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The split of surface plasmon resonance of self-assembled gold nanoparticles on Si substrate is observed from the dielectric functions of the nanoparticles. The split plasmon resonances are modeled with two Lorentz oscillators: one oscillator at ~1 eV models the polarization parallel to the substrate while the other at ~2 eV represents the polarization perpendicular to the substrate. Both parallel and perpendicular resonances are red-shifted when the nanoparticle size increases. The red shifts in both resonances are explained by the image charge effect of the Si substrate.
©2010 Optical Society of America
For metallic nanoparticles, whose sizes are significantly smaller than the wavelength of light, a strong optical absorption peak in the visible range of the spectrum can be identified; and this phenomenon is related to the localized surface plasmon resonance (LSPR). The LSPR is a collective oscillation of conduction electrons inside nanoparticles, whose frequency is strongly dependent on the size and shape of the particles, the interparticle distance, and the refractive index of surrounding medium [1–3]. For anisotropic nanoparticles, more than one plasmon excitation bands (longitudinal or transverse waves) may be simultaneously observable according to the symmetric axes of excitation [1,4,5]. For instance, multipolar surface plasmon peaks have been observed on gold nanotriangles [6]. Moreover, some researchers reported that near-field coupling between neighboring nanoparticles may give rise to the plasmon band splitting [7,8]. The collective effects has been described by many authors, especially the work by Kooij et. al. gives an indication of the extent of peak splitting [9]. Besides the coupling effect, the influence of the substrate can also be significant [7,10,11]. However, the effective dielectric function study on the effects of near-field coupling and image dipole is so far limited.
In this work, the effective dielectric functions of the self-assembled gold nanoparticles on silicon substrate under collective excitations have been determined from spectroscopic ellipsometry (SE) measurement. The effective dielectric functions of the nanoparticles were well represented by a Drude term and three Lorentz oscillators: one Lorentz oscillator and Drude term modeled the inter-band and free electron transitions, respectively; while the other two Lorentz oscillators each modeled the polarization parallel and perpendicular to the substrate. The structural properties of the nanoparticles were obtained using scanning electron microscope (SEM) measurement. The results revealed that the response of the gold nanoparticles was more related to the image effect of the Si substrate.
A p-type silicon wafer was cleaned and its native oxide was removed by diluted HF solution. Au films of 3, 5 and 8 nm thick were deposited on the silicon wafer by electron-beam evaporation. During the deposition, the base pressure was below 5 × 10−6 mbar, and the deposition rate was 0.1 Å per second. After the deposition, these samples were annealed using rapid thermal annealing (RTA) at 400°C for 30 seconds in N2 ambient. SEM was used to characterize the structural properties of the gold nanoparticles formed on the silicon substrate. The SE measurements were performed using a variable angle spectroscopic ellipsometer (J. A. Woollam, Inc). The ellipsometric angles (Ψ and Δ) were measured in the wavelength range of 300-1100 nm with the step of 5 nm at three different angles (65°, 70° and 75°) of incidence, respectively. The detailed methodology in determining the effective dielectric functions of gold nanoparticles from the spectral fitting of ellipsometric angles is presented elsewhere [12].
Figure 1 shows the SEM images of Au thin film of various thicknesses after RTA. It was observed that the Au thin films break into particles due to surface tension and compressive stress associated with the mismatch of the thermal expansion coefficients of Si and Au [13]. Although the fabricated nanoparticles have a large size distribution, their mean particle size varies proportionately to the initial Au layer thickness. The thicker the Au film was deposited, the more inter-links between particles can be observed, which gradually turned into irregular interlocked islands [14]. In more details, for the 3 nm thick Au thin film (sample 1), the mean size of Au nanoparticles obtained was 24.5 nm, with density of 9.88 × 1011 cm−2 and average particle-particle distance (assume a square distribution) of approximately 14.2 nm. For the 5 nm (sample 2) and 8 nm (sample 3) thick Au thin films, the mean sizes of nanoparticles were 31.7 and 53.9 nm, with densities of 4.94 × 1011 and 1.61 × 1011 cm−2, and average separations of approximately 20.1 and 35.2 nm, respectively.
Fig. 1 Size distribution of the Au nanoparticles: (a) sample 1 (mean size: 24.5nm; average separation: 14.2nm), (b) sample 2 (mean size: 31.7nm; average separation: 20.1nm) and (c) sample 3 (mean size: 53.9nm; average separation: 35.2nm). The inserts show the SEM micrographs of the samples.
The effective dielectric function of gold nanoparticles are related to free and bound electrons transitions, which can be described by the Drude term and Lorentz oscillators, and the corresponding energy-dependent function is described by [15]
where ε∞ is a background constant or an offset, Ai is the amplitude of the oscillator with the unit of (eV)2, Ei is the resonance energy with the unit of eV, Γi is the damping factor of the oscillator with the unit of eV, Ep is the unscreened plasma energy with the unit of eV and τD is electron relaxation time with unit of fs. The number (n) of Lorentz oscillators was determined to be 3 in the present study. The spectral fittings to the experimental ellipsometric angles (Ψ and Δ) were performed by adjusting the parameters in Eq. (1) together with effective layer thickness and void volume faction to minimize the mean-square error between the measured and calculated ellipsometric angles. As an example, Fig. 2 shows the spectral fitting for sample 1. All spectral features can be fitted excellently. As reported earlier [12], one oscillator is due to the 3d energy band-to-Fermi level interband transitions, while the other two Lorentz oscillators are required to describe the plasmon band splitting with the energy separation of ~1 eV. On the other hand, our study shows that although the contribution of the Drude term increases with the nanoparticle size, it is much smaller as compared to that of the Lorentz oscillators for all the samples. As such, we will focus on the Lorentz oscillators only in the discussions below.Fig. 2 Spectral fittings to the experimental ellipsometric data at different angles of incidence for sample 1.
Figure 3 shows the effective dielectric functions of gold nanoparticles with different mean sizes and interparticle spacing, and the dielectric function of Au film with thickness of 80 nm considered as bulk Au is also included for comparison. It was observed that the effective dielectric functions of Au nanoparticles become more similar to that of bulk Au as their mean size and interparticle distance increase. As shown in Fig. 3(a), the real part (ε1) of dielectric function is partially positive for samples 1 and 2, while it becomes fully negative over the entire spectral range like bulk Au for sample 3. Similar observation has been reported for discrete metal island films [16]. In addition, a prominent increase in ε1 for sample 1 can be observed when the photon energy decreases below ~1.3 eV and a positive value of ε1 is achieved at the photon energy of ~1.1 eV. On the other hand, some peak structures in the imaginary part ε2 at ~3.6, ~2 and ~1 eV can be also observed from Fig. 3(b). Figure 4 shows the absorption coefficients of the gold nanoparticles of samples 1, 2 and 3, and the bulk Au film is also included for comparison. The absorption peaks corresponding to the interband transition and the surface plasmon resonances can be observed. Note that due to the limited spectral range of the SE measurement, the plasmon resonance at ~1 eV (~1240 nm) cannot be fully displayed in the spectra of both ε2 and the absorption coefficient.
Fig. 3 (a) Real part (ε1) and (b) imaginary part (ε2) of the effective dielectric function ε of the gold nanoparticles. The dielectric function of bulk Au film is also included in the figure for comparison.
Fig. 4 Absorption coefficient α ( = 4πk/λ where k is the extinction coefficient and λ is the wavelength) of the gold nanoparticles. The absorption coefficient of bulk Au film is also included in the figure for comparison.
The inhomogeneous polarizations parallel and perpendicular to the substrate can cause splitting of the plasmon band. One of the possible reasons for the inhomogeneous polarizations is the non-sphericity of the nanoparticles [17,1]. However, the dielectric functions obtained from the spectral fittings to the experimental ellipsometric angles at three different angles of incidence are found to be independent of the angles of incidence. Therefore, the non-sphericity of the nanoparticles should not be the major reason for the plasmon resonance splitting observed in this work. The near-field coupling between the neighboring nanoparticles and/or the image charge effect of the Si substrate could be the main factors responsible for the inhomogeneous polarizations. Such argument is supported by the dependence of the Lorentz oscillators on the structural properties of the nanoparticles. Figure 5 shows the imaginary part of the three Lorentz oscillators as a function of photon energy for different samples. As shown in Fig. 5(a), the resonance energy of Lorentz 1 corresponding to the interband transitions is about the same for different samples (i.e., samples 1 to 3), indicating that the interband transitions are not largely affected by the structural properties of the nanoparticles. However, Fig. 5(b) and (c) demonstrate a clear structural dependence of the two other Lorentz oscillators which represent the two plasmon resonance bands. It has been pointed out that the low energy band corresponding to the resonance parallel to the substrate is a dominant one, while the perpendicular resonance is less significant [18]. Therefore, Lorentz 2 at ~2 eV and Lorentz 3 at ~1 eV are attributed to the polarizations perpendicular and parallel to the substrate, respectively. It can be seen from Figs. 5(b) and (c) that both perpendicular and parallel resonances are red-shifted when both the nanoparticle size and separation increase. It has been reported that interparticle coupling could split the plasmon resonance band into a blue-shifted perpendicular resonance and a red-shifted parallel resonance [10]. If a nanoparticle is regarded as a harmonic oscillator, in the perpendicular direction, the near-field coupling effect between neighboring nanoparticles can increase the effective restoring force, resulting in a blue shift in the resonance energy; but in the parallel direction, the coupling effect can reduce the effective restoring force, leading to a red shift [10]. Therefore, with increasing the interparticle separation, a weaker coupling effect is expected, and thus a red shift in the perpendicular resonance and a blue shift in the parallel resonance should be observed. However, as shown in Fig. 5(b) and (c), when the average interparticle separation increases from 14.2 to 35.2 nm, both the perpendicular and parallel resonances show a red shift. This could suggest that the coupling effect is not the dominant factor responsible for the splitting of the plasmon band as a result of the relatively large interparticle separations. On the other hand, the plasmon resonances are also sensitive to the image charge effect of the Si substrate. Assuming the nanoparticle acts like a point dipole, the interaction between the induced image point dipole in the substrate and the nanoparticle itself should modify the polarizations, and thus lead to changes in the plasmon resonance bands. The induced image charge in the substrate reduces the net effective restoring forces in both directions as the induced point dipole offsets the restoring forces of the nanoparticle [10]. Therefore, although the strength of the image dipole contribution is dependent on the dielectric functions of the substrate as well as the separation between the image and the nanoparticle [11], red shifts in both resonances are expected. An enlarged contact area is achieved as the particles become flatter when the film thickness (or nanoparticle size) grows [19], and this can lead to a more prominent substrate effect. In addition, as the size of the nanoparticles increases, the image charge in the substrate will be increased also [18]. Therefore, the red shifts in both resonances with increasing nanoparticle size shown in Fig. 5(b) and (c) could be explained by the image charge effect of the Si substrate. A similar observation of red-shifts of the plasmon resonance bands as a result of growing silver islands has been reported also [17].
Fig. 5 Influence of structural properties on the three Lorentz oscillators: (a) Lorentz 1; (b) Lorentz 2; (c) Lorentz 3.
In summary, the split of surface plasmon resonance of self-assembled gold nanoparticles on Si substrate has been observed from the dielectric functions of the nanoparticles. The split is attributed to the inhomogeneous polarizations parallel and perpendicular to the substrate. Both parallel and perpendicular resonances are red-shifted when the nanoparticle size increases. The split and the red shifts in both resonances could be explained by the image charge effect of the Si substrate.
Acknowledgements
This work has been financially supported by National Research Foundation of Singapore (NRF-G-CRP 2007-01). Y. Liu acknowledges the National Science Foundation of China (NSFC) under project No. 60806040, and the Grant under project No. 2008ZC80.
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