Plasmonics DOI 10.1007/s11468-014-9677-4
Tunable Properties of Surface Plasmon Resonances: The Influence of Core–Shell Thickness and Dielectric Environment Nilesh Kumar Pathak & Alok Ji & R. P. Sharma
Received: 23 November 2013 / Accepted: 22 January 2014 # Springer Science+Business Media New York 2014
Abstract In the present study, we have investigated the extinction spectra of coated sphere (using dipole model) with different core–shell radius, in which the core is TiO2 and the shell is made up of silver or gold nanoparticles. Nanoparticles exhibit surface plasmon resonance peak; these plasmonic peaks are highly tunable in wavelength range of 300 to 1,100 nm; in fact, the blue and red shifting of resonance peak highly depends on the core–shell thickness. The broadness of resonance peaks are analysed in terms of full width at half maxima (FWHM), and the width of these resonance peaks is also the function of core–shell radius. Keywords Core–shell geometry . Surface plasmon resonance . Noble metal nanoparticle and extinction spectra
Introduction Metal nanoparticle embedded in the dielectric medium shows unique optical properties in particular regions of the electromagnetic spectrum. When these nanoparticles are irradiated by incident light photon, there is an oscillation of conduction electron with certain oscillating frequency known as plasma frequency. If frequency of incoming radiation matches with the plasma frequency, a resonance condition takes place known as surface plasmon resonance (SPR) [1–4]. Under this resonance condition, the optical field is highly localised and enhanced near the surface of the nanoparticles [5]. The effect of these surface plasmon resonance in metallic nanoparticle shows a significant role in plasmonics applications, such as N. K. Pathak (*) : A. Ji : R. P. Sharma Centre for Energy Studies, Indian Institute of Technology, Delhi 110016, India e-mail:
[email protected]
chemical and biological sensing and plasmonic photovoltaics [6–8]. For most of the cases, we have seen that SPR peaks of noble metal nanoparticle lie in the range of ultraviolet to infrared regions of the electromagnetic spectrum. These SPR positions are actually controlled by controlling the size, shape, surface coverage and local dielectric environment [9]. In the recent years, several theoretical and experimental efforts have been done to study the tunability of SPR of metallic nanoparticles. The tunable property of these SPR peak positions can be tuned by tuning the parameter such as the particle size, shape and surrounding media. Core–shell geometry is also one of the ways through which we can tune SPR peak positions as desirable ranges of electromagnetic spectrum. Here, we are considering the spherical core–shell metal nanoparticle in which the core is TiO2 and the shell is a noble metal such as silver or gold. The choice of material, which we are using in our present paper, is the highly tunable wavelength spectra ranging from ultraviolet, visible and infrared regions [10–14]. There are several models that have been developed to see the effect of optical properties such as absorption, scattering and extinction of core–shell nanoparticles [15]. In this paper, we have endeavoured to show an analytical approach to discuss surface plasmon resonances, magnitude of extinction peak and full width at half maxima (FWHM) of coated sphere in the visible and infrared regions of the electromagnetic spectrum. The coated geometry is one of the ways to tune the dielectric property of composites, and it also plays a significant role in tailoring of the SPR peak position. The present manuscript gives the researchers the idea that they can take different materials for coated geometry to see the effects of SPR peak positions and its broadening in the different regimes of the solar spectrum. Our analytical approach may also be applied to a broad solar spectrum of three-component composite systems. These concepts are of course beneficial for scientists and the research community.
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Method We have considered the wavelength-dependent dielectric constant of metallic nanoparticles to harvest solar light ranging from the visible to the infrared regions of the electromagnetic spectrum. The bulk dielectric constant of the core–shell system and embedding medium has been taken from the literature [16]. The choice of different embedding media would affect the resonance position, and these resonance positions are red shifted as we are increasing refractive index of embedding media. To analyse the resonance spectra of core–shell composite nanostructure, we have taken two types of embedding media having constant refractive index of n=1.05 for air and n=1.54 for silica [17]. In order to study the extinction spectra of the composite nanostructure, we have taken a certain well-known assumption, i.e., in quasistatic approximation under this approximation, the particle size is much smaller than the wavelength of incident light. It means that the phase of harmonically oscillating electromagnetic field is practically constant throughout the particle volume so that particle simply experience electrostatic field. With this quasistatic approximation, the expression of electric field outside the nanoparticle can be found by solving the Laplace equation with the appropriate boundary condition [18]. The expression of electric field due to spherical nanoparticle is the superposition of two fields: (1) applied field and (2) field of an ideal dipole. In our case, we are considering the core–shell spherical geometry; hence, the field induced by this composite (core+shell) geometry can be written in the form of effective polarisability and dipole moment [19]. p ¼ εm αeff E 0 αeff ¼ 4πr32 ½ðε2 εa −εm εb Þ=ðε2 εa þ εm εb Þ For our convenience, we have introduced a dielectric function which is the ratio of the shell volume to the core volume [11, 12]. εa ¼ ε1 ð3−2 f Þ þ 2ε2 f εb ¼ ε1 f þ ε2 ð3−f Þ f ¼ 1−ða=bÞ3 Where ε1 and ε2 are the dielectric constants of the core and the shell, εm is the dielectric constant of embedding media, ‘f’ is the ratio of the shell volume to the total volume (sum of the core and the shell volume), ‘a’ is the core radius and ‘b’ is the total radius of the core–shell system, ‘p’ is the effective dipole moment of the core–shell system, E0 is the incident electric field and αeff is the effective dipolar polarisability. In the core– shell nanostructure, we can take materials such as semiconductor, metal or dielectrics. There are two internal boundaries
in the core–shell geometry in which the electromagnetic boundary condition must be satisfied individually. Corresponding to these boundaries, there are separate excitations of surface plasmon resonance mode in the core as well as the shell. These two separately excited modes couple together at the interface of the core–shell structure and hence produce the complex extinction spectra. In order to understand the scattering and absorption cross-section of metallic nanoparticles, we have used an electrostatic model in which the size of the particle is much smaller than the wavelength of light [20]. k4 jαeff j2 6π ¼ kImðαeff Þ
C scat ¼ C absa
The sum of absorption and scattering is known as extinction cross-section, and normalising this extinction crosssection to the total area of (sum of radius of core and shell) the core–shell geometry gives rise to extinction efficiency of the core–shell nanostructure. Qextn ¼ ðC abs þ C scat Þ=πb2
ð1Þ
To calculate the absorption and scattering efficiency of the core–shell metal nanoparticle, dielectric constants of various materials are key requirements. However, the dielectric function of the metal nanoparticle at the nanolevel is completely different from the bulk material. For the larger-sized nanoparticle, the dielectric constant of the noble metal (silver and gold) is the same as the bulk; but for small particles, surface scattering obviously becomes the dominant contribution, hence there is a strong need for modification in the dielectric constant of the nanoparticle [21]. The size of the nanoparticle is smaller than the bulk mean free path of the noble metal nanoparticle. Hence, the size of the nanoparticle is an interesting topic for studying optical properties; therefore, there is a need to determine the size-dependent dielectric function of the metallic nanoparticle which can be found by solving the Drude–Lorentz model as [22]: εðωÞ ¼ εbulk ðωÞ þ
ω2p ω2
þ jγ bulk ω
−
ω2p ω2
− jγω
Where ωp is the bulk plasmon frequency, ω is the frequency of incident electromagnetic waves and γbulk is the damping constant of bulk silver. When the size of the particle is smaller than the mean free path, there is interaction between the free electron and particle boundary. Due to this effect, there is a need for modification in the damping constant of bulk silver. The modified damping constant of bulk silver is γ ¼ γ bulk þ A
vf aeff
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Where τ=1/γ is the effective relaxation time, τbulk =1/γbulk is the bulk metal free scattering time, vf =1.39×106 m/s is the Fermi velocity of electron in silver, A is geometrical parameter and its value lies between 2 and 1 (in our case, we have chosen A=1 [23]) and aeff is the effective radius of the core–shell system; for the core–shell nanoparticles, it can be expressed in terms of inner and outer radii as
aeff ¼
1 = 1 3 ðb − aÞ b2 − a2 2
The bulk optical property of gold and silver nanoparticle is different at nanolevel properties. Here, we have used the core–shell spherical geometry in which effective shell thickness is smaller than the mean free path of bulk metallic materials, and the mean free path is 42 nm for gold and 52 nm for silver [22]. However, the dielectric constant of the nanoparticle becomes thickness dependent. Hence, the spectral response of the coated geometry is much more tunable.
Result and Discussion The extinction peak of the different core–shell radius with wavelength is shown in Fig.1a–c for silver nanoparticles. Firstly, we have taken Tio2 as a core, silver as a shell and air having dielectric constant of 1.05 is the embedding media. The thickness of the silver shell is taken at 2 nm which is fixed and with varying core radius from 7 to 13 nm with difference of 2 nm. We have seen that the extinction spectra with fixed shell thickness and varying core radius have wide tunability of the resonance peaks position [24]. There are two extinction peaks (for silver shell) found by our analytical expression indicated by Eq. (1); the first peak lies in the ultraviolet range at a wavelength of nearly 330 nm, and the second peak is highly tunable from the visible to the infrared region of the solar spectrum. This tunability of resonance peaks can be controlled by controlling the core–shell thickness and surrounding dielectric media. For 2-nm shell thickness and 7nm core radius, the value of extinction efficiency at SPR wavelength (585 nm) is 0.6343 with a FWHM nearly at 136 nm shown in Table 1. Figure 2a–c shows the calculated extinction spectra of TiO2/Au (core–shell) system embedded
Fig. 1 a–c Extinction spectra of TiO2/Ag core–shell nanoparticles embedded in air with different core radius at the thickness of shell set to 2, 3 and 4 nm
Plasmonics Table 1 Resonance wavelength and FWHM of core–shell system embedded in air (1.05) with different core–shell radius
Shell thickness (nm)
Core radius a (nm)
SPR peak for Ag (nm)
SPR peak for Au (nm)
FWHMF for Ag (nm)
WHM for Au (nm)
2
7 9 11 13 7 9 11 13 7 9
585 642 695 743 509 550 592 631 471 505
676 722 770 826 612 653 693 721 590 621
136 157 174 178 78 90 100 108 58 62
210 226 243 262 144 149 151 160 151 154
11 13
535 569
639 667
67 71
115 117
3
4
in air (1.05). It can be seen that the resonance position is also blue shifted as we are increasing the shell thickness, but in the case of TiO2/Au (core/shell), peak broadening is more as compared to the TiO2/Ag (core/shell) system. This gradual increase in the spectral width is due to the scattering of surface
electron in thin metallic nanoshell. For the same example, 2nm gold shell thickness and 7-nm core radius SPR peaks were obtained at a wavelength of 676 nm with an extinction value of 0.3324 and width of the resonance peak (FWHM) of 210 nm. With the same value of the core–shell radius, TiO2/
Fig. 2 a–c Extinction spectra of TiO2/Au core–shell nanoparticles embedded in air with different core radius at the thickness of shell set to 2, 3 and 4 nm
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Fig. 3 a Extinction spectra of TiO2/Ag core–shell nanoparticles embedded in silica with different core radius at the thickness of shell set to 2, 3 and 4 nm
Ag and TiO2/Au shows the different behaviour of resonance peak, extinction value and spectral width. Table 1 illustrates the SPR peak and FWHM of silver and gold nanoparticle. Figure 3a–c shows the extinction spectra of the core–shell (TiO2/Ag) nanostructure embedded in silica matrix with Table 2 Resonance wavelength of core–shell system embedded in SiO2 (2.37) with different core– shell radius
dielectric constant of 2.37. It can be seen that when increasing the refractive index of embedding media, a gradual red shifting of resonance will occur. The higher the refractive index of the embedding medium, the more will the polarisation be which will weaken the restoring forces inside
Shell thickness (nm)
Core radius a (nm)
λAg (nm)
λAu (nm)
FWHM for Ag (nm)
FWHM for Au (nm)
2
7 9 11 13 7 9 11 13 7 9 11 13
671 742 802 863 581 634 682 725 533 576 616 652
747 812 878 922 673 717 764 806 638 670 704 738
183 199 222 243 105 120 130 139 75 82 92 100
259 285 305 324 162 175 188 202 129 120 137 145
3
4
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the polarised particles. This gives rise to the excitation of other oscillating mode resulting in shifting of resonance towards the higher wavelength side. For the case of TiO2/Ag core–shell system embedded in silica (SiO2), two SPR peaks were obtained. The first resonance peak occurs at 330 nm, and it does not show any variation with the core–shell thickness while the second peak is highly tunable and depends on the core–shell parameter. For 2-nm shell thickness and 13-nm core radius, SPR peak was obtained at 863 nm; for the case of 4-nm shell thickness and 13-nm core radius, LSPR peak was obtained at 652 nm. Hence, from Table 2, we conclude that as we increase the shell thickness, our resonance is blue shifted because the effect of the core becomes weaker. Figure 4a–c shows the extinction spectra of TiO2/Au nanoparticle embedded in SiO2. For the 2-nm shell thickness and different core radius, we have tunable resonance spectra ranging from 300 to 1,100 nm. From the figure, we conclude that the advantage of shell thickness is twofold: firstly, shifting of resonance position (resonance is blue shifted as we are increasing the shell thickness and vice versa) and, secondly, broadening of the resonance peak [25]. Table 1 illustrates
the thickness-dependent SPR peak and FWHM of silver and gold metallic nanoshell. For 2-nm shell thickness, there is consistent increase in the FWHM value and gradual shift in the plasmon peak position. The width of the SPR peak is due to the decreased mean free path of conduction electron of noble metallic nanoshell. Table 2 exhibits thicknessdependent SPR peak positions and width of the resonance peak (FWHM) with silica as the embedding media.
Conclusion In this work, we have explained the optical properties such as extinction spectra of core–shell spherical geometry based on analytical calculation by using electrostatic approximation. The importance of this nanoshell geometry can be seen in tuning of plasmonic peak position and its broadening. The SPR peak position of gold nanoparticle can be tuned from 590 to 922 nm with air and silica as embedding media; for silver, it can be tuned from 505 to 863 nm, and tuning of these plasmonics peak can be controlled by controlling the core–
Fig. 4 a Extinction spectra of TiO2/Au core–shell nanoparticles embedded in silica with different core radius at the thickness of shell set to 2, 3 and 4 nm
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shell radius. Hence, the core–shell nanostructure is an open channel for scientists and researchers so that they can tune the plasmonics resonance position and spectral width according their own requirement by considering different types of core– shell material. Acknowledgements This research is financially supported by MNRE India.
References 1. 2. 3. 4. 5. 6. 7. 8. 9.
Homola J (2008) Chem Rev 108:462–493 Dostalek J, Knoll W (2008) Biointerphases 3:12–22 Hutter E, Fendler JH (2004) Adv Mater 16:1685–1706 Catchpole KR, Polman A (2008) Opt Express 6:21793–21800 Sangita AJ, Sharma RP (2012) J Phys D Appl Phys 45:275101– 25107 Lal S, Grady NK, Kundu J, Levin CS, Lassiter JB, Halas NJ (2008) Chem Soc Rev 37:898–911 Willets KA, Van Duyne RP (2007) Annu Rev Phys Chem 58:267–97 Nilesh K, Pathak Alok Ji, R. P. Sharma (2013). Appl Phy A. doi: 10. 1007/s00339-013-8061-0 Matthew J, Lane D, Grest GS (2010) Phy Rev Lett 104:235501– 235504
10. Niesen B, Rand BP, Van Dorpe P, Shen HH, Maes B, Genoe J, Heremans P (2010) Opt Express 18:19032–19038 11. Ruppin Surface R (1975) Science 51:140–148 12. Lim SK, Chung KJ, Kim CK, Shin DW, Kim YH, Yoon CS. J. Appl. Phys.98 (2005) 084309 13. Biswas A, Aktas OC, Schurmann U, Saeed U, Zaporojtchenko V, Faupel F, Strunskus T (2004) Appl Phys Lett 84:2655 14. Kelly KL, Coronado E, Zhao LL, Schatz GC (2003) J Phys Chem B 107:668 15. Alok Ji, Sharma, Kumari A, Pathak NK (2013) Plasmonics. Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, India, 7 pp 16. Palik ED (ed) (1985) Handbook of optical constants of solids. Academic, Orlando 17. Zheng YB, Huang TJ, Desai AY, Wang SJ, Tan LK, Gao H, Huan ACH (2007) Appl Phys Lett 90:18311 18. Maier S (2007) Plasmonics: fundamentals and applications. Springer, Berlin 19. Jackson JD (1999) Classical electrodynamics, 3rd edn. Wiley, New York 20. Bohren C, Huffmann D (1983) Absorption and scattering of light by small particles. Wiley, New York 21. Noguez CJ (2007) Phys Chem C 111:3806 22. Kreibig U, Vollmer M (1995) Optical properties of metal clusters. Springer, Berlin 23. Johnson PB, Christy RW (1972) Optical constants of noble metals. Phys Rev B 6(12):4370–4379 24. Gabudean AM et al (2011) Opt Mater 33:1377–1381 25. viste A, Plain JR, Jaffiol R, Vial A, Adam PM, Royer P (2010) ACS Nano 4:759–764
