Tailoring the plasmonic properties of ultrathin TiN films at metal-dielectric interfaces &#x0005B;Invited&#x0005D;

Alessandra Catellani; Arrigo Calzolari

doi:10.1364/OME.9.001459

1. Introduction

Optical metamaterials are artificially engineered compounds that are optimized to manipulate light in terms of amplitude, phase and polarization, by a keen control of light-matter interaction [1]. Miniaturization of metal/dielectric interfaces or arrangement of structural elements at the material surface with subwavelength periodicity imparts to the system peculiar optical and electronic properties, different from those of the original constituents, that in most cases can not be found in nature [2]. The metamaterial thus obtained allows to control light at extremely small scales, and paves the wave to the design of compact and planar optical or sensing devices.

Among this class of artificial compounds, a particular intriguing subgroup is covered by hyperbolic metamaterials (HMMs) [3]: here, the principal characteristic is an indefinite, i.e. hyperbolic, dispersion of the refracted electromagnetic wavevector. This behavior originates from the fact that one principal component of their permittivity (or permeability) effective tensors has an opposite sign with respect to the other two principal components: thus, the product $ε_{/ /} \cdot i l o n_{⊥} < 0$ , where $ε_{/ /}$ and $ε_{⊥}$ are the parallel and perpendicular components of the dielectric tensor, respectively, with respect to the optical axis. This, along with the exploitation of confinement effects and the choice of the costituent compounds, offers several degrees of freedom to the design of the final device and determines working environment and range of application, which includes high-resolution imaging and subwavelength lithography [4], hyperlens [5], spontaneous photon [6] and thermal [7] emitters (see also Ref. [8]).

Research in the field of plasmonics is rapidly moving towards materials different from noble metals, that have too low melting temperatures and high electronic losses to be effectively employed in HMM [9]. Examples of promising alternative optical materials include 2D materials (e.g. graphene, black phosporus and transition metal dichalcogenides) [10–12], transparent conductive oxides (e.g. Al:ZnO, Ta:TiO₂) [13–16] and refractory nitrides and carbides (e.g. TiN, TiC, ZrN) [17]. In particular, it was recently shown that TiN can be profitably used as plasmonic material in the visible (vis) and infrared (IR) range, offering extraordinary mechanical stability over a large range of temperatures ( $\sim e q$ 2000 $^{o}$ C) and pressures ( $≃$ 3.5 Mbar) [18, 19]. Furthermore, TiN can be epitaxially grown in ultrathin films, due to its lower surface energy with respect to noble metals [20, 21].

In order to realize high-performance metamaterials, the coupling with a proper dielectric is crucial: the dielectric component should fulfil both structural (e.g. lattice match and low surface energy) and optical (e.g. frequency-dependent sign of the dielectric function) requirements so to allow for the deposition of ordered layers on the metallic surface (TiN) and the completion of the hyperbolicity condition $ε_{/ /} \cdot ε_{⊥} < 0$ . Meeting all of these requirements is a huge challenge and the characterization of TiN/dielectric properties is a mandatory step to design and control the characteristics of the final metamaterial. The optimal choice to build an HMM superlattice for applications in the vis-IR optical range would then be obtained exploiting the couple TiN and the nitrides. Group III-metal nitrides have been largely adopted in the past for optoelectronic devices [22]; more recently they indeed found application as the dielectric component in metal/dielectric superlattices for thermionic and plasmonic devices [18, 23, 24].

Inspired by the recent experimental work on ultrathin TiN/(Al,SC)N superlattices [18, 23, 25], we present a first principles study of the optoelectronic properties for this kind of interfaces, addressing in particular the possibility to optimize HMM performances, and the role of the MgO substrate. We further discuss the results obtained from and effective medium approximation in comparison with those obtained from first-principles calculations of periodic buried interfaces and we show that the full ab initio treatment is mandatory to properly describe ultrathin films.

Fig. 1 Scheme of a TiN/(Al,Sc)N superlattice deposited on MgO substrate. Gray, yellow and blue layers represent MgO, TiN and Al $_{0.7}$ Sc $_{0.3}$ N materials, respectively. Atomic structures of the simulated MgO/TiN and TiN/(Al,Sc)N interfaces are shown on the lateral sides.

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2. Method

All calculations are carried out with the Quantum-Espresso simulation package [26, 27] within the framework of density functional theory (DFT), by using the PBE generalized gradient approximation [28] to describe the exchange-correlation functional. Single particle wavefunctions are expanded in a planewave basis set up to an energy cut-off of 200 Ry; atomic potentials for each chemical species are described by means of norm-conserving pseudopotentials [29]. A uniform (20 $\times$ 20) k-point grid is used for summations over the 2D Brillouin zone. In the case of MgO and (Al,Sc)N compounds, we employed a recent pseudohybrid Hubbard implementation of DFT+U, namely ACBN0 [30], that profitably corrects the DFT energy bandgap [31] as well as the dielectric and vibrational properties of semiconductors [32]. The U values resulting from the ACBN0 cycle are: U(Mg $_{s}$ )=0.52 eV, U(O $_{p}$ )=8.30 eV, U(Al $_{s}$ )=0.05 eV, and U(N $_{p}$ )=4.76 eV, respectively.

TiN, MgO and (Al,Sc)N films are simulated in the rocksalt phase and along the [001] direction. In order to evaluate the different contributions to the optical response of the system, and to complement experimental results, [18, 23, 25] we performed two different sets of calculations: (i) a superlattice, where the system presents periodic buried interfaces, and (ii) an open structure, which better resembles an experimental thin film deposited on a substrate (see Fig. 1). Studying both buried short-period interfaces and films on a substrate allows us to evaluate and decouple different contributions, namely the effect of surfaces and/or of thickness on the electronic and optical properties of TiN films; furthermore it opens the way to propose novel systems such as the multilayer.

Extended structures are simulated using periodically repeated supercells. The TiN/(Al,Sc)N superlattice (i.e. periodic buried interfaces) is simulated including 10 layers of TiN(001) and 10 layers of (Al,Sc)N(001) in the supercell, which corresponds to 2nm-thick film per material. The same number of layers is used to simulate the single TiN/(Al,Sc)N interface (open structure); in this case 12 Å of vacuum is also included in the simulation cell to separate adjacent replica. The MgO substrate is modelled through a periodic slab composed of 15 layers (3 nm-thick), as shown in Fig. 1. The lateral periodicity of each unit cell (4.24 $\times$ 4.24)Å² is fixed at the lattice crystal of TiN(001), obtained from optimization of the corresponding bulk crystal [19]. All structures are fully relaxed until forces on all atoms become lower than 0.03 eV/Å $^{- 1}$ [33]. The optical properties of films and buried interfaces are determined using the epsilon.x code, contained in the Quantum-Espresso package, which implements a band-to-band independent-particle formulation of the energy-dependent Drude-Lorentz model for the dielectric function $\hat{ε} (E)$ , where both intraband (Drude-like) and interband (Lorentz-like) contributions are explicitly considered [15].

3. Results and discussion

The HMM samples realized in the experimental setup [18, 23, 25] are composed of a stacked alternation of ultrathin layers of TiN and (Al,Sc)N grown on MgO(001), as shown in Fig. 1. The three materials have the same cubic (rocksalt) crystal structure and are almost lattice matched: a $_{0}^{T i N}$ =4.24 Å, a $_{0}^{M g O}$ =4.21 Å, a $_{0}^{(A l, S c) N}$ =4.26 Å, for an Al content of 70%, where $a_{0}^{i}$ is the lattice parameter of i-th material. In order to gain insights on both the microscopic characteristics of the TiN/dielectric interfaces and on periodic superlattices, we separately simulated the single TiN/MgO and TiN/(Al,Sc)N interfaces, as well as the periodic TiN/(Al,Sc)N multilayer.

3.1. Single interfaces

TiN/MgO. The TiN/MgO interface has been simulated facing 2nm-thick film of TiN(001) on 3-nm-thick substrate of MgO(001), as shown in Fig. 1 (left panel). The atomic relaxation hardly modifies the structure of the two constituent materials, resulting in a sharp and abrupt interface, in agreement with the X-ray and TEM experimental evidence [18]. In particular, Ti atoms at the interface maintain their original coordination and do not form oxynitride compounds with the oxygen atoms of the substrate [21].

Fig. 2 Real (a) and imaginary (b) part of the complex dielectric function of TiN(001) film (black), MgO (001) substrate (blue) and TiN/MgO single interface (orange). Black (orange) vertical dashed lines mark the position of TiN (TiN/MgO) crossover energy E $_{p}$ , respectively. (c) Total and projected density of states of the TiN/MgO interface; color assignement follows panels (a) and (b). Zero energy reference in panel is set to the Fermi level of the interface. Vertical blue dashed lines mark the bandgap (E $_{g}$ ) of MgO.

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The optical properties of the TiN/MgO interface and of its separate constituent films are displayed in Fig. 2(a,b). Both components of the dielectric function of the interface closely resemble the TiN film ones: At low energies the ultrathin TiN film is metallic (i.e. $ε_{r} < 0$ ) up to the crossover energy E_p=2.33 eV, after which the film assumes a dielectric character (i.e. $ε_{r} > 0$ ). At the crossover energy, the ε_i also has a minimum: the condition $\hat{ε} (E_{p}) = ε_{r} + i ε_{i} \approx 0$ corresponds to a plasmon-like excitation in the visible range, in agreement with recent findings [20, 21]. The microscopic origin of this plasmonic excitation in TiN has been discussed in our previous works for both bulk [19] and thin film [21] phases. Briefly, the electron density of states (DOS) of TiN films close to the Fermi energy(E $_{F}$ ) is characterized by two contiguous groups of bands, labeled and in Fig. 2(c). Bands forming the multiplet have a predominant N( $2 p$ ) character, while bands of group mostly derive from Ti( $t_{2 g}$ ) orbitals [19]. The plasmonic behavior of TiN originates from intraband transitions of group- bands that cross the Fermi level, giving rise to the negative Drude-like tail in the real part of the dielectric function for $E \to 0$ . For energies E $> 2.5$ eV, the excitation of interband $\to$ transitions gives a positive contribution to the (negative) Drude component of ε_r that becomes globally positive at the crossover energy E_p. This corresponds to collective electronic excitations (i.e. plasmons) in the visible range that effectively involve only a fraction of the overall electron density. For this reason, these excitations are often known as screened plasmons. We refer to original papers for further discussions [19, 21].

The presence of the MgO substrate does not to modify this picture: the formation of the interface realizes a Schottky barrier where the Fermi level of the metal lies in the bandgap (E $_{g}$ =7.5 eV) of MgO, at $\sim 2.5$ eV from the conduction band minimum, i.e. with band groups and hosted in MgO bandgap. Thus, for low-energy excitations ( $\leq 2.5$ eV), only the states around the Fermi level (i.e. TiN states) are involved in the optical response of the interface, along the scheme described above. In this energy range, MgO states do not participate to optical excitations. The crossover energy E $_{p}$ of the interface almost coincides with the TiN one (see vertical in Fig. 2), indicating that the formation of the interface does not change the free electron density (i.e. the plasmonic character) of the TiN layer. At higher energy mixed TiN $\to$ MgO interband transitions cause the increase of the real part of the dielectric function of the interface in the UV range, with respect to the TiN film. Finally, for energies higher than the MgO bandgap direct interband transitions become optically active and contribute to the dielectric character of the system. Summarizing, the actual band alignment at the TiN/MgO interface prevents any contribution of MgO to the pristine optical properties of TiN in the visible range: the substrate acts as a passive transparent support for the plasmonic TiN film.

TiN/(Al,Sc)N. In the production of HMM heterostructures, the primary dielectric target to couple to TiN would be AlN. Being a nitride compound with a wide gap semiconductor and a low surface energy, AlN would be expected to generate reduced interface defects, giving thus rise to the possibility of pseudomorphic growth of flat layers. However, native AlN grows in a hexagonal (wurtzite) phase that does not easily match the structural parameters of TiN(001) [25]. This prevents the realization of stable and thickness-controlled multilayers. The inclusion of a small amount of Sc ( $x \leq 0.88$ ) is sufficient to stabilize the growth of a cubic phase of Al $_{x}$ Sc $_{1 - x}$ N alloy [34] on TiN(001) and to realize ordered superlattices. Here, following experimental Refs. [18, 25], we assumed Al $_{0.7}$ Sc $_{0.3}$ N as reference model for the TiN/dielectric interface. As for MgO case, the atomic relaxation does not impart any in-plane symmetry breaking or modification of the ideal Ti coordination.

The incorporation of Sc modifies not only the crystalline phase of AlN, but largely affects its electronic properties. For instance, the energy bandgap of Al $_{0.7}$ Sc $_{0.3}$ N reduces to E $_{g}$ =3.5 eV, i.e. well smaller than cubic AlN bulk (E $_{g}$ =5.2 eV),in agreement with the experimental findings E $_{g}$ (Al $_{0.7}$ Sc $_{0.3}$ N) $\sim$ 3.0 eV [18]. The reduction of the bandgap with respect to the AlN host corresponds to an increase of the static dielectric constant and a red-shift of the absorption edge, as shown in Fig. 3 (red lines).

Fig. 3 Real (a) and imaginary (b) part of the complex dielectric function of TiN(001) film (black), Al $_{0.7}$ Sc $_{0.3}$ N(001) (red) and TiN/(Al,Sc)N single interface (green). Dashed red lines correspond to the AlN layer in the rocksalt phase. Black(green) vertical dashed lines mark the position of TiN (TiN/Al $_{0.7}$ Sc $_{0.3}$ N) crossover energy E $_{p}$ ( ${E^{'}}_{p}$ ), respectively. (c) Total and projected density of states of TiN/(Al,Sc)N interface; color assignement follows panels (a) and (b). Zero energy reference in panel is set to the Fermi level of the interface. Vertical red dashed lines mark the bandgap (E $_{g}$ ) of (Al,Sc)N dielectric.

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The presence of a nitride layer imparts a net modification of the plasmonic response of the TiN film [green line, Fig. 3(a)]. In this case, the band alignment deriving from the formation of the interface generates a completely different scenario.Even though the Fermi level of TiN remains in the bandgap of the dielectric film, now the TiN band-group is at higher binding energies than the valence band maximum of Al $_{0.7}$ Sc $_{0.3}$ N [Fig. 3(c)], which lines up at $\sim 1.85$ eV below the system Fermi level. As a consequence, mixed (Al,Sc)N $\to$ TiN interband transitions take place at lower energies than for TiN, redshifting the plasmon energy to ${E^{'}}_{p} = 2.09$ eV. This explains the differences in the crossover energy for TiN (black line) and TiN/Al $_{0.7}$ Sc $_{0.3}$ N (green line), ${E^{'}}_{p} < E_{p}$ , shown in Fig. 3(a).

Fig. 4 Parallel ( $/ /$ ) and perpendicular ( $⊥$ ) components of the real part of the dielectric function ε_r, obtained from (a) effective medium theory and (b) slab buried interface.

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3.2. Periodic multilayer

Experimentally, periodic multilayers have been recently realized by stacking TiN and Al $_{0.7}$ Sc $_{0.3}$ N layers with thickness of 5-10 nm [18, 24, 25]. The mixed metal/dielectric hetrostructures thus obtained present a high structural anisotropy along the growth [001] direction (i.e. vertical stacking), which is associated to a hyperbolic optical response with an alternation of type-I and type-II dispersion. Provided that the incident wavelength is large compared to the size of the costituent layers, the mixed system can be described by an effective dielectric function $\tilde{ε}$ within the effective medium theory (EMT) [35]. In this case, we can easily distinguish two spatial components of the (complex) dielectric function: the direction parallel ( ${\tilde{ε}}_{/ /}$ ) or perpendicular ( ${\tilde{v a r e p s i l o n}}_{⊥}$ ) to the film surfaces, as shown in Fig. 1:

\begin{array}{l} {\tilde{ε}}_{/ /} = \frac{ε_{m} ε_{d}}{f ε_{d} + (1 - f) ε_{m}} \\ {\tilde{ε}}_{⊥} = f ε_{m} + (1 - f) ε_{d}; \end{array}

ε_m and ε_d are the dielectric functions of the metal and dielectric constituents, respectively. The filling fraction

f = d_{m} / (d_{m} + d_{d})

indicates the volume fraction of the metallic phase within the multilayer, where d_m and d_d the thickness of the metallic and dielectric layers.

Here, ε_m and ε_d are calculated from first principles for TiN and Al $_{0.7}$ Sc $_{0.3}$ N bulk crystals separately, by using the same approach described above; f is set to 0.5 that corresponds to an equal amount of metal and dielectric compounds, as in the experimental samples [18]. Results are summarized in Fig. 4(a). The structural spatial anisotropy of the heterostructure clearly reflects on the optical response: for $E < {E^{'}}_{p}$ the parallel component of the dielectric function is negative (i.e. metal-like) as for the single interface, while the out-of-plane component ${\tilde{ε}}_{⊥}$ is positive (i.e. dielectric-like). This condition corresponds to a type-II hyperbolic metamaterial [Fig. 4(a), gray area]. In the energy range [2.09–2.50] eV the opposite condition takes place: ${\tilde{ε}}_{⊥} < 0$ and ${\tilde{ε}}_{/ /} > 0$ (cyan area) identify a type-I HMM [36]. Interestingly, E=2.50 eV is the plasmon energy of TiN bulk [19]. For higher energies both TiN and (Al,Sc)N have a dielectric character and consequently the multilayer itself act as a dielectric. For $E > 7$ eV both components of effective permittivity are almost zero. The energy alternation of the hyperbolic behavior of the stack perfectly reproduces the experimental results [18] that report a type-II dispersion for E $< 1.9$ eV ( $λ > 650$ nm) and type-II character in the range 2.07-2.30 eV ( $λ \in [540 - 600]$ nm). More closely, the simulated permettivity $ε_{/ /}$ =-2.1 at 1.8 eV (λ=650 nm) and $ε_{/ /}$ =1.35 at 2.33 eV (λ=532 nm) perfectly match the experimental values $ε_{/ /}$ =-2.3 and $ε_{/ /}$ =1.27 at the same energies for the TiN/Al $_{0.7}$ Sc $_{0.3}$ N multilayer characterized in Ref. [24].

It is worth noticing that the filling fraction f is not associated to any specific layer thickness, this means that within the EMT formulation the optical response of the multilayer depends on the metal-to-dielectric ratio and not on the thickness of its components. In order to investigate the role of the composition on the optical properties of the multilayer, we calculated the sign function $S (E, f) = R e [{\tilde{ε}}_{∥}] R e [{\tilde{ε}}_{⊥}] / | R e [{\tilde{ε}}_{∥}] R e [{\tilde{ε}}_{⊥}] |$ , as a function of the incoming radiation energy E and the filling fraction f.The results are summarized in Fig. 5. Black areas identify the regions where the sign function $S$ is negative, i.e. where the multilayer has a hyperbolic behavior; the horizontal dashed line marks the value $f = 0.5$ , whose optical properties are shown in Fig. 4a. The optical hyperbolicity depends on the energy of the incident radiation as well as on the composition in a non-obviuos way. Values f = 0 and f = 1 correspond to dielectric-only (i.e. Al $_{0.7}$ Sc $_{0.3}$ N) and metallic-only (i.e. TiN) samples, respectively, that are intrinsically non-hyperbolic over the entire energy spectrum. For all other compositions different hyperbolic dispersions alternate to standard (dielectric or metallic) character as a function of incoming radiadion energy. From Fig. 5 it follows also that the hyperbolic behavior in the THz-visible range (e.g. E $<$ 3.0 eV) requires an almost uniform combination of metal and dielectric components.

Fig. 5 2D plot of sign function $S (E, f)$ as a function of the incoming radiation energy E and the filling fraction f. Black areas identify regions where S is negative, i.e. where a hyperbolic behavior is expected. Horizontal dashed line corresponds to the selected filling fraction $f = 0.5$ , whose optical properties are shown in Fig. 4a.

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We can thus conclude that EMT is able to reproduce the experimental results, at least for samples composed of layers thicker than 5nm [18]. On the other hand, thinner layers may require the explicit treatment of quantum effects not included in the EMT approach. In order to estimate the effect of quantum confinement in the case of ultrathin layers, we compare the results from EMT with the results deriving from first-principles calculations of the periodic buried TiN(2nm)/Al $_{0.7}$ Sc $_{0.3}$ N(2nm)interface. This composition formally corresponds to a filling fraction $f = 0.5$ in EMT, as in the case discussed above. Albeit such ultrathin multilayers have not been realized yet, 2nm-thick films of TiN have been successfully grown on MgO substrate, indicating a metallic character and a plasmonic resonance in the visible range. Thus, it is interesting to understand how the hyperbolic dispersion is modified by the thickness reduction and whether EMT still holds in this ultrathin regime.

The DFT results of the simulated dielectric function in the direction parallel and perpendicular to the interface are displayed in Fig. 4(b). First principles spectra have evidently similarities with EMT results in particular: (i) the parallel component $ε_{/ /}$ (black curve) is very similar to the single interface [Fig. 3(a)], (ii) for $E > 2.3$ eV the superlattice has an overall dielectric character, (iii) a strong anisotropy with respect to the optical axis (i.e. stacking direction) is present. However, a few quantitative differences clearly appear: first of all, the crossover energy of $ε_{⊥}$ is strongly redshifted to E $_{p}$ =0.7 eV. Further, we do not observe anymore the sign inversion of the parallel and perpendicular components responsible for the type-I character of the system, which exhibits instead a standard metallic behavior (brown area). These differences indicate the important role of a proper evaluation of the dielectric component in the realization of good HMMs: while metallic films maintain their major plasmonic properties even at ultrathin thickness [20, 21], dielectric compounds necessitate of higher thicknesses ( $> 2$ nm) to exhibit a dielectric screening similar to the bulk (or thick film) phase. This also implies that, while EMT well reproduces the overall optical properties of the (thicker) experimental stacks ( $\sim 5$ nm, [18]), it would not be accurate enough to describe multilayers as thin as those considered here (2nm).

4. Conclusion

We presented a first principles study of the optoelectronic properties of ultrathin (Al,Sc)N/TiN interfaces and compare to recent experimental data in view of potential HMM application in the vis-IR range. We discuss the role of the substrate and show that a MgO substrate does not modify the overall properties of the plasmonic layer. On the contrary, coupling with nitride semiconductors changes the optical response of the metallic film. A detailed comparison of the effective medium approximation against a full ab initio treatment reveals the important contribution of the dielectric film, whose thickness fixes a structural lower limit to the hyperbolic behavior of the metamaterial.

Funding

European Union Seventh Framework Programme (265073 (ITN-Nanowiring)).

Acknowledgments

The research leading to these results has received partial funding from the European Union Seventh Framework Programme under grant agreement No. 265073 (ITN-Nanowiring).

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Tailoring the plasmonic properties of ultrathin TiN films at metal-dielectric interfaces [Invited]

Abstract

1. Introduction

2. Method

3. Results and discussion

3.1. Single interfaces

3.2. Periodic multilayer

4. Conclusion

Funding

Acknowledgments

References

Cited By

Figures (5)

Equations (1)

Optical Materials Express