Efficient Simulation for light scattering from plasmonic core-shell nanospheres on a substrate for biosensing
Huai-Yi Xie,1,2 Minfeng Chen,1 Yia-Chung Chang,1,3,* and Rakesh Singh Moirangthem1,4
1Research Center for Applied Sciences, Academia Sinica, 128 Academia Road, Sec. 2, Taipei 11529, Taiwan
2National Center for Theoretical Sciences (South), National Cheng Kung University, Tainan 701, Taiwan
3Department of Physics, National Cheng Kung University, Tainan, 701 Taiwan
4Department of Applied Physics, Indian School of Mines, Dhanbad – 826004, Jharkhand, India
We have developed an efficient and accurate numerical method to investigate light scattering from plasmonic nanospheres on a substrate covered by a shell, based on the Green’s function approach with suitable spherical harmonic basis. We use this method to study optical scattering from DNA molecules attached to metallic nanoparticles on a substrate and compare with experimental results. We obtain fairly good agreement between theoretical predictions and the measured ellipsometric spectra. The metallic nanoparticles were used to detect the binding with DNA molecules in a microfluidic setup via spectroscopic ellipsometry (SE), and a detectable change in ellipsometric spectra was found when DNA molecules are captured on Au nanoparticles surface. Our theoretical simulation indicates that the coverage of Au nanosphere by a submonolayer of DNA molecules, which is modeled by a thin layer of dielectric material, can indeed lead to a small but detectable change in ellipsometric spectra. Our studies demonstrated the ultra- sensitive capability of SE for sensing submonolayer coverage of DNA molecules on Au nanospheres. Hence the spectroscopic ellipsometric measurements coupled with theoretical analysis via an efficient and accurate computation method can be an effective tool for detecting DNA molecules attached on Au nanoparticles, thus achieving label-free, non-destructive, and high-sensitivity biosensing with nanometer resolution.
A variable-angle spectroscopic ellipsometer (VASE, J. A. Woollam Co.) system was used to conduct the spectroscopic ellipsometry (SE) measurements of Au nanoparticles covered by DNA molecules with a setup as shown in Fig. 1(a). Gold nanoparticles with average diameter of 13nm were prepared by reduction of chloroauric acid (HAuCl4) solution. The Au nanoparticles solution was poured on a chemically modified glass surface and dried with nitrogen gas. The DNA sequence containing 16 bases single strand oligonucleotides 5′ C T A C C T T T T T T T T C T G 3′(Thiol (SH) group modified) and 5′ C A G A A A A A A A G G T A G 3′were used for hybridization. The DNA molecules were diluted in 5x saline-sodium citrate buffer (SSC, pH= 7.0). One micromole (µM) of probe SH-DNA molecules was injected onto gold nanoparticle sample surface integrated with micro-fluidic cell. The solution is kept for 3 hours to achieve sufficient coverage of DNA molecules on surface of gold nanoparticle layer. The sample is further rinsed with SSC buffer to remove unbound probe DNAs. Finally, 1 µM of target DNA solution was injected into the micro-fluidic cell and kept for another 5 hours to undergo DNA hybridization. Rinsing process is repeated after the experiment to remove the non-hybridized target DNAs. Fig. 1(b) shows the AFM picture of the hybridized DNA sequence attached on Au nanoparticles.
Figure 1. (a) Optical setup of surface plasmon resonance ellipsometry used in the present study with the illustration of polarization of incident and reflected light within the prism (treated as ambient) (b) AFM image of DNA molecules attached on Au nanoparticles with diameter 13 nm.
The detail theoretical formulation of Green’s function method which calculates the light scattering from nanoparticles on the substrate partially covered by DNA shells is given in Ref. . We model the DNA coverage by an effective dielectric thin shell which encloses the Au nanosphere as shown in Fig. 2 since the Au nanoparticles are attached to the glass before the coverage of DNA molecules. We consider the effective-medium dielectric constant of the DNA-filled shell as an adjustable parameter and fit the experimental data for ellipsometric spectra. Fig. 3(a) shows the measured ellipsometric spectra (Ψ and Δ) obtained by VASE for a random distribution of closely-spaced nanospheres on a BK7 prism without (black solid line) and with (red dash-dotted line) the DNA coverage. We observed a small but detectable red shift of the plasmonic peak in both Ψ and Δ spectra when DNA molecules are attached. We find that the shift in Δ spectrum is much more pronounced than the Ψ spectrum, indicating a better sensitivity for sensing by using the Δ signal. In Fig. 3(b) we show the theoretical results for a random distribution of closely-spaced Au nanospheres with (red dash-dotted line) and without (black solid line) the DNA coverage obtained by the GF method adapted to random scatterers . Here, we have used the dielectric constant of a Au film measured by ellipsometry as the input parameter for describing the Au nanoparticle and the average distance between Au nanoparticles is taken to be 30 nm. For the DNA filled layer, we choose an effective layer thickness of 2.5 nm, which corresponds to the diameter of a double-strand DNA , and treat the dielectric constant of the effective medium layer as an adjustable parameter. The best fit is obtained with an effective-medium dielectric constant of 1.96 for the shell of solution loosely filled by DNA strands as indicated by the red dash-dotted curve in Fig. 3(b). The simulation results indicate a small red shift of the plasmonic peak in the Ψ spectrum when the DNA molecules are attached, which is in reasonable agreement with the experimental result.
To check the reliability of the current GF method, we also performed the calculation for a periodic array of Au nanospheres compare with the results obtained by using the COMSOL package and the results obtained by these two methods agree quite well . However, it is difficult to use the COMSOL package to calculate the scattering spectra from a random distribution of Au nanoparticles, as it will take prohibitively long time. We found that our current GF method is more efficient than the COMSOL package, since the finite-element method requires very high mesh density to simulate the strongly localized electromagnetic fields near the plasmonic resonance. For example, it took about 3.3 hours to obtain the corresponding spectrum for the black curve in Fig. 3(b) by using COMSOL (for a periodic array) with a single Intel 1.7GHz i5 processor, while it took 3 minutes for the GF calculation for the same periodic array, and only 30 (210) seconds to generate the spectrum for the random distribution of Au nanoparticles without (with) DNA coverage as shown by the black (red dash-dotted) line in Fig. 3(b) by using a single Intel 1.7GHz i5 processor. So, our GF method is especially effective for treating random distribution of core-shell nanoparticles on a substrate.
We further considered the nonlocal quantum effect for the Au nanoparticle by adding the quantum correction to the imaginary part of the dielectric constant according to the model described in Ref. 4. The results for the random distribution of Au nanoparticles without (with) DNA coverage as shown by the black (red dashdotted) line in Fig. 3(c) with the average interparticle distance taken to be 26.5 nm and the best-fit effective medium dielectric constant for the DNA filled layer to be 1.96+0.2i. The imaginary part used for the effective-medium dielectric constant describes the Au-nanoparticle induced absorption of the DNA molecules near the resonance frequency, which could be caused by the charge transfer from Au to DNA. Comparing this with Fig. 3(a) and (b), we found that including the non-local effect gives even better agreement with the experimental data, especially for the Δ spectra.
The close agreement between our GF method and COMSOL package indicates that our current GF approach for treating core-shell nanoparticles is reliable. Including the effect of random distribution and nonlocal effect gives very good agreement with the experimental results shown in Fig. 3(a).
Figure 2. Schematic diagram of light scattering from a Au nanoparticle on a substrate partially covered by DNA molecules.
The importance of the study
We use an efficient and accurate theoretical method to model the DNA coverage on metallic spheres on a substrate. First, we illustrate how to use the model calculation based on the Green’s function approach to interpret the ellipsometric spectra of randomly distributed coupled Au nanospheres placed on a BK7 dove prism. We found fairly good agreement between the model calculation and experiment. Importantly, we have used spectroscopic ellipsometry to detect the coverage of Au nanoparticles by DNA molecules. We found a small but detectable spectroscopic shift in both the Ψ and Δ spectra with more significant change in Δ spectra in both experimental and theoretical results. So, we have demonstrated that the spectroscopic ellipsometric measurements coupled with theoretical analysis via an efficient and accurate computation method can be an effective tool for detecting DNA molecules attached on Au nanoparticles, thus achieving label-free, non-destructive, and high-sensitivity biosensing with nanometer resolution.
Figure 3. (a) Experimental ellisometry spectra (Ψ and Δ) obtained by VASE for a random distribution of Au nanoparticles placed on a BK7 prism without (black line) and with (red dash-dotted line) the DNA molecules attached. (b) Calculated ellisometry spectra (Ψ and Δ) for a random distribution of Au nanoparticles obtained by the GF method without (black line) and with DNA coverage (red dash-dotted line). In the fitting, the thickness of DNA shell used is 2.5nm, the effective dielectric constant of the DNA shell is 1.96, and The pitch is 30nm. (c) Calculated ellisometry spectra (Ψ and Δ) for a random distribution of Au nanoparticles obtained by the GF method without (black line) and with DNA coverage (red dash-dotted line). The thickness of DNA shell used is 2.5nm and the effective dielectric constant of the DNA shell is 1.96+0.2i. The nonlocal effect of Au nanoparticle is included, while the pitch is reduced to 26.5nm in the fitting.
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This work was supported in part by Academia Sinica and Ministry of Science and Technology, Taiwan under Contract Nos. MOST 104-2112-M-001-009-MY2, MOST 103-2221-E-001-011-MY3 and NSC 101-2112-M-001-024-YM3.