Decoupling and tuning the light absorption and scattering resonances in metallic composite nanostructures

Yossef Danan; Yehonatan Ramon; Jonathan Azougi; Alexandre Douplik; Zeev Zalevsky

doi:10.1364/OE.23.029089

1. Introduction

Metallic composite nanostructures are recently considered and explored as contrast agents for medical diagnostics and treatment and optical integrated circuits [1–5]. The main interest stems from special properties of the nanostructures such as a strong dependence of the plasmonic resonance on the size and shape of the nanoparticle as well as modifications of the Localized Surface Plasmon Resonance (LSPR) peak by the surrounding environment such as exterior coating or binding with proteins, and/or membrane structures [6–8]. The LSPR can be considered as a collective motion of free electron on the surface of metal nanoparticle within certain characteristic geometrical boundaries that is being coupled with the incident light [9,10]. Thus, when the incident electromagnetic frequency matches the electrons resonant frequency, a strong amplification of the optical absorption and scattering of the nanoparticle occurs [11]. As the size or shape of metallic composite nanoparticle changes, the surface geometry changes, causing an altering in the electric field on the surface. Thus, the oscillation frequency of the electrons will be changed, generating different optical cross-sections [10,12]. The efficiency of the metallic composite nanostructures as biomedical imaging contrast and therapeutic agents depends on their optical properties. The optical contrast can be based either on light absorptions or light scattering or both. The approach based on the absorption contrast is widely used, for instance for bright field imaging and laser thermal therapy [13–15]. The light scattering contrast is essential for cell imaging applications based on light-scattering modalities such as optical coherence tomography [16,17] or dark field microscopy [18,19].

For the absolute majority of known synthesized metal nanostructures sized up to tens of nanometers, the light absorption and scattering peaks spectral displacement is only few nanometers, so it is impractical to resolve the light scattering and light absorption resonances. However, spectral displacement between the absorption and scattering peaks for large metallic antenna, length of 1.7- 4.4μm, with and without dielectric cover [20], and metallic nanorods with a large ε_i value [21] have been observed. The resonance wavelength drift between the scattering and absorption is believed to arise from the differences between the far- field (scattering) and the near field (absorption) [20,22]. The resonance shift is also attributed to the frequency dependent inter-band transitions generated due to the suppression of the scattering at shorter wavelength, causing drift of the scattering from the absorption [23]. Moreover, the absorption is determined by the imaginary part of the polarizability and the scattering is determined by both the real as well as the imaginary parts of the polarizabilities. Therefore, there is a different phase between the absorption and the scattering [24]. Furthermore, Pablo Albella et al. showed, using numerical analysis of hemispherical gallium nanostructures on dielectric substrates, that resonance frequencies displacement depends on nanostructure’s size, shape and substrate. He did so by means of varying the illumination angle and the polarization [12].

There are certain biomedical applications where domination at a certain wavelength band of the light absorption over the light scattering or vice versa would be an advantage [6]. For instance, the photo-thermal therapy or optoacoustic diagnostics requires a high nanoparticle absorption cross-section at low scattering losses to minimize the laser attenuation, and consequently the irradiation dose [25]. The metal nanostructures such as solid nanospheres, nanorods and nanoshells have the absorption and scattering resonance peaks at practically the same wavelength. Hari P. Paudel et al. simulated nanoshell of 3.5nm silver core coated with 4nm TiO₂ and achieved up to 126 nm blue shift [26]. In the experiment of Martina Abb and associates [27] they showed resonance’s wavelength blue shift of up to 170nm for a rectangular dimer antenna with dimensions of 200x1120x24nm for the individual arms and a gap width of 2nm completely embedded in ITO. Those works demonstrate an approach to achieve larger wavelength shifts. However, they only shift the resonance wavelength without investigating the ratio between absorption and scattering.

In this paper we aim to design, simulate and demonstrate feasibility to fabricate composite metallic-silicon nanostructures, where the absorption and scattering resonance peaks are (1) changing their order and (2) such a change can be tuned across the spectrum. Particularly, we simulated Gold Nano Rod (GNR) coated with silicon that switches the order between the scattering and the absorption at the resonance peak. GNRs have two plasmon resonances, one due to the transverse oscillation of the electrons and the other because of the longitudinal. The transverse surface plasmon resonance does not depend on the aspect ratio and is at the same wavelength as the one of nano-spheres. While, the longitudinal surface plasmon resonance occurs at longer wavelengths and it is red shifted for larger aspect ratios. The tunability is obtained via modification of the refractive index of the silicon coating of the nanoparticle by a pumping light radiation. One of possible applications for the proposed nanoparticles is the capability to switch a bright field into a dark field microscope one merely by swapping between the scattering and the absorption resonance peaks at neither moving the sample nor modifying the microscope itself.

2. Methods

The relative contribution of scattering and absorption to the total extinction for the longitudinal mode was found to be significantly dependent on the size and the aspect ratio of the nanorods. For example, decreasing the aspect ratio of the nanoparticle causes a blue shift of the longitudinal plasmonic resonance [28]. The most effective way to enhance the scattering cross section relative to the absorption cross section is to increase the particle size, thus enhancing the volumetric radiative capacity [29].

We examine a GNR coated with silicon. The GNR and the silicon shell are examined in different sizes .This nanoparticle is continuously illuminated by two light beams, (1) a pump beam at a constant wavelength and (2) a reference beam with a wavelength in the range of interest for either imaging or for therapeutic application, as is described in Fig. 1 When the pump illumination is off we have light excitation at a resonant wavelength that corresponds to the geometry of the nanoparticle and the refractive index of the surroundings. By using a high intensity pump illumination, which is absorbed by the silicon coating of the GNR, the silicon free charge carrier density is changed and so is the refractive index of the coating due to the plasma dispersion effect [30]. When the carrier density inside the silicon coating becomes significantly high, we essentially obtain a metallic like nanoparticle coating, which in turn results in a different effective radius of the core gold nanoparticle. Using this approach we can control and modify the effective radius and aspect ratio of the structure by means of external illumination, hence changing the ratio between the absorption and scattering cross sections, and tuning the wavelength of the peak power excitation directly in “sampling” regime.

Fig. 1 Sketch of the gold core silicon shell nanostructure. The core consists of GNR with semi-major axis of 40-58nm, semi-minor axis of 26-35nm and silicon coating of 2-5nm. The nanostructure is illuminated by two light beams: pump beam at constant wavelength and a reference beam with a wavelength in the range of interest.

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The plasma dispersion effect causes the modification of the refractive index in the silicon coating as a result of alteration of the free carrier concentration. This alteration is given by [30]:

Δ n = \frac{- e^{2} λ_{0}^{2}}{8 π^{2} c^{2} ε_{0} n} (\frac{Δ N_{e}}{m_{e}^{*}} + \frac{Δ N_{h}}{m_{h}^{*}})

Δ α = \frac{e^{3} λ_{0}^{2}}{4 π^{2} c^{3} ε_{0} n} (\frac{Δ N_{e}}{μ_{e} m^{*} {_{e}}^{2}} + \frac{Δ N_{h}}{μ_{h} m^{*} {_{h}}^{2}})

where e is the electron charge, λ₀ is the wavelength in free space, c is the speed of light, n is the refractive index, ε₀ is the vacuum permittivity, m*_e and m*_h are the effective electron and hole masses. ΔN_e and ΔN_h are the change of the carrier concentration of the electrons and holes,

μ_{h}

and

μ_{e}

are the mobility of the electrons and holes.

The change of the free carrier concentration is given by:

Δ N_{e} = Δ N_{h} = \frac{η \cdot P}{h \cdot υ}

where η is the quantum efficiency, P is the intensity of the pump illumination and hυ is the energy of each photon.

Analysis of the refractive index change was conducted only for the silicon shell due to its semi-conducting nature which enables PDE, as described above. While the refractive index change of the gold core due to the pump and the reference beam is neglected. The pump beam is performed in different wavelength from the one of LSPR, and thus, although the high pump intensity, no significant change of the refractive index of the gold core occurs due to nonlinear absorption effects (such as two-photon absorption [31]). The reference beam does not have high intensity and thus it does not cause any non-linear effects what so ever. Several research groups show increase of the induced two photon-absorption from metallic nanoparticle, due to the high near field intensity on the nanoparticles surface at LSPR [31,32].

3. Numerical analysis

The calculation of the optical absorption and scattering coefficients of the nanoparticles is performed by using the discrete dipole approximation (DDA) method. In this method the target is divided into an array of N dipoles (j = 1…N), and Maxwell's equations are solved by finding the oscillating dipole moment [33].

The electric field at each of the N dipoles can be found by writing a sum of the incident field and the fields radiated by the others dipoles:

E_{j} = E_{i n c, j} - \sum_{k \neq j} A_{j k} \cdot P_{k}

where

E_{i n c, j}

is the incident field,

A_{j k}

is an interaction matrix between the j and k dipoles and

P_{k}

is the k dipole. Each interaction matrix

A_{j k}

is a 3X3 tensor:

A_{j k} = \frac{exp (i k r_{j k})}{r_{j k}} \cdot [k^{2} (\hat{r_{j k}} \hat{r_{j k}} - 1_{3}) + \frac{i k r_{j k} - 1}{r_{j k}^{2}} (3 \hat{r_{j k}} \hat{r_{j k}} - 1_{3})], j \neq k

where

k = \frac{ω}{c}

is the wave vector,

r_{j k}

is the distance between the dipoles j and k,

\hat{r_{j k}}

is a vector with unit length in the direction of the vector r_j-r_k and

1_{3}

is the identity matrix [33]. The matrix equation is solved in order to find the dipole moment:

A \cdot P = E_{i n c, j}

Once the dipole moment has been found, the absorption and scattering cross section can be calculated according to:

Q_{e x t} = \frac{4 π k}{{| E_{0} |}^{2}} \sum_{j = 1}^{N} i m (E_{i n c, j}^{*} \cdot P_{j})

Q_{a b s} = \frac{4 π k}{{| E_{0} |}^{2}} \sum_{j = 1}^{N} {i m [P_{j} \cdot {(α_{j}^{- 1})}^{*} P_{j}] - \frac{2}{3} k^{3} {| P_{j} |}^{2}}

The scattering cross section equals to:

Q_{s c a} = Q_{e x t} - Q_{a b s}

DDSCAT 7.3 [34] was employed for the calculations required in our design. We characterized the size of the target by the “Effective Radius” R_eff:

R_{e f f} \equiv {(\frac{3 V}{4 π})}^{\frac{1}{3}}

where V is the actual volume of the nanoparticle.

The resonance wavelength excitation was tested at the range of 500nm to 800nm. The inter dipole separation was chosen to be around 1nm, depending mostly on each nanostructure’s smallest feature. In order to obtain accurate solution without significantly increasing the computational complexity there was a limitation to use an inter dipole separation d to be small compared to any structural lengths in the target [34] and the wavelength λ to meet the condition [33]:

| m | k d < 1

Where m is the complex refractive index of the target material, and k ≡ 2π/λ, where λ is the wavelength in vacuum. The polarization of the incident light was parallel and perpendicular to the long axis of the nanoparticle in order to calculate the contribution of both, the longitudinal as well as the latitudinal plasmonic resonance. The light is incident from a direction perpendicular to the long axis of the nanoparticle. In Fig. 2 we show the convergence of the scattering and the absorption spectra for different inter dipole separations (the inter dipole separation affects the accuracy of the solution, while a denser inter dipole matrix will improve the accuracy of the solution, however, it will also increase the computational cost). In the convergence plot we chose GNR with aspect ratio of 2.12, overall effective radius of 45nm and silicon coating of 2nm for 1000W/cm² intensities of the pump radiation. We chose the thinnest silicon shell simulated in the simulation results section, 2nm, in order to demonstrate the convergence for the smallest feature. For d>3.4nm the spectra changed significantly, the LSPR wavelength changed and additional resonances were added.

Fig. 2 Scattering and absorption spectra convergence for GNR with aspect ratio of 2.12, overall effective radius of 45nm and silicon coating of 2nm for 1000W/cm² intensities of the pump radiation. The spectra are calculated for dipole separation of 3.4nm, 1.7nm, 1.1nm and 0.85nm.

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4. Simulation results

The results were obtained for three different cases: (1) changing the aspect ratio at fixed effective radius and silicon coating width, (2) changing the effective radius at fixed aspect ratio and silicon coating width and (3) changing the silicon coating width at fixed aspect ratio and effective radius. Those cases were chosen to get an overall view of the factors affecting the ratio between the optical cross sections and the location of the plasmonic resonance. The pump radiation could be at any wavelength in the region of absorbance of silicon. In those simulations 532nm wavelength was chosen. From now and on the dimensions of the overall particle will be attributed to the effective radius and aspect ratio in order to simplify the analysis.

First, GNR coated with 3nm Silicon with overall effective radius of 40nm and aspect ratio of 2, 2.25, 2.57 and 3 for 0W/cm², 500W/cm² and 1000W/cm² intensities of the pump radiation was examined. When the pump radiation intensity increases, the shape gradually changes from said a “GNR-Coated-by-Insulator” to “Solid-Metallic-Nanorod”, thus increasing the effective radius of the composite nanostructure and decreasing its aspect ratio (A.R). This blue shifts the plasmonic resonance by up to 56nm and increases the scattering-to-absorption ratio, as shown in Fig. 3 and Fig. 4 respectively. One can see the red shift and strengthening of the absorption on account of the scattering when the aspect ratio gets higher. In Fig. 3(c) and Fig. 3(d) there is an actual change of order between scattering and absorption after using pump light of 1000W/cm² and 500W/cm² respectively. There is slight spectral deviation of the resonance position between the absorption and scattering cross sections [24,35]. This spectral deviation is practically negligible in our simulations.

Fig. 3 Calculated spectra of Q_sca (dashed line), Q_abs (solid line) for gold nanorods at fixed silicon coating of 3nm and overall effective radius of 40nm with aspect ratio of: (a) A.R = 2 (b) A.R = 2.25 (c) A.R = 2.57 (d) A.R = 3, and three pump intensities: 0W/cm², 500W/cm² and 1000W/cm².

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Fig. 4 Effect of the pump radiation intensity on the scattering-to-absorption ratio. The effective radius and the silicon coating were fixed to 40nm and 3nm respectively.

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Second, GNR coated with 2nm silicon with aspect ratio of 2.3 and overall effective radius of 37nm, 39nm, 41nm and 43nm for 0W/cm², 500W/cm² and 1000W/cm² intensities of the pump radiation was examined. As mentioned before, when the pump radiation intensity increases the silicon coating became metal like due to the plasma dispersion effect. Thus, changing the dimensions of the overall nanoparticle and altering the spectral location of the LSPR and the scattering-to-absorption ratio as can be seen in Fig. 5 and Fig. 6 The blue shift of the plasmonic resonance is 30nm for all the different R_eff values because the main attribute to the LSPR spectral location is the aspect ratio and the silicon coating thickness. One can see strengthening of the scattering on account of the absorption when the particle volume gets higher. In Fig. 5(c) there is an actual change of order between scattering and absorption after using pump light of 500W/cm².

Fig. 5 Calculated spectra of Q_sca (dashed line), Q_abs (solid line) for gold nanorods at fixed silicon coating of 2nm and aspect ratio of 2.3 with overall effective radius of: (a) R_eff = 37nm (b) R_eff = 39nm (c) R_eff = 41nm (d) R_eff = 43nm, and three pump intensities: 0W/cm², 500W/cm² and 1000W/cm².

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Fig. 6 Effect of the pump radiation intensity on the scattering-to-absorption ratio. The aspect ratio and the silicon coating were fixed to 2.3 and 2nm respectively.

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Last, GNR with aspect ratio of 2.12, overall effective radius of 45nm and silicon coating of 2nm, 3nm, 4nm and 5nm for 0W/cm², 500W/cm² and 1000W/cm² intensities of the pump radiation was examined. The results can be seen in Fig. 7 and Fig. 8 One can see more significant spectral displacement of the LSPR for higher pump intensity when the silicon coating becomes thicker. This occurs because the particle volume changes more significantly due to the plasma dispersion effect for thicker silicon coating. Fig. 8 shows an increase of 34% between the ratio sca/abs for 0W/cm² to 1000W/cm² intensity of illumination with 3nm silicon coating.

Fig. 7 Calculated spectra of Qsca (dashed line), Qabs (solid line) for gold nanorods at fixed aspect ratio of 2.12 and effective radius of 45nm with silicon coating of (a) 1nm (b) 2nm (c) 3nm (d) 5nm, and three pump intensities: 0W/cm², 500W/cm² and 1000W/cm².

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Fig. 8 Effect of the pump radiation intensity on the scattering-to-absorption ratio. The aspect ratio and the effective radius were fixed to 2.12 and 45nm respectively.

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5. Feasibility experimental results

An array pattern of the nanoparticles was fabricated on top of SiO₂ by spin-coating SOI (Silicon on Insulator) chip with E-beam lithography resist (Poly-methyl-methacrylate A2), providing GNR dimensions of 10x50x80nm and 5-10nm silicon coating. The sample coated with PMMA was subsequently baked for 120 seconds on hotplate at 180 Celsius degrees. The desired pattern was exposed in the PMMA layer using CRESTEC CABLE-9000C high-resolution Electron-beam lithography system using different doses to control line and pitch width. Following this, the sample was developed for 50 seconds using MIBK (Methyl-isobutyl-ketone) and rinsed with IPA. Afterwards, the sample was deposited with 3nm of chrome, as an adhesive, and 10nm of Au and immersed in 100 KHz ultrasonic bath with Acetone for 3 hours for the resist liftoff. We ended up the sample fabrication process with deposition of another 10nm of silicon using BESTEC 2” DC magnetron sputtering process. One can see in Fig. 9 SEM (Helios 600, FEI) image and TEM (JEM 2100, JEOL) cross-sections of the coated gold nanoparticles. The substrate underneath the composite nanoparticle is SiO₂, the insulator of the SOI wafer, and the layer above the silicon is platinum, coated in order to protect the multi-layer structure from being damaged by the FIB processing. This FIB processing is not part of the fabrication process, but only intended for the preparation of our specimen for the TEM inspection. Our next step is to fabricate the same nanoparticles array with more accurate separation between two different nanoparticles by means of completely etching the silicon layer between them. This layer causes the whole surface to become more conducting under strong pump illumination. Thus, the overall composite became larger than the wavelength and the LSPR will not occur.

Fig. 9 Images of the fabricated GNR with dimensions of 10x50x80nm and 5-10nm silicon coating. (a) SEM image of the GNR array on top of silicon before the upper silicon layer deposition. (b) High resolution micrograph cross-section of the specimen detached using FIB. The GNR and the silicon coating are clearly seen. (c) Computed Fourier transform taken from the marked area in (d), showing sets of reflections corresponding to the inter planer spacing of Au. Inset (e) shows the magnified image of the area outlined by the white square.

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6. Conclusions

We have shown that changing the absorption-scattering order and ratio up to 34% in scattering-absorption ratio and tuning the plasmon resonance over the spectrum by up to 56nm is possible to obtain when designing silicon coated gold nanoparticle. Both the absorption and scattering resonance frequencies can be tuned in tens nm by external pumping radiation with varied intensity within the range of 0 to 1000W/cm². The proposed nanoparticles can be very applicable e.g. in microscopy by converting a bright field microscope into a dark field only by changing the power of the external pump illumination. As it has been shown in the feasibility experimental results, such nanoparticles can be physically synthesized and fabricated.

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Decoupling and tuning the light absorption and scattering resonances in metallic composite nanostructures

Abstract

1. Introduction

2. Methods

3. Numerical analysis

4. Simulation results

5. Feasibility experimental results

6. Conclusions

References and links

Cited By

Figures (9)

Equations (10)

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