Omnidirectional wavelength selective emitters/absorbers based on dielectric-filled anti-reflection coated twodimensional metallic photonic crystals The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Yeng, Yi Xiang, Jeffrey B. Chou, Veronika Rinnerbauer, Yichen Shen, Sang-Gook Kim, John D. Joannopoulos, Marin Soljacic, and Ivan Celanovic. “Omnidirectional Wavelength Selective Emitters/absorbers Based on Dielectric-Filled Anti-Reflection Coated Two-Dimensional Metallic Photonic Crystals.” Edited by Eva M. Campo, Elizabeth A. Dobisz, and Louay A. Eldada. Nanoengineering: Fabrication, Properties, Optics, and Devices XI (August 28, 2014). © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) As Published http://dx.doi.org/10.1117/12.2067796 Publisher SPIE Version Final published version Accessed Thu May 26 18:39:14 EDT 2016 Citable Link http://hdl.handle.net/1721.1/97550 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Detailed Terms Omnidirectional wavelength selective emitters/absorbers based on dielectric-filled anti-reflection coated two-dimensional metallic photonic crystals Yi Xiang Yeng*ab, Jeffrey B. Chouc, Veronika Rinnerbauerd, Yichen Shena, Sang-Gook Kimc, John D. Joannopoulosab, Marin Soljačićab, Ivan Čelanovićb a Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; b Institute of Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; c Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; d Johannes Kepler University, Institute of Semiconductor and Solid State Physics, Altenbergerstraße 69, 4040 Linz, Austria ABSTRACT We demonstrate designs of dielectric-filled anti-reflection coated (ARC) two-dimensional (2D) metallic photonic crystals (MPhCs) capable of omnidirectional, polarization insensitive, wavelength selective emission/absorption. Up to 26% improvement in hemispherically averaged emittance/absorptance below the cutoff wavelength is observed for optimized hafnium oxide filled 2D tantalum (Ta) PhCs over the unfilled 2D Ta PhCs. The optimized designs possess high hemispherically averaged emittance/absorptance of 0.86 at wavelengths below the cutoff wavelength and low hemispherically averaged emittance/absorptance of 0.12 at wavelengths above the cutoff wavelength, which is extremely promising for applications such as thermophotovoltaic energy conversion, solar absorption, and infrared spectroscopy. Keywords: Photonic crystals, selective emitter/absorber, thermal emission, nanophotonics, high-temperature. 1. INTRODUCTION Naturally occurring materials usually exhibit thermal emission profiles that are broadband, and have a magnitude far weaker compared to the ideal blackbody. This is inefficient for many applications, for instance as an infrared source in sensing applications,1,2 as an emitter in thermophotovoltaic (TPV) energy conversion,3,4 and as a solar absorber.5,6 For many of these applications, it is desirable to accurately control thermal radiation such that thermal emission occurs only in certain wavelength ranges over an optimum angular spread. For instance, TPV energy conversion systems benefit from the use of omnidirectional polarization insensitive selective emitters,4 while solar absorbers that possess angularly selective absorptance are more efficient.6 To-date, various one-dimensional (1D),2,7–9 2D,10–17 and 3D18–20 periodic structures have been investigated both theoretically and experimentally in order to achieve accurate control of thermal radiation. The first class of these relies on excitation of surface phonon-polaritons,7 surface plasmon-polaritons,2,11,21 and localized plasmon resonances.22 These mechanisms usually result in very sharp and narrow thermal emission linewidths with respect to wavelength, and can be designed to emit over restricted,7,21 or wide polar angles.16,22 Thermal emission can also be enhanced by coupling to magnetic polaritons to obtain narrowband emission over wide polar angles.23 In certain applications, for instance as a selective emitter in TPV energy conversion systems, it is more advantageous to possess broader emission bandwidth such that high emittance is retained at wavelengths λ smaller than a particular cutoff wavelength λcut, while maintaining ultra-low emittance at λ > λcut over all exitance angles and polarizations. In this respect, metamaterial designs based on metal dielectric stacks9 and 2D metallic pyramid arrays15 show great promise. *[email protected]; phone +1-617-324-6442 Nanoengineering: Fabrication, Properties, Optics, and Devices XI, edited by Eva M. Campo, Elizabeth A. Dobisz, Louay A. Eldada, Proc. of SPIE Vol. 9170, 91700X · © 2014 SPIE · CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2067796 Proc. of SPIE Vol. 9170 91700X-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/26/2015 Terms of Use: http://spiedl.org/terms However, they are difficult to fabricate, and have not been experimentally demonstrated at high temperatures under extended operation. Here, we present a simpler approach based on dielectric-filled anti-reflection coated (ARC) 2D metallic photonic crystals (MPhCs) to obtain omnidirectional polarization insensitive wavelength selective thermal emission. 2. DESIGN AND OPTIMIZATION The traditional unfilled 2D MPhCs consists of a square array of cylindrical holes with period a, radius r, and depth d etched onto a metallic substrate, as shown in Figure 1(a).13,17 This design achieves selective emission by relying on cavity resonances, whereby λcut is determined by the fundamental cavity resonance mode. When the absorptive and radiative rates of the MPhC’s cavity resonances are matched, i.e. Q-matched, it is possible to achieve near-blackbody emittance ε at λ < λcut as well as emittance almost as low as a polished metal at λ > λcut, with a sharp cutoff separating the two regimes.17,24 This approach is general, and therefore applicable to any highly reflective metallic material of choice, for instance silver, platinum, tungsten, etc. In this investigation, tantalum (Ta) is our material of choice given its ultralow emittance at λ > λcut, and high temperature stability. Furthermore, 2D Ta PhCs have been demonstrated at scale,25 and have been shown to be thermally stable at high temperatures under high vacuum conditions.26 While Q-matching can successfully be used to quickly obtain designs with high emittance at λ < λcut, it is not a globally optimum design as it is impossible to satisfy Q-matching conditions for all higher order modes simultaneously, which is important in broadening the bandwidth for maximum emittance at λ < λcut. In addition, the optimization problem is highly non-convex marked by a large number of local optima. Hence, non-linear global optimization methods were used to uncover the optimum a, r, and d of the 2D Ta PhC that would possess maximum emittance at λ < λcut as local search algorithms may potentially get trapped in a localized peak.27 The global optimum was found via the multi-level singlelinkage (MLSL) method, which executes a quasi-random low-discrepancy sequence (LDS) of local searches using constrained optimization by linear approximation (COBYLA).28,29 We have also verified that other global search algorithms, such as the controlled random search (CRS) algorithm,30 yielded similar results. The global optimization routines were implemented via NLOpt, a free software packaged developed at MIT that allows comparison between various global optimization algorithms.31 Note that in all optimization routines, the design provided by Q-matching of the fundamental mode was used as the initial estimate. In addition, the following constraints were implemented: a-2r < 100nm to ensure integrity of sidewalls; d < 8.50μm based on fabrication limits using an SF6 based Bosch deep reactive ion etching (DRIE) process.25 - L 2r r d (b) (a) Figure 1: (a) Traditional unfilled two-dimensional metallic photonic crystal (2D MPhC) with period a, radius r, and depth d. (b) Dielectric-filled 2D MPhC with additional anti-reflection coating (ARC) of the same dielectric material of thickness t. θ and ϕ respectively denotes the polar and azimuthal angle. Proc. of SPIE Vol. 9170 91700X-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/26/2015 Terms of Use: http://spiedl.org/terms The emittance of the 2D Ta PhC can easily be determined via finite-difference time-domain (FDTD) numerical methods32 coupled with the Lorentz−Drude model fitted to measured room and elevated temperature emittance33 to capture the optical dispersion of Ta. However, high memory requirements and slow computational speed of FDTD methods limit its application, particularly in determining the globally optimum design for a particular application. Thus, to obtain quicker estimates, we utilized rigorous coupled wave analysis (RCWA) methods.34 To ensure accuracy, the number of Fourier components were doubled until the results converged. We have also verified that FDTD methods agree very well with RCWA formulations based on both polarization decomposition and normalized vector bases when more than 320 Fourier expansion orders were used. Figure 2(a) shows the emittance as a function of wavelength and polar angle of the traditional unfilled 2D Ta PhC optimized for maximum emittance at λ < λcut. As can be seen, the average emittance at λ < λcut is high at near-normal incidence polar angles. However, as the polar angle increases, the average emittance at λ < λcut falls significantly. The reason for this is the presence of diffraction losses, which is governed by the grating equation: a (sin θ i + sin θ m ) = mλ , m = ±1, ±2, ±3, … (1) where θi is the angle of incidence, and θm is the angle where the m-th order diffraction exists. The onset of diffraction occurs when m = 1 and θm = 90˚. Thus, for radiation with a specific wavelength, diffraction sets in when θi is larger than the cutoff angle given by: ⎛λ ⎞ − 1⎟ ⎝a ⎠ θ d = sin −1 ⎜ (2) Above this diffraction threshold, there are more channels to couple into, resulting in a smaller radiative Q. The initial match with the absorptive Q is thus lost, resulting in severe reduction in average emittance at λ < λcut. This effect is clearly observed in Figure 2(a) as indicated by the white lines, which are the diffraction thresholds as determined by Equation (2). 3 3 1 1 0.9 2.5 0.9 2.5 0.8 0.8 0.7 0.7 ¿ c 0.6 U. 2 0.5 0.6 2 C 0.5 :J° É t5 0.4 w 'E m 1.5 0.4 w 0.3 0.3 ............. 1 . 0.50 --.,. , 20 r 40 60 Polar Angle 0 ( °) 0.2 0.2 1 0.1 0.1 80 0 0.50 20 40 60 Polar Angle 0 ( °) 80 0 Figure 2: Emittance as a function of wavelength λ and polar angle θ averaged over azimuthal angle ϕ and over all polarizations for optimized (a) unfilled 2D Ta PhC (a = 1.16μm, r = 0.53μm, d = 8.50μm) and (b) HfO2-filled ARC 2D Ta PhC (a = 0.57μm, r = 0.23μm, d = 4.31μm, t = 78nm). Both designs are optimized for a cutoff wavelength λcut of 2μm. The white lines indicate the diffraction thresholds as defined in Equation (2). Proc. of SPIE Vol. 9170 91700X-3 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/26/2015 Terms of Use: http://spiedl.org/terms In order to reduce diffraction losses, θd has to be increased by reducing a as much as possible. A simple solution to reduce a is filling the cylindrical cavities with an appropriate dielectric, thereby increasing θd by virtue of a reduced r, d, and hence a to obtain the same λcut due to a reduced effective wavelength by a factor of n in dielectrics.35 In addition, we consider an additional coating of the same dielectric with thickness t that enhances the emittance at λ < λcut by functioning as an ARC. In this investigation, we have selected hafnium oxide (HfO2) because of its transparency in the visible and infrared (IR) region, its compatible thermal expansion coefficient, and its high melting point. HfO2 can also be easily deposited via atomic layer deposition (ALD),26 and sol-gel deposition methods.36 Furthermore, the HfO2 layer promotes stable operation at high temperatures by preventing debilitating chemical reactions that attack the top surface of Ta, and preventing geometry deformation due to surface diffusion.26,36 In our numerical simulations, the refractive index n of HfO2 was assumed to be 1.9 for 0.5μm < λ < 5.0μm, which is consistent with results reported in literature,37 and our measurements of HfO2 thin films deposited via ALD (Cambridge NanoTech Savannah). Results of non-linear global optimization routines applied to HfO2-filled ARC 2D Ta PhC for λcut of 2μm are shown in Figure 2(b). As can be seen, the optimized HfO2-filled ARC 2D Ta PhC more closely approaches the ideal cutoff emitter (hemispherically averaged emittance of 1 at λ < λcut and hemispherically averaged emittance of 0 at λ > λcut); the emittance is essentially unchanged up to θ = 40˚, and is > 0.8 for θ > 70˚, a significant improvement compared to the traditional unfilled 2D Ta PhC. The HfO2-filled ARC 2D Ta PhC can also be easily optimized for different λcut's as illustrated in Figure 3(a) using the aforementioned optimization methods. In addition, other suitable dielectric materials could be used, for instance silicon dioxide (SiO2) which has n ≈ 1.45.38 As shown in Figure 3(b), optimized HfO2-filled and SiO2-filled ARC 2D Ta PhCs show very similar performance. However, when using dielectrics with smaller n, larger a, r, d, and t are necessary to achieve optimal performance as shown in Table 1. The eventual choice will nevertheless depend more on thermal stability, ease of fabrication, and overall cost. Table 1: Dimensions of optimized dielectric-filled ARC 2D Ta PhCs with λcut = 2.0μm using different dielectric material choices. Dielectric Period, a (μm) Depth, d (μm) Radius, r (μm) Thickness, t (μm) Air (n = 1) 1.16 8.50 0.53 N/A SiO2 (n = 1.45) 0.80 6.28 0.35 125 HfO2 (n = 1.90) 0.57 4.31 0.23 78 9 04 0.8 0.7 at 0.8 Q c 0.5 L4.4 0ß 0.2 7.5 4 2. h5 1 1.5 2 2.5 3 3.5 4 4.5 wavelength 4.+m) (b) (a) Figure 3: (a) Optimized HfO2-filled ARC 2D Ta PhC designs for λcut = 1.7μm (a = 0.49μm, r = 0.19μm, d = 3.62μm, t = 63nm), λcut = 2.0μm (a = 0.57μm, r = 0.23μm, d = 4.31μm, t = 78nm), and λcut = 2.3μm (a = 0.64μm, r = 0.27μm, d = 5.28μm, r = 80nm). λcut can easily be shifted by altering a, r, d, and t, and further fine-tuned using global non-linear optimization routines. (b) Comparison between optimized HfO2-filled (n ≈ 1.9) and SiO2-filled (n ≈ 1.45) ARC 2D Ta PhCs for λcut = 2.0μm. Similar performance is obtained, albeit at a penalty of larger a, r, d, and t when using dielectrics with smaller n as shown in Table 1. Proc. of SPIE Vol. 9170 91700X-4 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/26/2015 Terms of Use: http://spiedl.org/terms 3. ANALYSIS: THERMOPHOTOVOLTAIC ENERGY CONVERSION In this section, we analyze the performance of optimized HfO2-filled ARC 2D Ta PhCs as a selective emitter in an InGaAsSb TPV energy conversion system. Using the numerical model outlined in Ref. 4, we can determine the following figure of merit for optimization purposes: FOM = xηTPV + (1 − x ) PhC J elec BB J elec (3) PhC BB captures the TPV system power density where ηTPV is the radiative heat-to-electricity efficiency and J elec / J elec performance of the optimized PhC selective emitter compared to the blackbody, and x ∈ [0,1] is the weighting given to ηTPV. Here, we are mainly concerned on obtaining the highest ηTPV possible, thus x = 0.9 was used. Results of the optimization of an indium gallium arsenide antimonide (InGaAsSb) TPV energy conversion system for a temperature of 1250K with a view factor of 0.99 (achievable with 100mm X 100mm flat plate geometry with emitter-TPV cell separation of 500μm) are shown in Table 2. Note that high temperature optical constants of Ta were used in the simulations. Clearly, when operated at higher temperatures, a much smaller d is sufficient for optimum performance due to increased intrinsic absorption of Ta, and is thus easier to fabricate. Table 2: Comparison of radiant heat-to-electricity efficiency ηTPV and electrical power density generated Jelec between a greybody emitter (ε = 0.9), optimized unfilled 2D Ta PhC (a = 1.23μm, r = 0.57μm, d = 4.00μm), and optimized HfO2filled ARC 2D Ta PhC (a = 0.73μm, r = 0.22μm, d = 0.75μm, t = 146 nm) in indium gallium arsenide antimonide (InGaAsSb) thermophotovoltaic (TPV) energy conversion systems at temperature of 1250 K and view factor of 0.99 (achievable with 100mm X 100mm flat plate geometry with emitter-TPV cell separation of 500μm). Emitter Filter η (%) Jelec (W/cm2) Greybody (ε = 0.9) N/A 6.38 0.781 Optimized 2D Ta PhC N/A 12.03 0.621 Optimized HfO2-filled ARC 2D Ta PhC N/A 12.71 0.713 Greybody (ε = 0.9) 10 layer Si/SiO2 12.52 0.700 Optimized 2D Ta PhC 10 layer Si/SiO2 18.31 0.568 Optimized HfO2-filled ARC 2D Ta PhC 10 layer Si/SiO2 19.34 0.646 Greybody (ε = 0.9) Rugate Tandem Filter 23.44 0.726 Optimized 2D Ta PhC Rugate Tandem Filter 23.68 0.588 Optimized HfO2-filled ARC 2D Ta PhC Rugate Tandem Filter 23.76 0.671 TPV In TPV systems without a cold-side filter, the optimized HfO2 ARC 2D Ta PhC enables up to 99% and 6% relative improvement in ηTPV over the greybody emitter (ε = 0.9) and the optimized unfilled 2D Ta PhC respectively. More importantly, up to 15% relative improvement is seen in Jelec with the optimized HfO2-filled ARC 2D Ta PhC compared to the unfilled 2D Ta PhC due to 26% relative improvement in hemispherically averaged emittance at λ < λcut. The improved electrical power density is especially vital in many portable power applications where power generated per kilogram of weight (W/kg) is the primary figure of merit. It is also interesting to compare the performance when coupled with notable experimentally realized reflective spectral control devices, namely the 10 layer Si/SiO2 filter39 or the Rugate tandem filter40. As can be seen, the improvement in Jelec is observed even when either filter is included. However, as better filters are used (e.g. Rugate tandem filter), the improvement in ηTPV from implementing MPhCs over a greybody becomes insignificant. Nevertheless, it is also Proc. of SPIE Vol. 9170 91700X-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/26/2015 Terms of Use: http://spiedl.org/terms important to note that Rugate tandem filters are extremely costly and difficult to fabricate, given the sheer number of layers (> 50 layers) and the specialty materials used (antimony selenide, yttrium fluoride, and heavily doped indium phosphide arsenide). When the much more practical 10 layer Si/SiO2 filter stack is used instead, the 2D Ta PhC selective emitter enables > 45% relative improvement over the greybody emitter. Additionally, the performance of the optimized 2D Ta PhC selective emitter based TPV system is improved by > 50% when the simple 10 layer Si/SiO2 filter is used. Ultimately, the optimum combination would depend on cost and design goals of a specific application. 4. CONCLUSIONS In summary, we have demonstrated optimized designs of dielectric-filled ARC 2D MPhCs for broadband wavelength selective emission. Using non-linear global optimization methods, optimized HfO2-filled ARC 2D MPhC designs exhibiting up to 26% improvement in hemispherically averaged emittance at λ < λcut over the unfilled 2D MPhC are demonstrated. The optimized designs possess high hemispherically averaged emittance of 0.86 at λ < λcut and low hemispherically averaged emittance of 0.12 at λ > λcut over all polar angles and polarizations at T < 100˚C, whereby λcut can easily be shifted and optimized via non-linear global optimization tools. At high temperatures (T ≈ 1250K), the hemispherically averaged emittance at λ > λcut increases to 0.26 due to primarily the reduction in DC-conductivity, hence making the metal more lossy at long wavelengths. This limitation is inherent to all metal based selective emitters, and is thus unavoidable. Regardless, the dielectric-filled ARC 2D MPhC design drastically reduces diffraction losses at λ < λcut compared to the unfilled 2D MPhC. This translates into ≈ 15% improvement in generated electrical power density for TPV systems, which is vital in many portable power applications. These designs also provide the platform necessary for many applications, ranging from solar absorbers for solar thermal applications, to near- to mid-IR radiation sources for IR spectroscopy. Our current work on realizing the dielectric-filled ARC 2D MPhCs experimentally has proven promising thus far, and will be presented in future publications. ACKNOWLEDGEMENTS This work is partially supported by the Army Research Office through the Institute for Soldier Nanotechnologies under Contract No. W911NF-13-D-0001. Y. X. Y., J. B. C., S.-G. Kim, and M. S. are partially supported by the MIT S3TEC Energy Research Frontier Center of the Department of Energy under Grant No. DE-SC0001299. V. 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# Omnidirectional wavelength selective emitters/absorbers based on dielectric-filled anti-reflection coated two-