation at 60 keV. X-ray photoelectron spectroscopy was used to identify Ta and the oxide formation in the matrix. Optical absorption clearly indicated a surface plasmon peak at 2.2 eV and the peak resulted from formation of nanoparticles embedded in the matrix. The measured absorption was compared with calculated ones, evaluated by Maxwell-Garnett theory. Nonlinear absorption was measured with a pump-probe method using a femtosecond laser system. The pumping laser transiently bleached the surface plasmon band and lead to the nonlinearity. The transient response recovered in several picoseconds and behaved in terms of electron dynamics in metallic nanoparticles. The Ta nanoparticle composite is one of the promising candidates for nonlinear optical materials with good thermal stability. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 42.70.Nq; 78.47.+p; 78.67.Bf Keywords: Ion implantation; Ta nanoparticle; Optical absorption; Transient absorption; Core shell nanoparticle
1. Introduction All-optical devices, which directly operate optical signals with optical gate pulses, are attractive for future ultrafast networks and circuits ahead of semiconductor devices. The metal nanoparticles are of great interests for the photonic applications due to photo-induced nonlinear optical properties [1–3]. The nanoparticle composites consist of metal nanoparticles embedded in a transparent insulator and have the large optical nonlinearity with
*
Corresponding author. Tel.: +81-298-59-5058; fax: +81298-59-5010. E-mail address: [email protected] (Y. Takeda).
picosecond response around surface plasmon resonance in the visible light region. For device applications, it is imperative to tune the resonance band for the demanded wavelengths of optical circuits. The resonance of the composites depends on both dielectric constants of a matrix and of nanoparticles. The negative ion implantation has the advantage of application to various ion species and insulating substrates, and has enabled us to form self-assembled Cu nanoparticles in SiO2 and other insulators [4]. We have reported that tuning of the surface plasmon band and transient nonlinear absorption band is possible by selecting appropriate substrates [5,6]. Flexible selection of ions, not only applying to noble metals, is also vital to
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(03)00797-3
Y. Takeda, N. Kishimoto / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 620–623
tune the optical band of nanoparticle composites. Refractory metals, such as Ta and W, with high thermal stability are of high interests in optical properties for device applications. Applicability of refractory metal ions, in a nonequilibrium manner, is a unique merit of ion implantation techniques. In this paper, we present X-ray photoelectron spectroscopy, steady-state optical absorption and nonlinear transient response of Ta-implanted silica glass. We discuss the chemical state of Ta nanoparticles and performance of the composite as a nonlinear optical material.
2. Experimental Negative Ta ions of 60 keV were produced by a Cs-assisted plasma-sputter-type ion source with a cusp magnetic field. The detailed techniques have already been described elsewhere [7]. The dose rate and total dose were 0.3 lA/cm2 and 3 1016 ions/ cm2 , respectively. Insulating substrates used were optical-grade amorphous (a-)SiO2 (KU-1: 820 ppm OH ). The projectile range predicted by the SRIM 2000 [8] is 29 nm for SiO2 . A sample was annealed at 900 °C for 1 h in an Ar gas flow after the ion implantation. X-ray photoelectron spectroscopy data were obtained with an X-ray source of 15 kV–400 W Mg Ka (hm ¼ 1253:6 eV). Steady-state optical measurements were made in a photon energy range from 0.5 to 6.5 eV using a dual beam spectrometer. The measurements were carried out from both surfaces, i.e. the implanted- and the rear surface. Absorbance of the metal nanoparticle composites was measured after rigorous evaluation of incoherent multiple reflections [9]. Optical parameters of the substrate were determined by spectroscopic ellipsometry. Transient absorption experiments were performed using the femtosecond pump-probe method [10]. We used an output pulse from an optical parametric amplifier with sum-frequency generation as a pump pulse. The wavelength of the pump pulse was tuned near the surface-plasmon resonance, 574 nm (2.16 eV). The pulse duration was a few hundreds of femtoseconds. All the optical experiments were carried out at room temperature.
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3. Results and discussion X-ray photoelectron spectrum in Fig. 1 exhibits Ta 4f signals for an annealed sample after Ta ion implantation. Overlapped peaks are observed ranging from 20 to 30 eV of the binding energy in the spectrum. The strongest and the second peaks are assigned to the binding energy of Ta5þ 4f7=2 (26.1 eV) and 4f5=2 (28.5 eV), corresponding to oxide [11,12]. The shoulders at the lower energy are identified as the binding energy of Ta0 4f7=2 (21.8 eV) and 4f5=2 (23.7 eV), associated with metal [11,12]. The XPS result shows implanted Ta ions exist as both oxide and metal in silica glass. According to a cross-sectional TEM image of annealed sample, spheres of particles of 10–40 nm in diameter are distributed near the surface. Fig. 2 shows absorbance spectra of as-implanted sample and annealed sample. The as-implanted sample shows a broad peak at 2.2 eV in absorption, corresponding to the surface plasmon resonance, and the peak structure results from the formation of nanoparticle dispersed in the matrix
Fig. 1. XPS spectrum of Ta 4f of annealed a-SiO2 in Ar at 900 °C for 1 h, after implantation with 60 keV Ta to a total fluence of 3 1016 ions/cm2 at a flux of 0.3 lA/cm2 .
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Y. Takeda, N. Kishimoto / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 620–623
Fig. 2. Steady-state absorption spectra of as-implanted a-SiO2 and annealed a-SiO2 after Ta implantation with 60 keV, where a total dose and dose rate are 3 1016 ions/cm2 and 0.3 lA/cm2 , respectively.
[13]. In the annealed sample, the plasmon peak is enhanced, corresponding to the growth of nanoparticles, and slightly shifts to blue. The absorption above the peak position bleaches due to annihilation of defects in the matrix and nanoparticles [14]. Numerical calculations of absorption spectra of various nanoparticle composites in silica glass are also shown in Fig. 3. In the calculation the effective dielectric constants of the composites are evaluated by the Maxwell-Garnett formula [9,15], where the thickness of the composites is 50 nm and the volume fraction of
Fig. 3. Numerical calculations of absorption spectra of metal Ta, TaSi2 , TaOx and Ta + TaOx nanoparticle composites, evaluated by Maxwell-Garnett theory.
nanoparticles in the composites is 0.10. Tantalum silicide and oxide nanoparticle composites have no peak around 2 eV, while metal Ta nanoparticle composites clearly shows a surface plasmon peak at 1.8 eV. A composite, which consists of independent metal and oxide nanoparticles, has the spectrum averaged with them and the peak is held at the same position. Core-shell nanoparticles have been reported as a composite including of two components [16–18]. However the oxide shell largely attenuates the absorption [16]. The sharply plasmon peak results from metallic nanoparticles in the matrix. The optical and XPS results suggest that the composite form metal Ta nanoparticles and solute Ta oxides. The free enthalpies of formation, from tantalum and oxygen to tantalum oxide, are )762 and )532 kJ at 300 and 1700 K at 1 atm for 1 mol of oxygen molecular, respectively and slightly higher than those of silicon oxide, which are )824 and )578 kJ [19]. Coexistence of tantalum oxide and silicon oxide in the matrix is reasonable because the difference of the enthalpy is relatively small. The measured plasmon peak shifts to blue in comparison with the calculated one. Dielectric constants constant of nanoparticles varies by size effects of intraband and interband transition [20,21]. The peak position is almost independent of a size effect of the intraband transition, derived from the Drude model. The size effect causes change of the peak shape, which is not shown here. The interband transition has a large peak at 2 eV and dominates the dielectric constant of metal tantalum in the range [22]. The difference of the peak position may be due to the size effect of interband transition near the Fermi level. Nonlinear optical response in picoseconds is important to apply the composites to ultrafast alloptical switching devices, working at THz. Laser irradiation excites electrons in the metal nanoparticles and finally modulates the absorbance and transmittance. Fig. 4 shows temporal change of the absorption of an annealed sample. Immediately after the laser pumping near the plasmon band, the surface plasmon band of the nanoparticle composite is bleached around the center of 2.2 eV as shown in the inset in Fig. 4. The bleaching spectrum recovers within several picoseconds. The behavior shows typical conduction electron dynamics
Y. Takeda, N. Kishimoto / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 620–623
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Acknowledgements A part of this study was financially supported by the Budget for Nuclear Research of the MEXT, based on the screening and counseling by the Atomic Energy Commission. The authors are grateful to Dr. H. Amekura, Mr. K. Kono, Dr. T. Suga, Ms. J. Lu and Mr. N. Umeda for their assistance in the experiments.
References
Fig. 4. Time resolved data of laser-excited transient absorption for Ta nanoparticles in a-SiO2 , where the probe is at surface plasmon peak. The inset shows transient absorption spectrum, right after the laser excitation at 2.16 eV.
in metal nanoparticles and also suggests the existence of metallic nanoparticles in the composite. The tantalum nanoparticles have comparable transient response to noble metal nanoparticles and are potential as a nonlinear optical material for device applications. The ion implantation technique would be applied for optical design to fabricate nanoparticles by appropriate choice of refractory metal ions and a substrate.
4. Conclusions Negative Ta ions at 60 keV have been implanted into a-SiO2 and fabricated nanoparticles. XPS spectrum indicates both metal tantalum and the oxide embedded in the matrix. The Ta-implanted a-SiO2 shows a surface plasmon peak in the absorption spectrum and the peak is enhanced after annealing. TEM images show particles of 10– 40 nm in diameter distributed near the surface. The optical and XPS results suggest that the composite form metal Ta nanoparticles and solute Ta oxides in a-SiO2 . The nonlinear transient absorption obeys electron dynamics in the metallic nanoparticles. The transient response with several picoseconds bears comparison with that of noble metal nanoparticles.
[1] R.F. Haglund Jr., L. Yang, R.H. Magruder III, C.W. White, R.A. Zuhr, L. Yang, R. Dorsinville, R.R. Alfano, Nucl. Instr. and Meth. B 91 (1994) 493. [2] R.F. Haglund Jr., Mater. Sci. Eng. A 253 (1998) 275. [3] J.-Y. Bigot, J.-C. Merle, O. Cregut, A. Daunois, Phys. Rev. Lett. 75 (1995) 4702. [4] N. Kishimoto, N. Umeda, Y. Takeda, C.G. Lee, V.T. Gritsyna, Nucl. Instr. and Meth. B 148 (1999) 1017. [5] Y. Takeda, C.G. Lee, N. Kishimoto, Nucl. Instr. and Meth. B 190 (2002) 797. [6] Y. Takeda, C.G. Lee, V.V. Bandourko, N. Kishimoto, Mater. Trans. 43 (2002) 1057. [7] N. Kishimoto, V.T. Gritsyna, Y. Takeda, C.G. Lee, J. Surf. Sci. 4 (1998) 220. [8] J.F. Zieger, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon Press, New York, 1985 (http://www.srim.org/). [9] Y. Takeda, V.T. Gritsyna, N. Umeda, C.G. Lee, N. Kishimoto, Nucl. Instr. and Meth. B 148 (1999) 1029. [10] Y. Takeda, N. Umeda, V.T. Gritsyna, N. Kishimoto, Nucl. Instr. and Meth. B 175–177 (2001) 463. [11] J.Y. Zhang, I.W. Boyd, Appl. Surf. Sci. 168 (2000) 234. [12] A.Y. Mao, K.A. Son, J.M. White, D.L. Kwong, D.A. Roberts, R.N. Vrtis, J. Vac. Sci. Technol. A 17 (1999) 954. [13] U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer-Verlag, Berlin, 1995. [14] Y. Takeda, J.P. Zhao, C.G. Lee, V.T. Gritsyna, N. Kishimoto, Nucl. Instr. and Meth. B 166–167 (2000) 877. [15] J.C. Maxwell-Garnett, Philos. R. Soc. London 205 (1906) 237. [16] C.G. Granqvist, O. Hunderi, Phys. Rev. B 16 (1977) 3513. [17] J.H. Hodak, A. Henglein, G.V. Hartland, J. Phys. Chem. B 104 (2000) 5053. [18] J. Sinzig, M. Quinten, Appl. Phys. A 58 (1994) 157. [19] R.A. Swlin, Thermodynamics of Solid, John Wiley & Sons, Inc., New York, 1962. [20] U. Kreibig, in: J. Bourdon (Ed.), Growth and Properties of Metal Cluster, Elsevier, Amsterdam, 1980, p. 371. [21] F. Hache, D. Ricard, C. Flytzanis, U. Kreibig, Appl. Phys. A 47 (1988) 347. [22] J.E. Nestell Jr., R.W. Christy, Phys. Rev. B 21 (1980) 3173.