1. Introduction

The growing interest in metamaterials and plasmonics can be attributed to many unparalleled applications and properties that they enable [1]. However, traditional plasmonic metals, such as gold and silver, suffer from large losses at optical frequencies, which can be detrimental to their applicability in realistic devices. Recently, researchers have been on the lookout for alternatives to traditional plasmonic materials, which not only have lower losses, but can also be integrated onto practical semiconductor devices. A wide variety of materials have been suggested in various spectral ranges [2], but one of the most promising is Titanium Nitride (TiN), which has recently received considerable attention [3]. For instance, the optical properties of TiN resemble those of gold, with reasonably low loss [4]. This material has a high melting point (>2900°C) [3,5], it is chemically stable, mechanically hard, bio-compatible, well-suited with standard semiconducting devices, can be grown epitaxially on substrates such as magnesium oxide, c-sapphire and silicon, and its physical properties can be tuned by varying the stoichiometry and the growth conditions [6]. These attributes make TiN a promising material for visible and near infrared plasmonic applications.

In recent years, metallic gyroid metamaterials – 3D self-assembled structures (Fig. 1) – have gained a lot of attention [7], as they have been predicted to show a range of interesting optical properties, including negative index of refraction in the visible and near infrared spectral ranges (for low-loss metals) as well as a bulk photonic band gap [7]. Due to chiral structure of gyroid networks, these materials can propagate circularly polarized light [7]. Furthermore, the optical behavior of these composite media can be tuned by optimizing the filling fractions of metal and lattice dimensions of the gyroid structures [8]. In this work, we have attempted to combine the potential advantages of TiN and gyroid materials. We have synthesized self-assembled TiN gyroidal metamaterials, studied their optical properties, and compared them with those of planar TiN thin films.

 

Fig. 1 Schematic of the gyroid network.

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2. Synthesis of gyroidal mesoporous TiN monoliths and TiN thin films

Titanium nitride (TiN) gyroids were generated by the heat treatment of gyroidal mesoporous titanium dioxide (TiO₂) under flowing ammonia (NH₃) gas. The TiO₂ gyroids were synthesized by the coassembly of an amphiphilic block terpolymer polyisoprene-block-styrene-block-ethylene oxide (ISO) [9]. Titanium (IV) isopropoxide was added to the hydrochloric acid and tetrahydrofuran to generate the TiO₂ sol that is added to the ISO block terpolymer. Evaporation of the solvent at 50 °C induces the coassembly of an ISO/TiO₂ hybrid gyroid structure. For some samples, to remove surface lamellae, the hybrid film was subjected to CF₄ plasma etching on its top and bottom. Subsequently, the ISO/TiO₂ hybrids were converted to freestanding gyroidal mesoporous oxides by calcination in air at 450 °C for 3 hours, which removed the organic material. Finally, the freestanding TiO₂ hybrids were converted to TiN gyroidal mesoporous samples by heating under dry flowing NH₃ in a tube furnace at 600 °C for 6 hours. The tube furnace was cooled under flowing NH₃ and the samples were slowly exposed to ambient temperature. For in depth understanding of X-ray diffraction and scanning electron microscopy characterization of these mesoporous TiN gyroid materials the reader is referred to a separate publication [10].

Thin films of TiN were deposited using reactive magnetron sputtering in a nitrogen/argon environment at the pressure equal to 5 mTorr. Since TiN is a nonstoichiometric material, the optical properties can be drastically altered by controlling the deposition conditions such as the substrate, deposition pressure, gas ratios, and temperature. For example, the TiN film on fused silica deposited at 350 °C and a TiN film on sapphire deposited at 800 °C exhibit significantly different properties. The TiN film on sapphire is epitaxial in nature and has a permittivity cross-over frequency nearly 200 nm shorter than the polycrystalline TiN film on glass. This tunability allows for an amazing flexibility when real devices are considered, enabling an optimized material for a given application.

3. Studies of optical properties

The thicknesses of three gyroidal TiN samples, two of which were plasma treated, were determined by optical microscopy to be equal to 436 μm, 98 μm, and 279 μm respectively. The samples were opaque and too thick for transmission measurements (transmittance was below the noise level). The reflectance spectra of these samples were measured between 200 nm and 2460 nm using the Lambda 900 spectrophotometer equipped with an integrating sphere, Fig. 2(a).

 

Fig. 2 (a) Reflectance spectra of gyrodial TiN samples: (1) 98 μm, treated surface, (2) 437 μm, treated surface, and (3) 279 μm, no surface treatment. Inset: Reflectance spectrum of the Au gyroid; adopted and re-plotted from [12]. (b) Real ε’ and imaginary ε” parts of the effective dielectric permittivity of TiN gyroids obtained by fitting trace # 2 of Fig. 2(a) with the Drude model (at 610 nm<λ<2450 nm).

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In order to obtain the spectra of dielectric permittivity of TiN gyroids (in the effective medium approximation), the experimental reflection spectra were fitted with the known formulas [11] originating from the Fresnel equations (see Appendix). In this procedure, theparameters of the Drude model as well as the model accounting for the Drude response plus one Lorentz oscillator were used as the fitting parameters.

The spectra of dielectric permittivity, determined by fitting the experimental reflectance spectra with the Drude model are shown in Fig. 2(b).The corresponding values of the plasma frequency, ω_p, and the damping rate, γ_D, are summarized in Table 1. Although the dielectric permittivities obtained using the “Drude plus Lorentz” model resulted in a good agreement between calculated and experimental reflectance spectra, they did not appear to be plausible. (Note that although the reflectance spectra of TiN gyroids were qualitatively similar to those of Au gyroids studied in [12] (see inset in Fig. 2(a)), the latter were much better plasmonic materials, as their dielectric permittivity spectra crossed zero between 800 nm and 600 nm, depending on the refractive index of the fill medium [13].)

Table 1. Drude model parameters and free carrier density of TiN gyroidal structures and thin films

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Subsequently, the optical properties of TiN thin films grown on sapphire and glass substrates were studied and compared to those of TiN gyroids. The transmission and reflection spectra of thin films were measured and used in the fitting procedure (based on the known formulas for reflectance and transmittance [11], see Appendix) to determine the Drude parameters as well as the film thickness.

Alternatively, the material properties and the thickness of the TiN films were obtained using variable angle spectroscopic ellipsometry (J. A. Wollam and Co. V-VASE). The films were measured at two incident angles of 50 and 70 degree. To extract the linear optical properties from the ellipsometry measurements, a combination of three Lorentz oscillators and one Drude term was used, as it has been described in previous works [4]. Dielectric permittivity spectra and film thickness obtained by the two methods were in a good agreement with each other (Fig. 3(c)), which validates the experimental procedure used in the study.

 

Fig. 3 (a) Reflectance spectra of TiN thin films on (1) sapphire and (2) glass. (b) Transmittance spectra of TiN thin films on (1) sapphire and (2) glass. (c) Real ε’ and imaginary ε” parts of the dielectric permittivity of TiN thin film on glass obtained from fitting the experimental reflectance and transmittance spectra using the Drude model (solid line); the dielectric permittivity of the same sample obtained using the ellipsometry technique (dashed line).

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Comparison of the Drude model parameters for the TiN gyroids and thin films shows that the plasma frequency, ω_p, in gyroid structures is smaller than that in thin films, indicative of a smaller free carrier density, while the damping rate, γ_D, is larger, Table 1. The calculated plasma frequency and the known effective electron mass, m*, in TiN [14] were used to estimate the free carrier density

The anticipated free carrier concentration corresponds to one electron per one TiN formula unit, 5.25x10²² cm⁻³ [14]. A very similar value was determined for the thin TiN film grown on sapphire, i.e. 5.1x10²² cm⁻³. In contrast, the free electron density in the thin film grown on glass was almost two times lower, while the values of N in the gyroidal samples were three-to-five times lower. We infer that the low free carrier concentration, N, in TiN gyroidal samples as well as the large damping rate, γ_D, may be due to porous nanostructure, where free electrons scatter much more at surface or edges of the structure, as well as due to incomplete substitution of oxygen by nitrogen and the materials parameters can be improved by using higher nitriding temperatures during synthesis.

The gyroidal TiN samples appeared black and shiny to a naked eye. Remarkably, they showed ~100 μm domains of bright rainbow colors in the reflection mode of an optical microscope, see Fig. 5(a). Therefore, we collected reflectance spectra from different spots on the sample using a home-built setup schematically shown in Fig. 4.

 

Fig. 4 Schematic of collecting reflection spectra of gyroidal TiN.

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The sample was illuminated with white light and its surface was projected to the image plane of the 10/2X objective. A rainbow pattern, similar to that in Fig. 5(a), was observed on a white card placed in the image plane. When the optical fiber P400-2-Vis/NIR connected to the PC2000 Fiber Optics spectrometer was placed in different local spots in the image plane (displaying different colors), distinctly different reflection spectra were recorded, Fig. 5(b). The spectra obtained from different spots were normalized to the spectrum of the halogen lamp used to illuminate the sample. The positions of the spectral bands corresponded to the colors of the particular local spots seen by eye (see Fig. 5(b) in which each spectrum is coded with the color seen in Fig. 5(a)). Qualitatively similar rainbow patterns observed in gyroid samples composed of Au nanoparticles (studied in [9]) have been attributed to different orientations of the gyroid domains [10]. Different orientations of the gyroid domains can be used as a tentative explanation of the effect observed in our TiN gyroid samples, although the color patterns in our experiments were not highly sensitive to polarization.

 

Fig. 5 (a) Optical microscopy image of the TiN gyroidal samples illuminated with unpolarized light. (b) Unpolarized reflection spectra collected from different local spots on the sample’s surface.

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4. Summary

To summarize, in this study, we have synthesized gyroidal TiN metamaterials, studied their optical properties, and compared them with the optical properties of TiN thin films fabricated using reactive magnetron sputtering. When the spectra of the real and imaginary parts of the dielectric permittivity of gyroidal and thin film TiN were fitted with the Drude model, the plasma frequencies, ω_p (and the corresponding free carrier concentrations N) were found to be much lower in gyroids than in thin films. Furthermore, the plasma frequency in TiN gyroids was comparable to or smaller than the damping rate, γ_D. This makes the synthesized TiN gyroids poor plasmonic materials. We infer that the plasmonic properties of the TiN metamaterials can be improved by using higher nitriding temperatures during synthesis. At the same time, TiN gyroidal samples have demonstrated a bright rainbow pattern in reflection mode in optical microscopy experiments. Correspondingly, the reflection spectra collected from different spots on the sample surface had their maxima at different wavelength positions. Following [8], we explain the bright multi-color reflection pattern by different orientations of the gyroid domains

Appendix

Below, we describe the procedure for determining real and imaginary parts of dielectric permittivity from the reflection and transmission spectra and its implementation to the TiN samples studied.

The dielectric permittivity was modeled taking into account both Drude and (single) Lorentz terms,

(2)$$\begin{array}{l}\epsilon \left(\omega \right)={\epsilon }_b-\frac{{\omega }_p^2}{{\omega }^2+i{\gamma }_D\omega }+\frac{f}{{\omega }_0^2-{\omega }^2-i{\gamma }_L\omega }\\ \text{Drude}\text{Lorentz}\end{array}$$

where ε_b is the “bound electron” component of the dielectric permittivity that is due to distant high-frequency resonances, ${\omega }_p=\sqrt{N{e}^2/m^{*}{\epsilon }_0}$ is the plasma frequency, N is the free electron concentration, e is the electron charge, m* is the effective mass, ε₀ is the vacuum permittivity, γ_D is the free electron damping rate, ω is the frequency, f is the constant proportional (among other factors) to the concentration of Lorentz oscillators and the oscillator strength, ω₀ is the natural frequency of oscillation, and γ_L is the oscillator damping rate.

By substituting this dielectric permittivity to the known formulas [11] describing reflection and transmission in the three-layer structure depicted in Fig. 6, one can calculate the reflection R(ω) and transmission T(ω) spectra of TiN samples measured in our experiments,

(3)$$R={\left|\frac{r_{12}^p+r_{23}^p\exp \left(2i{k}_{z2}d\right)}{1+r_{12}^p{r}_{23}^p\exp \left(2i{k}_{z2}d\right)}\right|}^2\text{and}T=\mathrm{Re}\left\{{\left|\frac{t_{12}^p+t_{23}^p\exp \left(i{k}_{z2}d\right)}{1+t_{12}^p{t}_{23}^p\exp \left(2i{k}_{z2}d\right)}\right|}^2\frac{k_{z3}}{k_{z1}}\right\}.$$

Here $r_{ik}^p=\left(k_{zi}{\epsilon }_k-k_{zk}{\epsilon }_i\right)/\left(k_{zi}{\epsilon }_k+k_{zk}{\epsilon }_i\right)$ and $t_{ik}^p=\left(1+r_{ik}^p\right)\sqrt{{\epsilon }_i{\epsilon }_k}$ are the amplitude reflection and transmission coefficients for p polarized light at the interfaces between media i and k; ε_i and ε_k are the dielectric permittivities of media i and k; $k_{zi}=\pm \sqrt{\kappa }=\pm \sqrt{{\epsilon }_i{(\omega /c)}^2-k_x^2}\text{(}i\text{=0,1,2)}$ is the z component of the wavevector in medium i; $k_x=k_{phot}\sin \theta$is the x component of the wavevector in medium i; c is the speed of light; θ is the incidence angle (near normal incidence in our experiments); d is the thickness of layer 2; $k_{phot}=n_1\omega /c$ is the wavenumber for a photon in medium 1; and n₁ is the index of refraction of medium 1 (in our case, n₁ = 1 for air). (When medium 3 was not air, the calculated transmittance was corrected for the index of refraction of medium 3 as well as the reflection at the medium3/air interface.)

 

Fig. 6 Schematic of reflection and transmission in three layered media.

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The dielectric permittivities ε₁(ω) and ε₃(ω) as well as the angle of incidence θ were known. By varying parameters ε_b, ω_p, ω₀, γ_D, γ_L, and f, one can fit the experimental reflection R(ω) and transmission T(ω) spectra with the calculated ones. The thickness d can be known form independent measurements (e.g. profilometry) or be used as an extra fitting parameter. The modeled spectra of real and imaginary parts of dielectric permittivity ε₂(ω) corresponding to the best agreement between the calculated and the experimental R(ω) and T(ω) were considered to be effective dielectric permittivities of medium 2 (TiN films or gyroids).

The transmission of relatively thick (≥100 μm) gyroidal samples was negligibly small; therefore, for these samples, we fitted reflection spectra only. Both reflection and transmission spectra were fitted in thin film samples.

Note that at λ≥600 nm, the experimental spectra could be fitted reasonably well by using the Drude term only. Although adding the Lorentzian term to the fitting routine, resulted in a good match of the experimental and calculated reflection and transmission spectra, the derived spectra of dielectric permittivities did not look plausible. Therefore, the data reported in Fig. 2 and Table 1, was determined by using the Drude model without the Lorentzian term.

Acknowledgment

The authors acknowledge the support of the NSF PREM grant DMR 1205457, NSF IGERT grant DGE 0966188, ARO grant W911NF-14-1-0639, NSF grant DMR-1409105, AFOSR grant FA9550-14-1-0138DEF, and NSF MRSEC grant DMR 112092.

References and links

1. M. A. Noginov and V. A. Podolskiy, eds., Tutorials in Metamaterials, Series in Nano-optics and Nanophotonics (CRC Press, 2011), p.293.

2. P. West, S. Ishii, G. Naik, N. Emani, V. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. 4(6), 795–808 (2010). [CrossRef]  

3. A. Boltasseva and H. A. Atwater, “Materials science. Low-loss plasmonic metamaterials,” Science 331(6015), 290–291 (2011). [CrossRef]   [PubMed]  

4. G. Naik, J. L. Schroeder, X. Ni, A. V. Kildishev, T. D. Sands, and A. Boltasseva, “Titanium nitride as a plasmonic material for visible and near-infrared wavelengths,” Opt. Mater. Express 2(4), 478–489 (2012).

5. U. Guler, A. Boltasseva, and V. M. Shalaev, “Applied physics. Refractory Plasmonics,” Science 344(6181), 263–264 (2014). [CrossRef]   [PubMed]  

6. G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25(24), 3264–3294 (2013). [CrossRef]   [PubMed]  

7. K. Hur, Y. Francescato, V. Giannini, S. A. Maier, R. G. Hennig, and U. Wiesner, “Three-dimensionally isotropic negative refractive index materials from block copolymer self-assembled chiral gyroid networks,” Angew. Chem. Int. Ed. Engl. 50(50), 11985–11989 (2011). [CrossRef]   [PubMed]  

8. S. Salvatore, A. Demetriadou, S. Vignolini, S. S. Oh, S. Wuestner, N. A. Yufa, M. Stefik, U. Wiesner, J. J. Baumberg, O. Hess, and U. Steiner, “Tunable 3D Extended Self-Assembled Gold Metamaterials with Enhanced Light Transmission,” Adv. Mater. 25(19), 2713–2716 (2013). [CrossRef]   [PubMed]  

9. M. Stefik, S. Wang, R. Hovden, H. Sai, M. W. Tate, D. A. Muller, U. Steiner, S. M. Gruner, and U. Wiesner, “Networked and chiral nanocomposites from ABC triblock terpolymer coassembly with transition metal oxide nanoparticles,” J. Mater. Chem. 22(3), 1078–1087 (2011). [CrossRef]  

10. S. W. Robbins, Materials Science and Engineering Department, Cornell University, Ithaca, New York 14850, and H. Sai, K. W. Tan, J. Kim, F. J. DiSalvo, S. M. Gruner, U. Wiesner, are preparing a manuscript to be called “Mesoporous TiN, Ti_1-xNb_xN, and NbN Gyroids from Block Copolymer Self-Assembly and Nitridation.”

11. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Springer-Verlag, Berlin, 1988).

12. S. Vignolini, N. A. Yufa, P. S. Cunha, S. Guldin, I. Rushkin, M. Stefik, K. Hur, U. Wiesner, J. J. Baumberg, and U. Steiner, “A 3D optical metamaterial made by self-assembly,” Adv. Mater. 24(10), OP23–OP27 (2012). [CrossRef]   [PubMed]  

13. P. Farah, A. Demetriadou, S. Salvatore, S. Vignolini, M. Stefik, U. Wiesner, O. Hess, U. Steiner, V. K. Valev, and J. J. Baumberg, “Ultrafast Nonlinear Response of Gold Gyroid Three-Dimensional Metamaterials,” Phys. Rev. A 2(4), 044002 (2014). [CrossRef]  

14. J. S. Chawla, X. Y. Zhang, D. Gall, “Effective electron mean free path in TiN (001),” J. Appl. Phys. 113, 063704 (2013). [CrossRef]