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RCWA Simulation Study of Enhanced Infrared Absorption Spectroscopy by Au Nanoparticle Array Combined with Optical Cavity Effect

Written By

Daichi Mitobe and Yushi Suzuki

Submitted: 06 June 2022 Reviewed: 14 June 2022 Published: 07 July 2022

DOI: 10.5772/intechopen.105851

Gold Nanoparticles and Their Applications in Engineering IntechOpen
Gold Nanoparticles and Their Applications in Engineering Edited by Safaa Najah Saud Al-Humairi

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Gold Nanoparticles and Their Applications in Engineering

Edited by Safaa Najah Saud Al-Humairi

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Abstract

Surface-enhanced infrared absorption is a phenomenon by which the infrared absorption intensity of molecules near metal nanoparticles (NPs) is increased considerably. In surface-enhanced infrared absorption spectroscopy, the absorption intensity depends on the strength of the field acting on the NPs layer. The optical cavity effect generates a strong electric field. If this strong electric field is applied to the NPs, then the IR absorption intensity will be enhanced further. This simulation study assessed the possibility of applying the enhanced electric field generated by the pseudo-optical cavity effect to the NP array. Results indicated that the IR absorption is markedly enhanced.

Keywords

  • au nanoparticle array
  • enhanced infrared absorption
  • optical cavity effect
  • rigorous coupled wave analysis

1. Introduction

An optical cavity is a method of confining light in a cavity (air layer or transparent dielectric layer) and of generating a larger field by the interference of the confined light [1, 2]. In this case, a standing wave is formed in the cavity. In a complete optical cavity system, a transparent layer with a high refractive index is surrounded by an atmosphere with a low refractive index. By setting the incident angle from the high refractive index layer to the low refractive index layer as equal to or larger than the critical angle, the reflectance at both interfaces of the high refractive index layer becomes unity. Therefore, the light incident on this layer is confined in the layer completely: a large field is formed. In this system, a high refractive index prism is used to inject light into the high refractive index layer, so that the simplest system is at least a four-layer system. We realized a simpler three-phase pseudo-optical cavity system using a high refractive index prism—air layer—bulk metal layer [3]. In this system, an air layer with a low refractive index is in contact with a high refractive index prism. The other interface is air-metal, with reflectance that is almost unity in the infrared region. Experiments and calculations demonstrated that, even in this case, an enhanced electromagnetic field is obtained within the air film (air layer) as a result of reflection and interference, which indicates that the pseudo-optical cavity effect might occur, even if the reflectance at both interfaces of the layer is not unity, as long as the reflectance is higher than a certain value. For instance, the pseudo-cavity effect might be achieved even in a three-layer system composed of a low refractive index layer-medium refractive index layer-high refractive index layer. As one example, a three-layer system of air (or vacuum)-polymer (or fluoride)-silicon (or germanium) is proposed. If the pseudo-optical cavity is achieved in this system and if an anti-node of standing wave is formed at the air-polymer interface, then infrared absorption by molecules present near the air-polymer interface can be enhanced. By appropriately setting parameters such as the dielectric constant of the layer and the layer thickness, anti-nodes can be formed at the interface.

Surface enhanced infrared absorption (SEIRA) is a method of enhancing the infrared absorption intensity of molecules existing around the particles using nano-sized metal fine particles (NP) [4, 5]. The NPs used for this process, including research by which enhanced infrared absorption was discovered, have been used widely in evaporated films because they are easily prepared [6, 7, 8, 9]. In recent years, many studies using nano-sized metals with special shapes such as nano-antennas and nano-resonators have been reported [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. These structures are used to excite surface plasmons (polaritons) to create an enhanced field (called hotspots). These complex metal structures are manufactured using lithography technology and other techniques. These structures provide powerful hotspots, but their fabrication requires extensive apparatus, which is difficult to arrange at a laboratory level. If a metal structure that can be created more easily were to provide a sufficient enhanced field, then this limitation could be relaxed. Therefore, we aim at obtaining greater absorption enhancement using vapor-deposited films or metal films with similar structures. The enhanced infrared absorption can greatly improve the infrared spectroscopy detection limit, which might facilitate analysis in many fields. The infrared absorption intensity of molecules A has a relational expression of A∝Nα|E|2, wherein N represents the amount of the molecule, α is the absorption coefficient of the molecule, and E stands for is the electric field strength. In other words, the key factor for development of sensing technology such as infrared spectroscopy is obtaining a strong electric field. Enhanced infrared absorption is a method of obtaining large absorption by increasing the electric field strength around the NP [21, 22]. The enhanced field formed around the NP depends on the electric field strength acting on the NP. Put simply, by imposing a large electric field on the NP array, the electric field formed around it will be larger, resulting in greater absorption intensity of the molecules. If the large electric field generated by the optical cavity effect described above is applicable to the evaporated film, then large infrared absorption is obtainable, thereby further increasing the potential for infrared spectroscopy.

For this study, we examine the potential of enhanced infrared absorption coupled with optical cavity effects. For this purpose, we use rigorous coupled wave analysis (RCWA) [23] to simulate the enhanced mechanism numerically by combining the optical cavity with a square column array modeling the deposited metallic thin film.

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2. Calculation

Rigorous coupled wave analysis (RCWA) was used for the simulation examined for this study. Actually, RCWA is a semi-analytical method in computational electromagnetics, typically used to solve diffraction of a field by a given periodic grating structure [24, 25]. Because it is difficult to evaluate the evaporated metal thin film directly as a result of its irregular shape, we adopt a square column array that models the evaporated film. It has been confirmed that the RCWA simulation using a Au square column array shows good agreement with measurement results obtained using the nanoarray prepared using an evaporated film or electron beam lithography [26, 27]. For this study, we conducted simulations under the following three conditions.

2.1 Simulation of infrared absorption spectra of model molecules by pseudo-optical cavity effect

A three-layer system consisting of the low refractive index layer—medium refractive index layer—high refractive index layer can act as a pseudo-optical cavity. A simulation to assess that hypothesis was performed in a four-layer system with an additional model molecule layer to achieve infrared absorption (vacuum layer—model molecular layer—buffer layer—Si substrate layer). The buffer layer thickness was changed from 50 to 4000 nm to simulate absorption spectra. The model molecular layer thickness was set as 12 nm. As the buffer layer, a material with a refractive index of 1.442 (the imaginary part is 0) was used. This value was used to reduce, to the greatest extent possible, effects of the presence of a model molecular layer on the reflectance and phase shift at a low refractive index layer—medium refractive index layer interface. In this system, the transmission spectra were simulated. The absorbance values were obtained from the results. To obtain a reference spectrum, simulation was also performed with a vacuum layer—model molecular layer—substrate layer, without a buffer layer. The same optical constant as a buffer layer was set on the substrate to eliminate the influence of a refractive index of the substrate on a reference spectrum. The enhancement factor is calculated by dividing the absorption intensity of a model molecule on the buffer layer by the absorption intensity of a model molecule without a buffer layer.

Furthermore, for the cavity effect, a refractive index of a buffer layer is considered to affect the interference inside a cavity. Therefore, simulations for which the refractive indexes of buffer layers are set respectively to 1.2 and 1.6 are also performed to obtain the absorbances.

2.2 Simulation of infrared absorption spectra of model molecule by combination pseudo-optical cavity effect with a square column array

To clarify the applicability of the enhanced field generated by the pseudo-optical cavity formed in the medium refractive index layer to the enhanced infrared absorption, simulations were conducted with a vacuum layer—model molecule and Au NP array layer—buffer layer—Si substrate layer (Figure 1). The Au NP size was 80 × 80 nm. The height was 12 nm. In addition, the distance of NP was 20 nm. These morphological parameters were chosen to approximate the scale of the evaporated film. The model molecules were placed in gaps of the Au NP array. Also, the height was set as equal to the height of NP (12 nm). As the buffer layer, a material with a refractive index of 1.442 (the imaginary part is 0) was used. As in 2.1, the buffer layer thickness was varied from 50 to 4000 nm. The transmission spectra were simulated. Also, the absorbances were obtained from the results. In addition, the same optical constant as the buffer layer was used for the substrate. We performed simulation of the vacuum layer—model molecule and Au NP array layer—substrate layer, using the same parameters as those used above. The enhancement factors in the cavity effect by the buffer layer were evaluated from the ratio of absorbance with and without the buffer layer.

Figure 1.

Schematic diagram of the four-layer system used in the simulation, as seen from the side. The model molecules were placed in gaps of the Au NP array.

2.3 Simulation of infrared absorption spectra of model molecule by combination of pseudo-optical cavity effect with nanoarray and Au plane

In the system adopted for use in this study, the magnitude of the interference field generated by the pseudo-optical cavity is sensitive to the reflectance at both interfaces of the medium refractive index layer. As the amount of light confined in the cavity increases, the field generated by the interference strengthens; the cavity effect becomes greater. Therefore, to improve the reflectivity at the interface between the medium refractive index layer and the high refractive index layer (substrate), a metal plane layer is placed to act as a mirror (Figure 2a). The model molecule absorption intensity is simulated by this system. The Au layer thickness is 200 nm, which is sufficient to prevent infrared light transmission. The parameters of NP array and the buffer layer adopted the same values as in 2.2. Unlike 2.1 and 2.2, there is almost no transmitted light. Therefore, the reflection spectra were simulated. The values for absorbance were obtained from the results.

Figure 2.

Schematic diagram of (a) a five-layer system used in the simulation and (b) with a model molecular layer with a 10 nm thickness in the buffer layer.

To investigate details of the electric field enhancement mechanism, we simulate the distribution of the electric field in the normal direction inside the buffer layer. If the existence of standing waves in the layer is confirmed, then it can be proved that the electric field enhancement results from the optical cavity effect. A model molecule layer with 10 nm thickness is placed in the buffer layer in the in-plane direction. By changing the position of this layer in the plane normal direction, the electric field intensity at each position in the buffer layer is evaluated from the absorption intensity of the model molecule (Figure 2b). In this case, no model molecules are placed in the NP array gaps.

The Lorentz oscillator model, formulated as described below, was adopted as the model molecule.

ε(ω)=εint+f/(ω02−ω2+iγω)E1

herein, εinf = 2.08, f = 2.8 × 1027 s−2, γ = 8.0 × 1012 s−1, and ω0 = 3.216 × 1014 s−1.

The wavenumber range of calculation was 1900–1500 cm−1. The spectral resolution was 4 cm−1. The incident light of the TM mode was set at an incident angle of 0°. For calculations, S4 free software was used [28]. The dielectric constants of the substrate (Si) and metal particles (Au) were referred from values reported in the literature [29, 30].

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3. Results and discussion

3.1 Simulation results of infrared absorption spectra of model molecules by pseudo-optical cavity effect

The complete optical cavity system constitutes a four-layer system, forming an intense field within the cavity. A simpler three-layer pseudo-optical cavity system has been realized using a high index prism—air gap—bulk metal. Experiments and calculations have proved that an enhanced electromagnetic field is obtainable in the air gap, which indicates that the pseudo-optical cavity effect might occur even if the reflectance at both interfaces of the layer is not unity, as long as the reflectance is higher than a certain value. Therefore, we investigated that the three-layer system consisting of low refractive index layer (air)—medium refractive index layer—high refractive index layer (Si) can function as a pseudo-optical cavity.

Figure 3 shows the 3D infrared absorption spectra of model molecules simulated by RCWA in the four-layer, the vacuum layer—model molecular layer—buffer layer—Si substrate.

Figure 3.

3D infrared absorption spectra of the model molecule as a function of buffer layer thickness. The infrared absorption spectrum with buffer layer thickness of 0 is the spectrum of the model molecule on a bare substrate.

As depicted in Figure 3, the absorption intensity does not change monotonically with the buffer layer thickness. To assess the change in the maximum value of the absorption intensity clearly, Figure 4 shows a plot of the change in the absorption intensity with respect to the buffer layer thickness.

Figure 4.

Infrared absorption intensity of the model molecule as a function of buffer layer thickness. The dashed line represents the reference spectrum intensity.

As portrayed in Figure 4, the absorption intensity increases as the buffer layer thickness increases, reaches a maximum value (around 1000 nm), and then begins to decrease. After reaching the minimum value (2000 nm), it increases again. In short, as the buffer layer thickness increases, the absorption intensity increases and decreases periodically. As the buffer layer thickness increases, the light path length increases. The change in the light path length changes the interference conditions in the buffer layer, leading to electric field strengthening or weakening. The change in the absorption intensity portrayed in Figure 4 is explainable as a result of this interference effect. This behavior indicates that this system is acting as a pseudo-optical cavity. The maximum value of the periodically varying absorption intensity is about 0.017, which is larger than the absorption intensity of the reference spectrum: approximately 0.011. The enhancement attributable to the cavity effect is about 1.5 times.

The actual optical path length also depends on the refractive index of the buffer layer. Figure 5 presents the calculation with the refractive index changed and the other conditions being roughly equal.

Figure 5.

The absorption intensity as a function of buffer layer thickness with the refractive index is varied. Each mark represents the index of refraction of the buffer layer: 1.2 for black, 1.442 for red, and 1.6 for green. The dashed line shows the absorption intensity of the model molecule on the bare substrate.

From this figure, it is apparent that the period of the absorption intensity changes. The maximum value of the intensity depends on the refractive index of the buffer layer. These reasons are explainable as follows. An increase in the refractive index is associated with an increase in the light path length. In other words, the optical thickness increases for the same physical film thickness. Therefore, the period of the absorption intensity change against the physical film thickness becomes shorter. The reflectance at the interface between the buffer layer and the substrate becomes smaller as the difference in refractive index between the buffer layer and the substrate becomes smaller. When the refractive index of the buffer layer is close to the refractive index of the Si substrate (nSi = 3.42), the reflectance at the interface becomes lower, which reduces the light trapped in the buffer layer. Also, the standing wave formed in the buffer layer becomes weaker, thereby reducing the maximum peak intensity. These results support that the system acts as a pseudo-optical cavity and that it therefore affects the infrared absorption intensity of the model molecule.

3.2 Simulation results of spectra combining pseudo-optical cavity effect with enhanced infrared absorption in a square column array

The enhanced field formed around the NPs in enhanced infrared absorption depends on the electric field strength acting on the NP. The results of 3.1 showed that a three-layer system composed of the low refractive index layer—medium refractive index layer—high refractive index layer functions as a pseudo-optical cavity. Therefore, we investigate the infrared absorption spectra of the model molecule around the NP when the enhanced field generated by the pseudo-optical cavity acts on the NP placed at the vacuum layer—buffer layer interface.

Figure 6 shows RCWA simulation results of the 3D infrared absorption spectra of the model molecule of the model molecule placed in the gap of the Au NP array set at the vacuum layer—buffer layer interface and of the model molecule in the gap of the Au NP without the buffer layer.

Figure 6.

3D enhanced infrared absorption spectrum of the model molecule as a function of the buffer layer thickness. The infrared absorption spectrum with buffer layer thickness of 0 is the spectrum in a Au NP array without the buffer layer.

The change in the spectrum with increasing buffer layer thickness is the same as that in 3.1.

The dependence of the absorption intensity on the buffer thickness is portrayed in Figure 7 to clarify the change in the maximum absorption intensity with thickness.

Figure 7.

Variation of absorption intensity as a function of buffer layer thickness. The dashed line represents the reference spectrum intensity.

As portrayed in Figure 7, as the buffer layer thickness increases, the absorption intensity of the model molecule changes periodically dependently of it, confirming the same behavior as that presented in 3.1.

The enhancement factor in enhanced infrared absorption because of NP array is about 18.5 times. Moreover, the enhancement factor of the cavity effect is about 1.5 times. If it is a combination of the effects explained above, it is expected to be about 27.75 times, which is the product of each enhancement factor. The enhancement factor obtained from the simulation results is about 28 times, which is almost identical. From these findings, it can be confirmed that the electric field enhanced by the pseudo-cavity effect in the buffer layer acted on the NP array. Thereby, greater enhancement was obtained.

3.3 Simulation results of spectra combining pseudo-optical cavity effect with enhanced infrared absorption in a square column array with Au plane

The enhanced electric field in the pseudo-optical cavity layer (buffer) is sensitive to reflectance at both interfaces of the layer. Therefore, a Au planar layer is placed between the buffer layer and the substrate to increase the reflectivity at this interface, thereby enhancing the optical cavity effect.

The infrared absorption spectra of model molecules placed in the gap of NP array in the system with a Au planar layer between the buffer layer and the substrate are presented in Figure 8.

Figure 8.

3D infrared absorption spectra of the model molecule as a function of the buffer layer thickness when the Au plane layer is placed between the buffer layer and the substrate.

In this system, as in 3.1 and 3.2, it can be confirmed that the absorption intensity depends on the buffer layer thickness. Figure 9 presents variation of the absorption intensity with the buffer layer thickness.

Figure 9.

Infrared absorption intensity with a Au plane layer as a function of buffer layer thickness.

Even for systems in which the Au layer is added, a periodic change in absorption intensity with respect to the buffer layer thickness is observed, indicating the presence of a cavity effect. We confirmed that greater enhancement is obtainable by placing a Au planar layer at the buffer layer-substrate interface to improve the reflectivity at this interface. Although using a complex metal structure, Debbrecht et al. [31] reported results of a similar study of enhancement caused by the optical cavity effect.

Comparing the IR absorption enhancement factor of the model molecules with and without the Au layer, it is about 28 for the case without the Au layer and about 95 for the case with the Au layer because the presence of the Au layer increased the reflectivity at the interface (Figure 10) and created a larger cavity field in the buffer layer, which acted on the NP array.

Figure 10.

Comparison of infrared absorption enhancement factors in each system configuration. Horizontal axis labels represent the configurations. Cavity: the system consisting of the vacuum layer-buffer layer-Si substrate layer (Section 3.1). NP array: the system consisting of the vacuum layer-Au square column array layer-Si substrate layer (Section 3.2). Cavity & NP array: the system consisting of the vacuum layer-Au square column array layer-buffer layer-Si substrate layer (Section 3.2). Cavity & NP array & Au plane: the system consisting of the vacuum layer-Au square column array layer-buffer layer-Au planar layer-Si substrate layer (Section 3.3).

Next, the distribution of the electric field intensity formed in the buffer layer in the direction of the interface normal is simulated. The buffer layer thickness is 860 nm, which is the maximum absorption intensity, and 2000 nm, which is the minimum. The resulting electric field distribution in the buffer layer is presented in Figure 11.

Figure 11.

Distributions of the electric field intensity in the buffer layer with thicknesses of (a) 860 nm, which gives the maximum intensity, and (b) 2000 nm, which gives the minimum intensity.

The vertical axis represents the distance from the Au planar film interface on the substrate, the upper end of which is the NP layer interface. The behavior of the change in absorption intensity in Figure 11b is one cycle of the sine function, which indicates that a standing wave is established in the buffer layer. This standing wave is the result of interference of light within the buffer layer, indicating that this system realizes a pseudo-optical cavity effect. In this case, standing wave nodes are formed at the NP layer interface. As a result, the electric field acting on the NP layer is weak. The absorption intensity attributable to the model molecules in the NP layer is low. By contrast, in Figure 11a, a half-period sine wave is formed. Its antinode acts on the NP layer, resulting in large absorption. Although not shown, it was confirmed that the IR absorption intensity of the model molecules in the NP layer corresponds to the electric field intensity of the buffer layer acting on the NP layer, even for other buffer layer thicknesses. Results demonstrated that the absorption intensity of the model molecules in the NP layer changes depending on the strength of the electric field in the buffer layer acting on the NP layer. The sudden increase in the electric field around 860 nm thickness in Figure 11a is explainable by effects of the enhanced field in the NP layer penetrating the buffer layer.

For this study, we used a simpler NP array and buffer layer. The following results were obtained by adjusting the system configuration and by making the buffer layer thickness variable.

From findings reported in 3.1, it was demonstrated that the infrared absorption of the model molecules existing at the vacuum layer-buffer layer interface by the pseudo-optical cavity in the vacuum layer-buffer layer-substrate layer three-layer system can be enhanced. Findings reported in 3.2 demonstrated that the infrared absorption of the model molecules around the NPs is enhanced when the field enhanced because of the pseudo-optical cavity is applied to the NP layer. From findings presented in 3.3, it was confirmed that the addition of a Au planar layer can increase the buffer layer interface reflectivity and can further enhance IR absorption. This system, a nanostructured metal layer-buffer layer-planar metal layer-substrate layer, resembles the system reported in references [32, 33, 34, 35]. However, the references reported that the large enhancement is attributable to interaction between the long-range plasmons excited in the planar metal layer and the local plasmons excited in the array. An optimum distance can be derived for interaction between the plasmons of two types. The results presented herein confirm that the absorption intensity increases and decreases cyclically with increasing buffer layer thickness. This finding suggests that the infrared absorption enhancement in this paper cannot be explained by plasmon interaction. That is to say, when a metallic structure with a scale similar to that of the evaporated film is used, enhancement attributable to "plasmon interaction" with the planar metallic layer is not observed, but enhancement because of cavity effects, as shown in systems 3.1 and 3.2, does occur.

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4. Summary

As described in this paper, we verified by simulation that the enhanced field generated by the pseudo-optical cavity effect in a system consisting of a low-refractive-index layer—middle-refractive-index laye—high-refractive-index layer is applicable to metal nanoparticle (NP) arrays near the interface between the low-refractive-index layer and the middle-refractive-index layer to enhance enhanced IR absorption further. First, it was shown that the three-layer system with a vacuum layer—buffer layer—Si substrate layer functions as a pseudo-optical cavity and that it increases the infrared absorption of model molecules placed at the vacuum layer—buffer layer interface. Next, the IR absorption spectra of model molecules were simulated in a system with an array of Au NP layers at the vacuum layer–buffer layer interface to allow the enhanced field because of the pseudo-optical cavity to act on the NP layers. The enhancement factor in this system was the product of the enhancement factor because of the pseudo-optical cavity effect and the factor of the NP layer. Results clarified that a field enhanced because of the pseudo-optical cavity can be coupled to the enhanced field because of the NP layer. Finally, to obtain a more efficient optical cavity effect, a planar Au layer with reflectivity close to unity in the infrared region was set between the buffer layer and the Si substrate layer to simulate the infrared absorption spectra of model molecules between NPs. As expected, the addition of a planar Au layer provides greater IR absorption, thereby confirming that IR absorption can be enhanced further. This study demonstrates that enhanced infrared absorption spectroscopy can have higher performance and more flexible tuning capabilities using simple manufacturing methods.

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Acknowledgments

This work was supported financially by a Grant in-Aid for Scientific Research from JSPS KAKENHI Grant number 21K04858.

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Written By

Daichi Mitobe and Yushi Suzuki

Submitted: 06 June 2022 Reviewed: 14 June 2022 Published: 07 July 2022

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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