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We present an accurate method to determine the effective refractive index and thickness of biomolecular layer by using Fano resonance modes in dual-period gold nanogrid arrays. The effective refractive index changes along the x and y directions are simultaneously measured and obtained by using a modified dispersion relation. The thickness of the surface layer is calculated by a three-layer waveguide equation without any fitting parameters. The accuracy of the proposed method is verified by comparing the results with the known coated dielectric layer and self-assembly layers. The applications of this method and nanogrid chips for determining the thickness and surface concentration of antigen/antibody interactions are demonstrated.
© 2015 Optical Society of America
1. Introduction
Surface plasmon resonance (SPR) has been widely used in applications of biomedical sensors, food safety and environmental pollution monitoring [1–4]. The label-free, real-time detection and high surface sensitivity make SPR become more popular in measuring biomolecular and chemistry interactions. The signal of SPR wavevector comes from the change of surface molecular density and thickness due to biomolecular binding, protein dissociation, and cell metabolism [5–8]. However, the commonly used SPR methods can only measure the refractive index change, which is the average contribution of the molecular density and its corresponding thickness. Because most of biomolecular layer is much smaller than the evanescent length of SPR wave, there is no direct information of the film thickness. In comparison to refractive index, the surface thickness is an important parameter that represents the coverage of molecular, adsorption processes or concentration of analyte. There were several works demonstrating the thickness determination based on conventional prism-based SPR techniques [9–13]. However, these methods are complicated in optical configuration and have a limited linear response range of SPR signals.
In this paper, we present a dual-mode SPR methods based on gold nanogrid arrays with two different periods. The non-polarized transmission light from the two-period nanogrids shows two distinct Fano resonant modes. Both modes have different responses to the surface density and thickness. We developed a guiding mode equation with a modified dispersion relation to analyze the two Fano resonance signals. The proposed nanostructures and calculations match quite well with the known surface coating materials and ellipsometric measurements. Finally, the determination of thickness and surface concentration of the antibody-antigen interaction as a function of concentration is demonstrated.
2. Fabrication and measurement
2.1 Fabrication of two-period nanogrid array
The nanogrid array with two periods 680 × 810 nm is designed as shown in Fig. 1(a). The nanogrid structures were fabricated by using thermal-annealed template-stripping method. Figure 1(c) shows fabrication flow charts for the nanogrid sensor. First, a nanogrid structure was patterned on a 2 cm × 2 cm square silicon substrate by using electron-beam lithography and reactive-ion etching processes. After the silicon mold was fabricated, a 80nm thick gold film was deposited on it using e-gun evaporation. Then a polycarbonate (PC) film (Lexan8010, GE, USA) was placed on the goal-coated silicon mold. The nanoimprint machine has an air chamber to apply uniform pressure to the sample/mold and a heating system to raise the temperature above the Tg point (glass transition temperature) of the PC film. Because the week adhesion between the gold film and silicon substrate, the gold film together with nanogrid patterns was completely transferred to the PC film. The PC/gold chip was easily separated from the silicon mold. The silicon mold can be repeatedly used in another imprinting cycle after the cleaning. Figure 1(b) shows a scanning electron microscope (SEM) image of PC/gold based nanogrid chip. Compare with others processes, thermal-annealed template-stripping process has a smoother gold film surface and better Fano resonance modes as reported at our provirus work [14].
Fig. 1 (a) Schematic diagram of a nanogrid SPR sensor with dual period 680nm and 810nm in the X and Y-axis respectively. The width of wall between grids is 45nm (b) The tilt SEM image of the fabricated nanogrid SPR sensor based on PC/gold film. (c) The fabrication flow charts for PC/gold chip as a SPR sensor.
2.2 Thin film material and deposition process
Two kinds of thin films were deposited on the gold nanogrid sensor for verifying the functions of dual-mode chips. One was the SiO2 thin film which was deposited on the chip with a slow rate of 1Å/s using a thermal evaporator. The other was the polyelectrolyte film which was grown on the chip surface by using self-assembly multilayers (SAM) technique as referred to the work by Yang et. al. [15]. The SAM was consisted of polyethylenimine (PEI) (MW~25,000) and poly(acrylic acid) (PAA) (MW~100,000) (Sigma-Aldrich Co.). The 0.1 wt% PEI solution was prepared using ultrapure water (resistivity = 18MΩ). The PH value was adjusted to 4.0 with 1.0M hydrochloric acid (HCl). 0.2 wt% PAA solution was also prepared using ultrapure water and adjusted the pH value to 4.0 with 1.0M sodium hydroxide (NaOH). To immobilize PEI/PAA multilayer thin film on the gold surface, the chip was first dipped into PEI solution for 300 seconds to form a monolayer. The sample was then rinsed with ultrapure water and dried with nitrogen gas. Next, sample was dipped into PAA solution for 300 seconds to bind with the PEI, then rinsed by ultrapure water and dried by nitrogen gas. In the following deposited cycle, both PEI and PAA solution dipped time were changed from 300 seconds to 60 seconds. We note q layers of PEI/PAA as (PEI/PAA)q.
2.3 Optical measurement setup
Two optical setups were used in the experiments. One was a normal transmission spectra measurement system. A nanogrid sensor was put on the inverse microscopy and illumined by a light source (MI-150, Dolan-Jenner Industries). The light beam was focused on a nanogrid pattern, passed through the sensor and collected by a fiber-lens. The transmittance spectra were recorded by a linear charge coupled device (CCD) spectrometer (BRC111A, B&W Tek). The other was an angle-dependent transmission spectra measurement system. The white light source was a 150W halogen lamp and coupled to a 80-μm-core optical fiber. It illuminated the sample with a fiber lens in order to collimate the incident angle. All the spectra were taken by a fiber-based spectrometer with another fiber lens to collect the transmission light. The sample was fixed on a rotational stage (OptoSigma). The incident angle to the sample was controlled by the rotation of the stage.
3. Results and discussion
3.1 Optical properties of the dual period nanogrid sensor
The optical properties of the dual-period nanogrid sensor are depicted in Fig. 2. The optical setup was shown in Fig. 2(a), where is incident wavevector and is polarization direction. The measured transmission spectrum of the dual period nanogrid for unpolarized light is shown in Fig. 2(b). There are two major resonance peaks in the spectrum. Both peaks are the Fano resonances at the x-polarization and y-polarization, respectively. The Fano resonance is due to the interference between the SPR mode on the metallic surface and the cavity mode in the slit. The constructive and destructive interference of both modes results in an asymmetrical resonant spectrum [16]. For normal incidence, the peak wavelength is usually estimated by the phase matching condition of surface plasmon wave on periodic metallic surface.
Where P is the period of nanogrid, i is resonance order, εm is dielectric constant of metal, and n(t) denotes effective volume refractive index within evanescent tail when the t is thinner than d. To confirm the SPR properties on the grids, we calculated the plasmonic mode (Ez) by using three-dimension finite-difference time-domain (3D-FDTD) method. In the simulation, a plane wave with 680nm wavelength (x-polarization) and 810nm wavelength (y-polarization) were incident to the grids with the same configuration of the fabricated gold nanogrid sensor. The simulated Ez field distributions were shown in Fig. 2(c). Both fields were corresponding to the peaks of the experimental spectrum in Fig. 2(b). It shows that x- and y- polarized waves make strong standing wave along x and y axes on the nanogrid array, respectively.Fig. 2 (a) A schematic configuration of transmission spectrum measurement. (b) The measured transmission spectrum of 680 × 810nm nanogrid structure for unpolarized light. (c) 3D-FDTD calculation of normalized Ez field distributions for (left side) 680nm wavelength of x-polarization and (right side) 810nm wavelength of y-polarization incident light. The white dashed lines indicate the boundaries of the nanogrids.
It is noted that resonant peak obtained by Eq. (1) is an approximate value. For example, the calculated λ0 in the air are 704 nm (n = 1, P = 680 nm, εm = −14.9554 + 1.0506i) for x-polarization and 827 nm (P = 810 nm, εm = −24.7466 + 1.5537i) for y-polarization. The calculated values were close to the measured results but there are some deviations. A more accurate model to estimate λ0 is important for determining effective index and thickness of the coated layer. We modified Eq. (1) by considering the angle-dependent phase matching condition. For periodic metallic structures with different incident angle, the SPR dispersion relation in general can be expressed by Eq. (2).
Where β is the propagation constant, θ is the incident angle, is the effective index of surface plasmon wave, and m is the resonance order. For normal incidence, the SPR occurs when λ0 is equal to nspP (optical path length of a round trip). As indicated in Fig. 2(c), the optical path length of surface plasmon wave is only located in the metallic well. The nanogrids are the boundaries for non-plasmonic wave. Figure 3(a) shows the schematic of a periodic metallic nanogrid with pitch P and gap w. The correct optical pathlength of a roundtrip should be modified asWhere ngap is the refractive index of the substrate. This modified dispersion relation was experimentally verified by the angular spectra. To highlight the difference between Eq. (2) and Eq. (3), a gold grating with a period of 500-nm and gap of 200-nm width was fabricated. The transmission spectra were measured at different incident angles. Figure 3(c) shows the transmission diagram at various incident angles. Red and cyan lines indicate the uncorrected bottom and top SPR wavelengths as calculated by Eq. (2). In contrast, red and cyan dashed lines show the corrected bottom and top SPR wavelengths as calculated by Eq. (3). A detailed comparison between Eq. (2) and Eq. (3) is shown in Fig. 3(b). The SPR wavelength difference, λerr (λerr = ), as a function of incidence angle was plotted from to . The top SPR wavelengths calculated by Eq. (3) fit quite well with the experimental data at all angles, while Eq. (2) shows deviations at all angles. For normal incidence, the measured λ0 is modified as . The effective index (nsp) and propagation constant () of the surface plasmon wave can be directly calculated by the measured spectra (λ0) and structure parameters (P, w, ngap).Fig. 3 (a) Schematic diagram of top and bottom SPR waves exited on one dimension periodic nanostructure with an incident angle, q. (b) The SPR wavelength difference between the measured result and uncorrected/corrected theoretical SPR wavelength. (c) The measured normalized transmission spectrum diagram for different incident angles from −50° to 50°. The solid curves show the uncorrected top/ bottom SPR wavelengths using Eq. (2). The dashed lines show the corrected top/bottom SPR wavelengths Eq. (3).
3.2 Thickness determination
In the experiment, the resonant wavelength λ0 can be determined from the measured spectrum. The nsp is obtained by using Eq. (3). The propagation constant is then determined by . Because of chip is consisted of a three-layer waveguide structure, therefore the accurate thickness of the core layer can be calculated by the wave equation. The configuration of a metal-clad waveguide is shown Fig. 4, where t is the thickness of core layer. Cladding layers (both metal layer and environment) were assumed to be infinite. The relative permittivities are:
Where and km are the real part of refractive index and extinction coefficient of metal. Surface plasmon wave (TM mode) guided in the core layer has a propagation constant. The coated film (core layer) is much thinner than the wavelength, only fundamental SPR (TM00) mode is considered in the calculation. By calculating the Ez component and matching the continuity boundary condition at and , the thickness of the core layer can be determined as following:Where , and . Using the wave equation method (WEM), if the propagation constant is measured, the thickness can be directly calculated without any fitting parameter.We used two different transparent films to verify the modified equation and WEM. The films were deposited on nanogrid sensor chips with different thickness. First, 0 to 30nm-thick silicon dioxide (SiO2) thin film was used to imitate the ultrathin organic film such as molecular monolayers, lipid membranes and viruses [17–19]. SiO2 film was deposited using thermal evaporation with a slow deposition rate. The thickness was monitored by a quartz crystal resonator in the chamber and doubly checked using ellipsometry. Figure 5(a) illustrates the measured transmission spectra with various layers of SiO2. In accordance with Eq. (1), when the thickness increased, the resonance peaks were red shifted. The refractive index of SiO2 is 1.45 [20] and wavelength dependence permittivity of gold is obtained from elsewhere [21].
Fig. 5 The measured normalized transmission spectra of 680 × 810 mm nanogrid structure various layer numbers of (a) SiO2 and (c) PEI/PAA films. White arrows indicate the red shifted resonance peaks of x and y-resonances. (b) The calculated thicknesses of SiO2 from x and y-resonances in (a). (d)The calculated thicknesses of PEI/PAA film by BSM (blue-squares) and WEM (red-cycles) along the bilayer numbers with the reference [15].
Using Eq. (3) and Eq. (5), the thickness of the film can be directly calculated. Figure 5(b) shows the experimental thickness and the calculated thickness using Fano resonances at x and y axes, respectively. Both calculated curves fit quite well with the measurement thickness. It is noted that the x- and y- resonances have two different resonant wavelengths and the shorter resonant wavelength has a larger wavelength red-shift. Nevertheless, the thickness calculated by the wave equation shows similar results. It indicates that the wave equation can be well applied to the different periodic nanostructures. The other type of coating film was the polyelectrolyte film with thickness from 0 to 100 nm. The polyelectrolyte film imitates the organic thin film such as biofilm and self-assembly multilayer (SAM) [15, 22]. Figure 5(c) show measured transmission spectra with various PEI/PAA films deposited by layer-by-layer assembly process. The refractive index is 1.45 for PEI/PAA films. Figure 5(d) shows the calculated film thickness by Eq. (3) and the experimental thickness. The curve shows the grown thickness of (PEI/PAA) bilayers. The calculated curve by WEM fits quite well with the real film thickness. The calculated results were the mean values of the x- and y- resonances. The low deviations verified that WEM calculations for both resonant modes had similar results.
In previous works, the film thickness is usually estimated by bulk sensitivity method (BSM). The method uses the effective index of dielectric layer within the evanescent wave [9]. As indicated in Fig. 4, the evanescent wave is exponentially decayed along the z direction. The deposition layer occupied a thickness t, hence the effective index change due to the deposited film is approximated by
Where d is the depth of the evanescent tail. The resonant wavelength shift can be calculated by , where Sbulk is the bulk wavelength sensitivity of the sensor. When the thickness of analyte grows to infinity, . The bulk sensitivity can be measured by using different glycerol/water solution covering on the sensor surface. For finite film thickness, the bulk sensitivity method is a simple and quick way to determine the film thickness, where t is expressed asThe calculated film thickness by the BSM method is also plotted in Fig. 5(d). Experimental thickness, calculated thicknesses by BSM and WEM are denoted as black-rhombus, blue-squares and red-cycles, respectively. For film thickness below 30 nm, the BSM and WEM fit quite well with the experimental thickness. Both methods determined similar thicknesses from same spectra and close to the reference result when the layer number of (PEI/PAA) bilayer was lower than 5. An obvious difference between BSM and WEM was observed when the bilayer number was larger than 5. For the BSM, the d is determined under environment refractive index condition (ne). When the thickness of the core layer increases, the evanescent tail will be decreased due to a higher refractive index of the core (n1). As a result, the BSM would overestimate d value when the surface layer is thick enough. From Eq. (7), the error between the calculated t and reference thickness is increased with the thickness. In our measurement, the BSM is useful for film thickness below ~30nm. For film thickness larger than 30 nm, the WEM shows much better results. The WEM directly calculates the film thickness based on the wave equation and the measured propagation constant of surface plasmon wave. There is no thickness limit for this method.3.3 Thickness measurement of biomolecular layer
In the experiment, the dual period nanogrid array was used to determine the thickness of the surface layer. Compared with conventional one-dimensional gratings or nanoslit arrays, the dual period grid array has two resonant responses. Both resonances have different responses to the surface conditions along x and y axes. If the film is uniform, both x- and y-resonances show similar thickness. With more thickness information, the thickness calculation is done more accurately. We demonstrate the application of the nanogrid chip for detecting the thickness of the biomolecular film under different conditions. Figure 6(a) shows the transmission spectra of binding experiments of BSA and anti-BSA. In the protein/anti-protein interaction experiment, the 1mg/mL solution of bovine serum albumin (BSA) in 10mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) was dropped on the sensor surface for 1 hour. After reaction, the sensor was rinsed with ultrapure water to remove the unbound BSA and dried with the nitrogen gas. After BSA modification, various concentrations anti-BSA solution, from 10 μg/mL to 1 mg/mL were dropped onto the sensor for 30 minutes, rinsed with ultrapure water and dried with nitrogen. BSA and anti-BSA were purchased form Sigma-Aldrich. HEPES buffer was purchased from Life Technologies, Grand Island, NY, US.
Fig. 6 (a) The measured normalized transmission spectra of nanogrid sensors for various concentrations of Anti-BSA in bio-interaction experiment. (b) The calculated thicknesses using WEM method and corresponding surface concentrations. The error bars represent the standard deviation of calculation results from 5 different sensing chips.
The BSA immobilized on the nanogrid sensor was used to bind various concentrations of anti-BSA solutions. By analyzing the transmission spectra between 0 μg/mL to 10 μg/mL of anti-BSA solution, 1.65 nm and 0.87 nm in averaged wavelength red-shifts were measured at 680-nm-peak (x-resonance) and 810-nm-peak (y-resonance), respectively. Using the shift of the resonant wavelengths and the wave equations, the calculated film thickness was 1.21nm (for 680 nm) and 1.2nm (for 810 nm). The detection limit of anti-BSA is lower than 10 μg/mL. Moreover, the surface concentration could be determined by the thickness. It is reported that surface concentration [23]. Figure 6(b) shows the BSA/anti-BSA complex thickness and the corresponding surface concentrations. For the BSA/anti-BSA interactions, the anti-BSA thickness is increased with the concentration because of the increased binding events. Since the size of anti-BSA is bigger than BSA, the complex thickness was mainly due to the anti-BSA biomolecules. According to the saturation at bound BSA/anti-BSA interactions, the saturation condition reaches the value of ~6.5-nm-thick or ~0.78.
5. Conclusion
We theoretically and experimentally explore the determination of film thickness by using Fano responses on a dual periodic nanogrid sensor. The thickness measurements of different kinds of analyte with various thicknesses on nanogrid sensors were compared. The results verified that wave equation with a modified dispersion relation is more accurate and suitable for thickness determination. Moreover, with the information of thickness, the sensor can be applied to monitor the antibody-antigen binding events. In our work, the surface concentrations of BSA were demonstrated by nanogrid sensors. BSA can be directly bound to the gold surface through its sulfhydryl group. Other bio-interactions, such as immunoglobulin G (IgG)/anti-IgG, can be monitored by immobilizing IgG on the gold surface through the modification of protein A. Other kinds of antigen-antibody systems on gold surface can be found in the reference [24]. In addition to surface immobilization, other techniques, such as pulse UV-light can help antibody immobilization on gold surface for bio-sensing [25]. The proposed sensing chip and analytic method provide a good platform for label-free biological and chemical sensing.
Acknowledgment
This work was supported by the Ministry of Science and Technology, Taipei, Taiwan, under Contact no. 103-2221-E-001-013-MY3 and nanoscience program of Academia Sinica.
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