1. Introduction

Rapid advances of nanostructured metal particle synthesis in recent years have enabled their diverse applications [1–3]. Innovation of novel nanostructures is crucial for attaining exotic optical properties and designing exciting optoelectronic and plasmonic devices. Plasmons are a collective oscillation of electrons inside material along with the EM wave outside of material, resulting a dramatic enhancement of electric fields [4]. Plasmons in plasmonic structures have been used as a coloring medium since ancient times. Recently, plasmonic structures have been utilized in a wide range of applications such as photovoltaics [5], polarizers [6], modulators [7], optical tweezers [8], detectors [9], biosensors [10], super-lens [11], heat absorbers [12] and microscopy techniques including raman scattering microscopy [13], electrochemical tuning [14]. The majority of research on plasmonics are based on noble metals. Noble metals have traditionally been treated as most conventional plasmonic material due to their substantially lower loss as a consequence of limited intraband transition (Drude) and interband transition (Lorentz) loss [15]. In addition to these intrinsic properties, their fabrication is compatible with the existing Si-based fabrication industry enabling their ubiquitous presence in plasmon-based devices [16]. However, there are some issues with conventional plasmonic materials which motivated researchers to find a "more convenient" alternative. So far, ultra-thin metal films (UTMF), which support two-dimensional plasmon, got much attention in plasmonic device research for their near-wavelength size and magnetic properties. In actuality, UTMF can be considered as the successor of thin film technology. UTMF has diverse applications, including photovoltaic cells, transparent conductors, and infrared reflectors [17]. However, trapping centers due to the defects, that were introduced during the fabrication process of UTMF, result in a loss in the plasmonic medium [15]. The grain boundary roughness of plasmonic nanoparticles, utilized in solar cells, significantly contributes to the scattering [18]. To overcome these limitations, there is a need to explore materials that are "less lossy" and chemically stable, less prone to surface roughness and have a higher value of real permittivity. Besides, their carrier concentration should be easily tunable, and most importantly, their fabrication process should be compatible with growth techniques. A detailed study by Naik et al. illustrated that metal alloys, transparent conducting oxides (TCOs), III-V semiconductors, metal nitrides, and silicides could be used in plasmonic applications [15]. Various approaches have been adopted to obtain noble metal-like plasmonic properties, i.e., negative $\epsilon _1$ and low $\epsilon _2$. Transforming metals to a comparatively "less metal" is one of those approaches. Metal silicides and germanides, ceramics such as oxides, carbides, borides and nitrides have negative real permittivity. However, most of these materials do not have sufficiently low imaginary permittivity. These issues prevent the widespread use of ultra-thin films based on alternative plasmonic materials in optical and optoelectronic devices.

However, TiN can be considered as a replacement for noble metals because stoichiometric TiN films on sapphire or other transparent substrates show lower imaginary permittivity profiles in visible and near-infrared (NIR) regions than other transitional metal nitrides [3,19]. In short wavelength region, Au suffers from interband transition loss [20]. TiN can be treated as the equivalent of Au with a loss factor of 3 [21]. Maniyara et al. reported a copper-seeded deposition technique that enables optical property tuning of noble metal-based ultra-thin film plasmonic devices [22]. The tunability of plasmonic resonance was demonstrated by varying geometric structures as well as external factors. Most recent reports varied external parameters for plasmon tuning, which are difficult to realize. Moreover, most reports were based on gold or similar noble metals. Most of these noble metals are lossy in certain wavelength regions and do not have stoichiometric properties, which is essential for fabricating plasmonic devices. Hence, the need for a less-lossy, easy-to-fabricate, and tunable plasmonic material for ultra-thin films encourages researchers to explore alternative materials. Importantly, easy and fine control of optical properties can be exciting attributes of optoelectronic devices as well as photonic devices. The extensive study on alternative plasmonic material-based nanoparticles is essential to explore their potential to tune optical properties. Although nanoribbon-shaped structures were reported, different unique nanostructures where various plasmonic modes can be confined are yet to be explored.

In this paper, we explored the plasmon tuning behavior of ultra-thin film based on alternative plasmonic materials using the finite-difference time-domain (FDTD) method. We analyzed the effect of surface roughness on the scattering and transmission spectra of ultra-thin films on a transparent substrate. We performed a comparative analysis of TiN, an alternative plasmonic material, with Au, a noble metal. Moreover, we investigated the impact of shapes and dimensions of nanostructures on the plasmonic resonance modes. We studied the incident light polarization sensitivity of the structures. Since electric gating is a simple mechanism, we proposed this technique to vary carrier concentration, and consequently, the possibility of around 30${\% }$ transmittance modulation was proven. Here, we presented a unique report on the possibility of using TiN as an alternative material replacing noble metals and explored the scope of plasmon resonance tuning using TiN.

2. Device design and simulation methodology

Our proposed structures comprised plasmonic nanoparticle patterns on CaF$_{2}$ substrate. CaF$_{2}$ is effectively transparent in visible and near-infrared regimes, which is convenient for light-transmitting structures studied here. Moreover, it has thermodynamic stability [23], high band-gap, high dielectric constant as well as high dielectric strength. Although amorphous glass also has transparency at the NIR range, here CaF$_{2}$ was used as it allows smoother metal thin film growth on it. A detailed study on the growth of metal films on CaF$_{2}$ substrate by Albert et al. [24] was a strong motivation for using CaF$_2$ instead on amorphous glass or its derivatives. Additionally, CaF$_2$ and TiN both have same atomic space group Fm3m [25], which is beneficial in TiN film growth over CaF$_2$ than other transparent substrates such as amorphous glass. The surface roughness on the substrate was introduced by using modeled objects which were created utilizing modeling and scripting tool. To make the rough surface environment over the substrate plane, we used a Python script to model a random amplitude block and applied the script to FDTD solver to build a 15$\times$10.5 $\mu$m CaF$_2$ substrate block. This rough surface was characterized by an RMS amplitude and correlation length. The roughness was generated by creating a random matrix of values in reciprocal space (i.e., k-space). A Gaussian filter was applied to this matrix, then Fourier transform was used to transform the matrix back to real space. The surface height was determined by utilizing the pre-developed random number generator function. The normalized height distribution of our modeled surface is shown in Fig. S2 of Supplement 1. We investigated structures for four different shapes of nanoparticles- nanoribbons, triangular nanoplates, nanospheres, and nanodisks. These four types of nanostructures are illustrated on Fig. 1.

 

Fig. 1. Four different structures of nanoparticle on CaF$_2$ substrate; (a) nanoribbons with t = 9 nm, w = 506 nm, (b) triangular nanoplates with t = 9 nm and vertically stretched with a base length of 670 nm, (c) nanospheres of radius, r= 200 nm and (d) nanodisks of radius, r = 200 nm.

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We analyzed the nanostructures using FDTD method. In the FDTD method, continuous recursive upgradation of the magnetic and electric fields gave the complete electric as well as magnetic field profile inside the structure in time domain [26]. Chirped z–transform, czt as expressed in Eq. (1) was used to get the frequency spectrum from the time-domain field signal.

Here, ${E_{x}}$ is the electric field magnitude along x direction, ${n}$ represents the refractive index of the medium and $k$ denotes the frequency index. When studying periodic structures, choosing periodic boundary conditions through periodic axis can effectively reduce simulation time and machine throughput. Nanoribbon and triangular nanoplate-based structures were periodic along x axis whereas nanosphere and nanodisk-based structures had periodicity along the x and z axes. FDTD equations on a unit cell were solved considering periodic boundary conditions along the periodic axes. On the aperiodic axes, we chose perfectly matched layer boundary conditions. A generic material with high absorbance and minimal reflection was chosen at the boundary points of the aperiodic axis of the structure to ensure minimal reflection. Although an ideal perfectly matched layer should have zero reflectance, the sudden change of material parameter at the boundary resulted in a small reflection at boundary edges in this study.

Initially, the nanoribbon thickness was 9 nm. These nanoribbons were uniformly spaced for the nanoribbon structure. We considered the gap between two adjacent ribbon equal to the half width of a single ribbon. Triangular nanoplates were vertically stretched with a base of 670 nm and the height of 10.5 $\mu$m. The thickness of the nanoplates was 9 nm. Uniformly distributed nanospheres with a radius of 200 nm and periodically arranged nanodisk arrays with a radius of 200 nm were initially considered for nanosphere and nanodisk-based structures, respectively. These dimensions were varied and optimized subsequently. The structures were illuminated by a simple plain wave source. We analyzed nanoparticles consisting of different materials such as Ag, Graphene, and TiN. We used two separate monitors to measure the transmittance and reflectance of the structures. The transmission measuring monitor was placed after the structures where the reflectance measuring monitor was placed behind the light source to avoid inclusion of front propagating light wave emitted from light source. To determine the effect of structural parameters on plasmon resonance wavelength, we varied thickness, width and shape of nanoparticles. Moreover, incident light polarization was varied and polarization sensitivity of the structures was studied. Electric field variation changes the carrier concentration. We modeled the electric field variation by sweeping carrier concentration from $2\times 10^{28}$ m$^{-3}$ to $5\times 10^{28}$ m$^{-3}$. A possible way to incorporate the effect of an external electric field into the permittivity of a material is by developing a model to describe permittivity as a function of the electric field. Yu et al. formulated a self-consistent model where they expressed the frequency-dependent electric field of plasmonic material as a function of permittivity of medium and host [27]. To characterize the relation between carrier concentration and permittivity of TiN, we applied a similar method. To accurately define the relationship between carrier concentration and permittivity, we considered the Drude-Lorentz formula up to two Lorentzian terms [28],

Here, $\epsilon _{\infty }$ is the background permittivity. In the above-mentioned equation, we considered the system as a two-sided split system. One side contains fixed ions and the other one consists of mobile electrons. When we considered the atomic polarization due to any external field, we took into account the fact that the ionic cores can also be polarized by the field. Polarization is always a function of frequency, which is true for determining background permittivity. However, we considered frequency independent characteristics of $\epsilon _{\infty }$ in Eq. (2) for simplicity. $\Gamma _D$ represents damping coefficient in Drude term and the subsequent $\gamma _{j}$ (j=1,2) are damping coefficients in Lorentzian terms. Similarly, $\omega _p$ and $\omega _l$ (l=1,2) are the plasma frequencies for Drude and Lorentz portions respectively that represent their resonant frequencies for respective transitions. $k_{i}$ (i=1, 2) are the constants associated with each of the Lorentzian expansion term. These constants reflect the Lorentz oscillation strength and can be derived by fitting experimental data. The plasma frequency, $\omega _{p}$ can be expressed as a function of carrier concentration, $n_b$ as given by,

Here, $m^*$ represents the effective mass of the electron and $e$ is the charge of the electron. Moreover, the effective mass of electrons is carrier concentration dependent which requires further analysis to establish a relation between them. We developed an empirical relation between $n_b$ and $m^{*}$ utilizing previously reported experimental data [29],

This empirical relation allowed us to theoretically estimate the effective mass for a specific carrier density and plug it into Eq. (3) to calculate $\omega _p$. This $\omega _p$ was employed to calculate $n_{b}$ dependent permittivity.

It is crucial to manufacture plasmonic nanoparticles for fabricating plasmonic devices. Noble metals are typically fabricated using CMOS-compatible methods. Our proposed structures can be produced using both the chemical vapor deposition (CVD) technique and DC reactive magnetron sputtering. Even though the latter is more expensive, various devices including plasmonic interconnect employing titanium nitride have been demonstrated using reactive sputtering of TiN inside an N$_2$:Ar chamber [30]. The recent development of TiN nanoparticle fabrication via the CVD process emerges with new hope to implement cheap, low loss, and wide range of plasmonic devices ranging from nanoantenna to biosensors based on TiN.

3. Results and discussion

3.1 Material dependency of LSPR

Au is consistently considered as an ideal plasmonic material. We focused on finding an alternative of Au that have lower $\epsilon ''$. Nitrides could be promising candidate for ultra-thin film-based devices from the standpoint of the fabrication process. Alongside the nitrides, transitional metal oxides and graphene can be used in plasmonic applications. Chen et al. reported that moderate charge carrier variation ($\sim$ 10$^{13}$cm$^{-2}$) in graphene can lead to a Fermi level change of around 0.37 eV which can be extended to around 1 eV by using ion gel gating [31]. Along with graphene, we utilized TiN to test its plasmonic tunability. We considered nanoribbon arrays of 9 nm thickness. We calculated the absorption spectra for the nanoribbon array structures based on Au, Graphene, and TiN as shown in Fig. 2(a). The refractive index of Au and graphene was derived from experimental findings of Ciesielski et al. [32] and Falkovsky et al. [33] respectively. The sharpness of the absorption peak as well as the transmission trough depends on the imaginary part of the dielectric constant. Materials having near zero epsilon and permittivity crossover wavelength at near-infrared region exhibited better result in our study which agreed with previously reported experimental results [34]. Graphene exhibited plasmonic resonance in the NIR and mid-infrared (MIR) wavelength region. However, TiN substantially followed the trend of noble metal Au in the studied wavelength regime. It is notable that TiN had an absorption peak at 2000 nm which was around 800 nm red-shifted and also higher than that of Au. As we focused on NIR wavelength, We chose TiN to further investigate its viability in ultra-thin film-based applications. We reported the findings of our comprehensive study in the subsequent sections.

 

Fig. 2. (a) Absorption spectra of different alternative plasmonic materials compared to that of Au. Nanoribbon structures were considered with a thickness of 9 nm and a width of 400 nm. (b) Absorption spectra of Au nanoribbons, triangular nanoplates, nanospheres, and nanodisks structures exhibited absorption peaks at different wavelengths.

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3.2 Shape and surface dependency

According to Mie theory’s extension, there is a strong correlation between particle shape and LSPR frequency. Additionally, the plasmonic resonance shift is directly influenced by the permittivity profile, which is directly controlled by the carrier concentration. The plasmonic oscillation occurs at sharp edges of the nanostructure where heterogeneous dielectric index results in light-matter interaction. Free electrons in nanoparticles oscillate with incident light at LSPR wavelength. This effect can be explained by the Mie Theory for a metal sphere surrounded by a dielectric medium. Hence, the extinction cross-section, $\sigma$ can be expressed by the following simplified formula [35],

In bulk materials, the mean free path of charge is significantly smaller compared to the dimensions of the system. However, the transport characteristics are governed by dimensions when the structure is comparable to or smaller than the mean free path of charge. The same applies to optical phenomena. The formulations for bulk material were adapted in nanostructures to consider the mesoscopic effect [36]. Hence, we comprehensively analyzed the impact of nanostructure shapes, dimensions, and surface roughness during plasmonic structure modeling.

The surface roughness of ultra-thin film on the substrate can vary depending on the deposition process. Moreover, there are reports on the introduction of surface roughness by island-like growth [37] and percolated films [38]. Each material has a percolation threshold level [22]. In some cases, it is much more cumbersome to maintain the thickness under the threshold. The permittivity of a thin film depends on grain boundary scattering as stated by Eq. (6). The relaxation rate, $\gamma$, which is in the denominator term of the Drude-Lorentz equation, is inversely proportional to the grain size, d is given by [39],

Here $\gamma _{0}$ is the relaxation rate without considering grain effect, $v_{f}$ is the Fermi velocity, and $A$ is a constant. The increment of grain size reduces the relaxation rate, resulting in a sharp increment of imaginary permittivity. Consequently, the loss factor of the material increases with the increment of grain size. The importance of surface roughness in the nanometer-level plasmonic event can be understood from Fig. 3 (a). Here, a comparative study of Au and TiN thin film was performed. Rougher films resulted in sharp spikes in the transmission and absorption spectrum. The critical observation from Fig. 3 (a) is that TiN was found less susceptible to surface roughness than Au. TiN has a good substrate adhesion property. Bhushan et al. investigated the adhesive strength of TiN deposition on a substrate by physical vapor deposition and got impressive adhesive strength and lower fraction coefficient [40]. This property can be relatable to the roughness-tolerant behavior of TiN, which implies better adaptability of TiN on a wide variety of substrates.

 

Fig. 3. (a) Effect of surface roughness on the transmission of 6 nm thick Au and TiN films. The solid lines represent the transmission on smooth surfaces, whereas the dash-dotted ones are for rough surfaces (b) Comparison of transmittance spectra for Au and TiN thin films by sweeping the thickness from 0.5 nm to 10 nm. The inset plot denotes the non-linear relationship between thin film thickness and transmission peak frequency.

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In Fig. 3(a), the transmittance spectra of 6 nm thick films have been plotted for both smooth and rough surfaces. For Au, the rough substrate introduced scattering centers, resulting in sharp spikes in the transmission spectrum. On the contrary, TiN was less sensitive to roughness, resulting in a much smoother transmittance spectrum than Au. Shah et al. reported thickness-dependent optical property tunability of the TiN-based thin films through variable angle spectroscopic ellipsometry and Hall measurements [41]. The parameters of the Drude-Lorentz equation are dependent on the thickness of the thin film, and consequently, permittivity is thickness dependent [41]. To further investigate the effect of thickness on thin film transparency, we swept the thickness of our thin film from 0.5 nm to 9 nm and observed a decrement in transmission through both Au and TiN films. The results from our study, as shown in Fig. 3, agreed with the reported proportional relationship between plasma frequency $\omega$ with film thickness [41]. Consequently, a gradual increment of the film thickness resulted in blue shift of peak wavelength, $\lambda _{peak}$. A similar trend was followed for the case of nanoribbons for variation of thickness as presented in a later section. To determine the relationship between transmission peak wavelength and film thickness, we fitted the calculated transmission peak wavelength data using the non-linear regression model. We found that $R^{2}$, the goodness of the fitting model, was significantly better for quadratic fitting than linear fitting. The calculated and fitted data plot is shown in the inset figure of Fig. 3(b). The non-linear relationship between transmission peak wavelength and film thickness can be expressed by empirical quadratic relationships given below,

Here, $t$ represents the thickness of the thin film on the substrate in nm. In the inset of Fig. 3(b), we illustrated the curve from the empirical relationship with solid lines. Whereas the calculated data from the numerical simulations are shown with square markers. Apart from Drude-Lorentzian parametric analysis, from intuition, it was expected that the thicker films had higher absorbance. The results from our absorption calculation supported this (see Fig. S3(b) of Supplement 1).

3.3 Polarization selectivity

We investigated the effect of incident light polarization on transmission through nanoribbon structure by varying the incident polarization angle from 0$^\circ$ to 90$^\circ$. The dependence of incident wave polarization in Au and TiN nanoribbon nanostructures was quite prominent as can be seen in Fig. 4. Each pixel-column of Fig. 4 represents a wavelength sweep for a specific polarization angle. For both Au and TiN, MIR waves through the nanoribbon structure were transmitted when the polarization angle was below 50$^\circ$. More than 80${\% }$ transmittance change was observed in the case of Au nanoribbon whereas it was 59${\% }$ in the case of TiN nanoribbon. Besides, the wavelength-dependent transparency of Au and TiN is prominent as can be seen in Fig. 4. Both Au and TiN were transparent for wavelengths longer than 2000 nm when the light was p-polarized (0$^\circ$). On the contrary, The transparency of the nanostructure was very low for wavelengths > 2000 nm. However, we found this behavior was reversed when the incident light polarization angle was > 50$^\circ$. Moreover, the attenuated transmission band (blue region in Fig. 4) of TiN was much wider than that of Au. This finding can be extended to the scope of these types of nanostructures as polarization-sensitive filters. Besides nanoribbon-based structures, there is a possibility for developing wire grid-structured TiN constituents to implement polarizers with a high extinction ratio.

 

Fig. 4. Polarization sensitive characteristics of (a) Au and (b) TiN nanoribbons. The wavelength was swept from 1 $\mu$m to 5 $\mu$m for each polarization angle.

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4. TiN as an alternative plasmon tuning material

4.1 Plasmonic tuning by varying shape of TiN nanoparticle

TiN has been proven to be an efficient, refractory alternative plasmonic nitride in diverse applications. In the nanometer range, plasmonic particles, size, shape, and material selection are key factors in the determination of resonant frequency as demonstrated in Fig. 2. TiN has substantially lower $\epsilon _2$ and its fabrication is CMOS-compatible. Moreover, the promising tunability scope of TiN-based nanoparticles necessitates a more detailed study of its plasmonic shift and the possibility of using it as an alternative to Au. To evaluate its performance, we simulated TiN-based nanoparticles with various shapes. We considered the normal incidence of light illumination upon the structures and swept the wavelength from 0.4 $\mu$m to 5 $\mu$m. The resultant reflection, transmission and absorption spectra are shown in Fig. 5. TiN-based nanostructures illustrated a similar trend as Au. Nanoribbons, nanospheres, nanodisks, triangular nanoplates, nano ribbon-triangle combination, and hexagonal nanoblocks were simulated here. The transmission spectra of the nanostructures with promising results are reported in Fig. 5. Results of other simulated shapes were described in Supplement 1. In most cases, TiN showed a comparatively broader reflection peak and broader transmission dip than Au. The plasmon resonance wavelength could be modulated from 800 nm up to 2200 nm by varying shapes. The periodicity of structures can also be tuned to modulate the plasmon resonance. A shorter gap between subsequent nanoparticles resulted in higher particle volume which resulted in red-shifted plasmonic resonance.

 

Fig. 5. Comparison of (a) reflectance, (b) transmittance, and (c) absorption spectra for various Au and TiN nanostructures.

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4.2 Plasmonic tuning by varying ribbon thickness and width

To develop any tunable plasmonic device, the roles of size, shape, aspect ratio and other geometrical parameters bear much importance. The periodicity of nanoparticle arrangement can be changed by varying their width. Transmittance profile for ribbon width variation is shown In Fig. 6, where an extraordinary spectral broadening was observed for broader ribbons. Calculations with varying ribbon width was performed for 3 nm, 6 nm, and 9 nm thick films. Each increment in ribbon width resulted in red-shifting of plasmon resonant wavelength. An important observation form Fig. 6 is, transmission dip broadening for thinner films at the same ribbon width. Hence, thickness variation is one of the prominent way to modulate the absorption as well as transmission band of ultra-thin films [42]. In Fig. 3(b), it was seen that the thinnest film with 0.5 nm thickness resulted in much higher transmission. From an almost transparent state (90% transmission) to semi-transparent (maximum 65% transmission) state was achieved by varying ribbon thickness from 0.5 nm to 9 nm. The same characteristics got echoed in case of Fig. 6 (a), (b), and (c); where a gradual decrement of transmission along with nanoribbon thickness increment suggests a dependency of transparency on aspect ratio.

 

Fig. 6. Influence of ribbon width on transmission profile of TiN nanoribbons on CaF$_2$ substrate. Structures with (a) t = 3 nm, (b) t = 6 nm, and (c) t = 9 nm were simulated for ribbon widths ranging from 400nm to 800nm.

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Fig. 7. (a) Complex TiN permittivity in visible and infrared region for different carrier densities ranging from $2\times 10^{28}$ m$^{-3}$ to $5\times 10^{28}$ m$^{-3}$. The solid lines represent the real part of permittivity whereas the dashed lines direct to the imaginary permittivity. (b) Effect of electric gating on plasmon resonant wavelength of TiN ultra-thin film ribbon.

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4.3 Plasmonic tuning by carrier concentration modulation of TiN

A fundamental feature of contemporary optoelectronic and photonic devices is external electric field-assisted modulation. By simply applying an external electric field, the transmittance of metal or metal-like particles can be modified. In this case, free carrier concentration allows the modulation of optical response via gating which results in transmittance and absorption tuning. However, in most metals, excessive carrier concentration results in the repulsion of the external electric field effect on optical characteristics. One of the possible solutions to this problem is to use "lesser metals" such as TiN instead of metals. In our proposed structure, we designed 3, 6, and 9 nm thick TiN films that can be considered transdimensional materials which were neither monolayer nor three-dimensional bulk materials. This thickness selection allowed us to achieve enough field penetration to achieve modulation for implementing dynamic nanophotonic devices. We calculated the optical properties of TiN nanoribbon to observe the effect of carrier concentration on plasmonic properties. When an external electric field applied to a plasmonic material, the Fermi energy level shifts. Consequently, a change in electric current can be observed. By reducing the relaxation rate $\gamma$, or tuning the plasma frequency, we can reduce the optical loss. We determined the permittivity profile of TiN for different carrier concentration levels as shown in Fig. 7(a). In Fig. 7(b), a gradual shift of resonant wavelength and broadening of transmission dip can be seen due to carrier concentration variation.

As discussed before, the effective mass of electrons for different carrier concentrations was required to calculate the variable permittivity profile of TiN. The relationship between carrier concentration and effective electron mass for TiN is plotted in Fig. 8(a). The relationship between carrier concentration and effective electron mass follows a non-linear relationship already expressed by a polynomial function in Eq. (4). This effective mass approximation can effectively be used to determine the relationship between plasma frequency and carrier concentration. We have utilized our calculated $m^*$ to determine the relation between $\omega _p$ and $n_b$. The blue curve on Fig. 8(b) explains the carrier concentration-dependent plasma frequency for TiN which is not entirely linear. This is because the slope of $\omega _p^2$ vs $n_b$ curve is a function of $m*$ and different $m^*$ at different $n_b$ results in different slopes. However, Shah et al. [41] reported similar results from hall measurement and ellipsometry data. But they used the linear fit of $\omega _p^2$ vs $n_b$ curve to determine the average $m^*$, equals to 1.31 whereas we first predicted the values of $m*$ for different carrier concentration utilizing the measurements from [29] and then used it to plot $\omega _p^2$ vs $n_b$ curve. To evaluate the accuracy of our numerical approach to determine the permittivity of TiN, we employed average effective mass of electron determined bt Shah et al. in our function and got a similar result to their reported one, which is depicted as the red curve in Fig. 8(b).

 

Fig. 8. (a) Relationship between carrier concentration and effective mass of electron for TiN. (b) Plasma frequency squared as a function of carrier concentration. Fixed effective mass assumption and $n_b$ dependent calculated effective mass consideration gives different results.

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5. Conclusions

This study comprehensively analyzed TiN as an alternative material to Au and other noble metals in ultra-thin film-based plasmonic devices. One of the interesting findings of this study was that transmission on TiN was tolerant to substrate roughness. This behavior encouraged us to design a plasmonic device based on TiN on CaF$_2$ substrate. Moreover, a detailed analysis of physical parameters and a comparison between Au and TiN were performed in this study. The polarization selective property study of Au and TiN on CaF$_2$ substrate-based nanoribbon structure showed that transmission spectra in NIR and MIR range were polarization angle dependent. A transmission modulation of 59% was observed via incident light polarization angle tuning. We not only studied the dependency of plasmonic properties on the material and shape but also proposed convenient ways to modulate transmission through varying periodicity, incident polarization angle, and external electric field. Amazingly, we found a shift of over 1100 nm plasmon resonant frequency by varying the carrier concentration from $2\times 10^{28}$ m$^{-3}$ to $5\times 10^{28}$ m$^{-3}$. Our study will give an insight into the stoichiometric properties of TiN and help researchers in a deeper understanding of the plasmon tuning mechanism which will lead to the further development of tunable novel electro-optical devices including smart windows, organic compound sensors, and electrochromic displays.