# A practical Tamm plasmon sensor based on porous Si

Alexandre Juneau-Fecteau, Rémy Savin, Abderraouf Boucherif, Luc Frechette

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Alexandre Juneau-Fecteau, Rémy Savin, Abderraouf Boucherif, Luc Frechette. A practical Tamm plasmon sensor based on porous Si. AIP Advances, 2021, 11 (6), pp.065305. 10.1063/5.0054629. hal-03683604

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# A practical Tamm plasmon sensor based on porous Si

Alexandre Juneau-Fecteau ; Rémy Savin ; Abderraouf Boucherif; Luc G. Fréchette

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# A practical Tamm plasmon sensor based on porous Si EP

Cite as: AIP Advances 11, 065305 (2021); doi: 10.1063/5.0054629

Submitted: 27 April 2021 • Accepted: 21 May 2021 •

Published Online: 3 June 2021

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Alexandre Juneau-Fecteau,<sup>1,2,a)</sup> ID Rémy Savin,<sup>1,2)</sup> ID Abderraouf Boucherif,<sup>1,2)</sup> and Luc G. Fréchette<sup>1,2,b)</sup> ID

## AFFILIATIONS

## ABSTRACT

We report the fabrication and characterization of a new type of porous Si sensor using the Tamm plasmon resonance. The sensor consists of a photonic crystal created by periodic electrochemical anodization of crystalline Si, followed by partial thermal oxidation. The photonic crystal is transferred to a Au-coated glass substrate to allow optical measurements of surface modes at the metal/porous Si interface. This configuration greatly simplifies sensing since an analyte can be introduced in the pores from the opposite side of the metal layer without disrupting the optical path. The fabricated device exhibits a Tamm plasmon resonance within the photonic bandgap at a wavelength of 794 nm with a quality factor of 25. We observe a wavelength shift of the resonance when the nanosized pores are infiltrated with different concentrations of a toluene/ethanol solution. The measured sensitivity reaches 139 nm/RIU, in agreement with scattering matrix simulations and more than twice larger than those previously reported for Tamm plasmons. The quality factor and sensitivity yield a sensor figure of merit of 4. We also show that the electric field within the Tamm device is confined within a mode volume twice smaller than within a Fabry-Pérot resonator of comparable size according to calculations.

© 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0054629

## I. INTRODUCTION

Surface plasmons (SPs) on metal films have been widely exploited in sensors due to a high sensitivity to a change in the refractive index in their environment.<fnref n="1" /> Tamm plasmons (TPs), a novel type of optical surface waves at the interface of a metal and a 1D photonic crystal (PC), have been actively researched in recent times for the same reason.<fnref n="2" />⁻⁴ Contrary to a SP resonance, a TP resonance can be excited at any angles of incidence for both polarizations without requiring a coupling prism or grating, which can be advantageous for sensing.⁵ An important limitation to this approach is that the electric field is located within the PC, so openings must be made in the device for the analyte to reach the detection volume.⁶ One way around this issue is to use porous layers in the PC, such as porous metal oxides deposited by spin-coating.⁷ Inspired by this approach, we have previously demonstrated the existence of a TP resonance in a PC made of porous Si (PSi) and coated with gold.⁸ PSi is an

interesting nanomaterial for PC fabrication because of the simple preparation of a periodic PSi multilayer with high refractive index contrast from a bulk Si wafer using a simple electrochemical process.⁹,¹⁰ Furthermore, PSi transmits light with very low absorption from visible to infrared,¹¹ and the nanosized pores reduce the energy necessary for vapor condensation, thus facilitating detection of volatile compounds.¹²,¹³ The very high specific surface of PSi, around 300 m<fnref n="2" /> cm⁻³,¹⁴ would be especially useful to capture molecules in gas sensing applications. However, the metal film on the top of the structure prevents access to the porous PC underneath, making the TP resonance impractical for sensing. In this work, we solve this problem by placing the PC above the metal layer, allowing the sensing layers to be infiltrated from the top.

We present the experimental validation of a practical optical TP sensor constructed by liftoff of a PSi multilayer through electropolishing,¹⁵ followed by a transfer of the resulting freestanding structure to a substrate coated with Au, as shown in Fig. 1. The process is

<footnote n="1"><sup>1</sup> Institut Interdisciplinaire d'Innovation Technologique (3IT), Université de Sherbrooke, 3000 Boulevard Université, Sherbrooke, Québec J1K OA5, Canada</footnote>

<footnote n="2"><sup>2</sup> Laboratoire Nanotechnologies Nanosystèmes (LN2) - CNRS UMI-3463, Université de Sherbrooke, 3000 Boulevard Université, Sherbrooke, Québec J1K OA5, Canada</footnote>

<footnote><sup>a)</sup> Author to whom correspondence should be addressed: alexandre.juneau.fecteau@usherbrooke.ca</footnote>

<footnote><sup>b)</sup> Electronic mail: luc.frechette@usherbrooke.ca</footnote>
<figure><img src="image_14.png" /><figcaption>FIG. 1. Schematic of the porous Si sensor. The incident beam reaches the Au film from the bottom, and the analyte is introduced from the top.</figcaption></figure>

similar to bonding of PSi to quartz¹⁶ and SiC.¹⁷ The resulting TP sensor is made of a PSi PC between two glass slides, where one of the slides is coated with Au, giving rise to the TP resonance inside the PC, while the other is perforated to allow passage of an analyte. We tested the sensor using solutions with varying concentrations of toluene in ethanol. Toluene is a widely available organic chemical with molecular weight and structure comparable to many target compounds, such as trinitrotoluene (TNT), in sensing applications. The refractive index of the toluene/ethanol mixture was determined from an effective model and the sensitivity of the device evaluated by fitting the wavelength of the resonance as a function of refractive index.

## II. FABRICATION

We fabricated the PSi PC in a silicon wafer by leveraging the well-established electrochemical etching method.¹⁸ A boron-doped crystalline Si wafer with a resistivity of ~0.01 Ω cm was placed inside a Teflon cell and exposed to an electrolyte of HF/water/ethanol in the volumetric ratio 1 : 1 : 2. Each unit cell of the PC is made of two layers fabricated by applying a current density of 31.6 mA/cm² for 2.16 s and 184 mA/cm² for 0.773 s for low and high porosities, respectively, with an 8 s delay between each pulse to allow regeneration of the electrolyte inside the pores. This sequence was repeated ten times to form the periodic PC. We calibrated the process by making single layers of both types. We determined the porosity of each layer by loss of mass after porosification, while we calculated the etching rates by measuring the layer thickness with a scanning electron microscope (SEM) and dividing by the etch time. The measured porosities for each layer type are 37% for low porosity and 59% for high porosity, with etching rates of 34.9 and 134 nm/s, respectively. According to these parameters, the PC is made of 75.5 nm thick low porosity layers and 104 nm thick high porosity layers, with an expected photonic bandgap centered around a wavelength of 800 nm at normal

<figure><img src="image_15.png" /><figcaption>FIG. 2. (a) SEM cross section of the PSi multilayer. The PC is located at the bottom of the structure. (b) Photograph of a PSi PC on a glass slide. (c) Photograph of a finished device with two PSi PCs on a glass slide covered with a Au film.</figcaption></figure>

incidence. SEM cross section of the PC is shown in Fig. 2(a). To facilitate handling of the freestanding PC, we fabricated an additional 20 µm thick supporting layer of high porosity below the multilayer. This layer also provides the benefit of delaying evaporation of the volatile analyte during sensing experiments. After porosification, the PC is detached from the substrate by electropolishing with a series of three 1 A current pulses of 5 s duration separated by 1 s pauses. The resulting freestanding PC is transferred to a 1 mm thick microscope glass slide coated by evaporation with 25 nm of Au on a 3 nm thick Cr adhesion layer. The PSi PC is further processed through thermal oxidation at 300 °C for 1 h in order to stabilize the nanostructure and enhance hydrophilicity in the pores. The Au film is compatible with this thermal treatment, as was previously demonstrated by heating a Au based TPP thermal emitter up to 360 °C with no significant change in the resonance.¹⁹ After oxidation, another microscope slide is positioned on top of the PC and secured to the bottom slide using crystalbond 509 by SPI Supplies, as shown in Fig. 2(b). Prior to bonding, we create a circular opening of 6 mm in diameter in the top glass slide using an LPKF Protolaser U3 to provide access to the PC from the top. Figure 2(c) shows a picture of the finished structure with two sensors.

## III. RESULTS AND DISCUSSION

We measured the reflectance of the TP sensors at normal incidence with a Filmetrics F10-RT-EXR spectrometer. Since the reflectance is measured from the bottom, the introduction of a drop of liquid from the top does not disturb the optical path to the spectrometer.

### A. TP sensor in air

Figure 3(a) shows the measured reflectance of a PC still attached to the Si substrate following porosification, as well as a 25 nm thick Au film on glass for comparison. The photonic bandgap of the PC is the region of the spectrum marked in blue where the reflectance reaches near unity because of destructive interference
<figure><img src="image_16.png" /><figcaption>FIG. 3. (a) Measured reflectance of a PC still attached to a Si wafer (red) and a 25 nm thick Au film deposited on glass (yellow). The photonic bandgap of the PC is marked in blue. (b) Measured reflectance of a PC on a Au-coated glass slide before (red) and after (blue) thermal oxidation of PSi. Large dips in reflectance within the bandgap are TP resonances. (c) Simulated reflectance of the oxidized PC on Au-coated glass. The inset shows the refractive indices of bulk Si (black), the low porosities (orange) and (magenta) layers of the PC. (d) Product of the simulated complex reflection coefficients $r_{Au}$ and $r_{PC}$ of the Au layer and PC, respectively. The modulus (blue) and phase (green) of $r_{Au}r_{PC}$ are plotted as a function of wavelength.</figcaption></figure>

within the multilayer. Figure 3(b) shows the results of the same measurement for a TP sensor made of a PSi PC fabricated with the same porosification parameters and transferred to a glass slide coated with Au. The reflectance spectrum was measured before and after the partial thermal oxidation of the PC. The sharp drop in reflectance within the bandgap corresponds to the TP resonance. The localized optical state at this wavelength absorbs energy, hence the decreased reflectance. The resonance wavelength, $\lambda_{TP}$, is blueshifted from 820 to 794 nm following PC oxidation since the partial conversion of Si to SiO$_2$ lowers the effective refractive index of PSi layers. To determine the quality factor, we fitted the resonance in Fig. 3(b) with a Lorentz function,

$$R(\omega) = R_0 - \frac{A}{1 + \left[ 2\frac{\omega - \omega_{TP}}{\Delta\omega} \right]^2}, \quad (1)$$

$$\Rightarrow R(\lambda) = R_0 - \frac{A}{1 + \left[ 2Q\left(\frac{\lambda_{TP}}{\lambda} - 1\right) \right]^2}, \quad (2)$$

with angular frequency $\omega = 2\pi/\lambda$ and quality factor $Q = \omega_{TP}/\Delta\omega$, where $\Delta\omega$ is the full width at half minimum (FWHM) of the resonance on the frequency scale and $\omega_{TP} = 2\pi/\lambda_{TP}$ is the resonance frequency. The fit gives a quality factor of $Q \approx 25$ and a FWHM of $\Delta\lambda \approx 32$ nm. The quality factor is unaffected by partial oxidation of PSi.

In addition to experimental measurements, we simulated the propagation of electromagnetic waves within the multilayer using our own C++ implementation of the scattering matrix method.²⁰ As shown by the schematic in Fig. 3(b), the simulated multilayer is a PSi PC made of 75.5 nm thick low porosity layers and 104 nm thick high porosity layers, on top of a 25 nm thick Au layer on a 3 nm thick

Cr layer. The multilayer is located on a semi-infinite glass medium and is surrounded by air. The incident light beam comes from the bottom of the glass slide. The support layer is not included in the simulations since we verified it has negligible impact on the TP resonance. We obtained from the literature the permittivities of soda lime glass,²¹ Au,²² Cr,²³ crystalline Si,²⁴ and thermally grown SiO$_2$²⁵ from Si. We then calculated the permittivities, $\epsilon_{layer}$, of both layer types in the oxidized PSi PC from the permittivities of Si and SiO$_2$ using the Bruggeman effective medium model as follows:²⁶

$$f_{\text{Si}} \frac{\epsilon_{\text{Si}} - \epsilon_{\text{layer}}}{\epsilon_{\text{Si}} + 2\epsilon_{\text{layer}}} + f_{\text{SiO}_2} \frac{\epsilon_{\text{SiO}_2} - \epsilon_{\text{layer}}}{\epsilon_{\text{SiO}_2} + 2\epsilon_{\text{layer}}} + f_{\text{pores}} \frac{\epsilon_{\text{pores}} - \epsilon_{\text{layer}}}{\epsilon_{\text{pores}} + 2\epsilon_{\text{layer}}} = 0, \quad (3)$$

where $f_{Si}$, $f_{SiO_2}$, and $f_{pores}$ are, respectively, the volume fractions occupied by Si, SiO$_2$, and the pores. As previously mentioned, the measured $f_{pores}$ is 0.37 or 0.59 depending on porosity. The 26 nm blueshift observed in experimental data after PSi oxidation is reproduced in the simulation by setting $f_{SiO_2} = 0.03$. The volume fraction of Si is determined with $f_{Si} = 1 - f_{pores} - f_{SiO_2}$. The inset in Fig. 3(b) shows the simulated electrical field intensity of the TP resonance within the volume of the PC with a maximum intensity close to the metal film. The fact that the electric field is located within the PC suggests that the resonance frequency is sensitive to a change in the refractive index inside the pores of the PC. The calculated reflectance spectrum is shown in Fig. 3(c). We notice a larger drop in reflectance from the simulated TP resonance than measured. However, the theoretical model does not take into account diffuse scattering at the interfaces, which is expected to decrease the magnitude of specular reflections within the multilayer. The refractive indices calculated for the low and high porosity PSi layers using Eq. (3) are shown in the
inset of Fig. 3(c) with the refractive index of bulk Si for comparison. The TP resonance occurs at the wavelength where the complex reflection coefficients of the metal, $r_{Au}$, and the PC, $r_{PC}$, approach the condition $r_{Au}r_{PC} = 1$, meaning that the reflection phases are related by $\phi_{Au} + \phi_{PC} = 0$ at the resonance.²,³ This condition is fulfilled at 844 nm according to the simulated product $r_{Au}r_{PC}$ plotted in Fig. 3(d). The difference with the measured resonance wavelength of 794 nm for the oxidized PC is thus only 6%, which can be explained by small discrepancies between the expected and actual porosities and layer thicknesses in the PC.

## B. TP sensor with analyte

We tested the response of both fabricated TP sensors by measuring the reflectance spectra after infiltration of the PSi pores with different concentrations of toluene/ethanol. We used five volumetric ratios $f_{tol/eth}$ of 1%, 5%, 10%, 44%, and 100% of toluene in ethanol for each sensor and cleaned the PSi pores with pure ethanol between each experiment. Figure 4(a) shows the results for one of the devices. The resonance shifts to longer wavelengths as the toluene concentration increases, but the width of the dip in reflectance is not affected by the change in concentration. In order to assess the sensitivity, we converted the concentration of chemicals infiltrated in the pores, in this case toluene in ethanol, to a refractive index once again using the Bruggeman model. The effective permittivity, $\epsilon_{pores}$, of the analyte in the pores is calculated by solving

$$f_{tol/eth} \frac{\epsilon_{tol} - \epsilon_{pores}}{\epsilon_{tol} + 2\epsilon_{pores}} + (1 - f_{tol/eth}) \frac{\epsilon_{eth} - \epsilon_{pores}}{\epsilon_{eth} + 2\epsilon_{pores}} = 0, \quad (4)$$

where the wavelength-dependent permittivities of both compounds, $\epsilon_{tol}$ and $\epsilon_{eth}$, come from the literature.²⁷ The refractive index in the pores, $n_{pores} = \text{Re}(\sqrt{\epsilon_{pores}})$, is plotted in Fig. 4(b) for all toluene concentrations with the location of the shifting TP resonance marked by dots. The wavelength of the resonance is also plotted as a function of the refractive index of the analyte in Fig. 4(c). A linear fit on these data reveals a sensitivity of $S_{\lambda} \approx 139$ nm/RIU. Through the same procedure, we measured a sensitivity of 121 nm/RIU for the other fabricated TP sensor. For comparison, Auguié et al. reported a sensitivity of 55 nm/RIU in a TP sensor with a seven-layer PC made

of porous metal oxides deposited on Au.⁷ Thus, the PSi based TP sensor has two times higher sensitivity, with a comparable FWHM. The sensitivity ($S_{\lambda}$) and FWHM ($\Delta\lambda$) can be combined in a single figure of merit, FOM = $S_{\lambda}/\Delta\lambda$, to compare the performance of different sensing platforms. The resulting FOM for the TP sensors is ~4, comparable to the measured FOMs of 2–10 for localized surface plasmon resonance sensors²⁸,²⁹ and close to the FOM predicted to be between 10 and 20 for a recently proposed self-referenced TP sensor design.³⁰ We validated the measured values of sensitivity for the TP sensors with the scattering matrix model. Using Eqs. (3) and (4), we calculated the refractive indices of the PC layers with pores filled with toluene in ethanol solutions at volumetric ratios from 0% to 100% toluene in 20% increments and computed the associated sensor reflectance spectra. The first ratio corresponds to pure ethanol in the pores, with a refractive index of $n_{pores} = 1.356$. The associated simulated reflectance of the sensor is shown in Fig. 5(a). The inset shows the linear response of the sensor to a change in refractive index as the TP resonance redshifts to larger wavelengths when the refractive index in the pores increases due to a larger fraction of toluene in the analyte. The fitted sensitivity is $S_{\lambda} \approx 166$ nm/RIU, close to the experimental value of 139 nm/RIU. Once again, small differences in parameters, such as porosities, thicknesses, and permittivities, between the real and simulated structures could account for the discrepancy in the measured and calculated sensitivities of the Tamm resonance. Still, the scattering matrix model has proven itself to be a valuable design tool to simulate the expected behavior of the TP sensor. Furthermore, the wavelength shift is also visible in Fig. 5(b) in the calculated reflectance of a PC with the same geometry deposited on a glass substrate without Au. We present two cases: pure ethanol and pure toluene in the pores. In this configuration, the point of maximum reflectance in the photonic bandgap is redshifted by 15 nm by changing the analyte. The corresponding sensitivity of 120 nm/RIU is of the same order of magnitude as the value for the TP sensor.

## C. Comparison with Fabry-Pérot resonance

We now compare the TP sensor to the Fabry-Pérot (FP) sensor, another well-studied refractive index sensing concept that can

<figure><img src="image_17.png" /><figcaption>FIG. 4. (a) Measured reflectance of the Tamm structure for five volumetric ratios of toluene in ethanol from 1% to 100% of toluene. The curves beyond 1% are shifted by 0.25 in reflectance from each other for clarity. (b) Simulated refractive index for each toluene/ethanol mix according to the Bruggeman effective medium model. (c) Wavelength shift of the TP resonance for each refractive index.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>FIG. 5. (a) Simulated reflectance of the TP sensor with pure ethanol in the PC pores. The inset shows the simulated TP wavelength as a function of the refractive index in the pores. The first data point at n = 1.356 corresponds to pure ethanol. (b) Simulated reflectance of the PC on glass with ethanol (green) and toluene (blue) in the pores.</figcaption></figure>

be implemented in a PSi multilayer.31 FP cavities are fabricated by embedding a defect within a periodic multilayer, usually a layer with a thickness such as to break the periodicity of the PC. This creates a localized optical state around the defect layer, which manifests itself as a resonance in the reflectance and transmittance spectra of the device. Provided the multilayer is porous, the infiltration of an analyte within the pores shifts the resonance frequency, as in the case of the TP sensor, with the same benefits of high specific surface and low optical absorption if a PSi multilayer is employed. However, the FP sensor does not require a metal film and is thus a purely dielectric structure, which is expected to have a finer resonance linewidth than a TP sensor due to the absence of absorption in metal. Volk et al. reported on refractive index sensing with a FP cavity made of 25 PSi layers with similar porosities to the PSi layers in our work.26 They demonstrated a sensitivity of 140 nm/RIU by infiltrating the pores with several organic solvents, a value identical to the ones measured for the PSi TP sensors. They also reported a FWHM of only 5 nm, indeed lower than the value of 32 nm measured for the TP resonance, which yields a FOM of 28 for the FP sensor. However, the TP resonance presents other advantages, as can be realized by simulating the electric field spatial distribution. The calculated field intensity of a TP resonance is shown in Fig. 6(a) for a simplified multilayer made of a 25 nm thick Au film on a PC with alternating layers A ($n_A = 2.5$, $d_A = 80$ nm) and B ($n_B = 1.5$, $d_B = 133$ nm). Figure 6(b) shows the field intensity in a FP cavity made by embedding a 215 nm thick defect layer of index $n_s = 2.5$ within the same PC.

We notice from the simulations that the electric field of the FP resonance is localized around the defect layer, whereas in the

<figure><img src="image_19.png" /><figcaption>FIG. 6. Simulated electric field intensity of (a) the TP resonance within a Au-coated PC structure and (b) a Fabry-Pérot cavity with the same number of layers. Both curves are normalized by the incident field intensity $|E_{inc}|^2$. The resonance occurs in both cases at a wavelength of 905 nm.</figcaption></figure>

case of the TP resonance the field intensity reaches a maximum very close to the multilayer surface. We can compare the degree of spatial confinement of electric field intensity, $|E(z)|^2$, in both structures by introducing the concept of mode volume,32

$$V_{\text{mode}} = \frac{A}{\max(\varepsilon(z)|E(z)|^2)} \int \varepsilon(z)|E(z)|^2 dz, \quad (5)$$

where z is the direction perpendicular to the layers, $\varepsilon(z)$ is the permittivity, which changes as a function of z as the integration is performed from layer to layer, and A is the sample surface area. A smaller $V_{\text{mode}}$ means a more confined electric field, which leads to increased light-matter interaction beneficial to many applications, such as sensing and light emission. The mode volumes per unit of surface, $V_{\text{mode}}/A$, calculated with the data in Fig. 6, are 145 nm for the TP resonance and 282 nm for the FP resonance. The field is therefore twice more confined for the TP structure. The fact that the field is located close to the surface in this configuration is also advantageous since it can be further confined in the two other dimensions parallel to the surface by patterning the metal film. For example, Fränzl et al. followed this approach to achieve the surface-enhanced Raman effect by fabricating silver nanosized triangles on a PSi PC.33 The high field intensity close to the surface of the PC due to a TP resonance combined with spatial confinement in the triangles generates a thousand times greater Raman intensity from organic molecules compared to the same analyte on bulk Si. In a similar manner, the lateral confinement of TPs by patterning of the metal film was used to realize enhanced spontaneous emission from quantum dots via the Purcell effect,34 single photon sources,35 and even micro-fabricated lasers.36,37 Furthermore, TPs have been shown to couple to other polaritonic quasiparticles, such as surface plasmons38 and exciton-polaritons.39 The coupling of TP and FP resonances in particular is predicted to significantly increase the performance of a Tamm sensor by exploiting a phenomenon known as electromagnetically induced reflection.40 To achieve this effect, a defect is introduced within the PC, giving rise to a FP optical state. The destructive interference between this new localized state and the TP resonance can lead to an extremely narrowband peak of high reflectance inside
the dip in reflectance. The sharpness of this predicted peak could be exploited to create TP sensors with a FOM potentially as high as 682 according to calculations.⁴¹

## IV. CONCLUSION

In summary, we have demonstrated that porous Si (PSi) is a viable platform to realize a sensor using the Tamm plasmon (TP) resonance as the transduction mechanism. We fabricated a porous photonic crystal (PC) using the anodization of Si, which we detached electrochemically from the Si wafer and transferred to a Au-coated glass substrate. The fact that the porous multilayer is located on top of the metal is a crucial advance since it allows an analyte to diffuse within the body of the sensor where it can affect the TP resonance. Furthermore, PSi retains the single crystal nature of bulk Si with very low optical absorption across a wide range of the spectrum, as well as a high specific surface facilitating analyte capture. The reflectance spectrum of the resulting sensor presents a dip within the photonic bandgap associated with the TP resonance. This phenomenon is in agreement with scattering matrix simulations using Bruggeman effective medium theory to simulate the optical properties of porous layers. We measured the response of two TP sensors by filling the PC pores with different concentrations of toluene in ethanol. The measured sensitivities of 139 and 121 nm/RIU are close to the simulated value of 166 nm/RIU. This work brings the sensitivity of porous TP sensors at more than twice the previously reported sensitivity of 55 nm/RIU. The associated sensor figure of merit (FOM) is 4, comparable to localized surface plasmon sensors. We also compared the TP resonance to a Fabry-Pérot (FP) resonance created by inserting a defect within a PC. Although FP resonances are sharper due to less optical absorption, TPs have twice the electric field confinement as measured by the mode volume and permit additional lateral confinement by patterning of the metal film at the surface, opening the way for many practical applications relying on light-matter interactions. Finally, we remark that the FOM of the TP refractive index sensor could be further improved by two orders of magnitude by coupling the TP resonance to a FP cavity fabricated in the same multilayer. The large FOM combined with the high specific surface and low optical losses of PSi makes the TP sensor design investigated in this work a promising avenue for gas detection and biosensing.

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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