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Abstract
In this paper, a surface-enhanced Raman scattering (SERS) sensor with a giant field enhancement factor based on the coupling of surface plasmon polaritons (SPPs) is designed and studied theoretically. The proposed sensor adopts a metal-dielectric layered hybrid slot waveguide structure, combining thin metal (gold) layers and silicon nitride strip waveguides. Unlike other similar sensors, the silicon nitride waveguide structure does not serve as an excitation signal channel, conventionally loaded with the guided modes, but as an auxiliary layer, making it easier to concentrate the light field in the slot. Therefore, the sensor has a higher enhancement factor compared to the pure metal or dielectric slot structure. The results exhibit that we can obtain a maximum enhancement factor exceeding 10^6 under the compact configuration of 510 × 300 × 225nm^3 at the wavelength of 785 nm. By analyzing the dependence of the sensor performance on the structural parameters, we show that the structure of such sensor can directly be applied to SERS spectroscopic analysis as well as integrated with micro-and nano-photonic platform to perform on-chip detection system.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Efficient confinement and enhancement of light field at the nanoscale are significant for photonic devices or light-on-chip integration. Plasmonic structures and high refractive index (HRI) materials have been extensively studied due to their excellent ability to manipulate optical field, like surface-enhanced Raman scattering [1–4], surface plasmon resonance [5,6], biological sensing [7–9], metamaterials and so on based on their applications [10–14]. As a crucial component of photonic devices, waveguide optical sensors based on the nanoscale dimensions have also attracted much attention [15–19]. Specifically, research in sensitivity improvement of sensors, including enhancing the electric field and enlarging sensing volume, is always a hot issue in optical sensor research [20–23]. A. Cherouan [24] used the electric field to induce the guiding film (LiNbO3) to produce birefringence and improved the sensitivity of the planar waveguide sensor through the coupling effect of evanescent waves. S. Zouheir [25], P. Jaromír [26] applied metal materials with negative complex-valued permittivity into the structure design of the sensors to enhance the electric field. P. Raknoi [27] has attempted to apply metal array waveguides to the detection of metal (Au, Ag and Al) nanoparticles. S. A. Taya [28], U. Anurag [29] tried to use the left-handed material as a waveguide layer to improve the detection sensitivity. D.Y. Lu [30] adopted the method of strong coupling between SPP and planar waveguide mode, and improved the sensitivity by 2-3 orders of magnitude over conventional surface plasmon resonance sensors.
The hybrid plasmonic waveguide sensors, commonly containing dielectric strip waveguide that operates as an excitation signal channel (i.e., guided modes do exist in the strip waveguide.), are discussed in a lot of literature [3,23,24,30,31]. However, the case of the dielectric strip waveguide that serves only as auxiliary layers (in which there is no guide mode) has rarely been reported. In this paper, we present a hybrid plasmonic slot waveguide sensor formed by two adjacent insulator-metal-insulator structures. Compared with other similar sensors, the outstanding feature of the waveguide sensor is that the guided modes will not exist in the silicon nitride dielectric layer. Therefore, it will ensure that the light field can highly concentrate within the slot, so that the electric field intensity inside the slot is strongly enhanced arising from the coupling of the two surface plasmon polaritons (SPPs) along the metal surfaces on both sides of the slot. Considering the trend towards miniaturization, compactness of sensors and on-chip integration, we attempt to realize sensor configurations as small as possible. By calculating the dependence of field enhancement on structural parameters of the sensor, we show that the local field enhancement factor above 10^6 can be theoretically obtained when the sensor configuration is optimally miniaturized. Our work in this paper has potential scalability for the design of the light-on-chip detection system based on plasmonic waveguide structure.
2. Sensor scheme and configuration
Insulator-metal-insulator (IMI) structures, which are well known to support symmetric and anti-symmetric surface plasmon polaritons (SPPs) propagating along the metal-insulator interfaces, are schematically shown in Figs. 1(a) and 1(b), corresponding to symmetric and asymmetric IMI structures, respectively. Here, the symmetric IMI structure means the dielectric on both sides of the metal is of the same material, and otherwise, it's asymmetric. As shown in Fig. 1(a) and 1(b), the mechanism underlying electric field enhancement based on SPPs can be illuminated visually and theoretically. For the three-layer IMI waveguide [e.g., the dotted box in Figs. 1(a), 1(b)], the maximum value of the electric field intensity will appear at the metal-dielectric interfaces, beginning to fade away from it exponentially into the dielectric layers. When such two IMI waveguides approach each other, the electric field intensity in the core layer (the ${n_4}$ region) will be enhanced due to the superposition of the two exponential attenuation fields. The solid curves in the core layer represent the field intensity profile after superposition. And those dotted curves represent the field distribution in the core layer for individual IMI structures without considering their interaction. The sensing structure we investigated in this paper has just been performed based on this.
Fig. 1. Schematic illustration of electric field enhancement related to the hybrid slot waveguide structure. (a), and (b) visualize the field enhancement more understandably, representing field intensity distribution of symmetric and asymmetric metal planar waveguide structures, respectively. (c) shows the proposed sensor structure together with the light excitation and collection of Raman scattering signal. (d) Longitudinal section of the sensor showing the configuration parameters of the waveguide structure. The TM-polarized light is incident on the end-facet of the structure from the top, with the electric field vector orthogonal to the interfaces between different layers.
Fig. 2. Theoretical calculations of electric field enhancement related to the hybrid slot waveguide structure. (a) Eigenvalue curves of symmetric [i.e., the dotted box in Fig. 1(a)] and asymmetric [i.e., the dotted box in Fig. 1(b)] IMI structures, respectively. (b) and (c) represent the field function curves (${E_x}$) of the symmetric and asymmetric IMI structures, where the parameters in the calculation are assumed as: ${n_1}$=1.997, ${n_2}$=${n_4}$=1.33, ${n_3}$=0.18262, ${\kappa _3}$=4.5627, $\lambda $ = 785 nm, and the metal-layer thickness ranging from 10∼50 nm.
The proposed hybrid slot waveguide sensor is schematically shown in Fig. 1(c), formed by two same asymmetric IMI units, including an auxiliary dielectric layer with excellent optical property and a thin metal layer. The sensor is located on a SiO2 substrate. The light is propagating along the –z direction from top. The dielectric layer can effectively help the light field to concentrate in the slot. Meanwhile, the thin metal layer can further enhance the electric field near the metal-dielectric interfaces. Due to low loss, the SPPs can propagate over a long distance, thus having access to a large sensing volume. The sample prepared to be detected can diffuse into the slot, where detection of SERS spectroscopy can be performed sensitively attributed to the electric field enhanced significantly there. As we know, it is difficult to miniaturize the sensing system by using prism coupling (e.g., Kretschmann or Otto configuration) to excite the SPPs, so the SPPs coupling scheme we adopted here is end-fire coupling, in which a TM-polarized optical beam is focused on the end-facet of the waveguide. The light excitation (${\omega _i},{k_i}$) and the collection of Raman scattering signal (${\omega _{sc}},{k_{sc}}$) are also indicated with the red and blue wavy lines in Fig. 1(c). The longitudinal section of the sensor is shown in Fig. 1(d), illustrating the structural parameters of such sensor for use in the following discussion. ${l_D}$ and ${l_m}$ represent respectively the lengths of the dielectric and the metal layer. ${l_D}$ is more slightly longer ($\Delta l$) than ${l_m}$ in order to better couple the light into the metal layer. ${W_D}$, ${D_{ms}}$ are the widths of the dielectric layer and the slot, respectively. The thickness of metal layer denotes as ${t_m}$, and the height is h as the same as the dielectric layer. The incident light wavelength of 785 nm, which is commonly used in SERS spectroscopy, is considered to adopt in the calculation.
Aimed to the structures of Fig. 1(a) and 1(b), the field distributions have been theoretically calculated and shown in Fig. 2. Figure 2(a) represents the eigenvalue curves of the symmetric (red curve) and anti-symmetric modes (blue curve) of the symmetric IMI structure corresponding to Fig. 1(a), together with the eigenvalue curve of the anti-symmetric modes (purple curve) of the asymmetric structure [ see Fig. 1(b)]. One can see that the symmetric and anti-symmetric modes exist in the symmetric IMI structure, while the asymmetric IMI only has the corresponding anti-symmetric modes. In the case of the symmetric structure, the curves of field function based on the symmetric modes are plotted in Fig. 2(b) with the gold thickness varied from 10∼50 nm, exhibiting that the electric field intensity begins to exponentially attenuate from the same value at both sides of the metal. The field function curves of the asymmetric structure are shown in Fig. 2(c). In contrast to the symmetric structure, the maximum values of both sides of the metal layer will not equal, and the larger maximum will appear on the low-index side, revealing that the field intensity on the high-index side is suppressed. Therefore, we can obtain a strongly enhanced field in the core compared to the symmetric structure.
To confirm the feasibility of the scheme fore-mentioned, the trial calculations were performed by using the finite-element method (FEM) and shown in Fig. 3. In the visible and near-infrared spectral range, silicon nitride (Si3N4) has been actively pursued in the design of optical waveguide sensors because of its almost zero loss [32]. And gold is also employed as a crucial metallic material in interesting electromagnetic problems in the optical frequency range. Therefore, the two kinds of materials still were exploited in our simulation. The optical parameters of silicon nitride and Au are taken from the Phillip and Rakia database [32], and their refractive indices are 1.997 and 0.18262-j4.5627, respectively. The refractive index of aqueous environment (slot and cladding) is ${n_4}$=1.33. In Figs. 3(a) and 3(b), the field distribution of symmetric structure contained two 10nm-thick gold layers, are calculated demonstrating the enhanced field intensity inside the slots, which are 50 and 100 nm in width, respectively. And the field functions through the center transversal line of the structure are plotted in the Fig. 3(e) and (f), corresponding to Figs. 3(a) and 3(b). Here, as a layered slab waveguide, it is assumed that the parameters of the waveguide configuration ${t_m}$=10 nm, ${l_m}$=1.0µm. When added silicon nitride layers (${W_D}$=100 nm) outside of the metal layers, we can obtain higher enhanced field intensity in the slot [see Figs. 3(c), 3(d)] compared to the pure metal structure such as the cases of Figs. 3(a) and 3(b). These simulation results agree well with the theoretical scheme above. Note that only the TM modes (${E_x} > > {E_z}$, $|{{E_x}} |\approx |E |$) can exist, propagating along the metal-dielectric interfaces and inter-coupling in the slot.
Fig. 3. 2D cross-sectional Field images of normalized $|{{E_x}} |$[i.e.,(a)-(d)] and the curves of the field function through the centre transversal line [i.e.,(e)-(h)], the distance between the two gold layers, i.e., the slot width ${D_{ms}}$=50 nm and 100 nm, and other parameters of configuration ${t_m}$=10 nm, ${l_m}$=1.0µm, ${n_4}$ = 1.33. (a)-(d) exhibit the field distributions in x-y plane from the top view angle [see Fig. 1(c)]. (a) and (b) represent pure gold-layer slot waveguide, (c) and (d) represent hybrid plasmonic slot waveguide added a silicon nitride dielectric layer at the outside of the gold layers. These calculations were performed by the FEM method using COMSOL software.
As for the guided modes of the sensor, for simplicity, they can be discussed approximately by a four-layer planar waveguide with a metal layer, which can be seen as a half of our whole sensor configuration. Here, the eigenvalue equations can be expressed by [33]
From Eqs. (1)–(4), the eigenvalue curves can be calculated and plotted in Fig. 4. Figure 4(a) represents the relationship curves of the TM1, TM-1(SPPs) modes, together with an inset illustrating the materials configuration. Notice that the TM0 mode does not exist. It is assumed that ${\varepsilon _2} = {\varepsilon _4}$=1.332, ${\varepsilon _1}$ = 1.9972, ${n_3}$ = 0.18262, ${\kappa _3}$=4.5627. The gold relative permittivity is obtained from the relation of ${\tilde{\varepsilon }_3} = {\varepsilon _3} - j{K_3}$, ${\varepsilon _3} = n_3^2 - \kappa _3^2$, ${K_3} = 2{n_3}{\kappa _3}$. One can see that there is a cut-off width ${W_{D,cf}}$ in the width range, demonstrating that the TM1 guided modes cannot exist in the auxiliary dielectric layer (i.e., Si3N4 layer) at small widths. The proposed sensor is just explored based on this point. ${W_{D,cf}}$ will approximately appear at ∼200 nm at ${t_m}$ = 20 nm and shift to the right with an increase of ${t_m}$. The cutoff width ${W_{D,cf}}$ can be theoretically given by below
In the case of ${t_m}$ = 20 nm, we have ${W_{D,cf}}$=232.13 nm. Figure 4(b) represents the effect of ${t_m}$ on the modes TM1 and TM-1 at three different ${W_D}$ of 150, 250, and 350 nm. One can see that TM-1 modes almost don’t depend on the width ${W_D}$ and absolutely exist at any case [see dotted curves in Fig. 4(b)]. However, TM1 modes only exist at large value of ${W_D}$(see blue solid curve). if it still exists at small ${W_D}$, the smaller ${t_m}$ will be required (see purple and brown solid curves). As can be seen from the above calculation, the cut-off width of 232.13 nm means that the width of the Si3N4 layer we consider in the simulation will not exceed this value. It should be emphasized that the four-layer structure is beneficial to the simplification of calculation compared with the whole seven-layer analogue and here, we just consider the cut-off value of guided modes in the auxiliary layer (silicon nitride). Admittedly, the cut-off width of the four-layer structure maybe has somewhat difference from that of the seven-layer structure, but it is not very big. In fact, the subsequent modeled calculation also confirmed this point.
Fig. 4. Theoretical calculations of the eigenvalue relationship of the TM-1 and TM1 related to the four-layer asymmetric structure corresponding to the inset. (a) represents eigenvalue curves of TM-1 and TM1 considered to change the width of the auxiliary layer, demonstrating the presence of the cut-off width ${W_{D,cf}}$ from the solid curves (see blue, purple and brown solid curves). (b) represents the dependence of the eigenvalue curves of TM-1 and TM1 modes on the thickness ${t_m}$, where the structural parameters are assumed as: ${n_1}$=1.997, ${n_2} = {n_4}$=1.33, ${n_3}$=0.18262, ${\kappa _3}$=4.5627, and $\lambda $ = 785 nm.
To evaluate the dependence of the field enhancement on the structural parameters of the sensor, the local field enhancement factor will be adopted, expressed by
4. Simulation analysis
First, given the rigor of the analysis, it is necessary to examine the rationality of using silicon nitride (Si3N4) as an auxiliary layer, and its suitable width ${W_D}$ as well as on the thickness of gold layer ${t_m}$. By calculating the local enhancement factor of the center point in the slot, the results have been shown in Fig. 5. In the simulation, we have assumed the case of the layered slab waveguide, where ${W_D}$=200 nm, ${D_{ms}}$=30 nm, ${t_m}$=20 nm, and ${l_m} = {l_D}$=1.0µm. Figure 5(a) exhibits Si3N4 has great advantage over other typical photonics materials, where ${L_c}$ denotes the local enhancement factor at the waveguide center, ‘sn’ and ‘j’ in parentheses denote silicon nitride and other materials, respectively.
Fig. 5. The dependence of the field enhancement on the structural configuration of the sensor. (a) A comparison of the local field enhancement factor ${L_c}$ for several key dielectric materials. Silicon nitride exhibits the priority over other dielectric materials, where ${W_D}$=200 nm, ${D_{ms}}$=30 nm, ${t_m}$ = 20 nm, ${l_m}$=${l_D}$ = 1.0µm. (b) The effect of the auxiliary layer thickness ${W_D}$ on the field intensity in the slot at ${D_{ms}}$=30 nm, ${t_m}$ = 20 nm, ${l_m}$=${l_D}$ = 1.0µm. (c) The effect of the thickness ${t_m}$ on the field intensity for two kinds of slot width ${D_{ms}}$=30, 50 nm. (d) The dependence of field distribution inside the slot on the length ${l_m}$, at two slot widths of ${D_{ms}}$=30 and 50 nm, respectively.
The ${L_c}$ with the width ${W_D}$ varied from 30 to 250 nm can also be calculated and plotted in Fig. 5(b), revealing that Si3N4 also has an advantage at relatively larger sizes, which can be fabricated easily. One can see that, at ${W_D}$=200 nm, the situation corresponds to the case of Fig. 5(a). From the theoretical calculation of Eq. (5), we have ${W_{D,cf}}$=232.13 nm, so we can find that the theoretical calculation is well in agreement with the numerical simulation results. At the width of ${W_D}$>${W_{D,cf}}$, ${L_c}$ will decrease, resulting from the TM guided modes beginning to appear in the Si3N4 layer. In the cases of other material such as Ge, Si, and SiC, etc., their corresponding cut-off widths all will be less than the cut-off width of the Si3N4 layer [${W_{D,cf}}(sn)$] due to their smaller refractive indices (see other marked curves in colored). Considering a bit of calculation bias, the width ${W_D}$ of 220 nm will conservatively be chosen in the following calculation. In Fig. 5(c), at ${W_D}$=220 nm, the effect of the thickness of gold ${t_m}$ on ${L_c}$ was calculated for the slot widths of ${D_{ms}}$=30 and 50 nm. It is shown that, the range of ${t_m}$ marked in ellipse A is more suitable. Here, we can choose ${t_m}$=20 nm as a fixed parameter of gold layer. To further improve the uniformity of the light field distribution in the slot and compactness of the whole sensor, a gold layer length (${l_m}$) as short as possible is required, so the dependence of field distribution on ${l_m}$ was calculated and plotted in Fig. 5(d). Considering both the enhancement of electric field and the shorter length of gold layer, ${l_m}$ should be determined from the elliptical region B in Fig. 5(d), so we choose 300 nm as the value of ${l_m}$. Up to now, as a result we have tentatively determined three parameters of the sensor, i.e., ${W_D}$=220 nm, ${t_m}$=20 nm, and ${l_m}$=300 nm. Based on these values, the relation of the field enhancement on other parameters such as h, ${D_{ms}}$, and $\Delta l$ will be further investigated and discussed in the following 3D modeled geometry.
For the slot widths of ${D_{ms}}$=30, 50, and 70 nm, the dependence on sensor height $h$ is calculated at $\Delta l$=40 nm, as shown in Fig. 6. Figures 6(a), 6(b) and 6(c) represent the relationship of the evaluation factors ${L_c}$, $EF$ and $NVEF$ to the variable $h$, demonstrating two well-defined peaks in the height range, which can be attributed to the SPPs resonance (like standing wave) at the height dimension. One can see clearly that $EF$ beyond 104 can be obtained at ${D_{ms}}$=30 and 50 nm. $NVEF$ is evaluated by normalizing to the maximum value at ${D_{ms}}$=30 nm. One can see that a higher field enhancement appears at ${D_{ms}}$=30 nm, compared with other different ${D_{ms}}$. Zoom extents from the two peak positions are respectively shown in Figs. 6(d) and 6(e), exhibiting narrow peak width of just several nanometers. $h$ of approximately 440 nm will be the best choice due to the higher $NVEF$, though almost the same values of ${L_c}$ and $EF$ do exist at around 220 and 440 nm. The 2D images of the evaluation factors are also calculated and plotted in Figs. 6(f)–6(h), which can show visually the dependence of the field enhancement factors on ${D_{ms}}$, and $h$. As a result, the electric field enhancement is almost entirely dependent on ${D_{ms}}$ and has a strict selectivity to $h$, i.e., the field can be enhanced in a certain height range, but cannot in another. In addition, it is clearly shown from Figs. 6(f) and 6(h) that, if you want to choose an expected width ${D_{ms}}$ reaching the upmost enhancement factor, the width of 30 nm is dominant.
Fig. 6. The evaluation of the field enhancement ability on the sensor using three factors: ${L_c}$, $EF$ and $NVEF$, for three different slot widths of ${D_{ms}}$=30, 50, 70 nm. Parameters assumed: ${W_D}$=220 nm, ${l_m}$=300 nm, ${t_m}$=20 nm, ${l_D}$=380 nm, $\Delta l$=40 nm. (a), (b), and (c) show the relationship curves of the enhancement factors at three slot widths. (d) and (e) show the zoom extents at two discrete height ranges corresponding to (c), where $NVEF$ of three slot widths is normalized to the maximum of the case of ${D_{ms}}$=30 nm. (f), (g), and (h) present 2D images of the three evaluation factors when both the distance ${D_{ms}}$ and the height h change simultaneously, demonstrating the dependence of the field enhancement on ${D_{ms}}$ and the selectivity on $h$.
From the view of a fixed $h$, the dependence on ${D_{ms}}$ is also calculated and plotted in Fig. 7. One can see from Fig. 7(a) that an optimal ${D_{ms}}$ corresponding to the fixed $h$ can be obtained at the single peak position, which ${L_c}$ reaches the maximum value. And it is shown that the maximum shifts towards larger ${D_{ms}}$ with an increase of h, such as the cases of 220, 450, and 480 nm. In Fig. 7(b), $EF$ and $NVEF$ are plotted demonstrating the high enhancement factors exceeding 104 exist at around 30 and 40 nm. It can be seen clearly that the case of ${D_{ms}}$=31 nm and $h$=220 nm strongly dominates because of a larger value of $NVEF$. In addition, one can see that a great enhanced field cannot be obtained at ${D_{ms}}$>60 nm.
Fig. 7. The effect of the slot width on the enhancement ability with fixed sensor height. At three different sensor heights of 220, 450, and 480 nm, other assumed parameters as aforementioned : ${W_D}$=220 nm, ${l_m}$=300 nm, ${t_m}$=20 nm, ${l_D}$=380 nm, $\Delta l$=40 nm. (a) represents the relationship curves of the field ratio ${L_c}$ at three different heights, exhibiting well defined single peak and its shift toward a large ${D_{ms}}$ with an increase of h . (b) represents the enhancement factors $EF$ and $NVEF$, where $NVEF$ is normalized to the maximum value at $h$=220 nm. The enhancement factor exceeding 104 can be obtained around widths of 30, 40 nm in the cases of $h$=220, and 450 nm.
It must be emphasized that, the results above have obtained from a preset $\Delta l$(40 nm), which can effectively adjust the field enhancement by affecting the coupling efficiency of light into the slot. The evaluation factors ${L_c}$, $EF$, and $NVEF$ are calculated and plotted in Fig. 8 at several different $\Delta l$. As shown in the Figs. 8(a), 8(b), and 8(c), it can be seen clearly that each curve has two well-defined peaks in the height range, which can be termed as the first (∼220 nm) and the second (∼440 nm) maxima (or peaks). However, we can see a noticeable difference at the amplitudes, but the corresponding positions ($h$) of the peaks don’t have any shifts, demonstrating that the variable $\Delta l$ has no effect on the SPPs resonance at the height dimension. The curves of ${L_c}$ with respect to $\Delta l$ derived from the first and the second maxima [Fig. 8(a)] are plotted in Fig. 8(d). As can be seen from the curves, an enhancement factor of ${L_c}$>30 (i.e., ${L_c}$=32.3, $EF$=1.09 × 10^6) is obtained at Δ/20nm and h=225nm. The two largest values among the first and second peaks appear accidentally at the same $\Delta l$(20 nm), exhibiting that the condition of $\Delta l$=20 nm will be optimal. As a comparison, in the cases of $\Delta l$ = 20 and 40 nm, the field intensity patterns are exhibited to (e)∼(l), it can be seen that the difference between them is not very obvious to some extent, but the enhancement factors are very different, as shown the red and yellow curves in Figs. 8(a)–8(c).
Fig. 8. The effect of the excessive length $\Delta l$ on the enhancement ability with a fixed slot width of ${D_{ms}}$=30 nm, Parameters assumed as aforementioned: ${W_D}$=220 nm, ${l_m}$=300 nm, ${t_m}$=20 nm. (a) shows the relationship curves of the field enhancement ratio ${L_c}$ with varied height $h$ at several different $\Delta l$, demonstrating well-defined two maxima on each curve. (b) shows the dependence of $EF$ on $h$, revealing that the factor can easily reach a large value beyond 104. (c) shows the relationship of $NVEF$ with respect to h. (d) represents the relationship between two sets of maxima of the electric field intensity in the slot and the variable $\Delta l$, demonstrating that a suitable $\Delta l$ can have great advantage of concentrating light into the slot to obtain high enhancement factor. The optical field distribution in y-z plane corresponding to different $h$ at $\Delta l$=20 nm, i.e.,(e)-(h), and $\Delta l$=40 nm, i.e., (i)-(l), have some slightly difference between the patterns of the images.
So far, we have thoroughly investigated the dependence of the field enhancement on the structural parameters of the proposed sensor. From the three evaluation factors ${L_c}$, $EF$, and $NVEF$ in the figures exhibited above (see Fig. 6–Fig. 8), one can see that the curves of ${L_c}$, $EF$, and $NVEF$ all have two narrow peak value ranges, revealing that the structural parameters to realize the enhanced field intensity in the slot likewise have a small corresponding floating range. Based on a fixed slot width ${D_{ms}}$, we can obtain the allowable error range of h, as shown in Fig. 9. Figures 9(a) and 9(b) represent the tolerances of $h$ and ${D_{ms}}$ in the cases of $EF > {10^3}$ and $EF > {10^4}$, respectively. As it can be seen that the points with an error bar marked in red and orange denote the first maxima, whereas the blue and green ones denote the second maxima, at the same time, the length of the error bar at each point represents the quantity of the tolerance. The tolerance of the height $h$ at a fixed slot width ${D_{ms}}$ denotes with $\delta h$, and similarly, $\delta {D_{ms}}$ is the tolerance of ${D_{ms}}$ at a fixed height $h$. Other structural parameters are assumed as aforementioned, $\delta h$ and $\delta {D_{ms}}$ can be calculated and discretely plotted in Fig. 9. One can see from Fig. 9(a) that the electric field in the slot can be enhanced completely in a large slot width range of 30∼80 nm, and $\delta h$ can reach 20 nm at ${D_{ms}}$=60 nm, but it will reduce at a smaller or larger value of ${D_{ms}}$. Additionally, it can be seen clearly that the tolerance in the first maximum range (200∼260 nm) is less than it in the second maximum range (430∼510 nm). In the case of $\delta {D_{ms}}$, similar results can also be obtained. However, it is worth noting that the maximum of $\delta {D_{ms}}$ still reaches about 20 nm, and most importantly, $\delta {D_{ms}}$ obviously has a larger range compared with $\delta h$, indicating the fact that the etching process aimed at the slot width is easier to achieve the desired effect when the sensor is fabricated based on a determined height. In the case of $EF > {10^4}$, from Fig. 9(b), it can be shown that the extremely enhanced field with a giant factor almost cannot be obtained at a large slot width. Meanwhile, the tolerances $\delta h$ and $\delta {D_{ms}}$ will become smaller ($\delta h$<10 nm). As you may know, the sensors with a high factor require much lower tolerances. Similarly, the tolerances of ${t_m}$ and ${l_m}$ can be determined in the same way, and we will omit it here to avoid the repetition of the contents.
Fig. 9. The tolerance of the height $\delta h$ to realise high enhancement factor based on fixed slot width ${D_{ms}}$, and the tolerance of the slot width $\delta {D_{ms}}$ based on fixed height $h$. (a) represents the tolerances $\delta h$ and $\delta {D_{ms}}$ in the case of $EF$>10^3, where $\delta h$ can be obtained at the given slot widths of 30∼80 nm, in steps of 10 nm. And $\delta {D_{ms}}$ corresponds to the given heights such as 225, 230, 240, 450, 460, and 480 nm. (b) represents the case of $EF$>10^4. At ${D_{ms}}$>50 nm, $\delta h$ does not exist, showing that the enhanced field with $EF$>10^4 cannot be achieved. On the other hand, $\delta {D_{ms}}$ all exists except for the height of 480 nm, demonstrating that a highly enhanced optical field can be obtained easily at the height range of 200∼260 nm compared to the range of 430∼510 nm.
Modern nanotechnology allows one to scale down different types important devices such as sensors, chips and thus opens up new paths for their particular applications. The hybrid plamonic slot sensor we present here has been miniaturized to the geometrical dimensions of approximately 510 × 300 × 225 nm (i.e., width × length × height) while ensuring excellent performance. The value of 510 nm refers to the total width of the sensor structure in the layered direction. The proposed structure of the sensor can be fabricated with the well-established CMOS craft. A 225nm-thick Si3N4 layer was first deposited on a glass substrate of 2µm thick by plasma-enhanced chemical vapor deposition (PECVD). The 30nm-thick Si3N4 strip will be reserved through the processes patterned with electron-beam lithography (EBL)and etched by a fluorine-based inductive coupled plasma-reactive ion etching (ICPE). Then the deposition and subsequent lift-off of the gold are performed leaving a 20nm-thick gold layer on the outer both sides of the Si3N4 strip. Similarly, the 220nm-width Si3N4 layer is attached outer side of the gold layers by the PECVD and EBL processes. Finally, the slot can be obtained by etching the core of the structure to remove the 30nm-thick Si3N4 trip. By the way, the etching at the length dimension (300 nm) should be carried out at the same time, which is easier to be achieved technologically.
5. Conclusion
In summary, aimed to the field enhancement for the application of SERS spectroscopy measurements, a compact hybrid plasmonic slot waveguide sensor based on SPPs is investigated theoretically. Considering the existing Micro-nanometer technology, we present a feasible hybrid IMI structure of the slot waveguide sensor, which can be fabricated relatively easily using the well-established COMS etching process. By calculating the evaluation factors ${L_c}$, $EF$, and $NVEF$, the dependence of the electric field enhancement depending upon the structural parameters of the sensor is discussed. The results show that, in the height range of $h$<600 nm, the electric field intensity in the slot can be strongly enhanced at two heights ${h_0}$ and ${h_1}$, which can be attributed to the SPPs resonance like standing wave along the direction of propagation of the light. From the distributions of ${L_c}$, $EF$, and $NVEF$, one can see two well-defined narrow peaks on each curve. The narrow peaks indicate that the field can only be enhanced within a strict allowable range of error. The proposed waveguide structure can achieve an enhancement factor of up to 1.09 × 10^6 at a compact configuration of ${W_D}$ = 220 nm, ${t_m}$=20 nm, ${D_{ms}}$=30 nm, ${l_m}$=300 nm, Δ/=20nm, and $h$=225 nm. Our results can be exploited to design slot waveguide optical sensors with an extremely enhanced field, or a SERS substrate that can directly be employed for spectral analysis. Furthermore, our work in the paper has a good guiding role in the sensing application fields of light-on-chip integration.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analysed in the presented research.
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