Absorption and scattering in perfect thermal radiation absorber-emitter metasurfaces

Detailed spectral analysis of radiation absorption and scattering behaviors of metasurfaces was carried out via finite-difference time-domain (FDTD) photonic s imulations. It revealed that, for typical metal-insulator-metal (MIM) nanodisc metasurfaces, absorbance and scattering cross-sections exhibit a ratio of fabs/fsca = 1 at the absorption peak spectral position. This relationship was likewise found to limit the attainable photo-thermal conversion efficiency in experimental and application contexts. By increasing the absorption due to optical materials, such as Cr metal nano-films typically used as an adhesion layer, it is possible to control the total absorption efficiency [ = fabs/fsca and to to make it the dominant extinction mechanism. This guided the design of MIM metasurfaces tailored for near-perfect-absorption and emission of thermal radiation. We present the fabrication as well as the numerical and experimental spectral characterisation of such optical surfaces.


Introduction
Radiation absorption in metal-insulator-metal (MIM) metasurfaces, which generally consist of a metal back-plate, dielectric layer, and a metal nano-structure, is currently applied for realizing a great variety of efficient photo-thermal energy converter designs . Such converters also show significant promise in the mid-infrared (IR) wavelength range, where they are used as both IR radiation sources as well as detectors, notably for applications in optical sensing of volatile organic compounds (VOCs) [27][28][29][30][31][32][33][34][35][36][37]. Also, owing to their spectrally selective emissivity, metasurfaces can be harnessed as passive yet efficient radiative coolers at specific atmospheric IR transmission windows.
In most studies, the absorbance exhibited by a MIM metasurface is among its most important properties -implicitly treated as = − , where is energy incident on the sample ( = 1 in the normalised presentation), whereas is the reflectance. This absorption relies on dissipation of optical energy in metals, although realization of perfect absorption is also considered using epsilon near zero (ENZ) materials [38][39][40][41][42] with permittivity ≡ ˜2 → 0. Similarly, coupling of ENZ and a meteasurfaces provides a viable path for attaining a highly absorbing layers [40]. For example, indium tin oxide (ITO) is a notable ENZ material candidate, however, its operation wavelength is highly dependent on specifically tailored optical constants. Therefore, precise control over dopant concentrations becomes an acute challenge in achieving a well-defined ENZ wavelength. In designing metasurfaces, nano-structures and functional layers are usually treated rigorously, but the absorbance in the metal back plate of a MIM structure is scrutinised to a far lesser degree due to experimental difficulties in directly measuring the fraction of optical energy absorbed in it. The metal back plate is understood as a reflector with negligible transmittance owing to its considerable thickness. Hence, the scattered portion of radiation energy is either ignored or not explicitly accounted for, since it is assumed to be incorporated in or and is distributed among them.
As illustrated in Fig. 1, the relevant optical power balance equation is = + + + and ( − − ) corresponds to the extinction = + , which accounts for all the energy removed from a propagating beam in a far-field measurement. In this representation corresponds to the specular and to the diffuse reflectance respectively. Due to a zero transmittance = 0 of the MIM metasurface, both and manifest as a backward reflection of light. In the case of nanoparticles (nanodiscs in this work), their plasmonic resonance-related optical properties are derived from the Mie scattering by the structures. The the resonance bandwidth is defined by scattering rather than the inherently broadband absorption exhibited by electron plasmas in metals [43][44][45][46][47][48][49].
Our previous reports on emissivity of metasurfaces with 10-nm-thin insulator layers confirmed that their thermal radiation spectral output qualitatively follows Kirchhoff's law [30]. However, it was noticed that thermal radiation emittance from metasurfaces was quantitatively lower than would be expected if Kirchhoff's law was rigorously obeyed, given the near-perfect antireflectance exhibited by the structure. This prompted the present study. MIM metasurfaces confine a significant portion of the resonant electro-magnetic field in the insulator layer, but a fraction of radiation energy is nevertheless localized around nanodsics and subject to scattering. Therefore, scattering effects are expected to notably effect metasurface optical response and its characterisation, and their control is vital to realization and demonstration perfect optical absorber performance. This issue was highlighted by Maccaferri et. al and a mitigation strategy by multi-layered metasurface design was proposed to spectrally separate the absorption and scattering effects [50].
The target of this study is a comparative analysis of absorption and its cross-section in fabricated MIM samples and FDTD simulations. It involved extensive metasurface parameter sweepsincluding disk diameter , period , insulator thickness -and optimisation of the final design that was subsequently fabricated. Such analysis also revealed the effect of scattering on the thermal radiation emission behavior of such metasurfaces. According the Kirchhoff's law of thermal radiation, emittance is related to the absorbance = but not to the scattered portion of energy . Therefore, by increasing the absorption cross-section compared to the scattering one, the radiation emissivity would be also expected to increase. This conjecture is put to the test by way of numerical analysis and experimental verification, whereby we show interplay of the scattering and absorbance contributions in optical response of a MIM metasurface and the way to maximise absorbance towards a true perfect absorber with → 1 (or = = 100%).

FDTD simulations
FDTD simulations were performed using a commercially available solver software (AN-SYS/Lumerical) on a homemade workstation with Dual CPU (AMD EPYC 7302 16 core × 2), 512 GB (32 GB × 16) of DDR4 memory. To simulate metasurface response in a broad wavelength range from visible to mid-infrared (MIR) wavelengths, material permittivity data for Au, Cr and SiO 2 reported by Palik was employed [51]. In this study, reflectance spectra simulations were performed using a plane wave source set to illuminate the MIM structures from the top nanodisk-patterned side, incident along z-axis. The reflection readout monitor was placed above the light source. The MIM structure was framed along the x-and y-directions using periodic boundary conditions, whereas a perfectly matched layer (PML) was used for termination along the the z-coordinate axis. Absorption and scattering cross-section simulations Fig. 1. Schematic illustration of the redistribution of incident optical energy once it impinges onto the MIM metasurface. When calculating absorbance , scattered energy portion is usually incorporated into reflectance or transmittance so that their total ammounts to unity + + = 1. were conducted on same configuration of MIM structures, key difference being that a total-field scattered-field (TFSF) light source was initialized. Two sets of power monitors were placed inside and outside of the TFSF source volume, respectively for calculating the absorbed and scattered optical powers.

Fabrication of metasurfaces
MIM structures were defined on a mirror-polished Si wafer substrate surface by first depositing a 5 nm Cr adhesion layer and 200 nm Au reflector metal films by thermal evaporation. Then, either 5 nm or 50 nm of Cr and 100, 150, 200 nm of SiO 2 were deposited using electron beam (EB)-evaporation. Electron beam lithography (EBL) was used to define periodic nanodisk patterns with individual feature diameters ranging form 600 nm to 4000 nm over 1 × 1 mm 2 areas in a spin-coated ZEP520A positive tone resist. Pattern development was again followed by thermal evaporation deposition of 5 nm or 50 nm thickness Cr adhesion/absorber film, followed by 50 nm thickness of Au. Then, resist lift-off was performed using a heated organic solvent, N-Methyl-2-pyrolidone (NMP) at 100 • C, until a metal layer deposited over the resist fully removed. Lastly, MIM metasurface samples were washed in acetone and methanol and blow-dried in air.

Optical measurements
Metasurface reflectace characterization was performed using a FTIR spectroscope system (FTIR-6600) with a microscopy attachment unit IRT-1000. Thermal radiation emission was likewise measured with the same FTIR-6600 and IRT-1000 setup by using the MIM metasurface as an external illumination source, connected to the spectroscope via a side port. The reference for reflection was a Au-mirror (98% reflectance at MIR wavelengths) and a paint with 94% emissivity was employed as a blackbody radiation standard. For best comparability the paint was applied directly onto the MIM sample chips near the 1 × 1 mm 2 metasurface areas. Heating in thermal radiation output measurements was applied to the substrate by placing on a Peltier device and fixed with a thermal conductive grease. The devices were heated up to 150 • C. Prior to measurement each sample was allowed to reach a steady thermal state over the course of at least a 30 minute a settling time. Figure 2 shows FDTD simulated extinction ≡ 1 − , as well as absorption, scattering and extinction cross-section (respectively abs , sca , ext ) spectra of MIM metasurfaces with fixed = 400 nm disc diameter and = 800 nm period values, but varying SiO 2 spacer thicknesses. At this period-to-diameter ratio of / = 2 the interaction between adjacent nanodiscs (plasmonic gap mode) is negligible. Even if a collective grating effect is present, the optical properties of the metasurface are primarily defined by the interaction between dipole resonance of the individual nanodiscs and their induced mirror-charge oscillations in the metal ground plate [52]. Therefore, when the spacing between nanodisc and ground plate become smaller, the dipole-induced interaction is enhanced, causing a red-shift in the resonance wavelength. Both absorption and scattering are defined by the resonant interaction between a nanodisc and ground plate; sca increases for a thicker SiO 2 layer. This series of simulations revealed that both abs and sca are prominent at the minimum specular reflectance condition when overall extinction = 1 − is at its maximum.

Results and discussion
This behavior is elaborated further in Figure 3 (a), which shows maximum abs , sca , ext at resonance wavelength plotted as a function of SiO 2 insulator thickness. The absorption cross-section abs rises until = 30 nm, but starts to decrease when thicknesses of SiO 2 are increased further. At the same time, the scattering cross-section sca continues to increase up to a considerably higher = 150 nm SiO 2 thickness. As shown in Figure 3 (b), at maximum extinction = 1 − , the absorption cross-section abs is likewise at its peak, yet the absorption/scattering cross section ratio = abs / sca at best becomes equal to 1.
The effect of MIM metasurface configuration on resonant mode localization is revealed by FDTD derived cross-sectional view plots in Figure 3 (c). It is evident that, until SiO 2 spacer thickness is at or below = 30 nm, the majority of the optical field is tightly confined inside the insulator layer. However, as thicknesses become larger, the localization in the insulator layer is diminished, and modes start to exhibit a more pronounced dipolar character, typical for isolated nanodisk plasmonic structures. A majority of the optical field portion localized in the insulator layer is bound to eventually be converted to thermal energy in the free-carrier plasma of metals in the MIM structure. However, the portion loosely confined around a nanodisc particle is liable to re-radiated into free space, and should be considered as scattered. Hence, for our = 400 nm disc diameter metasurfaces, = 30 nm insulator thickness defines a delimiting line between the absorption dominated mode ( ≤ 30 nm) and primarily scattering mode for ≥30 nm. Figure 4(a) summarizes FDTD simulated reflectance and absorbance/scattering behavior as a function of a comprehensive MIM metasurface parameter study, including sweeps of SiO 2 thickness from 10 to 100 nm in 10 nm increments, disc diameter from 400 to 800 nm in 100 nm steps, and the ratio of / from 1.5 to 3.0 in 0.5 steps. In both and = abs / sca plots, minimum reflectance (i.e. maximum extinction ) condition is observed along a relatively narrow parameter range band, corresponding to bright-yellow areas. This minimum reflectance condition closely matches the abs / sca = 1 dividing curve (white-band) between where the metasurface is primarily absorbing (red area) and mainly scattering (blue area). Overall, increasing the disc diameter relaxes the constraints on SiO 2 thickness , so that comparable localization can be achieved for larger insulator spacings. Furthermore, increasing nanodisk pattern periods tends to similarly increase the apparent contribution of absorbance, but this is likely due to a simple decrease in the number of dipolar scatterers per unit surface area.
When all minimum reflectance data points are plotted against abs / sca , as shown in Figure 4 (b), all the resulting dependences ca be readily fitted by the same Gaussian curve. This series of detailed FDTD simulation results reveal that at any geometrical condition, the MIM metasurfaces follow the same rule for the relationship between abs and sca . This tendency is of paramount importance and limits the achievable maximum of at the perfect anti-reflection → 0 condition. Panels in Figure 5 show abs / sca relationships with abs , sca , and ext , respectively, each normalized by the resonance wavelength. This graph reveals the maximum attainable absorbance, scattering and total extinction cross-section for a selected efficiency . All the plotted data points are clustered around the abs / sca = 1 condition. It is important to note that the maximum abs appears at abs / sca ≥ 1, whereas the maximum sca appears at abs / sca ≤ 1. Consequently, the maximum of ext is situated at abs / sca = 1. Estakhri et. al reported that gold/SiO 2 core-shell structures always exhibit maximum abs / 2 at abs / sca = 1 as well [44]. Therefore, the observed tendency of sca to be tied to abs is expected and is defined by general plasmonic particle scattering dynamics.
While the extinction cross-section ext underlies the extinction = 1 − , it is nevertheless challenging to maximize the abs at the minimal reflectance. This is a severe impediment for the realization of true perfect absorption → 1, and, by extension, perfect thermal emitters with emittance = as per Kirchhoff's law of thermal radiation. From the simulated far-field distribution of scattered radiation, even though specular reflection is dominant in the FDTD analysis of ideal structures, it can be recognised that there is appreciable output at angles up to 40 degrees from the normal incidence. Therefore it is required to separate the specular reflection from scattering for further qualitative analysis that would be predictive of metasurface behavior as observed in the far-field.

Increasing abs using an absorption layer: model and experiment
Model. One possible approach for increasing the total absorption cross-section involves increasing the absorbance of electromagnetic radiation in metasurface materials. The electricomagnetic field localized inside the SiO 2 insulator layer decays primarily the ohmic loss of the metals in MIM structure. However, Cr metal, widely used as an adhesion layer for noble metal plasmonic structures, exhibits a 5 times higher resistance than that of Au. This higher ohmic loss is expected to increase the rate of optical damping, thereby limit the fraction of energy that is available to be re-radiated by way of scattering to free-space. On the other hand, increasing the conductivity of the insulator layer causes the plasmon resonance to disappear [11]. Therefore, it is important not to compromise insulation between the metal reflector layer and the nanodiscs comprising a MIM structure.
In a previous study we have shown that the addition of Cr notably increased the extinction = 1 − of a metasurface even for layer thicknesses as low as 5 nm [9]. Therefore, it is expected that when the thickness of a Cr adhesion layer is increased further, the absorption cross-section also would be augmented. Figure 6 shows the results of FDTD simulations with different Cr layer thicknesses ranging between 0 nm and 50 nm. There was a clearly observable departure from the abs / sca = 1 condition, denoted by Δ, as the amount of Cr was increased. Indeed, Δ increased from 1 when adhesion layer effects were disregarded, up to 1.25 when Cr layer thickness was 50 nm. These simulation results strongly suggest that the absorption/scattering ratio can be adjusted by controlling the thickness of an absorption layer interspersed between insulator and Au on both sides of the MIM stack. As mentioned previously, then plasmon resonance vanishes if the electric conductivity of insulator layer is increased. However, this MIM structure with Cr absorber layers ensures that the SiO 2 layer insulation between both metallic parts of the MIM structure is maintained.
Experiment. We experimentally tested the effect of Cr absorption layer inclusion in a metasurface. MIM samples were made with 5 nm and 50 nm Cr adhesion layer thicknesses, as illustrated in the inset of Figure 6. In order to benchmark experimental finding against FDTD simulation results, other parameters of the fabricated samples were varied as well -thicknesses of SiO 2 insulator layers were 100, 150, 200 nm, disc diameters ranged from 600 to 4000 nm (with a 50 nm increment up to 2000 nm diameter, and 100 nm increment between 2000 nm and 4000 nm). The measured optical reflectance and thermal radiation emission spectra are shown in Figs. 7 and 8 for 5 nm and 50 nm Cr thickness cases, respectively. As predicted by FDTD simulations, the SiO 2 thickness alters the Au disc diameter value at which a near-perfect absorption condition is achieved. For a = 100 nm SiO 2 thickness, the mimimum reflection resonance was situated at ∼ 3.5 m; for 150 nm -∼ 4.5 m; and for 200 nm -∼ 6.5 m, respectively. For thinner 5 nm Cr layers, reflectance and radiation emission spectra closely mirror each other. However, the emittance was unable to exceed the 80% black body value, even when a metasurface exhibits near total reflectance suppression. This divergence between measured optical extinction and radiation emission is most apparent at higher wavelengths, likely due to lower optical absorbance of Au in that spectral region.
When Cr thickness was increased to 50 nm to aid in absorbance, spectral behaviors changed drastically. The reflectance at shorter wavelengths was further suppressed due to absorption in Cr, although this also involved the reduction in metasurface quality factor and an increased resonance linewidth. Furthermore, the minimum anti-reflection parameter range became broader than that for a thinner Cr layer. In case of SiO 2 = 100 nm, reflectance became less than 10% throughout the 2-to-6 m wavelength window. The thermal radiation output was also considerably improved compared to the MIM design using 5 nm Cr thickness, with maximum radiation exceeding 90% emittance. This illustrates that, due to absorption in the Cr layer, absorbance in MIM pattern became dominant relative to scattering. This can serve as a guideline for designing metasurfaces that perform closer to the true perfect absorption condition → 1.
Other possible metals for controling MIM absorbance as alternatives to chromium, which, as perviously mentioned, has a 5 times larger resistance than gold, are: Ti with 17 times larger resistance, Bi 45 times, and Mn 105 times. Titanium is also frequently used as an adhesion layer between Au and SiO 2 , and it is usually considered that its detrimental effect on plasmonic properties of Au is smaller than Cr. Furthermore, not only the conductivity of a metal, but also its optical permittivity should be considered for the realization of true-perfect absorber, hence, a perfect thermal black-body emitter = = 1 (100%).

Conclusions and outlook
In this study, we have quantitatively analyzed the scattering effects by numerical modeling as well as fabrication and characterization of MIM metasurfaces. We observed the considerable effect backwards scattering has on the optical response of metasurfaces, hence it is a prominent feature that cannot be ignored in their design. Also, there is further room for improvement in removing the specular reflection of metasurfaces, guided by detailed FDTD analysis. Light scattering under slanted incidence is the next required step for analysis of MIM response and can be achieved at a quantitative level using FDTD modeling. We show that it is possible to increase the absorption cross section via use of nano-thin layers of metals with strong absorbance such as Cr. This point was confirmed experimentally by showing that a higher Cr adhesion layer thickness was able to drastically improve thermal radiation output efficiency from MIM metasurfaces. Thermal radiation due to a large enhancement of infrared absorption together with a strong coupling disk and base-plate in MIM metasurfaces [25,37] provides a promising approach to realize a perfect absorber at the IR molecular fingerprinting spectral range with wide applicability in diverse sensing contexts.