1. Introduction

In recent years surface plasmon polariton (SPP) based nanoscale devices have attracted a lot of attention [1,2]. SPPs are exponentially decaying localized electromagnetic waves (EM) that propagate along the interface of a dielectric and a medium with high free-carrier concentrations [3]. SPPs have greater momentum than light of the same frequency; consequently, the electromagnetic field does not propagate away from the surface and is guided by it [4]. Previously, the size of optical devices was limited by the incident wavelength due to the diffraction limit, as stated according to Heisenberg’s uncertainty principle. SPPs has the unique capability of overcoming the diffraction limit [5] ($\lambda / 2n$) of light thus removing the restriction on the size of the optical devices. This led to the creation of subwavelength devices like Mach-Zehnder Interferometers (MZIs) [6], Fabry-Perot resonator [7], multimode interference demultiplexers and splitters [8], refractive index (RI) sensors [9–11], that was previously not possible. Different types of waveguides (WG) like ridge WG, hybrid WG, plasmonic slit type WG are used to guide the EM waves. The slit type WG shows two prevalent types of configurations namely Metal-Insulator-Metal (MIM) and Insulator-Metal-Insulator (IMI). MIM type of configuration is preferred more due to small mode size [12], higher confinement of EM wave [13], and good balance between propagation length and losses [14]. Due to their label-free detection of analytes and on-chip sensing capability, RI sensors based on MIM have attracted significant interest. Chau et al. [15] proposed a semicircular-ring resonator with a sensitivity of 2900 nm/RIU. Wang et al. [16] investigated a structure with an asymmetric MIM waveguide that had a sensitivity of 1114.3 nm/RIU. Rakhshani et al. [17] demonstrated a MIM plasmonic sensor with one rectangular and two square nanorod array resonators, and recorded a maximum sensitivity of 1090 nm/RIU. In 2020, a RI sensor was designed with two concentric double-square resonators to facilitate the sensing of human blood groups [11]. In 2023, a temperature sensor was proposed that uses an elliptical-shaped ring resonator coupled with a MIM waveguide as a RI sensor [13].

Noble metals like Ag and Au have been used widely in these subwavelength devices as they have sharp resonance, high conductivity [18] and large free carrier concentrations. However, the limitations of these noble metals prevent their widespread adaptation. The lack of tunable optical properties of metals is a significant drawback as the carrier concentration of metals cannot be altered significantly [18,19]. Their melting temperature is less which results in low thermal stability at higher temperatures [18], due to nanostructures’ high surface-to-volume ratios they may even liquify below their bulk melting point [20] and low conduction electron mobility causes significant conduction electron losses [21]. The deterioration of metals upon contact to air or oxygen or moisture would provide further challenges. The silver film tarnishes to form a layer of silver sulfide, and the nucleation on the film appears random, the nucleation site density is high, and the sulfide forms in clusters, degrading the optical properties [22]. Metals present significant difficulties in the field of nanofabrication, particularly when used to produce thin films. These films have distinct morphologies compared to bulk metals, which causes their optical properties to degrade. Due to the fact that thin-film grains are smaller than bulk metal grains, additional grain-boundary scattering degrades the optical properties, and methods with limited scalability are necessary to surmount the percolation threshold [19]. An additional technological barrier associated with noble metals is their incompatibility with conventional silicon manufacturing processes [23]. Incorporating noble metals into such processes is a formidable obstacle, and gold and silver are still regarded as impracticable for silicon production. In this article, we propose a CMOS-compactable comb-shaped plasmonic refractive index sensor based on ZrN-Insulator-ZrN configuration. It has the potential to overcome the limitations of traditional noble metal-based sensors and offer an alternative material with better properties for plasmonic devices. The sensor has a sensitivity of 1445.46 nm/RIU and a FOM of 140.96. The label free detection capability of the proposed ZrN-Insulator-ZrN optical sensor can be used for a wide range of applications with low volume of analytes. The proposed nanosensor is a strong contender for the CMOS compactable alternative plasmonic sensor regime which will remove the barriers of wide scale adaption of plasmonic optical sensors through creating a interconnection between plasmonic optical sensor and nanoelectronics.

2. Attributes of ZrN

The development of next-generation of optical sensors has made transition-metal nitrides (TMNs) a focal point of research due to their extraordinary properties and potential advantages over conventional noble metals. At visible and near-infrared wavelengths, Titanium Nitride (TiN), Zirconium Nitride (ZrN), and Hafnium Nitride (HfN) (group IV-B) exhibit behavior similar to that of metals [24] and have high carrier concentrations. The plasmonic properties of TMNs can be tuned by the metal/nitrogen stoichiometry, thereby affecting the structural composition (i.e., change in carrier concentration) which tunes optical properties [25]. These materials have refractory properties [19], high electron conductivity and mobility [26], metallurgical and thermal stability [27], high hardness [28], low work function [26], and are comparatively less expensive than noble metals [20]. TiN and ZrN have melting points of 2930$^{\circ }$C and 2952$^{\circ }$C, respectively, at 1 atmospheric pressure, whereas gold’s melting point is 1064$^{\circ }$C [25]. Compatibility of TMNs with CMOS technology [27,29] provides fabrication and integration advantages that may be beneficial for integrating plasmonics with existing CMOS technologies as a substitute to the incompatible Au and Ag [30]. TiN has received a great deal of attention as an alternative plasmonic material, whereas ZrN has received less attention despite its better performance. Among TMNs, ZrN is the most stable and reproducible material in terms of its optical performance, has higher mean free path of carriers, demonstrates the optimal balance of electronic and dielectric losses [31], has longer average value electron relaxation time than TiN [30], reduced dielectric losses in comparison to TiN, while maintaining nearly the same conduction electron density and oxidation resistance equal to or greater than TiN [27]. By tuning the nitrogen content of $\mathrm {ZrN_{x}}$ flims, the optical property can be controlled where carrier concentration of films increases with the nitrogen vacancy concentration [31]. Due to cubic lattices, ZrN can be grown epitaxially on cubic substrates like MgO that results in ultrasmooth and ultrathin films, suitable for plasmonic applications that require high-quality films with low losses and TiN has a lower carrier concentration under nitrogen-rich deposition conditions [19]. A large lattice constant permits heteroepitaxy of ZrN on Si, a unique property among transition metal nitrides [27]. As interband $\mathrm {p} \rightarrow \mathrm {d}$ transition energy of ZrN is higher than TiN, it exhibits stronger plasmonic resonance [32]. Lalisse et al. investigated plasmonic efficiencies of nanoparticles made of metal nitrides and found out that ZrN appears to be a more advantageous nanoplasmonic material than TiN, based on the parameters studied in their work with 10 times the near-field enhancement [25]. This study introduces the use of ZrN in plasmonic sensors, creating a high-performance, robust, and CMOS-compatible alternative to conventional noble metal-based sensors. The finding paves the way for the integration of plasmonics with existing technologies and promises a significant advance in the field of nanometric sensing devices.

3. Structure model and methodology

In Fig. 1(a), the overhead view of the proposed model of the sensor has been illustrated. The blue part indicates the ZrN and the orange part indicates the material under sensing (MUS) that has been used to fill the cavities. Table 1 provides the geometric parameter values for the designed sensor. The comb shaped cavity has been coupled to a WG with gratings. The introduction of teeth in the comb shaped cavity introduces additional parameters for design tunability and optimization. The electric field distribution at the resonant wavelength ($\mathrm {\lambda _{res}}$) of 1262.968 nm is given in Fig. 1(b).

In order to couple the light in and out of the MIM waveguide, a mode converter can be used, which can efficiently convert the dielectric mode to plasmonic mode and back to dielectric mode. Butt et al. [33] demonstrated a tapered waveguide mode converter that can be used for coupling the light in the MIM waveguide and to collect the light from the MIM waveguide with a conversion efficiency of -1.6dB. This research provides a comprehensive analysis of a sensing system with a light coupling and collecting mechanism that has not been thoroughly investigated in previous research. A dielectric-to-plasmonic mode converter was suggested for coupling the light into the input port, and a plasmonic-to-dielectric mode converter was suggested to capture light from the plasmonic WG [33]. This arrangement can be used to couple the light to the MIM waveguide for our proposed sensor. The structure has been simulated using finite element method (FEM) using COMSOL Multiphysics. FEM defines the material interfaces precisely, whether they are linear or curved, using an unstructured adaptive mesh, and high numerical resolution can be imposed wherever it is required [34]. Extremely fine triangular meshing has been used in the domains for better accuracy of the numerical results, with a maximum element size of 8 nm and a minimum element size of 0.016 nm. To presume that the proposed structure has an open geometry, scattering boundary conditions have been applied. The structure is built upon ZrN-Insulator-ZrN configuration. The permittivity of ZrN is given by the Lorentz-Drude equation [19]:

Here, $w_p$ is the plasma frequency, $\omega _1$ is the resonance frequency, $\gamma _1$ is the damping constant, $\gamma _p$ is the damping constant of drude part, $\epsilon _b$ identifies the background constant owing to transitions not taken into consideration by Lorentz terms, and $f_1$ is the oscillator strength of the material. To support the SPPs at the interface between ZrN and MUS, the permittivity of ZrN ($\epsilon _{ZrN}(\omega )$) and the permittivity of MUS ($\epsilon _{MUS}(\omega )$) must be of the opposite sign, as the electric field normal to the interface must also change sign across the ZrN-MUS interface [4]. As MUS are dielectrics with real and positive values, it follows that $\epsilon _{ZrN}(\omega )$ must also be real and negative. Fig. 1(c) shows the real and imaginary parts of the permittivities indicating that ZrN will be able to support SPPs at the ZrN-MUS interface. In spite of the fact that every particular geometry will have its own unique quality factor, a general limiting case may be obtained which indicates the quality factor of SPPs ($Q_{SPP}$) supported by the material [35]. The following equation indicates $Q_{SPP}$[35,36]:

Here $\epsilon '_{ZrN}$ is the real part of permittivity and $\epsilon ''_{ZrN}$ is the imaginary part of permittivity from the Lorentz-Drude model. We have compared the $Q_{SPP}$ of two popular TMNs, namely TiN and ZrN. The TiN has also been modeled using the Lorentz-Drude equation [19]. From Fig. 2(a) we can see that the quality of SPPs supported by ZrN exceeds TiN. Our sensor operates in the near-IR spectrum where the ZrN outperforms TiN by a large margin. Thus, our choice of TMNs is appropriate as it will be a better choice than TiN in terms of the quality of SPPs supported. The normalized ZrN SPP wavelength ($\lambda _{SPP} /\lambda _0$) is given by the following equation [4]:

Here, $\lambda _{0}$ is the free space wavelength. In Fig. 2(b) the normalized ZrN SPP wavelength is given where we have taken the MUS as air. This graph shows the bound nature of SPPs [4] on ZrN-MUS interface as the SPP wavelength is less than free space wavelength. The wave is restricted to the interface between the two materials which gives us the ability to create an RI sensor. The propagation length ($\delta _{SPP}$) along the ZrN-MUS interface is given by the following equation [4]:

In order to create a RI sensor manipulating SPPs and using ZrN as the functional material, the dimension of the structure has to be much smaller than the attenuation or propagation length in a ZrN-MUS interface. Fig. 2(c) shows the propagation length in the visible and near-IR spectrum which is in the order of ${\mathrm{\mu} \mathrm{m}}$. Our sensor operates in the near-IR spectrum. The dimensions of our sensor lies in the range of several hundred nanometers which is way smaller than this attenuation limit. Researchers can use this attenuation limit when designing optical devices using ZrN so that their dimension is within the attenuation limit. The penetration depth ($\delta _{MUS}$) into the MUS (in this case air) is given by the following equation [4]:

Figure 2(d) illustrates the penetration depth into the MUS in the visible and near-IR spectrum. Initially at visible wavelengths the penetration depth is smaller than the free space wavelength but as the wavelength increases it becomes larger and exceeds the free space wavelength values at near-IR spectrum which is also consistent with SPPs behavior in metal-air interface [4].

 

Fig. 1. (a) Schematic of the proposed sensor. (b) Electric field distribution at resonant wavelength (1262.968 nm). (c) Real and imaginary parts of permittivity of ZrN in the visible and near-IR spectrum.

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Fig. 2. (a) Quality factor of SPP between TiN and ZrN. (b) Normalized SPP wavelength. (c) Attenuation length along ZrN-MUS interface. (d) Penetration depth into the air.

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Table 1. Initial geometric parameters of the proposed design.

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The imaginary part of the dielectric permittivity represents loss in the system. If the imaginary part increases, the loss of the system increases which decreases the propagation length of SPPs. Perfect medium approximation (PMA), disregards the imaginary part of the dielectric permittivity which has an effect on SPPs properties [37]. That is why throughout the paper we have considered the dielectric permittivity of ZrN ($\epsilon _{ZrN}$) as a complex quantity which has been modeled with the renowned Lorentz-Drude model for material modeling which incorporates both the real and imaginary parts of the dielectric permittivity. The Lorentz-Drude model is renowned for its efficacy in approximation of the complex dielectric function in the optical frequency range where SPPs play a crucial role for which the obtained numerical results match closely with the experimental data when this model is employed [38]. The necessary condition of excitation of SPPs in an ZrN-MUS interface is [37]:

For ZrN-Air interface, this relation is satisfied which is evident from Fig. 1(c). The spatial period ($\Lambda$) needs to be calculated from the following formula for lossy materials [37]:

For ZrN-Air interface, at the wavelength 1262.96 nm (resonant wavelength of our sensor), the spatial period matches within 0.796% of wavelength.

The TM mode is defined by a magnetic field that is perpendicular to the direction of wave propagation and no electric field component parallel to the magnetic field. The dispersion relation for the TM mode can be expressed by the following equation [39].

Here, $\epsilon _{MUS}$ is the relative permittivity of the dielectric, $\epsilon _{ZrN}$ is the relative permittivity of ZrN, $n_{eff}$ is the effective refractive index, $W$ is the width of the waveguide, and $\lambda$ is the wavelength of the incoming light. The $n_{eff}$ can be calculated for our proposed structure using the following equations [40],

Here, $k_{MUS}$ is the transverse propagation constant of dielectric, $k_{ZrN}$ is the transverse propagation constant of ZrN, $k_0$ is the wavevector of free space, and $\beta _{SPP}$ is the propagation constant. One way to determine the resonant wavelength $\lambda _{res}$ of a plasmonic resonator is to use standing wave theory, which relates that $\lambda _{res}$ is proportional to the real part of $n_{eff}$, is expressed by the following equation [41],

Here, m is the order of resonant mode, $P_{eff}$ is the total effective route travelled by the SPP, and $\phi _{ref}$ is the phase shift experienced by the light upon reflection from the resonator.

4. Optimization and result analysis

In the case of a plasmonic refractive index sensor, the resonant wavelength varies linearly as the refractive index of the MUS varies. An essential aspect of a plasmonic refractive index sensor is the linear relationship between the refractive index and the resonant wavelength. Detecting extremely minor changes in the RI of the analyte facilitates fluorescent label-free detection, which reduces the risk of labeling agent interference. Cost-effective and point-of-care detection is crucial in many scientific disciplines. The sensitivity is a key performance metric in plasmonic sensor as it shows the ability of the sensor to distinguish between small amount of refractive index change. The sensitivity (S) is given by the following equation [42]:

Here, $\Delta \lambda _{res}$ is the change in resonant wavelength due to a change in refractive index ($\Delta n$). More change in $\Delta \lambda _{res}$ indicates that the sensor is more sensitive to a change in refractive index. Another important parameter for the sensor is figure of merit (FOM). It is given by the following equation [42]:

Here, FWHM is the full width at half maximum. FOM indicates the sharpness of resonance. A sharper resonance means that the differentiating capability between two resonant modes is increased. The reflectance is given by the following equation [43]:

A stronger reflectance dip indicates better performance. The sensing resolution (SR) is the limit on the sensor due to the optical spectrum analyzer resolution. SR can be expressed by the following equation [44]:

Here $\Delta \lambda _{Detection \ Limit}$ is the minimal resolution of optical spectrum analyzer taken as 0.001 nm [44]. The quality factor is another important performance metric that indicates the sharpness of resonance given by the following equation [45]:

Figure 3(a) shows the reflectance spectra for different values of ‘L’, sweeped from 260 nm to 420 nm with a step size of 40 nm. Fig. 3(b) displays the resonant wavelength ($\lambda _{res}$) versus change of ‘L’, indicating a redshift of resonant wavelength as the ‘L’ value increases which can be justified by the standing wave theory from Eq. (12). In Fig. 3(c), it is seen that initially sensitivity of the system increases as ‘L’ is increased, with a maximum value observed at L=380 nm, indicating that the system is most responsive to changes in RI of the analyte at this particular value. Fig. 3(d) and 3(e) show an increase in the FOM and a decrease in the reflectance dip as the ‘L’ value increases. Based on these results, it can be concluded that L=380 nm is the optimal value, providing a good balance between sensitivity and FOM. In Fig. 4(a), the reflectance spectra are shown for NG = 1, 3 and 5, while keeping L=380 nm and the rest of the parameters same as those in Table 1. Fig. 4(b) illustrates the $\lambda _{res}$ as a function of ‘NG’, demonstrating a blueshift of the resonant wavelength as ‘NG’ increases. Fig. 4(c) reveals an increase in the system’s sensitivity. Fig. 4(d) shows that the FOM initially decreases as the ‘NG’ value increases, but then experiences a sharp increase. Fig. 4(e) displays an initial increase in the reflectance dip followed by a decrease as ‘NG’ increases. The analysis concludes that NG=5 is the most appropriate value, as it yields a higher sensitivity and FOM. Fig. 5(a) shows the effect of varying the parameter ‘$g_2$’ on the reflectance spectra of the sensor with L=380 nm and NG=5 while keeping other parameters constant. Reflectance spectras were obtained by incrementally varying ‘$g_2$’ from 30 nm to 70 nm in steps of 10 nm, and the resulting redshift of the $\lambda _{res}$ is presented in Fig. 5(b) with increasing the value of ‘$g_2$’. To evaluate the performance of the sensor, its sensitivity, FOM, and reflectance dip were analyzed, which are illustrated in Fig. 5(c), (d), and (e), respectively and improvement in all performance parameters was observed with increasing ‘$g_2$’. Finally, the value of $g_2$=70 nm is selected to provide the maximum sensitivity, FOM, and reflectance dip. Fig. 6(a) shows the reflectance spectra for different values of ‘d’ ranging from 10 nm to 20 nm in increments of 2.5 nm, while keeping L=380 nm, NG=5, and $g_2$=70 nm, along with the other parameters held constant. The resulting redshift of the $\lambda _{res}$ is presented in Fig. 6(b). We investigated the sensor’s sensitivity, FOM, and reflectance dip, which are depicted in Fig. 6(c), (d), and (e), respectively, to further verify its performance. Our findings show an improvement in FOM and reflectance dip with increasing ‘d’, while sensitivity decreased. Finally, based on our analysis, we selected a value of d=20 nm to achieve the maximum FOM and reflectance dip. Fig. 7(a) displays the reflectance spectra obtained by varying ‘$g_3$’ from 15 nm to 35 nm in steps of 5 nm, while keeping L=380 nm, NG=5, $g_2$=70 nm, and d=20 nm. The redshift of the $\lambda _{res}$ with increasing ‘$g_3$’ is shown in Fig. 7(b). The sensitivity of the system is increasing which is shown in Fig. 7(c). Fig. 7(d) and 7(e) show the FOM and reflectance dip for different values of ‘$g_3$’. Notably, $g_3$=20 nm is chosen as it provides the maximum FOM and reflectance dip. Table 2 provides the optimal value of the parameters considering best performance of the sensor. Table 3 presents a comparative analysis of four distinct performance metrics. The table shows the initial and final values for each metric, as well as the percentage increase from the initial value to the final value. The first metric, sensitivity (nm/RIU), witnessed a significant increase of 25.5%, with the initial sensitivity being 1151.79 nm/RIU, and the final sensitivity being 1445.46 nm/RIU. The study employed a linear fitting technique to calculate sensitivity values for various parameters, including $L$, $g_2$, $g_3$, NG, and $d$. By determining the slope of the resonant wavelength vs refractive index line, accurate sensitivity values were obtained. For example, for $g_3$ the linear fitting process yielded an impressive adjusted $R^2$ value of approximately 0.9998, indicating a high level of precision in the results. Throughout our analysis, we found that the adjusted $R^2$ value was consistently close to 1. This strongly supports the characteristic of the refractive index sensor, which specifies a linear relationship between resonant wavelength and refractive index. Consequently, our calculations firmly support this linear theory, enhancing the dependability and precision of the behavior of the refractive index sensor. The second metric, figure of merit (FOM), experienced a staggering increase of 3048.99%. The initial FOM was 4.67, and the final FOM was 140.96, indicating that the device underwent massive improvements. The third metric, resonant dip (dB), also demonstrated a noteworthy improvement, with the final value of -156.87 dB being 200.81% higher than the initial value of -52.15 dB. Lastly, the fourth metric, Q-factor, experienced a substantial increase of 2548.6%, with the initial Q-factor being 4.65, and the final Q-factor being 123.16. Overall, the results indicate that the sensor underwent significant improvements in all four performance metrics, with particularly noteworthy increases in FOM and quality factor. Table 4 shows a summary of comparative analysis with recent literature where most of the refractive index is in the range of 1.0 to 1.10. We chose the refractive index values between 1.0 and 1.10 because these values correspond to the majority of the studies with which we compared our performance and the particular application we demonstrated. The refractive index range of 1.0 to 1.10 is commonly associated with gaseous analytes which shows the potential of our sensor being employed as a gas sensor. For the demonstrated operating range of our pressure sensor, the refractive index for this application lies between 1.0 and 1.10. For the refractive index of 1.33 of the MUS, the sensitivy and FOM of the sensor is 1414.897 nm/RIU and 7.993. As seen from the table most of the sensors employ noble metals like Ag or Au that is incompatible with CMOS technology thus creating a barrier in widescale adoption of plasmonics with nanoelectronics. Due to the inability of metals to undergo significant changes in their carrier concentration, metals do not possess the ability to adjust their optical properties, which is a significant disadvantage. In terms of its optical performance, ZrN is the TMN that is the most consistent and reproducible and providing many advantages over TiN as discussed earlier. Consequently, the introduction of this ZrN-Insulator-ZrN based plasmonic sensor presents a significant addition to the literature, offering novel possibilities for research and applications.

 

Fig. 3. (a) Reflectance spectrum. (b) Resonant wavelength shift. (c) Change in Sensitivity. (d) Change in FOM. (e) Change in Reflectance dip for L=260 nm to L=420 nm.

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Fig. 4. (a) Reflectance spectrum. (b) Resonant wavelength shift. (c) Change in Sensitivity. (d) Change in FOM. (e) Change in Reflectance dip for NG= 1, 3, 5.

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Fig. 5. (a) Reflectance spectrum. (b) Resonant wavelength shift. (c) Change in Sensitivity. (d) Change in FOM. (e) Change in Reflectance dip for $g_2$=30 nm to $g_2$=70 nm.

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Fig. 6. (a) Reflectance spectrum. (b) Resonant wavelength shift. (c) Change in Sensitivity. (d) Change in FOM. (e) Change in Reflectance dip for $d$=10 nm to $d$=20 nm.

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Fig. 7. (a) Reflectance spectrum. (b) Resonant wavelength shift. (c) Change in Sensitivity. (d) Change in FOM. (e) Change in Reflectance dip for $g_3$=15 nm to $g_3$=35 nm.

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Table 2. Overview of optimal parameter values for structural components.

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Table 3. Impact of optimization on performance metrics.

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Table 4. Comparative analysis with recent literature.

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The fabrication technique will depend of the purpose of the sensor like research and development or mass production. Ishii et al. [55] experimentally fabricated ZrN nano disk arrays. These were fabricated by physical vapor deposition (PVD)- DC sputtering (CFS-4EP-LL, Shibaura Mechatronics Co.) followed by spin coating a negative-tone resist (NEB-22A, Sumitomo Chemical Co., Ltd). After that the pattern was transferred using electron-beam lithography (EBL) system (ELS-7500EX, Elionix Inc.). Then development was done using NMD-3 and it was dry etched using using a reactive ion etching system (CE300I, Ulvac, Inc.). Then the resist stripping was done by the use of a plasma asher (PB-600Z; Yamato Scientific Co., Ltd.) [55]. Dutta et al. fabricated ZrN plasmonic waveguides using photolithography and plasma etching [56]. Some of the other deposition techniques that can be used for deposition of ZrN is reactive magnetron sputtering (MS), atomic layer deposition (ALD), ion beam assisted deposition, pulsed laser deposition [27]. For fabrication of our proposed sensor, we suggest a top-down fabrication approach. After deposition followed by electron beam lithography, our sensor can be fabricated. EBL’s primary advantage is its ability to create custom patterns with a resolution of less than 10 nanometers [43]. For PVD techniques like evaporation and sputtering directly from a nitride source, these TMNs with high mechanical strength and melting temperatures present obstacles. Due to the availability of numerous low-vapor-temperature metallo-organic sources, chemical vapor deposition (CVD) can be used [19]. So, ZrN is first deposited onto a substrate using CVD. The next step is Resist coating. A thin layer of a special material called an EBL resist has to be applied to the ZrN. This resist is sensitive to the electron beam and, when exposed to it, its solubility will alter. Next, the desired pattern is then transferred onto the resist using an electron beam. After creating the desired pattern, the electron beam modifies the solubility of the resist in the exposed areas. A computer controls this phase, ensuring that the electron beam moves in the correct pattern. Chemical development washes away the resist where the electron beam had hit. This exposes the ZrN on the places where the beam hit and on all the other places where electron beam did not hit, there is resist layer. After creating the desired pattern into the resist, the exposed ZrN portions can be etched away. This is accomplished using a reactive-ion etching (RIE) method. At last, the remaining resist is subsequently removed, leaving the desired pattern on the substrate. In electron beam lithography, resist removal, also known as resist stripping, can be accomplished in two primary ways: wet stripping and dry stripping. The major steps that are involved in the sensor fabrication process, has been illustrated in the Fig. 8.

 

Fig. 8. Major steps of fabricating the proposed sensor.

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5. Application as an air pressure sensor

For air pressure sensing using RI sensor, a method is employed wherein the relative pressure in the chamber is carefully adjusted in increments of 5 MPa. This range spans from 10 MPa to 40 MPa, covering a broad spectrum of pressures for comprehensive analysis. To ensure the integrity and consistency of the results, the simulations are conducted under standard conditions, maintaining a constant temperature of 27°C. In this context, the refractive index serves as a vital parameter that characterizes the behavior of light as it passes through the sensing medium. The RI can be expressed as a function of pressure (P) and temperature (T), as demonstrated by Zhang et al. [57]. Using Eq. (18), it’s possible to accurately relate the RI variations to pressure changes [58].

By utilizing this equation, we’ll be able to calculate the variations in RI resulting from the applied pressure changes. As expected, the RI demonstrated a correlation with pressure, indicating its suitability as a sensing mechanism. The calculated RI values can be further used to investigate the reflection spectra of the sensing medium. The changes in the reflection spectra can be observed through the use of an optical spectrum analyzer, providing valuable insights into the behavior of light as it interacted with the sensing material. As the air pressure within the chamber increased, notable shifts in the reflectance dip were observed. Specifically, these shifts were observed to occur towards longer wavelengths, as depicted in Fig. 9(a) and (b). This evidence further supported the relationship between pressure and the resulting optical response. The optical spectrum analyzer enables the detection and measurement of these shifts, providing a means to quantify the applied pressure. Overall, the pressure sensor developed using this approach exhibited a sensitivity of 3.7421 nm/MPa. For temperature values of other than 27°C, one can use Eq. (18) and perform necessary calculations. We investigated the change of temperature on the sensor’s performance. From the resonant wavelength vs temperature graph in Fig. 10, we can see that the resonant wavelength remains almost constant with variation in temperature. This means that the sensor performance is not affected considerably by change in temperature which is due to the fact that from Eq. (18), as the temperature changes, the change in refractive index is small. For 20°C, 25°C, 30°C, 35°C, and 40°C temperature, the change in the pressure sensitivity is 3.33%,1.32%,0.054%,2.05%, and 3.41%, respectively. This shows that the sensor will perform well at different temperatures. The efficacy of the sensors will not be substantially affected by temperature variations.

Fabrication error tolerance: Electron Beam Lithography (EBL) is renowned for its exceptional accuracy making it one of the most precise lithography techniques currently available. In general, the resolution of EBL can be less than 10 nm, with some systems achieving sub-nanometer resolution under optimal conditions. This level of precision permits for extremely small error tolerance, typically within a few nanometers. We have investigated the effect of error in fabrication of the sensor parameters by increasing and decreasing the sensor parameters by 1%. From table 5, as the sensors parameters are changed by 1%, we can see that the change in pressure sensitivity is very low. To further investigate the effect of fabrication error, we have rotated the comb shape part with respect to the center of the input waveguide as given in Fig. 11. The change in pressure sensitivity for 1°and -1°rotation is 1.07% and 0.39%. Consequently, it can be asserted that the performance of the sensor will remain largely unaltered by minor fabrication variations.

 

Fig. 9. (a) Reflectance characteristics for change in pressure. (b) Resonant wavelength vs pressure.

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Fig. 10. Variation of resonant wavelength for different temperature values.

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Fig. 11. Fabrication Error Tolerance.

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Table 5. Impact of fabrication error on performance metric.

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6. Conclusion

We proposed a ZrN-based plasmonic RI sensor that incorporates a comb-shaped structure integrated with a MIM waveguide, it demonstrates remarkable sensitivity with a maximum value of 1445.46 nm/RIU and a high figure of merit (FOM) of 140.96 within the RI range of 1 to 1.10. The reflection spectra and E-field distributions of the proposed sensor configurations are determined using the finite element method (FEM) with a scattering boundary condition. Noble metals, including Ag and Au, are not ideal for subwavelength device creation due to their limitations, such as the lack of tunable optical properties, low thermal stability at higher temperatures, low conduction electron mobility, and difficulty in nanofabrication. However, the application of transitional metal nitrides, like ZrN, effectively overcomes these constraints. Notably, they offer tunability of plasmonic properties, high carrier concentrations, high electron conductivity and mobility, superior metallurgical and thermal stability, high hardness, low work function, and relatively lower cost compared to noble metals. ZrN has the potential to be a strong candidate for a CMOS-compatible alternative plasmonic sensor, thereby facilitating the widespread implementation of plasmonic sensors.