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Double-plasmon broadband response of engineered titanium silicon oxynitride

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Abstract

Titanium nitride is a CMOS-compatible alternative material to conventional metals for plasmonics and metamaterials applications. We demonstrate complete tunability at visible and near-infrared frequencies of the optical dispersion of titanium nitride nanolayers deposited on Si (100) substrates from metallic to dielectric behavior by alteration of reactive magnetron sputtering growth conditions and, via co-deposition, the addition of Si and/or O2 elemental components. The dielectric function and region of metallic character is found to be further modified by post-deposition vacuum annealing. We categorize this dispersion behavior as anomalous due to a distinctive line shape that allows for double-plasmon resonances, which we investigate analytically using Mie scattering theory.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Alternative plasmonic materials to noble metals such as transition metal nitrides and transparent conductive oxides allow for controllable dispersion behavior, decreased losses, and realization and optimization of metamaterial and plasmonic devices [1,2]. Reduced free carrier concentrations in combination with robust structural properties promote novel applications such as large broadband metamaterial absorbers at visible [3] and mid-infrared [4] wavelengths.

Efforts to tune the optical dispersion of TiN and reduce optical losses have been rekindled with these proposed applications in metamaterials and plasmonics at visible to near-infrared wavelengths [5,6]. Transition-metal nitride materials combine ionic and covalent bonding character resulting in exceptional hardness and high melting points while still maintaining metallic character at visible and near-infrared wavelengths [7]. Likewise, the non-stochiometric nature of these materials allows for tunability via alteration of deposition conditions while preserving optical quality. In contrast, at visible and near-infrared wavelengths the dispersions of traditional plasmonic metallic materials such as Au and Ag cannot be tuned and have a much larger magnitude of negative real permittivity. Furthermore, noble metals possess low melting points and a lack CMOS-compatibility.

Epitaxial TiN thin films were demonstrated to be grown on c-sapphire substrates using a reactive magnetron sputtering (MSP) deposition with a Ti target in a 5 mTorr pressure N2:Ar gas ratio atmosphere at a substrate temperatures of 300°C and 500°C. These conditions show large metallic behavior with a minimum imaginary permittivity surrounding the screened plasma wavelength of approximately 3.5, with a screened plasma wavelength from about 650 nm to 500 nm [8]. In agreement, deposition temperature has been previously shown to be linearly correlated with the material’s unscreened plasma frequency [9]. Our group has grown polycrystalline TiN thin films via reactive DC MSP at relatively low N2 gas pressures (2.5 mTorr) and at room temperature on Si (100) substrates and found its optical dispersion can be adequately described by the Drude model at visible wavelengths, with a screened plasma wavelength that blue-shifts with increasing vacuum annealing temperature from 720 nm to 500 nm [5].

In this paper, we investigate the effect of deposition conditions and incorporation of O- and Si-dopants in a TiNx nanolayer materials platform grown by reactive MSP in a nitrogen gas environment. We show extremely large tunability of the optical properties of this material from metallic to completely dielectric behavior and the development of anomalous double crossover behavior in the optical dispersion, where the real permittivity is equal to zero at multiple points within a small wavelength region. Then, we further modulate the dielectric function of these materials using post-deposition annealing, observing that it promotes metallic character and modifies the position of both crossover wavelengths. Finally, we use Mie scattering theory to study the effects due to the anomalous optical dispersion and demonstrate a unique double plasmon behavior that allows for broadband optical responses in engineered silicon oxynitrides.

2. Growth, processing, and characterization methods

In all cases the films are grown to ~100 nm thicknesses with reactive MSP on p-type (100) Si substrates in a pure N2 gas atmosphere with a flow rate of 10 Sccm at a deposition rate of ~3.5 nm/min. Likewise, a DC cathode was incorporated using a Ti (99.995% purity) 3” diameter and 0.125” thick target and powered at 200W. When integrating Si-dopants, a reactive co-deposition was employed by adding a RF cathode using either a Si (99.999%) or a SiO2 (99.995%) 3” diameter and 0.125” thick target with Cu backing plates at multiple applied powers. The deposition was performed with a Denton Discovery 18 sputtering system with cathodes in a confocal arrangement distanced approximately 100 mm from the substrate and angled at about 30 degrees from the substrate normal. The sample was rotated at 10 rpm to improve nanolayer uniformity. The base pressure was kept below 5x10−7 Torr, the deposition pressure was varied between 1.5 and 7.5 mTorr, and the deposition temperature was either kept at room temperature or increased to 300°C.

Any post-deposition annealing was performed in vacuum at pressures less than 3 mTorr with a Mellen thermal furnace. The annealing was conducted for 1 hour at various temperatures with a maximum temperature of 1000°C.

2.1 Optical and structural characterization

The samples were characterized using variable angle spectroscopic ellipsometry (VASE, J.A. Woollam Co.) in the near-UV, visible, and near-IR wavelength ranges. The VASE data were fitted with best accuracy by describing the complex material permittivity, (ω), using the Drude-Lorentz model:

ε(ω)=ε'(ω)+iε"(ω)=εωp2ω2iΓDω+j=1nAjωoj2ωoj2ω2+iγjω
with a maximum of three Lorentz oscillators (n = 3). In Eq. (1), 𝜀 is the background permittivity in the limit of high optical frequency, which accounts for higher-energy resonances. The variables ωp and ΓD, are the unscreened plasma frequency and free charge carrier collision damping factor, respectively, and describe the free electron contribution to the optical response. The Lorentz terms describe interband transitions with a strength of Aj, a broadening of 𝛾j, and an energy of ωoj.

The Lorentz terms can be correlated with calculated electronic band structure [10]. Previous studies of nanocrystalline over-stoichoimeteric TiNx (x>1) thin films model ellipsometry data with Drude behavior and two Lorentz oscillators. The first oscillator, located at 3.0-3.7 eV, is attributed to the Γ12→ Γ15 interband absorption and the second oscillator, located at 5.2-6.2 eV, is attributed to the X5→X2 interband absorption. In many cases, the lowest bandgap transition from Γʹ25→ Γ12 of ~1.0 eV was found to be indistinguishable from loses due free charge carrier collisions [9].

Sample reflection was measured using a Cary 5000 UV-VIS-NIR Spectrophotometer. Reflection images were taken with an optical microscope illuminated by a tungsten-halogen lamp. X-ray diffraction (XRD) measurements were performed with a Bruker D8 Discover system using Cu k-α radiation and a Lynxeye detector.

3. Material parameters and results of characterization

This section contains the results of various growth conditions observed to induce the anomalous dispersion behavior in planar nanolayers.

3.1 Anomalous dispersion: influence of deposition pressure and temperature

Typical growth pressures via MSP of titanium nitride nanolayers range between 1.5 mTorr and 5 mTorr with deposition temperatures between 300°C and 600°C. If growth is performed at room temperature, then lower deposition pressures are required for a more energetic ion bombardment that promotes ion mobility at the material surface [5].

Figure 1 shows the dielectric functions VASE characterization of nanolayers deposited on Si substrates by room temperature MSP with increasing deposition pressure within the wavelength region of 300 nm to 2000 nm. A deposition pressure of 6.5 mTorr results in the anomalous optical dispersion behavior where 𝜀’ crosses zero at multiple points within a narrow wavelength region. Increasing the pressure to 7.0 mTorr and 7.5 mTorr is observed to cause 𝜀’ to become positive in magnitude while still retaining a similar line shape to the 6.5 mTorr deposition pressure condition.

 figure: Fig. 1

Fig. 1 Real (a) and imaginary (b) permittivity of titanium nitride nanolayers grown by room temperature MSP at high deposition pressures and with and without post-deposition annealing at 900°C.

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The results of post-deposition annealing at 900°C for each case are also shown in Fig. 1. At the 6.5 mTorr deposition pressure a blue-shift of both 𝜀’ = 0 crossovers and an increase in the negative magnitude of 𝜀’ are observed. At higher deposition pressures, post-deposition annealing induces a negative 𝜀’. Likewise, the annealing preserves the anomalous line shape features, yielding a double zero crossing of the real permittivity at different wavelengths.

Oxygen is extremely reactive and high levels of residual oxygen during deposition have been shown to induce similar dielectric-like dispersions at room temperature even at 1.5 mTorr deposition pressures [11]. Likewise, at 4.0 mTorr pressures the degree of oxygen incorporation was shown to depend on gas ratio, temperature, substrate type, and bias voltage [12]. Nitrogen incorporation in sputtered films with a Ti target and comparable O2 and N2 gas flow rates was found to be significantly low when compared to oxygen, and this is attributed to replacement of the metal nitride by oxide due to higher reactivity of the latter [13]. One method to overcome this involves a constant N2 gas flow with a periodic oxygen flow rate that cyclically introduces oxygen into the sputtering chamber [14].

Increasing MSP deposition temperature at high deposition pressures is also investigated. Figure 2 shows the measured dielectric function upon increasing deposition temperature to 300°C at 7.0 mTorr and 7.5 mTorr pressures. In both cases the optical dispersion is shifted so that 𝜀’ becomes negative within a certain wavelength region. Increasing deposition temperature increases surface ion mobility and, in this case, has an inverse correlation to increasing deposition pressure. Both of the first crossings of 𝜀’ = 0 at the 300°C deposition condition are blue-shifted relative to the 6.5 mTorr room temperature deposition. Likewise, the second crossing of the 7.5 mTorr deposition at 300°C is red-shifted.

 figure: Fig. 2

Fig. 2 Real (a) and imaginary (b) permittivity of titanium nitride nanolayers grown by MSP at room temperature and at 300°C at high deposition pressures.

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3.2 Ti and SiO2 reactive co-deposition

An alternative approach to systematically incorporates oxygen into TiN is demonstrated through reactive MSP co-deposition with both DC Ti and RF SiO2 targets at different power ratios DC:RF. The deposition pressure was kept low at 1.5 mTorr, and the deposition temperature was kept at 300°C to improve surface ion mobility during deposition and ensure metallic TiNx optical dispersion at an RF power of 0 W.

Figure 3 shows the material optical dispersion data as a function of increasing RF target power. Increasing the RF target power has a similar effect on the dielectric function of these materials as decreasing deposition temperature and increasing deposition pressure. With an RF power of 0 W, the optical dispersion is typical of TiN with a screened plasma frequency of around 600 nm. At a DC:RF ratio of 4:2, the real part of the permittivity 𝜀’ is nearly completely positive with the first crossing of 𝜀’ = 0 at 950 nm and the second crossing at 1300 nm.

 figure: Fig. 3

Fig. 3 Real (a) and imaginary (b) permittivity of titanium silicon oxynitride nanolayers grown by a MSP co-deposition with DC Ti and RF SiO2 targets with a DC:RF power ratio at a 300°C deposition temperature and 1.5 mTorr deposition pressure.

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The results of post-deposition annealing as a function increasing temperature are displayed in Fig. 4 for a DC:RF power ratio of 4:1, and in Fig. 5 for a DC:RF power ratio of 4:2. Similar to the results of post-deposition annealing in section 3.3, both the crossings where 𝜀’ = 0 for the 4:1 condition are blue-shifted. However, in the case of the 4:2 condition the low energy crossing is first red-shift and is then blue shifted with increasing annealing temperature.

 figure: Fig. 4

Fig. 4 Real (a) and imaginary (b) permittivity of 4:1 DC:RF titanium silicon oxynitride nanolayers as a function of increasing post-deposition annealing temperature.

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 figure: Fig. 5

Fig. 5 Real (a) and imaginary (b) permittivity of 4:2 DC:RF titanium silicon oxynitride nanolayers as a function of increasing post-deposition annealing temperature.

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Figure 6 shows the effect of these deposition and processing conditions on normal incident reflectance at visible wavelengths referenced to Ag. The color of the material shifts from a dark Si-like color to a brown and eventually Au-like luster as the condition occurs where the screened plasma frequency shifts across the visible spectrum and 𝜀’ at wavelengths larger than the screened plasma wavelength becomes more negative.

 figure: Fig. 6

Fig. 6 (a)-(g) Optical reflectance images of nanolayers on Si substrates deposited by DC Ti and RF SiO2 targets with a DC:RF power ratio 4:1 as deposited (a), annealed at 600°C (b), and annealed at 800°C (c), and 4:2 as deposited (d), annealed at 600°C (e), annealed at 800°C (f), and annealed at 1000°C (g). (h)-(n) Reflectance measurements of nanolayers on Si substrates deposited by DC Ti and RF SiO2 targets with a DC:RF power ratio 4:1 as deposited (h), annealed at 600°C (i), and annealed at 800°C (j), and 4:2 as deposited (k), annealed at 600°C (l), annealed at 800°C (m), and annealed at 1000°C (n).

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3.3 Ti and Si reactive co-deposition

A reactive MSP co-deposition was also performed with a DC Ti and an RF Si target. Again, the deposition pressure was kept low at 1.5 mTorr, and the deposition temperature was kept at 300°C. Figure 7 shows the material optical dispersion as a function of increasing RF target power. The results are very similar to those in Fig. 5 and indicate that the anomalous optical dispersion behavior can occur without oxygen incorporation.

 figure: Fig. 7

Fig. 7 Real (a) and imaginary (b) permittivity of tertiary compound titanium silicon nitride nanolayers grown by a MSP co-deposition with DC Ti and RF Si targets with a DC:RF power ratio at a 300°C deposition temperature and 1.5 mTorr deposition pressure.

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Tertiary titanium silicon nitride nanostructure compounds are known for their improved hardness and mechanical properties [15,16]. Likewise, these materials can be much less susceptible to oxidation that occurs when titanium nitride compounds are brought to high annealing temperatures in an oxygen atmosphere [17]. In these compounds, Si3N4 phases that are stable in oxygen atmospheres protect TiN phases against oxidation. This can allow the material to be utilized up to temperatures as high as the melting point of Si3N4.

3.4 Structure

XRD analysis was performed on all samples to help determine their physical structure. Figure 8 shows a representative XRD θ-2θ scan. In all cases the only peaks that were determined to be present are those that correspond to a TiN face-centered cubic rock salt structure and those of the Si substrate. The TiN (200) and (220) peaks were present, while the (111) peak that usually surrounds a 2θ value of 36.7° is absent. The lack of peaks that would correspond to crystallized oxide or silicon nitride phases indicates that these components are incorporated as amorphous phases.

 figure: Fig. 8

Fig. 8 Representative 2θ-θ X-ray diffraction scan showing peaks corresponding to the TiN cubic rock salt structure.

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In all cases both the TiN (200) and (220) peaks are shifted to a higher 2θ than is typical. From Bragg’s law the peak locations correspond to a lattice constant of ~4.1 Å while a lattice constant of 4.24 Å is normal for stochiometric TiN. A decrease in lattice constant is typically observed in TiNx compounds with x>1 [9]. Excess nitrogen concentrations induce Ti vacancies that cause the crystal structure to relax and lattice constant to reduce. Higher incorporation of nitrogen with x much larger than unity results in migration to and desorption at the films surface, superstructure formation [18], or precipitation of nitrogen into grain boundaries [19]. This is consistent with our system where MSP was conducted in a pure N2 atmosphere. The lack of Ar gas flow increases effective N2 partial pressures and causes excess nitrogen incorporation.

4. Origin of the anomalous dispersion behavior

In order to illustrate the origin of the anomalous dielectric function behavior, we consider in Fig. 9 an idealized phenomenological model described by Eq. (1) with a single Lorentz oscillator (n = 1) and 𝜀 equal to unity. If the transverse oscillation of the Lorentz oscillator ωt≡ωo1 is located at a lower energy than ωp so that the Lorentz oscillator’s positive contribution starts at a lower energy than ωp, then an anomalous optical dispersion behavior will be realized if A1 is large enough to overcome the negative contribution from the Drude term. Notice also that increasing the oscillator strength Aj will blue-shift the high energy screened plasma frequency unless there is an accompanying decrease in ωp or ωo1 or increase in ΓD or 𝛾1.

 figure: Fig. 9

Fig. 9 Real (a) and imaginary (b) permittivity as a function of frequency in eV of a phenomenological material system with a single Drude and Lorentz contribution to the optical response. Particular arrangement and strength of these two contributions results in a real component to the optical dispersion with two nearby crossings where 𝜀’ = 0.

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In realistic TiN materials, ωp is on the order of 5 eV while the interband Lorentz transitions previously discussed introduce a screened plasma frequency that is shifted to a lower energy. The intrinsic interband transitions of TiN are not of enough influence to explain the material’s transition to dielectric behavior and requires Lorentz oscillator contributions in the optical response from another polarization mechanism in the material. For example, TiO and TiO2 phases have been modeled and experimentally shown to possess fundamental electronic bandgaps, Γ→ Γ’ interband transition around ~1.9 eV and ~3.6 eV [10,20]. In our group’s previous study of TiN, an increase in the optical bandgap and an increase in grain size were found to be inversely correlated with a decrease in screened plasma wavelength without an obvious Burstein-Moss shift [5]. Thus, the tuning of the optical dispersion of the TiN system in that case originated from structural reconfigurations induced upon annealing and/or variations in the grain size [21]. However, in these multi-phase, multi-component materials, the morphology is much more complex. What we believe to be clear is that the tunablility of the dispersion data stems from the interplay between the Drude and Lorentz oscillator contributions associated to these phases.

Our phenomenological model is consistent with another study that proposes a Maxwell-Garnett homogenization with robust TiN and TiO2 phases [11]. Rather, our proposed model does not impose microstructural or morphology restrictions on the material system in question and allows for optical effects induced by crystal imperfections, e.g. vacancies.

5. Plasmonics and metamaterials applications

In this section, we assess the potential of the anomalous metal-nitride materials as building blocks for broadband plasmonic and metamaterial applications compared to Au and stochiometric TiN materials. The TiSixOyNz material with 4:2 Ti to SiO2 target power ratio and 600°C vacuum post-deposition annealing and with obtained dielectric function shown in Fig. 7 is chosen as representative example and dubbed “TiSiON”. However, the tunability and component versatility of these materials can enable optimization based on specific device application and geometry.

5.1 Plasmonics applications

We investigated scattering due to material plasmonic resonances analytically by applying Mie scattering theory for nanospheres of different radii (r). Figure 10(a) and 10(b) show the real permittivity of Au and TiSiON, respectively. The red dotted line indicates the wavelengths where the condition 𝜀’ = −2 is met, which describes the plasmonic resonance of a sphere in the quasi-static limit. It can be observed that the TiSiON material dispersion intersects this dotted line at multiple points, while the dispersion of Au intersects this line at only a single point.

 figure: Fig. 10

Fig. 10 Real component of dielectric function for (a) Au and (b) TiSiON with red dotted line to indicate ε’ = −2, the plasmonic resonance condition in the quasistatic limit of a sphere of each material. Mie theory is used to find the dipole scattering efficiencies of Au and TiSiON in (c) and (d), respectively, when modeled as a sphere of radius r = 80 nm, 100 nm, 120 nm with ε” = 0 in all cases.

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Figure 10(c) and 10(d) show the dipole scattering efficiencies in the idealized situation of zero optical losses for spheres of r = 80 nm, 100 nm, 120 nm found using the data from Fig. 10(a) and 10(b), respectively. The effects of realistic dispersion losses will be discussed in the next section. In the case of Au, there exists only a single dipole resonance from 0.3 to 2.0 µm for each radius condition. For TiSiON, there exists two distinct dipole resonances. This double-plasmon behavior is a unique phenomenon as it requires an anomalous real permittivity that cross the same resonance condition at multiple wavelengths. Although the real part of the permittivity of TiSiON nanolayers is similar to that of TiN nanolayers at shorter wavelengths [8], the reduced magnitude of real component of the permittivity at longer wavelengths, which induces the double-plasmon behavior, also reduces the quality factor for the surface plasmon resonance at these wavelengths. This makes the current materials platform more promising for broadband absorption enhancement device applications as opposed to sub-wavelength field guiding with surface plasmon polaritons.

5.2 Implications for broadband metamaterial absorbers

Metamaterial designs have large capability to control absorption and reflection properties of light. These devices are typically constructed with metals such as Au and Ag that are extremely limited in bandwidth because of their large reflectivity due to their large negative real permittivity that needs to be compensated for by complicated metamaterial structures that promote large plasmonic or surface plasmon resonances. Likewise, they are limited in application because of their lack of CMOS compatibility.

A demonstrated alternative plasmonic material at visible to near infrared wavelengths is stochiometric TiN. The design scheme targeted for thermophotovoltaics by Wei Li et al. [3] shows a broadband absorber with an average absorption of 95% over the range of 400-800 nm. This is accomplished by combining a planar film backing and ring-type metamaterial configuration. The TiN film backing absorbs largely at wavelengths below the screened plasma frequency and is covered by either a SiO2 or Si3N4 anti-reflection coating to eliminate reflections when the material behaves as a lossy dielectric. The reflections due to the metallic character are compensated by the dominate resonance of the TiN ring structure surrounding 700 nm. However, semiconductors used in thermophotovoltaics, such as Ge, SiGe, GaSb, and InGaAs, usually have a bandgap of 0.56-0.72 eV [22]. Naturally, these devices would benefit extremely from a broadband absorber with a high average absorption extending to wavelengths as large as 1.7 µm.

An advantage of these alternative anomalous materials is dielectric function tunability that allows reduced metallic character while still supporting plasmonic resonances that promote absorption. Likewise, because of the nature of the optical dispersion, simple meta-structures can produce dipole resonances at multiple wavelengths, which encourages broadband optical absorption responses. Equation (2) describes the power absorbed (Pabs) by a nonmagnetic material where ω is the frequency of light and |E| is the magnitude of the electric field integrated over the volume V, of the material.

Pabs=(1/2)ωε''|E|2dV

From this relationship it is favorable for power absorption from light to increase 𝜀” and |E| inside the material. Figure 11(a) shows the dielectric functions of Au, stoichiometric TiN, and the representative anomalous material. The reduction in magnitude of 𝜀’ for TiSiON relative to both Au and stoichiometric TiN decreases the reflectance of incident light. In addition, the 𝜀” remains like that of TiN and larger than that of Au at wavelengths above 0.5 µm. The skin depth (δ) quantifies the extent of light penetration into the material and is defined as in Eq. (3), where λ is wavelength and k is the imaginary component of the complex refractive index.

 figure: Fig. 11

Fig. 11 (a) Real and imaginary permittivity of Au (JC) [23], TiN (Palik) [24], and TiSiON. (b) Calculated skin depth for Au, TiN, and TiSiON using data from (a) and Eq. (3).

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δλ2πk

Figure 11(b) shows the calculated δ for each material from Fig. 11(a). Across the entire 0.3 to 2 µm wavelength range, δ of TiSiON is significantly larger than that of Au. Likewise, the δ of TiSiON is nearly twice as large as stochiometric TiN at wavelengths greater than 0.4 µm within this wavelength region. This combination of low metallic reflectance, large imaginary permittivity, and large skin depth is ideal for light absorption.

We investigated the potential for fabricated absorption due to plasmonic resonance analytically by using the dielectric function of each material, as displayed in Fig. 11(a), and applying Mie scattering theory for nanospheres of different radii (r) [25]. The absorption efficiencies (Qabs) for each material calculated from this method are shown in Fig. 12.

 figure: Fig. 12

Fig. 12 Mie theory absorption efficiencies of (a) Au (b) TiN and (c) TiSiON when modeled as a sphere of radius r = 40 nm, 80 nm, 100 nm, 120 nm.

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Although Qabs of Au is large at certain wavelengths, it is not broadband. It is determined with these geometries that, at maximum, Qabs of Au is larger than 1.5 from 0.3 to 0.55 µm and Qabs of TiN stays above 1.5 from 0.3 to 0.65 µm. In contrast, at maximum TiSiON maintains Qabs above 1.5 from 0.3 to 1.0 µm.

In the double plasmon materials, a further reduction of losses can promote an extremely broadband Qabs. Figure 13 shows the results of the same calculation as for Fig. 12, but with the value for the imaginary permittivity for each material replaced by 𝜀” = 3. In this case, Qabs for both Au and TiN remain relatively unchanged, but the TiSiON material can maintain Qabs above 1.5 from 0.3 to 1.7 µm, doubling the width of Qabs; hence the broadband plasmonic absorption in these materials can benefit dramatically from material studies that decrease the value of 𝜀” surrounding the secondary resonance. Comparing Fig. 10(d) and Fig. 13(c) it is clear that there is an optimal loss value that allows one to engineer the maximum broadband absorption over a desired bandwidth. This can be understood simply by the fact that if the losses are too small, then the two resonant peaks will not overlap effectively while in the opposite case (large losses) their absorption efficiency will be too low.

 figure: Fig. 13

Fig. 13 Mie theory absorption efficiencies of (a) Au (b) TiN and (c) TiSiON when modeled as a sphere of radius r = 40 nm, 80 nm, 100 nm, 120 nm with ε” = 3 in all cases.

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Naturally, more complex metastructure schemes can additionally be conceived to alter the peak locations in Qabs and the optimized loss value would vary depend on metamaterial component geometry. However, the broad resonances of a nanosphere with double-plasmon behavior serve as a basis for novel metamaterial designs. Likewise, nanosphere optical responses have been shown to be approximately equivalent to that of nano-cylinders with equal diameter and height [26,27], and these nano-cylinder structures can be readily fabricated with nanolithography methods.

6. Conclusions

We have shown that the dielectric function of optically robust TiN-based metal nitride nanolayer materials can exhibit an anomalous dispersion behavior over the visible to near-infrared wavelength regime that provides tunable metallic character from pure TiNx phases to completely dielectric ones with reduced losses. We show that this transition can be induced indirectly through reactive MSP by alteration of deposition conditions or directly through reactive MSP co-depositions with Ti and either Si or SiO2 targets. Likewise, the dielectric function can be further manipulated by post-deposition annealing. Nanolayers of these materials are Si-compatible and, depending on method of growth, stable up to extremely high temperatures. In addition, we have shown analytically through Mie theory that this material supports a unique double-plasmon resonance that is ideal for creating broadband optical responses, providing a new tool for plasmonic and metamaterial engineering.

Funding

National Science Foundation (ECCS 1709704, ECCS 1643118).

Acknowledgments

This work was supported by the NSF program “Tunable Si-compatible Nonlinear Materials for Active Metaphotonics” under Award No. ECCS 1709704 and the NSF EAGER program “Enhanced Solar Energy Conversion by Ultra-slow Photon Sub-diffusion in Aperiodic Media” under Award No. ECCS 1643118.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Figures (13)

Fig. 1
Fig. 1 Real (a) and imaginary (b) permittivity of titanium nitride nanolayers grown by room temperature MSP at high deposition pressures and with and without post-deposition annealing at 900°C.
Fig. 2
Fig. 2 Real (a) and imaginary (b) permittivity of titanium nitride nanolayers grown by MSP at room temperature and at 300°C at high deposition pressures.
Fig. 3
Fig. 3 Real (a) and imaginary (b) permittivity of titanium silicon oxynitride nanolayers grown by a MSP co-deposition with DC Ti and RF SiO2 targets with a DC:RF power ratio at a 300°C deposition temperature and 1.5 mTorr deposition pressure.
Fig. 4
Fig. 4 Real (a) and imaginary (b) permittivity of 4:1 DC:RF titanium silicon oxynitride nanolayers as a function of increasing post-deposition annealing temperature.
Fig. 5
Fig. 5 Real (a) and imaginary (b) permittivity of 4:2 DC:RF titanium silicon oxynitride nanolayers as a function of increasing post-deposition annealing temperature.
Fig. 6
Fig. 6 (a)-(g) Optical reflectance images of nanolayers on Si substrates deposited by DC Ti and RF SiO2 targets with a DC:RF power ratio 4:1 as deposited (a), annealed at 600°C (b), and annealed at 800°C (c), and 4:2 as deposited (d), annealed at 600°C (e), annealed at 800°C (f), and annealed at 1000°C (g). (h)-(n) Reflectance measurements of nanolayers on Si substrates deposited by DC Ti and RF SiO2 targets with a DC:RF power ratio 4:1 as deposited (h), annealed at 600°C (i), and annealed at 800°C (j), and 4:2 as deposited (k), annealed at 600°C (l), annealed at 800°C (m), and annealed at 1000°C (n).
Fig. 7
Fig. 7 Real (a) and imaginary (b) permittivity of tertiary compound titanium silicon nitride nanolayers grown by a MSP co-deposition with DC Ti and RF Si targets with a DC:RF power ratio at a 300°C deposition temperature and 1.5 mTorr deposition pressure.
Fig. 8
Fig. 8 Representative 2θ-θ X-ray diffraction scan showing peaks corresponding to the TiN cubic rock salt structure.
Fig. 9
Fig. 9 Real (a) and imaginary (b) permittivity as a function of frequency in eV of a phenomenological material system with a single Drude and Lorentz contribution to the optical response. Particular arrangement and strength of these two contributions results in a real component to the optical dispersion with two nearby crossings where 𝜀’ = 0.
Fig. 10
Fig. 10 Real component of dielectric function for (a) Au and (b) TiSiON with red dotted line to indicate ε’ = −2, the plasmonic resonance condition in the quasistatic limit of a sphere of each material. Mie theory is used to find the dipole scattering efficiencies of Au and TiSiON in (c) and (d), respectively, when modeled as a sphere of radius r = 80 nm, 100 nm, 120 nm with ε” = 0 in all cases.
Fig. 11
Fig. 11 (a) Real and imaginary permittivity of Au (JC) [23], TiN (Palik) [24], and TiSiON. (b) Calculated skin depth for Au, TiN, and TiSiON using data from (a) and Eq. (3).
Fig. 12
Fig. 12 Mie theory absorption efficiencies of (a) Au (b) TiN and (c) TiSiON when modeled as a sphere of radius r = 40 nm, 80 nm, 100 nm, 120 nm.
Fig. 13
Fig. 13 Mie theory absorption efficiencies of (a) Au (b) TiN and (c) TiSiON when modeled as a sphere of radius r = 40 nm, 80 nm, 100 nm, 120 nm with ε” = 3 in all cases.

Equations (3)

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ε(ω)=ε'(ω)+iε"(ω)= ε ω p 2 ω 2 i Γ D ω + j=1 n A j ω oj 2 ω oj 2 ω 2 +i γ j ω
P abs =(1/2)ωε'' | E | 2 dV
δ λ 2πk
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