Design of a gradient epsilon-near-zero refractory metamaterial with temperature-insensitive broadband directional emission

Directional control over the propagation of light (i.e., angular selectivity) is a fundamental capability in photonics with a broad range of applications, including photovoltaics,¹ solar thermal absorbers,^2,3 light emission,^4,5 sensing, and privacy.⁶ In these technologies, tailoring the angular range of emission and absorption is desirable. However, until recently, the spectral range of angular selectivity in photonic crystals and epsilon-near-zero (ENZ) metamaterials was limited. To address this challenge, researchers have established an approach to achieve broadband angular selectivity by layering directional photonic structures in a gradient stack, so that the property which dictates the spectral range of the angular selectivity changes across the thickness of the overall structure.^4,5 In the case of photonic crystals, broadband transmission at the Brewster angle is observed when stacking photonic crystals with gradually changing photonic bandgaps.⁴ In the latter case, layering materials with gradually changing ENZ frequency can result in broadband angular emission/absorption in the spectral range between the two ENZ frequency extremes.⁵ Both approaches represent advancements in broadband directional control; however, such capabilities have not been established in the harsh thermo-chemical environments associated with practical applications in thermal photonics.

Refractory oxides and nitrides are a promising class of materials to address this gap because they possess high melting temperatures, good chemical resistance, and a wide range of dielectric functions that are desirable for photonic applications.⁷ In inert environments, transition metal nitrides, such as titanium nitride (TiN), have become leading candidates for high-temperature solar absorbers due to their near-IR plasmonic behavior. TiN maintains excellent thermal stability, even when fabricated into periodic metamaterial arrays.^8,9 In addition to nitrides, there are several refractory oxides, such as hafnium oxide (HfO₂),¹⁰ that are commonly applied as both barrier and optically functional layers to extend the high-temperature operating range in air. Beyond conventional oxides, new materials, such as indium-doped cadmium oxide (In:CdO)¹¹ and indium tin oxide (ITO),¹² have shown tailored infrared ENZ frequencies based on growth conditions and doping levels.

Here, we design a refractory metamaterial that provides broadband directional control of thermal emission using a gradient ENZ approach and study the effect of temperature-dependent optical properties on the emission direction. We consider a multilayer stack of oxides that consists of nickel, magnesium, barium, hafnium, and zirconium. Our previous work demonstrated that a heterostructure containing two lattice-matched refractory oxides, MgO and BaZr_0.5Hf_0.5O₃ (BZHO), is stable up to 1100 °C in air.¹³ This photonic heterostructure overcame common high-temperature instabilities associated with oxidation, grain-growth degradation, and intermixing. Different crystal structures provided a barrier to intermixing, while lattice matching enabled high-quality epitaxial growth, thus mitigating degradation through grain growth. We also developed a high-throughput screening method for finding promising oxide pairs based on the principles implemented in selecting BZHO/MgO.

In this work, we make use of that materials screening method to design a refractory ENZ metamaterial with broadband angular selectivity made from MgO, BZHO, and NiO (Fig. 1). MgO and NiO exhibit a large difference in ENZ frequency, which makes broadband directional emission possible. Over this frequency range, there is an excitation of a leaky optical mode called the Berreman mode.^14–16 The longitudinal optical (LO) phonon frequency, which corresponds to the ENZ frequency, is varied linearly across the metamaterial as shown in Fig. 1(a). This structure enables broadband directional emission in the spectral range between the LO phonon frequencies of MgO and NiO. In our design, BZHO provides a barrier to mixing between MgO and NiO layers in the stack [Fig. 1(b)]. Numerical simulations of emissivity at 25 and 1000 °C show that the broadband angular selectivity is maintained at high operating temperatures, and BZHO has a negligible effect on the overall performance of the emitter. Finally, we discuss the limitations of the design (e.g., a reflective substrate is required) and potential fabrication routes to overcome them. Overall, this hybrid design, which takes advantage of the optical properties of MgO and NiO, and the diffusion resistance of BZHO, provides a pathway to directional emission at high temperatures.

The refractory ENZ design builds upon our prior work with BZHO/MgO superlattices, which exhibited high thermo-chemical stability.¹³ Here, we select NiO as a third material because it is soluble in MgO¹⁷ and has a different ENZ frequency than MgO, thus providing directional emission over a wide spectral range. Given the measured stability of BZHO/MgO, we expect that refractory oxides identified by our screening method should also exhibit enhanced high-temperature stability. Specifically, we expect that NiO and BZHO will not intermix at high temperatures for the same reason as MgO and BZHO. Incorporating Mg into the A-site of a BZHO lattice requires large formation energies. We hypothesize the same will be true for incorporating Ni in BZHO. Mg²⁺ and Ni²⁺ have similar ionic radii (72 and 69 pm), which are much smaller than Ba²⁺ (135 pm), and thus, incorporating Ni²⁺ into BZHO should be hindered by a similarly large formation energy.

Our refractory ENZ metamaterial consists of five Mg_1−xNi_xO layers (N = 5) for a total thickness of 750 nm. Each Mg_1−xNi_xO layer has a different stoichiometric concentration of Mg²⁺ and Ni²⁺ so that the LO frequency (ω_LO) linearly changes across the stack [Fig. 1(a)]. The real part of the relative permittivity (ε′) and the corresponding LO frequency of each proposed layer are shown in Fig. 2(a). Epsilon crosses zero twice, at each boundary of the Reststrahlen band, corresponding to the longitudinal optical (LO) and transverse optical (TO) phonon frequencies. However, intense directional emission, resulting from large electric field enhancements from the Berreman leaky mode, is only observed at the higher energy LO frequency because it has significantly lower optical losses (ε″) relative to the TO frequency.¹⁵ 

The TM-polarized emissivity of the metamaterial at 25 °C, calculated via the transfer matrix method, exhibits clear contributions from each layer as shown in Fig. 2(b). By stacking Mg_1−xNi_xO layers with varying cation concentrations and, thus, linearly changing the LO frequency, the directional emission provided by the Berreman leaky mode becomes a broadband effect between the LO frequencies of pure MgO and pure NiO.

The dispersion and local electric field enhancement of the Berreman mode depend on the layer thickness and lossiness. The thickness of each layer is optimized so that the peak emissivity, resulting from coupling to the Berreman leaky mode, occurs at an emission angle of ≈70°. At the long-wavelength edge of the gradient ENZ bandwidth, which corresponds to the LO frequency of pure NiO, coupling to the Berreman leaky mode is significantly weaker due to higher optical loss compared to MgO. This can be understood by comparing the relative values of imaginary permittivity (ε″) for NiO and MgO at their corresponding LO frequencies [see Fig. 2(a), bottom]. Higher optical loss results in weaker local field enhancement from the Berreman leaky mode and, thus, a lower peak emissivity as more Ni²⁺ is incorporated into the structure.

In between each Mg_1−xNi_xO layer, a thin 10 nm BZHO diffusion barrier is placed to prevent intermixing and preserve the LO frequencies of each discrete layer needed to observe broadband directional emission. Coincidentally, BZHO exhibits ENZ behavior in the same spectral range with an LO frequency of ≈15 μm. However, the contribution to the emissivity is negligible due to its small thickness of 10 nm. Even if the thickness of each BZHO diffusion barrier is increased to 100 nm, there is still a minimal effect on the emissivity (see Fig. S1).

This initial design is based on a five-layer structure, but the approach can be extended to a greater number of layers. Increasing the number of layers to 20 (N = 20) for the same total thickness provides a smoother emissivity over the ENZ bandwidth at 70° as shown in Fig. S2(a). Nevertheless, the five-layer design presented here provides broadband directional emission despite being relatively simple.

To understand how the ENZ bandwidth and angular selectivity of the structure change at high temperatures, we repeat the numerical study using the optical properties of MgO, NiO, and BZHO at 1000 °C. The gradient ENZ structure discussed above was designed using room-temperature optical properties for MgO,¹⁸ NiO,¹⁹ and BZHO.¹³ However, it is well known that the infrared optical properties of dielectrics can drastically change at high temperatures due to the relaxation of the crystal lattice and other effects.

The temperature-dependent permittivity of pure MgO (first layer) and NiO (last layer) is shown in Fig. 3(a). Increasing the temperature to 1000 °C produces a redshift of the LO frequency in both materials. However, because the redshift is small (<5%), the spectral bandwidth of angular selectivity remains similar overall. Specifically, the ENZ bandwidth changes from 13.8–16.8 to 14.0–17.5 μm. This minimal effect on the spectral range of angular selectivity is confirmed by simulating the emissivity at 1000 °C. Notably, the individual layer contributions at each LO frequency are less apparent, as increases in optical loss near the LO frequency provide a smoothing effect on the Berreman mode. Increases in optical loss are associated with higher values of the imaginary permittivity, which increase by a factor of 2.7 and 2.3 at 1000 °C for MgO and NiO, respectively [Fig. 3(a), bottom]. As a result of this smoothing effect, the emissivity of a five-layer (N = 5) and 20-layer (N = 20) structure, of the same thickness, show negligible differences [Fig. S2(b)].

The effects of temperature and emission angle on the emissivity are further illustrated in Fig. 4(a), which shows emissivity line scans at emission angles of 25° (off resonance) and 70° (on resonance) at 25 and 1000 °C. This result shows that the spectral bandwidth and selectivity of directional emission are both preserved. We also show the effect of total stack thickness (d) on the angle of peak emissivity in Fig. 4(b). The angle of peak emissivity increases with stack thickness. However, as the metamaterial gets thicker and attenuation increases, the stack becomes less directionally selective.

For temperatures above 1000 °C, we expect that the phonon scattering rate will continue to increase, leading to a higher optical loss in MgO and NiO. This will lead to weaker local field enhancement from the Berreman leaky mode and, thus, a lower emissivity. Nevertheless, the results presented here demonstrate a design in which directional emission is not highly sensitive to temperature changes. This property is important for several reasons, among those is that first principles calculation of optical properties at zero-temperature is significantly easier than at high temperatures.

Though the gradient ENZ design presented here is promising for applications at high temperatures, several challenges remained to be overcome. One key challenge is the necessity of a highly reflective and thermally stable substrate that can interface with the oxide metamaterial. The reflective substrate has a dual role: to provide high local field enhancements in the ENZ layers and to screen-out broadband angular-independent emission from the underlying substrate. In the above calculations, the substrate was assumed to be a perfect electrical conductor (PEC). Transitioning to a refractory metal, such as Ta, could provide comparable performance to a PEC substrate (see Fig. S3). A high-index dielectric substrate (a refractive index of 4) could similarly fill this role (see Fig. S4). The challenge arises in the growth/fabrication of the metamaterial with such substrates. To preserve high film quality and good oxidation resistance, the substrate should be lattice-matched to Mg_1−xNi_xO and BZHO.

As an alternative to a lattice-matched reflective substrate, it may be possible to leverage epitaxial liftoff to transfer the refractory metamaterial to another substrate. Sacrificial liftoff layers, such as the water-soluble Sr₃Al₂O₆²⁰ or solvent-soluble Ge,^21,22 could enable this transfer. Transfer of complex-oxide thin films has also been achieved through van-der-Walls epitaxy, which uses a graphene film between the growth substrate and oxide films to weaken out-of-plane bonding, enabling transfer to a new substrate.²³ 

In addition to addressing fabrication challenges, several improvements can be made to the design presented here. First, coupling to the Berreman leaky mode, which drives directional emissivity, is solely a TM-polarized effect. When accounting for TE-polarized light, the average directional emissivity drops. Achieving broadband directional emissivity for TE-polarized light would require mu-near-zero materials over the sample spectral range.^24,25 Additionally, for high-temperature technologies such as thermal photovoltaics, there is a general interest in the spectral and directional control of thermal emission at much lower wavelengths (1–5 μm). In our emitter, ≈15% of the total energy is emitted over the ENZ bandwidth at 1000 °C (compared to ≈2% for a blackbody). To achieve directional control at shorter wavelengths, a similar strategy discussed in this work could be explored but with tunable, mid-IR plasmonic materials. A potential candidate is In:CdO, which demonstrates a wide range of tunability over the ENZ frequency.^11,26

In summary, this work presented the design of a gradient ENZ metamaterial made with refractory MgO, BZHO, and NiO that provides broadband directional control of thermal emission. This structure is expected to have high thermal stability in air, based on an experimentally tested materials screening framework. Changes in the real and imaginary permittivity of MgO and NiO at 1000 °C do not significantly change the spectral bandwidth and selectivity of directional emission. Although promising, there are practical fabrication challenges such as the necessity of a reflective substrate that must be addressed to implement this structure. Provided these are addressed, the proposed gradient ENZ metamaterial should grant directional emitters and absorbers access to harsh thermo-chemical environments.

See the supplementary material for information regarding the effect of BZHO diffusion barrier layers on emissivity, the effect of number of layers on broadband direction emissivity, and the emissivity of a gradient ENZ metamaterial with a reflective Ta or arbitrary dielectric substrate.

This work was supported by the Department of Defense, Defense Advanced Research Projects Agency under Grant No. HR00112190005. The views, opinions, and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. This document has been cleared under the Distribution Statement “A” (Approved for Public Release, Distribution Unlimited). Additional support is by the National Science Foundation (NSF) Graduate Research Fellowship under Grant No. NSF DGE 1256260.