1. Introduction

Electromagnetic phenomena accompanying plasmon resonances underpin a rich diversity of optical metadevices [1]. Plasmonics offers solutions for many cutting-edge optical technologies including nano-imaging [2–4], frequency conversion [5], energy harvesting [6] and high-integrated optical circuitry [7–9]. Noble metals have long constituted a material platform for plasmonics. Recent years have witnessed a realization of photonic devices based on alternative plasmonic media. This enabled to implement novel functionalities previously unattainable with the conventional material platform [1]. There are several comprehensive reviews on the recent progress in the quest of alternative materials for plasmonics and nanophotonics [10–12]. The comparative study provided therein considers advantageous and limitations of such materials as noble metals, 2D materials, semiconductors, transition metal nitrides and carbides, metal oxides as well as ternary nitrides and carbides.

Among the variety of alternatives, a growing number of investigations have been devoted to TiN, which belongs to the class of transition metal nitrides pioneered by Shalaev’s and Boltasseva’s groups [13–15]. TiN enables to overcome many of limitations imposed by the noble metals. TiN is refractory, robust, chemically inert, CMOS- and bio-compatible material that demonstrate a good plasmonic response in the visible and NIR ranges – far beyond the capabilities of conventional metals [16–18]. The core advantage of TiN is that its optical properties are tunable, which is enabled by stoichiometry control at the synthesis stage. Recent advances that has been achieved with TiN-based plasmonic components are summarized in Section 2.

TiON thin films with the 2ENZ behavior are attractive for plasmonic applications. Consider the resonant condition to excite a surface plasmon polariton (SPP) [21]

 

Fig. 1. Real and imaginary parts of the dielectric permittivity of conventional and alternative plasmonic materials: Au – green curve (data from [19]), TiN – red curve (data from [13]), TiON – blue curve (data from [20]). A grey curve shows the permittivity of an arbitrary dielectric with the opposite sign.

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Herein, we highlight a promising class of alternative plasmonic media that exhibits the negative double-epsilon-near-zero (2ENZ) behavior. This unusual property of the dielectric function permits the excitation of the plasmon resonance with a dual-band shape [22]. Recently, it has been demonstrated by Mihai et al. that the 2ENZ behavior in the visible and NIR region can be achieved in TiON thin films [20]. As follows from Fig. 1(a), the function ${\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}(\lambda )} ]$ of TiON crosses the curve $- {\varepsilon _\textrm{d}}(\lambda )$ twice at two distinct wavelengths. As a result, the dual-band plasmon resonance can occur. Moreover, there is a dispersionless (${{d{\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}} ]} \mathord{\left/ {\vphantom {{d{\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}} ]} {d\lambda }}} \right.} {d\lambda }} \to 0$) part of the TiON dielectric function, resulting in the opportunity to fulfill the SPP excitation condition within the continuous spectral range. In other words, under certain conditions TiON-based plasmonic structure with the valley-type dispersion will have a broadband plasmon excitation spectra.

Another strategy for the realization of multi-resonant plasmonic components is based on localized surface plasmon resonances. It is well known that extended metallic structures can support several plasmonic modes at different wavelengths [21]. From this viewpoint, conventional materials, such as noble metals, can be successfully used as a material platform. For multiphoton applications of these structures it essential to ensure, that the optical near-fields not only exited at different wavelengths, but also located at the same spatial region. The advances in multi-resonant plasmonics with spatial mode overlap are provided in the recent Review by Safiabadi Tali et al. [23]. Interestingly, the utilization of 2ENZ media in this approach can provide a twofold increase in a number of available resonances. Moreover, 2ENZ materials enable to excite a plasmonic mode at two different wavelengths. These excitations will automatically be spatially overlapped, without the need of structures with sophisticated geometries.

In the second part of this work we will consider the results of characterization of 2ENZ plasmonic materials. The potential of 2ENZ materials in optical applications will be discussed.

2. Recent advances in TiN-based plasmonics

Since TiN has been established as good plasmonic media, many researches were devoted to application of TiN-based nanostructures in various optical applications [1]. In this section we briefly review the recent progress in TiN-based plasmonics.

Refractory properties of TiN-based plasmonic structures push its practical applications especially in those optical technologies where high operation temperatures are inherent. For instance, in solar thermophotovoltaics, highly concentrated sunlight heats up a thermal emitter to generate the photons with energies tuned to the bandgap of a photovoltaic cell [24,25]. This technique has a potential to significantly improve the efficiency of electrical power generation (theoretically up to 85%) compared to direct illumination of a solar cell. There are continuous efforts in the pursuit of perfect absorbers that can both efficiently collect the whole solar spectrum and survive at elevated temperatures (typically >1000 °C), required for high-performance thermophotovoltaic conversion. Much attention was devoted to metamaterial absorbers [26]. The noble metals are unsuitable for thermophotovoltaics because of low stability at high temperatures and melting point depression effects in nanostructures [27]. A refractory absorber with an average absorption of 95% in the visible region was first demonstrated in 2014 using a TiN-based metasurface [28]. The underlying mechanism of the wide spectral absorption benefit the broadband nature of the plasmon resonance in TiN as well as tunability of its dielectric function (the ability to place the plasma frequency in the visible region). In the subsequent years TiN has become a popular material of choice for thermophotovoltaic, thermal imaging and thermal emission applications [29–40]. In a more recent study, 3D TiN nanopillars were proposed for the ultrabroadband absorption exhibiting the average absorptivity of 94% over the wavelengths range of 300-2300 nm [29]. The ability of the absorber to withstand temperatures as high as 900 °C in an inert ambient was demonstrated through measuring the absorption spectra before and after 24 h long annealing. Incorporation of HfO₂ capping layer leads to the extra resistance and finally enabled to achieve spectral stability at 1200 °C. Importantly, nanopillars were fabricated by means of a lithography-free technique, thereby avoiding time consuming and expensive technological processes. This design criteria is crucial for mass production. Recently, a simple design for a perfect absorber has been reported, which is based on a thin film of TiN/AlN nanocomposite covered with an anti-reflection coating [30]. Magnetron multi-target co-sputtering were applied as an industrial technique for one-step large-area deposition of the constituent layers. The origin of the strong broadband absorption is the light trapping by percolating TiN nanoparticles throughout the nanocomposite film. As a result, this structure shows a continuous absorption spectrum between 400 and 750 nm with the average absorptivity of 99.6%. Impressive results were achieved with TiN-based plasmonic biomimetic nanocomposites, which absorptivity is above 90% in the region of 450-2500 nm [31]. It has been demonstrated that these nanostructured materials can be produced using a self-assembly approach, which is compatible with large-scale synthesis. Roberts and co-workers developed a thermal emitter based on few-nanometer-thick continuous TiN films incorporated in a layered metal-dielectric structure [32]. The device exhibits strong resistivity against temperature-induced damage (up to 800 °C) along with high spectral selectivity and flexible fine-tuning. A number of studies were performed to measure the temperature-dependent optical properties of TiN thin films [41,42]. Indeed, when the plasmonic components operate at elevated temperatures, the corresponding dielectric function should be used in electromagnetic simulations for optimization of the device parameters.

The advent of refractory plasmonic materials capable to withstand intense laser light has significantly promoted the development of nonlinear plasmonics. Being an emerging branch of nonlinear optics, this field aims at downscaling the nonlinear elements (frequency-, phase- and beam route converters, switches, modulators, sensors etc.) to nanosized dimensions for their further on-chip implementation. Progress in this subject, including advances in nonlinear matasurfaces, is reviewed in the following Refs. [5,43–47]. Conventionally, bulky samples and pulsed laser sources with high peak intensities are used in order to build up the nonlinear signal [48]. This stems from small higher-order susceptibilities of natural materials. Obtaining a strong nonlinear response at the nanoscale with available modest-power lasers can be accomplished using surface plasmons in metallic nanostructures. In this case manifold enhanced near-fields act as a localized optical pump. Another intriguing strategy to boost nonlinear optical interactions is the usage of ENZ resonances [49] as well as Mie resonances in high-index dielectric nanostructures [50]. Conventional material platform is unsuitable for nonlinear plasmonic applications due to low photo-induced damage threshold, which is considerably surpassed at the intensities required for efficient nonlinear optical regime. The pronounced properties of TiN together with large and broadband intrinsic nonlinearities [51,52] make this material a promising substitute of noble metals for nonlinear refractory plasmonics. Recently, exploiting robustness of TiN nanoparticles and its broadband plasmonic response in the NIR, Xian and co-workers have demonstrated a stable switching device, which is based on saturable absorption and operates at NIR frequencies [53]. This enabled to generate a pulsed laser light at 1030 nm and 1562 nm with a high modulation depth and the pulse duration down to 763 fs. The operation of the switch remained stable at extremely high peak intensities of the laser pump approaching to 557 GW cm⁻². TiN nanostructures have also been successfully used for enhanced nonlinear light frequency conversion, such as second-harmonic generation [54–56].

One particularly interesting feature of TiN is the combination of the plasmon resonance and the Raman-activity. This fact opens the route towards the observation of nonlinear Raman effects, such as coherent anti-Stokes Raman scattering [57], stimulated Raman scattering [58], hyper-Raman scattering [59] etc. The efficiency of these processes can be fairly high, with up to 50% of the incident power being converted into one of the Stokes/anti-Stokes waves. Thus, in contrast to Raman-silent metals, TiN-based components allow plasmon-enhanced nonlinear frequency conversion not only to even and odd harmonics, but also to Raman-shifted modes. Our group has recently demonstrated stimulated Raman emission from TiN nanoantennas using continuous-wave modest-intensity (∼1 MW/cm²) laser light [60]. Surface plasmons excited in a TiN structure by the laser pump experience inelastic scattering on phonons within a TiN lattice. This process leads to the launching of the plasmons at Stokes and anti-Stokes frequencies. Notably, given the smallness of the frequency shift in Raman scattering, the frequencies of the generated waves fall into plasmon excitation spectra. This makes them confined and enhanced. The third-order nonlinear interaction of the pump and Stokes plasmons leads to the exponential growth of the Stokes amplitude. Moreover, the threshold of the underlying SRS effect is greatly reduced since all the waves involved in nonlinear conversion are enhanced. In other words, this leads to enhancement of the effective third-order Raman susceptibility as follows [60]

TiN is extensively used as a material platform for plasmonic metasurfaces. Chaudhuri et al. have demonstrated a photonic spin Hall effect in a phase gradient metasurface made of TiN [63]. The authors pointed out that although gold-based designs exhibit a slightly higher power efficiency, TiN metasurface provides a broader working bandwidth of 0.9–1.6 µm. Recently, reversible tuning of optical responses with TiN metasurfaces has been reported [64]. In this study an evolutionary algorithm was developed and applied for the optimization of a nanohole array. Highly anisotropic TiN nanowires were produced for implementation of hyperbolic metamaterials suitable for applications at high temperatures [65]. In the work of Zakomirnyi et al. high-Q narrowband surface lattice resonances were achieved in TiN nanodisk arrays at the telecom bands [66].

The combination of CMOS-compatibility and good plasmonic response of TiN at the telecommunication wavelengths stimulates the investigations of TiN-based plasmonic waveguides for their on-chip applications. Saha et al. have demonstrated a hybrid photonic-plasmonic waveguides made of ultrathin TiN nanostripes [67]. The proposed configuration represents a robust all-solid-state platform that was produced by means of an industrial-compatible fabrication technique. It has been shown that surface plasmon polaritons at 1.55 µm propagating in these waveguides exhibit the propagation length of 7.2 mm and the mode size of 7.9 µm. This results in the large figure-of-merit (FOM) that is a twofold larger than that for previously reported Au and TiN wavegides. TiN nanoparticle chain waveguides were investigated in Ref. [68]. In addition to good optical transmission properties, the spectral stability at 800 °C was achieved.

Plasmonic TiN nanostructures were extensively used to generate hot carriers for a variety of applications [69]. In a recent study of Gusken et al. an on-chip IR photodetector based on sub-bandgap light absorption with a TiN thin film with a native TiO_2-x layer was demonstrated [70]. This device shows a photoresponsivity on the level of 1 mA/W that is one order of magnitude larger than that for conventional material such as gold. Further improvement of photodetection performance can be achieved using a nanostructured TiN film which permits the plasmon-enhanced absorption under direct illumination. The effect of plasmonic excitations on electron harvesting in TiN/TiO_2-x interfaces was explored in Ref. [71]. Meanwhile, broadband photodetection at NIR wavelengths (up to 2.6 µm) driven by hot electron excitations in TiN/Ge heterojunctions was realized [72]. Recent works have leveraged plasmon-enhanced hot carrier generation in TiN nanostructures for solar photocatalytic hydrogen production and photovoltaics [73–75]. In contrast to gold, the utilization of TiN enables to capture the entire solar spectrum.

TiN local heaters are currently under intensive study for photothermal treatment, since they offer a bio-compatibility and giant absorption in the NIR biowindows. Photoacoustic tumor imaging is the another field, where photo-responsive nanoagents with high photothermal conversion efficiencies in the spectral range of interest are in a great demand. Recent advances in these fields made with TiN-based plasmonic components are available in the following Refs. [76–79]. Plasmon-assisted photothermal nanomedicine is on the verge of its real-life applications.

It has been demonstrated that TiN is a promising material for active plasmonics in which an optical response can be tuned. A recent review on this subject can be found in Ref. [80]. Recently, Atwater and co-workers have proposed a new mechanism for dynamical control of quantum dot emission coupled to a plasmonic cavity, which is based on temporal modulation of the local density of states (LDOS) [81]. Quantum dots were embedded into a SiO₂ layer of a gated TiN/SiO₂/Ag heterostructure. Changes in LDOS were performed by tuning the permittivity of a TiN ultrathin film. In a theoretical study of Kildishev and co-workers, a gated TiN ultrathin (1 nm) film were incorporated in a gold metasurface for the phase control of light [82]. A 337° phase modulation was achieved at the telecommunication wavelength of 1.55 µm, which was induced by changing the carrier density in TiN by 3%. Alternative tunable materials (VO₂, graphene, GaAs, indium tin oxide) are either not suitable for visible and telecom bands, or exhibits a large response time (for TiN this quantity is ∼1 ns) leading to the slow modulation.

In addition to aforementioned recent applications of TiN-based plasmonic structures, there are also other fields where TiN has been used as a material platform, such as biosensing [83–85], optofluidics [86], random lasing [87] and enhanced spectroscopy [88–90].

3. Characterization of 2ENZ titanium oxynitride thin films

It has been recently demonstrated, that TiON thin films with the 2ENZ behavior of the dielectric function represent metal-dielectric nanocomposites consisting of TiN inclusions within a mixed-phase TiO_x/TiO_yN_z dielectric host [91]. The physics behind this unusual dispersion can be understood in a first approximation by considering the Maxwell-Garnett model [20]. In general, different synthesis conditions of TiON lead to various nanocomposite characteristics, such as intrinsic morphology, a volume filling factor of inclusions as well as the permittivity of TiN_x and TiO_y constituents. The permittivity of TiN_x and TiO_y change as their stoichiometry alters. According to the effective medium theory, these parameters contribute to the effective dielectric function that manages an electromagnetic response [92]. In this section, we deal with experimental techniques for characterization of TiON nanocomposites. The analysis of the obtained results is provided.

Figure 2 shows two representative examples of the dielectric function with the 2ENZ behavior, that has been observed in TiON thin films prepared at different conditions. TiON nanocomposites were prepared on Si substrates using magnetron sputter-deposition by following the procedure reported in Ref. [20]. In both cases, the real part of permittivity exhibits a valley-type dispersion with two crossover wavelengths located in the visible and NIR ranges. A plasmonic response of 2ENZ materials depend on the following characteristics: the spectral position of the cross-over wavelengths, the interval between them and the magnitude of ${\mathop{\rm Re}\nolimits} [\varepsilon ]$ in the minimum. These parameters, together with the magnitude of ${\mathop{\rm Im}\nolimits} [\varepsilon ]$, define the spectral position of the plasmon resonance peaks, their amplitude and width. As follows from Fig. 2, a flexible tuning of TiON optical constants can be performed at the synthesis stage. The similar functionalities were recently demonstrated with titanium silicon oxynitride (TiSi_xO_yN_z) thin films [22]. It is worth noting that considered TiON thin films exhibit rather high $\textrm{Im}[\varepsilon ]$ in the major part of the visible and NIR ranges (Fig. 2(b)). These values, however, are comparable with those typically observed in TiN [16,17].

 

Fig. 2. Real and imaginary part of the permittivity plotted as a function of the wavelength for TiON thin films prepared at different conditions. The optical constants of TiON film prepared in this work (green curve) were measured by spectroscopic ellipsometry. The data for the blue curve are taken from [20]).

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A chemical composition of the prepared TiON thin film was investigated using energy-dispersive X-ray spectroscopy (EDS). In contrast to X-ray photoelectron spectroscopy (XPS), this technique allows to obtain information on elemental concentration from the whole thickness of the film, rather than from the surface layer. By analyzing the measured EDS spectra (Fig. 3) the following chemical composition of the TiON film were estimated: titanium (40.75%), nitrogen (13.65%), oxygen (29.9%). Additionally, the presence of carbon (6.14%) has been observed, which is caused by surface contaminations. The peak at 1.73 keV arises from the Si substrate. These results confirm a high level of oxygen in the prepared TiON thin film. The exact stoichiometry of TiON cannot be determined through the EDS analysis due to the strong overlap of titanium L$\alpha $ and nitrogen K lines at 0.395 keV and 0.392 keV, respectively [93].

 

Fig. 3. EDS spectra obtained from TiON thin film with the 2ENZ behavior, as shown in Fig. 2 (green curve).

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A depth distribution of the chemical elements in the TiON layer was determined by means of secondary ion mass spectrometry (SIMS). The measurements were performed using Time-of-Flight SIMS spectrometer TOF.SIMS 5-100 (ION-TOF, Germany). The energy of the Bi₃⁺ analysis beam was 30 keV. Low-energy (500 eV) Cs⁺ and O₂⁺ sputter beams were applied for depth profiling in negative and positive ions, respectively. Figure 4 displays the positive ion intensities as a function of the sputtering time. As follows from the obtained data, there is a well-defined interface between the TiON film and the Si substrate, as evidenced by the dramatic increase of the Si⁺ and SiO⁺ signals at the sputtering time of 300-400 s and decrease of TiN⁺ and TiO⁺ signals. The TiSi⁺ profile indicates the intermixing of the TiON and Si layers. The considered TiON film is nonhomogeneous. The marked downward change of N⁺ and NO⁺ intensities at 150-200 s of sputtering suggests that the nitrogen presents mainly in the upper layer of the TiON film. The depth profile of TiN⁺ ions also shows an intensity shift, but less pronounced due to the mass overlap of ⁴⁸TiN⁺ and ⁴⁶TiO⁺ ions.

 

Fig. 4. ToF-SIMS depth profiling of TiON thin film, which has 2ENZ dielectric function as shown in Fig. 2(a) (green curve). The curves show the intensities of different positive ions against the sputtering time.

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The intrinsic morphology and chemical composition of the TiON thin film with the valley-type dielectric function (Fig. 2(a), green curve) were investigated using the TERS (Tip-enhanced Raman spectroscopy) method. Figure 5(a) displays the geometry of the TERS experiment. Detailed parameters of the TERS measurements can be found in Ref. [91]. A gold optical antenna with the tip apex size of ≈60 nm (Fig. 5(b)) was prepared via an adaptive electrochemical etching technique [94]. According to the registered far-filed Raman spectra (Fig. 5(d), blue curve), there is a wide band in 580-700 cm⁻¹ region, which is indicative for the presence of different phases of titanium oxide within the TiON film. It was further confirmed by capturing a TERS spectra (Fig. 5(d), red curve). The TERS method allowed to considerably enhance a Raman signal and hence resolve four peaks within the broad Raman band. The observed peaks correspond to different crystalline modifications of TiO₂: rutile (600 and 630 cm⁻¹) and anatase (655 and 680 cm⁻¹). The background is responsible for an amorphous TiO_x phase. A Raman peak at 480 cm⁻¹ corresponds to TiN [95]. Figure 5 (c) shows a TERS map of the TiON thin film at 480 cm⁻¹, thus the bright regions demonstrate the distribution of TiN phases. We observed disordered TiN inclusions with a typical size of 10 nm. The particles are embedded in a mixed-phase TiO₂/TiO_x host. Interestingly, the sub-tip spatial resolution of ${\approx} $10 nm ($\lambda /80$) were achieved (see the inset in the Fig. 5(c), which demonstrate the cross-section along the dashed line). This enabled to reveal the nanocomposite morphology of the TiON film.

 

Fig. 5. The results of TERS studies of the TiON thin film that exhibits a 2ENZ dielectric function as shown in Fig. 2 (green curve). (a) Sketch of the TERS experiment; (b) transmission electron image of the tip apex of a gold nanoantenna; (c) TERS map of the TiON thin film at 480 cm⁻¹; (d) far-field and near-field Raman spectra of the TiON film.

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Figure 6 shows the results of DC electrical current mapping of the TiN and TiON thin films. The TiN film was prepared on a Si substrate using magnetron sputtering, and the corresponding synthesis parameters can be found in Ref. [96]. The TiON thin film was taken the same one that for TERS studies. The DC current measurements were performed using scanning probe microscopy (SPM). We used SPM Smart1000 (AIST-NT) microscope and a Pt-coated probe CSG10/Pt (NT-MDT). A scheme of the experiment is shown in Fig. 6(a). A SPM tip serves as a working electrode, while a macroscopic counter electrode is connected to the top surface of the film. A distance between the electrodes was approximately 2 mm, and the applied bias voltage was 0.1 V (for more details see [91]). A value of a tip-sample force was typically in the range of 10-15 nN during the scanning. As follows from Fig. 6(b), the current pattern of the TiN film demonstrates a quasi-uniform character with a small-scale deviations caused by topography artefacts. This confirms that the prepared TiN layer represents a homogeneous metallic film. The picture is remarkably different for the TiON film, where a well-defined contrast was observed (Fig. 6(c)). The map clearly shows isolated areas with a high current values, which are surrounded by the regions of a zero level of current. It means that the TiON film incorporates dielectric and metallic components. These data are consistent with the results of TERS microscopy, where the nanosized TiN inclusions were observed within the TiO_x dielectric surrounding (Fig. 5(c)). The fact that a non-zero current was registered in this film indicates the presence of conducting TiN networks within the TiON layer. Once the volume filling factor of TiN particles approaches the percolation threshold, the particles come in contact and form continuous chains that permit dc current between electrodes to flow. TiN chains are embedded in the dielectric surrounding, which is verified by the complete absence of the current when probed in the points between chains (see Fig. 6(c)). Obviously, the neighboring phases of titanium nitride and titanium oxide automatically lead to the formation of TiO_xN_y phase at their interface.

 

Fig. 6. Scanning probe microscopy of titanium nitride (TiN) and titanium oxynitride (TiON) thin films. (a) Sketch of the experiment; (b), (c) DC electrical current maps probed for TiN and TiON, respectively. The current is measured in the nanoampers.

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In addition to valley-type dielectric functions presented in Fig. 2(a), there are another possible scenarios of ${\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}(\lambda )} ]$ behavior that can be realized in TiON nanocomposites. Figure 7 shows real and imaginary parts of the dielectric function of TiON thin films synthesized at different conditions. A series of TiON thin films were sputter-deposited by following the procedure described in Ref. [20], except for the temperature T_s of the Si substrate that has been varied for different depositions. As evident from Fig. 7(a), the real part of permittivity monotonically decreases with the wavelength. The curves of ${\mathop{\rm Re}\nolimits} [\varepsilon ]$ has only one cross-over wavelength, which depends on the T_s and hence can be adjusted at the synthesis stage. The variation of this parameter has also enabled to dramatically reduce the magnitude of ${{d{\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}} ]} \mathord{\left/ {\vphantom {{d{\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}} ]} {d\lambda }}} \right.} {d\lambda }}$ and make the film less metallic. Meanwhile, the imaginary part of permittivity became smaller in the spectral range 1-2 µm. The TiON film prepared at room temperature (Fig. 7(a), red curve) exhibits the negative permittivity at the wavelengths >1 µm and the almost flat dispersion in the wide wavelength region located in the NIR. Thus, the plasmon excitation condition in such a material can be fulfilled within the continuous region of spectra.

 

Fig. 7. Real (a) and imaginary (b) part of the dielectric permittivity of titanium oxynitride (TiON) thin films prepared at different temperatures of the Si substrate.

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As has been noted, the chemical composition of the nanocomposite is one of the important parameters that define the effective dielectric function. In order to monitor the changes in the concentration of different phases during the transformation from TiN to TiON, it is illustrative to analyze XPS (x-ray photoelectron spectroscopy) spectra. Figure 8 shows XPS core-level spectra obtained from TiN and TiON thin films. The corresponding dielectric function for TiON films is plotted in Fig. 7. TiN film was taken the same one as in SPM measurements. The color bars in Fig. 8 display the binding energies indicative for the presence of different phases in TiON as specified on the graph. The characteristic binding energies for each particular phase demonstrate a certain variation in accordance with the NIST data base [97]. The parameters of the XPS measurements were identical to those used in our previous work [96]. As follows from Fig. 8, the spectrum of the TiN film demonstrate two characteristic peaks centered at 455 keV and 460.8 keV, which are associated with the TiN phase. The peaks exhibit an asymmetric line shape typical for TiN. Only negligible signal rise is observed at characteristic energies of titanium oxide and oxynitride. This suggests that the oxygen content in the TiN film is low. For the set of TiON spectra a considerable redistribution between the peak intensities occurs. There is a remarkable trend of increasing of the signal associated with titanium oxide and oxynitride phases. The maximum effect was observed for the film prepared at the substrate temperature of 400 °C. It is evident that the growth of the relative percentage of titanium oxide and oxynitride phases resulted in drastic change of the dielectric function of TiON (see Fig. 7). The concentration of different phases within the TiON film can be extracted by deconvolution of XPS spectra. The approach for unambiguous XPS spectra deconvolution is reported in Ref. [98].

 

Fig. 8. Ti 2p XPS core-level spectra acquired from TiN as well as from a series of TiON thin films, sputtered at different substrate temperatures. Color areas demonstrate the energy regions of characteristic binding energies indicative for presence of different phases.

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The experimental approaches described above provide an insight into the structure and composition of TiON nanocomposites, that govern the effective dielectric function ${\varepsilon _{\textrm{eff}}}(\lambda )$ of 2ENZ media. Additionally, transmission electron microscopy (TEM) and EDS elemental mapping are highly informative.

Recently, Britton et al. have demonstrated that 2ENZ materials can exhibit dual-band plasmon resonance [22]. They used optical constants of TiSiON thin films that demonstrate valley-type dispersion with two cross-over wavelengths in the visible and near-infrared ranges. Thin films of TiSiON were deposited on Si substrates using magnetron multi-target (Ti and Si/SiO₂) co-sputtering in Ar-N₂ ambient. Figure 9 shows the dielectric function of TiSiON (Fig. 9(b)) and gold (Fig. 9(a)) for comparison. Authors of this work calculated scattering efficiencies for nanospheres made of gold (Fig. 9(c)) and TiSiON (Fig. 9(d)) placed in air as a function of the wavelength. The calculations were performed for different sphere radii applying the Mie theory. In both cases the resonant peaks occur at those wavelengths, when the curves of ${\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}} ]$ and $- 2{\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{d}}} ]$ cross each other (${\varepsilon _\textrm{m}}$ and ${\varepsilon _\textrm{d}}$ are permittivities of metal and dielectric (air), respectively). It means that the condition for the localized plasmon excitation is fulfilled (for a small sphere this condition is given as ${\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{m}}} ]={-} 2{\mathop{\rm Re}\nolimits} [{{\varepsilon_\textrm{d}}} ]$). In contrast to the gold sphere, there are two resonant bands for the sphere made of TiSiON with 2ENZ dielectric function (Fig. 9(d)). The similar picture was observed for absorption efficiency spectra [22]. The insets in the Fig. 9 display the distribution of the optical near-fields corresponding to resonant wavelengths. As follows from the patterns for TiSiON, the dipole plasmon mode is excited at two different wavelengths. It should be noted, that the same character of the plasmon excitation spectra as in Fig. 9(d) can be achieved, for example, with the sphere having a large size [21]. The multiple peaks will correspond to high-order localized plasmon modes (dipole, quadrupole, etc.). However, the near-field patterns of this modes have a vanishing spatial overlap. Hence, the enhancement of the non-degenerate multiphoton interactions will be negligible.

 

Fig. 9. Examination of 2ENZ materials to exhibit dual-band plasmonic response. (a), (b) dielectric functions of gold and TiSiON, respectively. (c), (d) scattering efficiencies calculated using Mie theory in the limit of negligible losses. The insets show the near-field distribution of the nanospheres at resonant wavelengths. The figure is reproduced from Ref. [22] with permission.

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Importantly, the above results were obtained in the limit of negligible optical losses. In reality, as noted by the authors [22], when material exhibits non-zero ${\mathop{\rm Im}\nolimits} [{{\varepsilon_\textrm{m}}} ]$, the analysis become not so trivial and the plasmon spectra will have a more complicated structure. Given the valley-type behavior of the permittivity, the second cross-over wavelength lies in the region of anomalous dispersion, where the inherent large absorption exists. It results in the decrease of the quality factor, which in turn leads to the broadening of the resonance shape and depression of its amplitude. Thus, the first and the secondary plasmonic peaks will be considerably overlapped. The shape of the resonance peak will be rather like a broadened band instead of having two distinct lines. When decreasing the imaginary part of the dielectric function, the secondary peak become pronounced and the material demonstrate the dual-band plasmonic response [22]. At this point, 2ENZ materials are more suitable for the realization of broadband perfect absorbers. For optical applications, where small dissipation of the energy is essential, the loss compensation is necessary [99]. On the other hand, there are great prospects in optimization of morphology and composition of 2ENZ materials. Thus, a great research remains to be done in the design of multi-resonant plasmonic materials with the negligible imaginary part of the permittivity.

4. Applications of 2ENZ titanium oxynitride thin films

As has already been noted, 2ENZ materials are promising for multi-resonant plasmonics. Practical applications, where plasmon enhancement at different wavelengths is demanded, are reviewed in Ref. [23]. Below, we provide some interesting results that can be obtained using TiON plasmonic nanocomposites as a material platform.

In order to demonstrate the benefits of 2ENZ materials in thermophotovoltaics, we have calculated the absorption spectra of a specifically designed metasurface, as reported in Ref. [28]. The calculations were performed using the FDTD method (Lumerical Solutions). The geometry of the unit cell is illustrated in Fig. 10(a). These building blocks constitute the metasurface as shown in the SEM (scanning electron microscopy) image (Fig. 10(b)). Figure 10(c) displays the absorption coefficient as a function of the wavelength for the metasurfaces made of various plasmonic materials. Solar spectra (AM 1.5 direct + circumsolar) is depicted as a grey curve. The gold metasurface has an almost perfect absorption only in the visible region (red curve). Additionally, the spectrum contains two strong absorption peaks centered at 0.7 and 2.0 µm. These peaks, however, are narrowband, and reflect the high-Q plasmon resonance in gold. As a corollary, this metasurface can absorb only 51% of the total power of the solar radiation. A significant improvement of the absorber efficiency can be achieved with TiN [28]. For simulations we used the dielectric function for two different TiN films, which were reported in Refs. [13] and [60]. This allows to evaluate the capabilities of this material platform to tune the absorption spectra. Both TiN-based matasurfaces demonstrate a nearly perfect absorption in the whole visible range, which then diminishes at larger wavelengths (see Fig. 10(c), green and blue curves). The absorption bands are considerably wider than that of the gold absorber, which is driven by the broadband nature of the plasmon resonance in TiN. The fraction of the absorbed power of the incoming solar spectrum is 79% and 82% for green and blue curves, respectively. This effect is even more dramatic for the TiON-based metasurface absorber. The dielectric function of TiON was taken in Ref. [20] and is shown in Fig. 2 (blue curve). TiON also yields a near-unity absorptivity at the visible wavelengths (Fig. 10(c), purple curve). The absorption coefficient is then gradually decreases with the increase of the wavelength. Within the spectral region where ${\mathop{\rm Re}\nolimits} [\varepsilon ]$ is positive, TiON behave as a lossy dielectric. As a result, the absorber efficiency reaches the level of 89% demonstrating a ca. 10% improvement compared to the case of TiN. It should be noted, that the geometrical parameters of the considered metasurface were optimized for the specific dielectric function of TiN film. Consequently, when the metasurface is optimized for the TiON nanocomposite, an additional increase of the absorber efficiency is expected.

 

Fig. 10. The performance of metasurface absorbers made of various plasmonic materials. (a), (b) Geometry of the unit cell of the metasurface and its scanning electron image, respectively; (c) The absorption spectra calculated for different material platforms: Au (red curve, dielectric function from [19]), TiN (green and blue curves, dielectric functions from [60] and [13], respectively); TiON (purple curve, dielectric function from [20]). Grey curve displays a solar spectra (AM 1.5 direct + circumsolar). For each material the fraction of the absorbed power of the solar light is indicated. The figures (a) and (b) are reproduced from Ref. [28] with permission.

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Our group has recently demonstrated that TiON nanocomposites with the valley-type dispersion can be applied for the realization of a multi-mode optical superlens [91]. This device enables to obtain optical images with the sub-diffraction spatial resolution at multiple wavelengths. For this purpose we used the TiON thin film with the dielectric function shown in Fig. 2 (green curve). By harnessing the broadband nature of the plasmonic response of such materials, it is possible to meet the condition of superlensing [100] within the continuous spectral range. Figure 11 shows the results of far-field optical microscopy of TiON-based planar nanostructure. This structure was prepared by means of focused ion beam (FIB) etching of the TiON thin film with the thickness of ≈50 nm. A SEM (scanning electron microscopy) image is shown in Fig. 11(a). Figure 11(d) displays far-field Raman spectra registered in the continuous TiON film (blue curve) and in the center of TiON nanostructure (pink curve). Yellow bars indicate the position of the peaks associated with TiN. Optical measurements were performed using a He-Ne laser source with the wavelength of 632.8 nm. The power of the laser light was on the order of 1 mW, which results in pumping intensity of ∼1 Mw/cm² in the focal plane of the exploited objective (100x, NA = 0.7). As follows from the spectra, the peak at 480 cm⁻¹, which corresponds to the SRS signal [60], was registered in the TiON nanostructure. TiON behave as a nonlinear media even under continuous wave illumination with modest intensity owing to its percolating metal-dielectric nature [91]. Figure 11(b) and 11(c) show Raman maps of the TiON nanostructure at 460 cm⁻¹ and 480 cm⁻¹ that correspond to spontaneous and stimulated Raman scattering, respectively. The map at 460 cm⁻¹ represents a diffraction-limited image of the TiON nanostructure. For the case of SRS microscopy, a sub-diffraction spatial resolution was achieved (Fig. 11(c)). Indeed, the edges of the nanostructure on the image are well-resolved: one can see a square-shaped spot blurred within a diffraction-limited background. It should be noted, that the obtained image of the nanostructure has a square shape whereas in fact the structure represents a circle (see Fig. 11(a)). The reason for this discrepancy is a pixelization of the image, which was obtained by raster scanning with a step size of ≈40 nm. Figure 11(e) plots the intensity of the Raman signal at 480 cm⁻¹ (red curve) along the dashed line denoted on the map (Fig. 11(c)). According to this graph, the sub-diffraction spatial resolution of ≈80 nm (λ/8) were achieved. To compare, a cross-section of the Raman map at 460 cm⁻¹ is shown on the same graph. It is evident that the edges of the nanostructure are not resolved, and the intensity distribution resembles the Airy function. The same analysis revealed that optical superresolution occurs at multiple frequencies corresponding to SRS overtones [91]. There are two principal mechanisms that underlie the observed far-field superresolution in TiON nanocomposites: (1) coherent amplification of the evanescent waves owing to the SRS effect and (2) decoupling of the enhanced waves from the TiON surface to the far-filed zone. These factors are the key to detection of large spatial frequencies in the far field. In paper [101] the far-field Raman color superlensing effect has been demonstrated by showing the spatial resolution of λ/6NA using multi-walled carbon nanotubes dispersed on the metalens surface.

 

Fig. 11. Superresolution stimulated Raman scattering microscopy of the TiON planar nanostructure. (a) SEM image of the TiON nanostructure with the size of 100 nm and (b), (c) corresponding Raman maps at 460 cm⁻¹ (spontaneous Raman scattering) and 480 cm⁻¹ (stimulated Raman scattering), respectively. (d) Far-field Raman spectra registered in the continuous TiON film (blue curve) and TiON nanostructure (pink curve). (e) Cross-sections along dashed lines that are shown in the Raman maps. For clarity, the line in the figure (c) is interrupted.

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So far, we have omitted a distinctive property of 2ENZ materials such as the near-zero permittivity. Owing to the valley-type dispersion, it is possible to achieve a broadband ENZ region, i.e. when the real part of the dielectric function is nearly zero. A zero-permittivity is a key to the wealth optical phenomena that poses near-zero refractive index (NZI) photonics. This field, being a current research hotspot, deals with an exciting effects such as photonic tunneling/superconducting, beamsteering, enhanced nonlinear optics, cavity-free stopped light, non-reciprocal and non-local wave dynamics, to name a few [49,102]. In general, the refractive index $n = \sqrt \varepsilon $ ($\mu = 1$, non-magnetic media) and permittivity $\varepsilon $ are complex quantities. When the ${\mathop{\rm Re}\nolimits} [\varepsilon ]$ approaches a zero value, there is usually a non-zero ${\mathop{\rm Im}\nolimits} [\varepsilon ]$. Hence, both ${\mathop{\rm Re}\nolimits} [n ]$ and ${\mathop{\rm Im}\nolimits} [n ]$ will not be vanishing. At the wavelength of zero-permittivity the real part of the refractive index is given as [49]

5. Conclusion

In summary, TiON thin films demonstrating the 2ENZ behavior in the visible and NIR ranges have been considered as the promising material platform for plasmonics. 2ENZ materials constitute a novel class of alternative plasmonic media, which provides a new way for excitation of multi-band plasmon resonance. The emergence of two cross-over wavelengths in TiON dielectric function were attributed to formation of the nanocomposite structure, consisting of metallic TiN inclusions within the multi-phase TiO_x/TiO_yN_z dielectric host. TiON nanocomposites can be produced through the magnetron sputtering of polycrystalline TiN films with the post- or in-situ oxidation. In view of the recent progress in TiN-based plasmonics, which is briefly reviewed in the first part of this work, TiON has a great potential to augment the TiN advantages. Addition of oxygen to TiN yields a new degree of freedom in the design of advanced plasmonic materials. Besides the creation of the valley-type dispersion, we have shown that the cross-over wavelengths can be tuned within the wide wavelength range at the synthesis stage. Moreover, it is possible to prepare TiON films with the flat dispersion in the considerable wavelength range. All these functionalities provide the unprecedented control on the plasmonic response of metallic structures. We have outlined the experimental techniques for characterization of TiON nanocomposites that provide an important information on its chemical composition and intrinsic morphology, which both govern the effective dielectric function. The potential of 2ENZ materials in plasmonics and near-zero refractive index photonics is discussed. Going beyond single-resonant plasmonics extends the scope of plasmonic applications and routes towards the efficient broad-bandwidth nanophotonic devices.