1. Introduction

The optical sensing and imaging techniques are often used to detect the specific biological or chemical samples with high precision in various applications, such as homeland security and environmental protection [1], virus or cancer cell detection [2, 3], glucose in blood or protein in urine [4, 5], food protection [6, 7], gas vapor detection [8, 9], etc. Thus, it is important to develop an efficient, sensitive, and low-cost method for quantification of specific biological or chemical molecules. Among the different techniques, the surface-enhanced Raman spectroscopy by using the light enhancement in plasmonic nanostructures becomes a popular tool in optical sensing and imaging because of its high precision and sensitivity [10–13]. It also gives the opportunity to detect the single molecule [10, 14]. Many different nanostructures have been designed to use in surface-enhanced Raman scattering (SERS) applications. One kind of the structures is the nanovoid structure which has the advantage to detect the samples in the nanovoid regions, where it often has strong field enhancements [15]. The periodic nanovoid structures support localized plasmons and can also provide necessary phase matching conditions for coupling of external radiation into propagating surface plasmon polaritons (SPPs), or Bloch modes under Bragg coupling conditions in 2D periodic nanostructures [16]. These plasmons are interacted with the detected molecules and then the lower frequency plasmons are scattered into the radiation light. The inverted pyramidal nanostructure, which is also called Klarite substrate, with gold overcoating is the nanovoid structure but its far field radiation pattern is often broad without specific direction [15, 17]. The three-dimensional numerical study confirms that the metallic inverted pyramidal nanostructures supports the localized plasmons in the pyramidal pits and the SPP modes propagating along the metal surface [18]. The other three-dimensional numerical study by comparing metal and perfect electric conductor suggests that thin metallic layer in pyramidal nanostructures can give stronger field enhancement, and it is found that the opposite charge can attract and accumulate on the pit for 2D V-shape nanostructure but the like charge can repel each other and result the strong field shifts upwards and away from the pit for 3D inverted pyramidal nanostructure [19]. The inverted pyramidal nanostructures for different metals, including Ag, Au, Al, Cu, and Pd, had been studied and the high refractive index sensitivity had been reported by narrow SPP resonances [20]. The angular beaming of plasmons was observed on plasmonic nanostructures because of the different angular dispersion of the plasmons at the pump wavelength and the scattered Raman wavelength [21]. The lamellar grating nanostructures with metal/organic multiple layers were shown to be able to control the surface plasmon polaritons for the specific directional emissions [22]. The angular beaming of plasmons can offer the opportunity to separate the incident light and the SERS signals, which can be useful in remote and portable optical sensing devices.

Conventional SERS substrates are typically designed to provide strong field enhancements. The high numerical-aperture (NA) lenses are often used to focus or to collect the SERS signals, and the far field radiation pattern of SERS signals from hot spots is not important because the lenses can collect the SERS signals in different directions. However, the compact and portable Raman detectors are needed for in situ and remote measurements in various applications, for example, the hazardous waste detection. In general, the NA of lenses used in the portable Raman devices is not as high as the micro-Raman system on optical table. Moreover, the SERS signals can be also coupled into the optical waveguide, like optical fiber, without any condenser lenses. In this consequence, the SERS plasmonic nanostructures need to excite strong local field with good control of far field radiation pattern to give enough SERS signals as it is coupled into low NA lenses or coupled directly into the optical fibers without lens focusing. Thus, it is important to study how to design the SERS structures with strong field intensity and preferred radiation pattern. We propose a new design of nanostructure which has the tips in the inverted pyramidal nanostructures, and we study its localized field enhancements and far field radiation patterns. Different tip shape, tip height, and tip tilt angle in the pyramidal nanostructures can give more functionality to control the localized and de-localized surface plasmons in the SERS substrate. In this paper, we study the near field enhancements and far field radiation patterns of different structures by the finite-difference time-domain (FDTD) method and investigate their physical mechanisms. We also fabricated the inverted pyramidal nanostructures with and without the tips and measured their reflection spectra and the SERS signals for the chemical molecules thiophenol.

2. Structure and simulation setup

Figure 1(a) shows the three-dimensional cartoon plotting of our proposed plasmonic nanostructure, which is the periodic inverted pyramidal nanostructure with the tips. Figure 1(b) is the cross section of Fig. 1(a), and it can be also seen as a 2D structure which looks like the W-shape. The plasmonic modes in 2D W-shaped waveguide had been discussed in [23]. If the tip height is zero in Fig. 1(a), it is the case of the inverted pyramidal nanostructures which was reported in [15]. Because the tip size and angle can be controlled by different etching solutions, temperature, and anisotropic etching processes, the tips with different angles, sizes, and shapes can be obtained by different fabrication procedures. For the silicon substrate, the tip shape is related to the silicon lattice structures. The angle between the faces of the inverted pyramids and the flat surface of silicon for <100>-oriented silicon wafer is 54.74° in Fig. 1. It should be also noted that the angle between the edges of the inverted pyramids and the flat surface of silicon is 45°. Thus, there are several parameters for the inverted pyramidal nanostructures with the tips. As shown in Fig. 1(b), h is the tip height from the bottom of the inverted pyramidal nanostructures to the top of the tips, α is the tilt angle of the tip, w and p are the width and the period of the inverted pyramidal nanostructure, and t is the thickness of the gold film. The optical constants of the silicon and gold can be found in [24]. Although we use silicon as the substrate in our numerical and experimental study, it is worthy to mention that different shapes of the structures with different angles can be obtained by using other materials and fabrication techniques such as nanoimprint lithography or self assembly method.

 

Fig. 1 (a) The three-dimensional view of the structure with the tips inside the inverted pyramidal nanostructures and (b) is the cross view with the defined parameters, where t is the thickness of the gold material, h is the tip height from the bottom of the inverted pyramid to the top of the tip, α is the tilt angle of the tip, and w and p are the width and the period of the inverted pyramidal nanostructure.

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We use the Lumerical FDTD Solutions [25], the commercial software based on the FDTD method, to simulate the near field intensities and far field radiation pattern for different structures. We investigate the performance of our proposed SERS structures and compare the results with the inverted pyramidal nanostructures without the tips. The 2D and 3D simulation domains are set as 2000 nm × 3000 nm and 2000 nm × 3000 nm × 2000 nm, respectively. We apply the non-uniform meshes, and the smallest mesh spacing is about 2 nm. In our simulations, the plasmonic nanostructures are coated by 180 nm-thick gold layers. The cavity width of the structure is 1768 nm with the tip height h range from 0 nm to 1070 nm and the tip tilt angle α from 0° to 30°. We use the transverse magnetic (TM) polarization for 2D nanostructures. For most simulations of 3D nanostructures, we use the linear polarization along the unit side. We also compare the results of the linear polarization along the unit side and along the diagonal direction. The periodic boundary conditions are applied to simulate the periodic structures, and the perfect matching layers (PML) are applied on the top and bottom boundaries.

3. Simulation results and discussions of 2D W-shape nanostructures

Excitation of plasmonic resonances is manifested as dips in the reflectance spectra, whose spectral positions can be varied for different width and the period of the inverted pyramidal nanostructures without the tip [15]. This phenomenon should be also found in 2D V-shape and W-shape nanostructures [23]. We fix the width and the period of the 2D W-shape nanostructure as 1768 nm and 2.0 μm respectively and assumed that the thickness of the gold t is 180 nm in our simulations as shown in Fig. 1. To show the plasmonic effects, our calculated reflection spectra of different 2D W-shape nanostructures are normalized by the reflection spectra of flat gold film. Figure 2(a-f) show the reflections of the structures with various tip height from h = 0 nm to h = 1070 nm for the illuminated light wavelength from 500 nm to 800 nm with polarization along the unit side and angle of incidence from 0° to 45°. Because the period of the structure 2.0 μm is larger than the visible light wavelength ranges, it is obvious that there are several diffractive orders can be existed in these periodic nanostructures. These diffractive orders can be analyzed by the grating theory [15] or they can be defined as the anomalies in the reflection spectra as shown in Fig. 2. Not only these anomalies but also the tip structure can influence the plasmon resonances. If the He-Ne laser with λ = 632.8 nm is used as the illumination light and the thiophenol is considered as the probe molecule, the Raman shifts are 1000.1, 1022.7, and 1071.4 cm⁻¹ with their corresponding scattered Raman wavelengths 675.5, 676.6, and 678.8 nm which can be found in [26] or our SERS experiment results. Because these three wavelengths are close to each other, we selected 677 nm as the observed scattered Raman wavelength in our FDTD simulations. To be easier to read the reflections of the pump wavelength and the scattered Raman wavelength, we plot the solid lines for λ = 632.8 nm and dash lines for λ = 677 nm in Fig. 2. The smaller reflection indicates stronger coupling to the plasmons. To obtain the larger SERS signals, the angle of incidence should be chosen in the strong plasmon coupling at λ = 632.8 nm and the detection angle should be chosen in the strong plasmon radiation at λ = 677 nm. Thus, Fig. 2 can be used as the guideline to design the structure with stronger SERS signals. The reflection map for the case of tip height smaller than h = 270 nm is similar as the results without the tip in Fig. 2(a). This means that the coupling plasmons are not affected by the smaller tip. The reflection map for the tip height h = 270 nm in Fig. 2(b) is different as comparing to Fig. 2(a). There are smaller reflections for the mid-band energy (λ ~677 nm) and angle of incidence larger than 30 degrees. It means that the other plasmons can be excited at larger tip height, and it is probably because the larger tip can give the other phase matching conditions. Similar things can be found for the tip heights h = 470 nm and h = 670 nm in Figs. 2(c) and 2(d). As the tip height is larger than 270 nm, the reflection maps are more complicated which reveals that there may be localized plasmons and delocalized plasmons in these cases. The case with the tip height h = 870 nm in Fig. 2(e) shows that it has the strong coupling to the plasmons for smaller angle of incidence at λ = 632.8 nm; however, the reflections for this structure are not small at λ = 677 nm. For the tip height h = 1070 nm in Fig. 2(f), the structure looks like a half-pitch V-shape grating as comparing to the structure in Fig. 2(a) although the tip height is still a little smaller than the depth of the groove. We simulate and discuss the near field intensities and far field directivities for the 2D W-shape nanostructures with different tip heights and tip tilt angles at λ = 632.8 nm and λ = 677 nm. Under these conditions, p = 2.0 μm, w = 1768 nm, and t = 180 nm, only two parameters can be varied in Fig. 1, the tip height h and tip tilt angle α. In our simulation cases, we focus on the study of the effects of the shape and size of the tips on the near field and far field intensities.

 

Fig. 2 The reflection maps for different angle of incidence and the illuminated light wavelength for the 2D W-shape nanostructures with the tip height h from 0 nm to 1070 nm. The tip tilt angle α is zero. The solid lines in each figure are for λ = 632.8 nm and the dash lines are for λ = 677 nm .The polarization is along the unit side. For better visualization, the scale for reflection intensities has been saturated from 0.5 to 1.

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We consider that the depth and the width of the inverted pyramidal nanostructures are 1250 nm and 1768 nm in 2D simulation, and we vary the tip height h from the bottom of the inverted pyramidal nanostructures. Figures 3(a) and 3(b) show the far field intensity of different tip height verse the azimuthal angle θ at λ = 632.8 nm and 677 nm. The pump light is at normal incidence with the polarization along the unit side. The bottom sub-figures in Figs. 3(a) and 3(b) represent the far field intensity of the structures with no tip. Because the period of the nanostructure is larger than the visible wavelength, there are several diffractive beams which can be radiated in different directions and can be interfered each other. Although the far field intensity calculations are like the interference results of these diffractive beams, they can give the information where to get the larger light signals. To understand how the far field intensity can vary with the tip height, we plot the near field intensities for the tip height h = 0 nm (no tip), 270 nm, and 870 nm, respectively, as shown in Figs. 3(c-e) for λ = 632.8 nm and Figs. 3(f-h) for λ = 677 nm. The far field intensity for the structure with no tip and λ = 632.8 nm in Fig. 3(a) expands broad verse θ which means that it lacks the specific radiation directions. From the observation of the near field intensity of the inverted pyramidal nanostructure without the tip for λ = 632.8 nm in Fig. 3(c), we can find that there are not only the hot spots on the pits but also the hot spots with lighter intensities along the metallic surface because the surface waves propagate on the metallic surface. Because of these hot spots, the far field radiation pattern is broad for the case without the tips for λ = 632.8 nm. Some cases with different tip height have strong intensities at θ = 0°. They behave like two light sources at the two pits which form the strongest intensity at θ = 0°. Because of the symmetric structure, the far field intensity is also symmetric. For the case with no tip for λ = 632.8 nm as shown in Fig. 3(c), there is the strongest field intensity on the pit and it results the broaden far field intensity as shown in the bottom sub-figure in Fig. 3(a) because it looks like that the far field pattern is induced from a single slit diffraction. But the case with no tip for λ = 677 nm in Fig. 3(f) has weak field intensity on the pit and its strong field intensities are in the locations above the pit and two angles in the top of the grooves. This results different far field intensity distributions as shown in the bottom sub-figure in Fig. 3(b). Interestingly, the near field intensities for the cases with the tip height h = 270 nm for λ = 632.8 nm and 677 nm in Figs. 3(d) and 3(g) are similar. Although the near field intensities are complicated, the near field intensities in the case with h = 270 nm are weaker than the case with no tip and there are two stronger field intensities separated symmetrically between the tip. This results the far field intensity as two radiation direction for h = 270 nm as shown in Figs. 3(a) and 3(b). This means that the plasmon coupling are not sensitive to λ = 632.8 nm and 677 nm for the structure with the tip height h = 270 nm as the illumination light is at normal incidence. This can be confirmed as reading the reflection data for the incident angle at zero degree in Fig. 2(b); however, Fig. 2(b) also hints that the situation for λ = 632.8 nm and 677 nm are different as the incident angle is larger. For the case with the tip height h = 870 nm for λ = 632.8 nm as shown in Fig. 3(e), the near field intensities have two localized hot spots around the two pits in W-shaped nanostructures. The far field intensities of the two hot spots is like the double slit interference, which has the strong main radiation direction and weak side lobes for h = 870 nm as shown in Fig. 3(a). For the case with the tip height h = 870 nm for λ = 677 nm as shown in Fig. 3(h), the field intensities also has two localized hot spots around the two pits in the W-shaped nanostructure but the field intensities along the gold surfaces are different as comparing to Fig. 3(e). This results the different far field intensity distributions as shown in Fig. 3(b).

 

Fig. 3 (a) and (b) are the far field intensity for the 2D W-shape nanostructures with different tip heights h for the incident light wavelength λ = 632.8 nm and 677 nm, respectively. The tip tilt angle α is zero. For comparison, the bottom figure is the far field intensity for the V-shape nanostructure without the tip. (c)-(e) for λ = 632.8 nm and (f)-(h) for λ = 677 nm are the near field intensities for the tip height h = 0 nm (no tip), h = 270 nm, and h = 870 nm, respectively. To be easy for visualization, (c)-(h) are in logarithmic scale and limited from 0 to 3. The maximums in (c)-(h) are 260.5, 32.6, 214.7, 47.5, 22.9, and 77.0, respectively. The pump light is at normal incidence with the polarization along the unit side.

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To study the effects of the tip tilt angle in 2D W-shape nanostructures, we choose the case of the tip height h = 870 nm for λ = 632.8 nm and 677 nm in Figs. 3(e) and 3(h). We simulate the near field and far field intensities by varying the tip tilt angle α. Figures 4(a) and 4(b) show the far field intensities for the cases with different tip tilt angle α at λ = 632.8 nm and 677 nm. The pump light is at normal incidence with the polarization along the unit side. To understand how the radiation pattern varies with the tip tilt angle, we plot the near field intensities for the tip tile angle α = 10°, 20°, and 30°, respectively, as shown in Figs. 4(c-e) for λ = 632.8 nm and Figs. 4(f-h) for λ = 677 nm. Varying the tip tilt angle can change the positions and the intensities of the surface plasmons, and it results the non-symmetrical far field intensities. For example, the far field intensities for the structure with the tip tilt angle α = 10° has two strong radiation directions in Fig. 4(a) which wavelength is 632.8 nm, one is about θ = 0° and the other is about θ = 35°. As the tilt angle becomes larger in Fig. 4(a), the intensity at θ = 0° decreases and the intensity at positive θ increases. The radiation pattern is broad from θ = 30° to θ = 70° for the structure with the tilt angle α = 20°. As the tilt angle increases from 20° to 30°, the far field intensity in negative θ becomes obvious. The far field intensity for λ = 677 nm shown in Fig. 4(b) has one dominate radiation intensity in θ ~ 40° and the other strong radiation intensity for smaller tile angle in θ ~ -30°. The simulation results in Figs. 4(a) and 4(b) show that the far field intensity in positive or negative θ can be varied by tip tilt angle. Notice that the near field intensity for the cases with α = 0° is already shown in Figs. 3(e) and 3(h). It can be found that the field intensity on the tip gets stronger as the tip tilt angle is larger and the localized field intensities in the two pits are different because the surface plasmons behave differently for the different tip tilt angle. Because of these changes in the near field intensities, the far field radiation pattern can be varied accordingly. From the study of near field intensities of different W-shape nanostructures with different tip heights and tip tilt angles and the comparisons of their corresponding far field intensities in Figs. 3 and 4, the physical mechanism are explained and it is expected that the far field radiation pattern can be controlled in the careful designs.

 

Fig. 4 (a) and (b) are the far field intensities for the 2D W-shape nanostructures with different tip tilt angle α for the incident light wavelength λ = 632.8 nm and 677 nm, respectively. (c)-(e) for λ = 632.8 nm and (f)-(h) for λ = 677 nm are the near field intensities for the tip tilt angle α = 10°, α = 20°, α = 30°, respectively. The tip height is 870 nm. To be easy for visualization, (c)-(h) are in logarithmic scale and limited from 0 to 3. The maximums in (c)-(h) are 153.5, 147.5, 122.8, 68.4, 67.0, and 79.1, respectively. Notice that Fig. 3(e) and (h) are the cases of α = 0°. The pump light is at normal incidence with the polarization along the unit side.

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4. Simulation results and discussions of 3D inverted pyramidal nanostructures with the tips

To understand the effects of the tip height on plasmonic resonance for 3D inverted pyramidal nanostructures with the tips, the reflection spectra for the structures with different tip height are required. It needs heavy 3D FDTD computation to simulate the reflection spectra for different incident angle and orientation of pits. The reflection spectra can be also obtained experimentally [15]; however, it is hard to fabricate the structures with controlled tip height in a university laboratory. There are more diffractive anomalies for 3D nanostructures than 2D nanostructures because it has one more degree of freedom. We consider the width and period of 3D nanostructure is same as 2D nanostructure and assumed that the thickness of the gold t is 180 nm in our 3D FDTD simulations. Figure 5 shows the simulated reflection spectra verse incident angle for different tip height from h = 0 nm to h = 1070 nm for the illuminated light wavelength from 500 nm to 800 nm with polarization along the unit side, i.e. fixing the orientation of pits, and angle of incidence from 0° to 45°. Our calculated reflection spectra are normalized by the reflection of flat gold film. Thus, Fig. 5 can be used as the guideline to design the structure with stronger SERS signal, and it is found that the reflection map for the case of tip height h = 670 nm at wavelength 632.8 nm in Fig. 5(d) is stronger than the other cases with different tip height. To understand the tip effects, we simulate the near field and far field intensities for different cases with tip height and tip tilt angles at λ = 632.8 nm and λ = 677 nm if He-Ne laser and thiophenol as the probe molecule are chosen for the SERS experiments.

 

Fig. 5 The reflection maps for different angle of incidence and the illuminated light wavelength for the inverted pyramidal nanostructures with the tip height h from 0 nm to 1070 nm. The tip tilt angle α is zero. The solid lines in each figure are for λ = 632.8 nm and the dash lines are for λ = 677 nm. The polarization is along the unit side. For better visualization, the scale for reflection intensities has been saturated from 0.5 to 1.

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The far field intensities of the 3D inverted pyramidal nanostructure with the symmetric tip in consideration of the tip height h are studied. It preserves its symmetric shape for the 3D nanostructure as same as the 2D W-shape nanostructure simulation results in Fig. 3. Figure 6 shows the near field and far field intensities simulation results for the 3D inverted pyramidal nanostructures with the tips for different tip height and wavelengths. The pump light is at normal incidence with the polarization along the unit side. For λ = 632.8 nm, the charge distributions of case with tip height h = 270 nm in Fig. 6(e) are similar to the case of no tip in Fig. 6(a). For λ = 677 nm, similar phenomena are also found in Figs. 6(c) and 6(g). The charges oscillate around the sidewall above the pitsdirectivities at λ = 632.8 nm and 677 nm in the case of no tip in Figs. 6(a) and 6(c) and in the case of tip height h = 270 nm in Figs. 6(e) and 6(g). The charge congregates at two pits in the case of tip height h = 670 nm in Fig. 6(m) for λ = 632.8 nm and in Fig. 6(o) for λ = 677 nm. In the case of tip height h = 670 nm in Figs. 6(m) and 6(o), the field enhancement is strongest and the two pits behave as two light sources and the far field forms like the diffraction pattern of double slit interference. Their corresponding far field intensity distributions for h = 670 nm are mostly in normal direction as shown in Figs. 6(n) and 6(p). This means that the tip height of the 3D inverted pyramidal nanostructure should be designed at h = 670 nm for strong near field enhancement with small incident angle and small detection angle. Comparing to the simulation results of 2D structures in Fig. 3, the strongest field enhancement for λ = 632.8 nm and 677 nm are the 2D structure with the tip height h = 870 nm; however, the far field radiation patterns for λ = 632.8 nm and 677 nm are different. Though the charge distributions in the case of h = 870 nm and in the case of h = 1070 nm for λ = 632.8 nm in Figs. 6(q) and 6(u) are similar, the directivities of far field intensity in Figs. 6(r) and 6(v) are quite different. Similar things also happen for the cases of λ = 677 nm for h = 870 nm and h = 1070 nm in Figs. 6(s), 6(w), 6(t), and 6(x). The case with h = 870 nm has the strong intensity at the center in the far field but the case with h = 1070 nm has weak intensity at the center in the far field. For the case with no tip as shown in Fig. 6(a) and 6(c), the strongest field intensity is not on the pit of the inverted pyramidal nanostructure. It is not the same as 2D V-shaped structure which has the strongest field on the pit as shown in Fig. 3(c). Because there are the other two side walls for the 3D inverted pyramidal nanostructures as comparing to the 2D V-shape nanostructures, the like charges have the repulsive force in 3D inverted pyramidal nanostructures but only the opposite charges attract each other in 2D V-shape nanostructure [19]. This results the field maximum away from the pits of 3D inverted pyramidal nanostructures. As the tip height gets larger, the strong field intensities are found in the two pits. For example, as h = 670 nm, the strong field intensities are larger in two pits. It is because the other two side walls are not close to the tips as the tip height is larger. Thus, the opposite charges can be existed on the two sides of the pits and it results in large field intensities.

 

Fig. 6 The near field and far field intensities for the 3D inverted pyramidal nanostructures with tip height from h = 0 nm to h = 1070 nm. The maximums of near field intensities for λ = 632.8 nm in (a), (e), (i), (m), (q), and (u) are 49.1, 53.0, 198.3, 1113.4, 257.0, and 221.9. The maximums of near field intensities for λ = 677 nm in (c), (g), (k), (o), (s), and (w) are 44.0, 43.6, 60.0, 600.8, 124.1, and 113.9. The corresponding far field intensities are in right-hand sides of each near field intensity figure. The pump light is at normal incidence with the polarization along the unit side. The scale bar for near field intensities is in logarithmic scale and limited from 0 to 3.

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To study the effects of the tip tilt angle in 3D inverted pyramidal nanostructures with the tips, we choose the case of the tip height h = 670 nm in Fig. 6(m) for λ = 632.8 nm and Fig. 6(o) for λ = 677 nm and then simulate the near field intensities and far field radiation patterns by varying the tip tilt angle α. Figure 7 shows the near field and far field intensities of different tip tilt angle α at λ = 632.8 nm and 677 nm. The pump light is at normal incidence with the polarization along the unit side. It is found that the charges not only exist in two pits but also congregates at the top of the tip and they turn from negative to positive as α = 10° to α = 30°. Although the strong far field radiation intensity is on the center region for different tip tilt angles, more side lobes are found for larger tip tilt angle. It is also found that stronger near field intensities for the cases with the tip tilt angles as comparing to the case without tip tilt angle.

 

Fig. 7 The near field and far field intensities for the 3D inverted pyramidal nanostructures with different tip tilt angle α = 10°, α = 20°, α = 30°, respectively. For λ = 632.8 nm, (a), (e) and (i) are the near field intensity and their corresponding far field intensities are in (b), (f), and (j). For λ = 677 nm, (c), (g) and (k) are the near field intensities and their corresponding far field intensities are in (d), (h), and (l). The scale bar for near field intensities is in logarithmic scale and limited from 0 to 3. The tip height h is 670 nm. The maximums in (a), (e) and (i) are 473.9, 1513.6, and 3373.4, and the maximums in (c), (g) and (k) are 2687.8, 5185.8, and 1720.2. The pump light is at normal incidence with the polarization along the unit side.

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Moreover, we also considered the incident light with diagonal polarization. We change the polarization along the unit side for the cases in Fig. 7 to the polarization along the diagonal direction and the corresponding simulation results are shown in Fig. 8 . The pump light is at normal incidence. As comparing to Figs. 7 and 8, the near field intensities are similar. The far field distribution for the cases at λ = 632.8 nm is elliptical for diagonal polarization but it does not happen for the case at λ = 677 nm. The far field radiation pattern properties are centralized for the diagonal polarization as shown in Fig. 8.

 

Fig. 8 The near field and far field intensities of diagonal polarization for the 3D inverted pyramidal nanostructures with different tip tilt angle α = 10°, α = 20°, α = 30°, respectively. For λ = 632.8 nm, (a), (e) and (i) are the near field intensities and their corresponding far field intensities are in (b), (f), and (j). For λ = 677 nm, (c), (g) and (k) are the near field intensities and their corresponding far field intensities are in (d), (h), and (l). The scale bar for near field intensities is in logarithmic scale and limited from 0 to 3. The tip height h is 670 nm. The maximums in (a), (e) and (i) are 477.9, 1514.0, and 3380.9, and the maximums in (c), (g) and (k) are 2688.7, 5186.9, and 1763.2. The pump light is at normal incidence with the polarization along the diagonal direction.

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5. Sample preparations and experimental results

We prepared three samples. One sample is the pyramidal nanostructures with the tips, the other sample is without the tips, and another sample is the flat gold film. The gold was coated in these structures. The fabrication procedures of the samples with nanostructures are shown in Fig. 9 . We used the <100>-oriented and p-type (1-100 Ω cm) silicon wafer for our substrate. Its surface was chemically mechanically polished to optical flatness. By using the plasma enhanced chemical vapor deposition (PECVD), the 180 nm-thick silicon nitride (Si₃N₄) layer was deposited and covered the entire structure as the hard masking layer for the chemical wet etching of the silicon bulk and the silicon nitride layer provides thermal and electrical isolations. Next, the 300 nm-thick high-resolution sacrificial positive electron beam resist (ZEP-520A, Zeon Corp) was spin-coated on to the silicon nitride layer. The desired mask pattern was fabricated by the electron beam lithography process (ELIONIX ELS-7500EX). The etching window was formed by removing silicon nitride using the reactive ion etching (RIE). Once the desired mask pattern was obtained by electively etching off the silicon nitride, commercially available 30 wt.% potassium hydroxide (KOH) aqueous solutions with surfactant was used as the etching solution for silicon. The time control during the process of chemical wet etching can affect the tip size and shape. By doing so, the expected tip height was achieved according to the etching time. Many different factors which can influence the etching processes should be well controlled, such as the etchant concentration, temperature, and other environmental parameters in the laboratory. Figure 10 shows the SEM photos of the fabricated pyramidal nanostructures with the tips and without the tips for 2 µm periods by using scanning electron microscopes (ERA-8800FE, ELIONIX). The tips of fabricated structures were successfully formed but the shapes were not perfect as an octahedral shape. The roughness around the structures and the tips can also help the SERS enhancement signals. After the etching was completed, the silicon nitride was removed in a phosphoric acid. Then, the 180 nm gold film was evaporated on the structures.

 

Fig. 9 The fabrication process for the inverted pyramidal nanostructures with the tips.

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Fig. 10 The scanning electron microscopy (SEM) images, where (a) and (b) are the inverted pyramidal nanostructures with and without the tips, respectively. The scale bars are 5 μm. Insets: respective zoom-in figure and the corresponding scale bar is 0.5 μm.

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The morphology of the fabricated nanostructures was characterized with the atomic force microscope (Digital Instrument Dimension 3100) in the tapping mode. For these morphology observations, the features (edges, centers, and in-betweens) of two samples were studied. The dimensions of structures obtained from AFM images were corrected by the tip features. Figure 11 shows an AFM image of SERS and inverted pyramidal nanostructures with and without the tips. It shows that the shape and the size of the nanostructures are well controlled during the sample preparation processes.

 

Fig. 11 The AFM images of inverted pyramidal nanostructures with and without the tips in (a) and (b), respectively. The cross section and the dimensions are given in (c) and (d).

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To better demonstrate the superiority of structured SERS substrate, we used thiophenol as a probe molecule to explore the enhanced electromagnetic fields and the subsequent SERS signals around the gold nanostructure arrays. Following the gold nanostructure array synthesis outlined above, the SERS substrates were immerged in 1 mM ethanolic thiophenol solution for 3.5 hours at room temperature. A self-assembled monolayer of thiophenol was formed around the gold nanostructures via S-Au bonds during this process. Following the reaction period, the samples were removed, copiously rinsed in ethanol, and dried in nitrogen gas to remove unreacted thiophenol and solvent.

We measured the Raman shift spectra by a high-resolution micro-Raman analysis using Lab RAM HR-Raman Microscope (Horiba, France), which has a transmission volume phase grating providing a spectral resolution of 10 cm⁻¹. An integrated sampling fiber probe was used to deliver the excitation laser to the sample and receive the Raman emissions from sample to the spectrometer. For Raman measurements, a linear polarized, continuous-wave (CW) 632.8 nm stabilized HeNe laser was guided into a microscope with a 100x (NA = 0.9) objective lens and finally was focused on the SERS substrate. The diameter and intensity of focus spot is about 2 μm and 200 μW, respectively. Figure 12 shows the Raman shift spectra of the thiophenol monolayers on three different kind of substrates, which are inverted pyramid without the tip (blue line), inverted pyramid with the tip (red line), and reference flat gold substrate (green line). The results show that the inverted pyramidal nanostructure with the octahedral tips can have stronger SERS signals than the inverted pyramidal nanostructure without the tips.

 

Fig. 12 The SERS spectra of adsorbed thiophenol on three different kinds of substrates. The red line is inverted pyramidal nanostructures with the tips, the blue line is the inverted pyramidal nanostructures without the tip, and the green line is the reference flat gold substrate.

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Figure 13 shows the measured reflection spectra for the fabricated inverted pyramidal nanostructure with and without the tips in Fig. 10. We also fabricated one gold film with thickness 180 nm and measured its reflection spectra for normalization. These measurements are done in an in-house measurement system. The incident light is a broad-band white light source (PerkinElmer, HX2) passing through a monochromator (HORIBA, Triax 180) and illuminating on the test structure which is fixed on a rotating stage in an integrating sphere (Labsphere, 3P-GPS-053-SL). The total reflection spectra is collected and analyzed by this system. As shown in Fig. 13, it is generally that the reflection of the inverted pyramidal nanostructures with the tip is lower than the structure without the tip. The lower reflection is caused by the stronger light coupling and localized field intensities. This gives the reason that SERS signal is enhanced for the inverted pyramidal nanostructures with the tips as shown in Fig. 12.

 

Fig. 13 (a) and (b) show the reflection spectra of inverted pyramidal nanostructures with and without the tips in Fig. 10 (a) and (b), respectively.

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According to the AFM measurements in Fig. 11, the near field and far field intensities for the fabricated structures are simulated with and without the tips for λ = 632.8 nm and 677 nm in Fig. 14 . The pump light is at normal incidence with the polarization along the unit side. Obviously, the near field intensity of the structures with tips in Figs. 14(e) and 14(g) are stronger than the structures without the tips in Figs. 14 (a) and 14(c). The far field radiation pattern properties are centralized for the structures with the tips in Figs. 14(f) and 14(h) as comparing to the far field intensities of the structure without the trips in Figs. 14(b) and 14(d). Both near field intensity results and far field intensity distributions show strong evidences that the stronger SERS signal can be measured for the structures with the tips as comparing to the structures without the tips in our experimental setup.

 

Fig. 14 The simulated near field and far field intensities for the fabricated 3D inverted pyramidal nanostructures with and without the tips in Fig. 10. Figures (a) and (e) are the near field intensities for λ = 632.8 nm and their corresponding far field intensities are in (b) and (f). Figures (c) and (g) are the near field intensities for λ = 677 nm and their far field intensities are in (d) and (h). The scale bar for near field intensities is in logarithmic scale and limited from 0 to 3. The maximums in (a), (c), (e), and (g) are 350.6, 259.2, 51.7, and 146.0, respectively. The pump light is at normal incidence with the polarization along the unit side.

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5. Conclusion

We have studied the periodic inverted pyramidal nanostructures with the tips and without the tips theoretically and experimentally. The effects of the structure parameters on its localized field enhancements and far field radiation pattern have been discussed. The devices with tips and without tips were fabricated and the measurement results were compared. We have studied the light enhancement properties of the structures with the tips inside the inverted pyramids by changing the tip height and the tilt angle in consideration of the light polarization and angle of incidence. The results were also compared with the case of the inverted pyramidal nanostructures without the tips. We found that our proposed structures with the tips have stronger field enhancement than the inverted pyramidal nanostructures without the tips, and the far field radiation pattern can be varied by changing the tip height and tip tilt angles. The hot spots are found around the pits and the radiation pattern can be varied by the tip height and tip angle from the simulation studies. This physical understanding can be used to explain the near field intensities and far field radiation patterns for different structures, and it can be also useful in the design of SERS nanostructures with strong field enhancement and preferred radiation pattern properties.