Omnidirectional wavelength selective emitters/absorbers
based on dielectric-filled anti-reflection coated twodimensional metallic photonic crystals
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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
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Final published version
Accessed
Thu May 26 18:39:14 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/97550
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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.
*yxyeng@mit.edu; 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
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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.
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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
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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.
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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
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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. R. gratefully
acknowledges funding by the Austrian Science Fund (FWF): J3161-N20. The authors would also like to thank Jay
Senkevich for valuable discussions.
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