of 7
1
SCIENTIFIC
RepoRts
| 6:31451 | DOI: 10.1038/srep31451
www.nature.com/scientificreports
Omnidirectional and broadband
absorption enhancement from
trapezoidal Mie resonators in
semiconductor metasurfaces
Ragip
A.
Pala
1
,
2
, Serkan
Butun
3
, Koray
Aydin
3
& Harry
A.
Atwater
1
,
2
Light trapping in planar ultrathin-film solar cells is limited due to a small number of optical modes
available in the thin-film slab. A nanostructured thin-film design could surpass this limit by providing
broadband increase in the local density of states in a subwavelength volume and maintaining efficient
coupling of light. Here we report a broadband metasurface design, enabling efficient and broadband
absorption enhancement by direct coupling of incoming light to resonant modes of subwavelengthscale
Mie nanoresonators defined in the thin-film active layer. Absorption was investigated both theoretically
and experimentally in prototypes consisting of lithographically patterned, two-dimensional
periodic arrays of silicon nanoresonators on silica substrates. A crossed trapezoid resonator shape
of rectangular cross section is used to excite broadband Mie resonances across visible and near-IR
spectra. Our numerical simulations, optical absorption measurements and photocurrent spectral
response measurements demonstrate that crossed trapezoidal Mie resonant structures enable angle-
insensitive, broadband absorption. A short circuit current density of 12.0
mA/cm
2
is achieved in 210
nm
thick patterned Si films, yielding a 4-fold increase compared to planar films of the same thickness. It
is suggested that silicon metasurfaces with Mie resonator arrays can provide useful insights to guide
future ultrathin-film solar cell designs incorporating nanostructured thin active layers.
Optically engineered nanostructures have opened new design paths for solar cells that feature light manage-
ment as an integral component of cell design
1–6
, leading to higher open-circuit voltages, and higher short-circuit
currents. In recent years it has also been shown that the ray optical light trapping limit
7
can in principle even be
surpassed using ultrathin film cell designs that operate in the wave optics regime
8–11
. Efficient light absorption in
ultrathin film solar cells requires both an increase in the number of optical states in the absorber layer across the
solar spectrum and an optimal broadband light-coupling scheme. Numerous solar cell designs have been pro-
posed to achieve light management by employing, e.g., plasmonic design
12
, photonic crystal architecture
13,14
and
excitation of dielectric waveguide modes
8
and Mie resonances
15
, all of which serve to increase the local density of
optical states in the active absorber layer. A second important requirement for efficient light trapping is effective
coupling into these modes, which is often realized over only a small bandwidth for resonant structures, as com-
pared to the solar spectrum. Separate efforts have been made to develop optical coupler designs for broadband
light coupling using non-periodic
16
and disordered
17
,18
structures. However achieving an increase in the band-
width of the coupling via of disordered systems results in a significant decrease in the coupling efficiency. It is thus
worth developing novel design architectures that enable both a high density of optical states and broadband light
coupling into ultrathin-film solar cells.
Ultrathin optical materials structured on the subwavelength scale offer an unprecedented opportunity to con-
trol the effective optical materials properties
19,20
, phase
21
and amplitude
22
of the transmission and reflection, and
potentially realize effective light trapping. Nonetheless these structures are composed of resonators with a particu-
lar design frequency
23
, limiting their performance to narrowband applications. Metasurfaces with multiple reso-
nant spectra can be obtained by interlacing semiconductor nanostructures with distinct resonance frequencies
24
,
1
California Institute of Technology, Thomas J. Watson Laboratories of Applied Physics, Pasadena, 91125,
United States.
2
California Institute of Technology, Kavli Nanoscience Institute, Pasadena, 91125, United States.
3
Northwestern University, Department of Electrical Engineering and Computer Science, Evanston, 60208, United
States. Correspondence and requests for materials should be addressed to H.A.A. (email: haa@caltech.edu)
r
eceived: 08 January 2016
A
ccepted: 27 June 2016
P
ublished: 19 September 2016
OPEN
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2
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RepoRts
| 6:31451 | DOI: 10.1038/srep31451
however only a limited number of resonances can be excited across the solar spectrum. In this work, we report a
broadband metasurface design, composed of subwavelength, multi-resonant Mie resonators that enhances light
trapping and increases absorption with a broadband spectral response. Efficient coupling is achieved to resonant
modes of subwavelength-scale nanoresonators incorporated into a thin film crystalline silicon absorber layer. In
a Mie resonator, the resonant wavelength and the bandwidth are simply determined by the design parameters of
the nanostructure. In our prototype structures, we break symmetry in a subwavelength volume by use of crossed
trapezoids
25
with rectangular cross section as absorbers, which enables formation and excitation of multiple Mie
and guided mode resonances and achieves broadband light trapping across the visible spectrum.
Results
Light Trapping in Resonant Si nanostructures.
To motivate the absorption enhancement mechanism
in trapezoidal Mie resonator structures, we focus first on a simple model system consisting of a structured Si thin
film on an SiO2 substrate patterned with a periodic array of Si ridges with rectangular (Fig. 1a, top) and trape
-
zoidal shape (Fig. 1a, bottom). Such a high-index dielectric ridge structure acts as an array of resonators, with
increased absorption arising from two distinct origins: 1) Mie resonances that localize light intensity in individual
high-index ridge regions, with the resonant frequencies determined by the size of the trapezoid or wire cross sec-
tion, and 2) delocalized resonant waveguide modes supported by the entire periodic ridge array in the Si film, with
incoupled frequencies determined by the periodic array properties. To investigate these two coupling regimes, we
performed full-field simulations and calculated the Si slab absorption for normally incident plane waves. In our
simulations we considered a relatively thin film Si of thickness
t
Si
=
210
nm to simplify the analysis of resonant
modes that are contributing to light trapping. In each resonator design presented in the manuscript, geometry
parameters are separately optimized to maximize the overall absorption using full-field simulations. In our first
example, we considered Si ridges of width
w
=
85 nm, thickness
t
=
100
nm, and a period of
P
=
400 nm. Figure 1b
shows the magnetic field profile for a transverse magnetic (TM) polarized plane wave at free space wavelengths
of 565
nm and 610
nm respectively. At 565
nm, light is localized within the Si ridges by coupling into Mie reso-
nances. On the other hand, at 610
nm Si ridges enable coupling into the waveguide modes of the Si slab. In both
cases the local H-field amplitudes are enhanced by more than an order of magnitude compared to incoming field.
To analyze the contributions of these resonances to absorption across the spectrum, we simulate the absorption
spectrum of the nanostructured Si film and the bare Si film of an equivalent thickness,
t
=
135
nm (Fig. 1c). The
absorption for the bare Si film is highest at short wavelengths and rapidly decreases towards the Si bandgap. The
peaks seen for the bare film arise from Fabry-Perot resonances in the Si layer. Several absorption enhancement
features can be identified in the absorption spectrum of the stripe array (in green), corresponding to different
orders of the Mie and guided mode resonances, yielding in total a 50% overall increase in photocurrent density.
At each resonance, the Si ridges act like nanoantennas, altering the flow of the light into the semiconductor, and
inducing an increase in light absorption. These resonances can be also identified by analyzing the abrupt phase
shifts of the reflected wave from the Si metasurface (Fig. 1d). Despite a significant overall photocurrent enhance-
ment from the rectangular stripe array, we observe that these resonances are quite sparse across the solar spectra.
Figure 1.
(
a
) A schematic representation of Si ridge grating model structure with rectangular stripe (top)
and trapezoid (bottom) cross-section. (
b
) Simulated H-field intensity distribution maps in xy plane of the
rectangular stripe array for plane wave incidence in TM-mode at 610
nm and 565
nm respectively. (
c
) Simulated
absorption spectrum for bare (blue) and nanostructured Si films with rectangular stripe (green) and trapezoidal
(red) ridges. (
d
) Calculated reflection phase from Si metasurfaces with rectangular stripe (green) and trapezoidal
(red) ridges. (
e
) Schematic of silicon-on-insulator lateral Schottky device with embedded nanostructures. The
regions where Au contact pads (yellow) are contacted with Si are indicated with blue and red colors for Ohmic
and Schottky contacts, respectively. (
f
) SEM images of fabricated device featuring crossed rectangular (top)
and trapezoidal (bottom) nanostructures. Scale bar is 0.5
μ
m. Insets are the corresponding unit cells of the
nanostructured patterns.
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3
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RepoRts
| 6:31451 | DOI: 10.1038/srep31451
Broadband Absorption Mechanism in Trapezoidal Structures.
Broadband light absorption is
achieved by using ridges with a trapezoid pattern (plotted in red). Varying the resonator width along the ridges
from 20
nm to 120
nm facilitates Mie resonance excitation of the same resonance order at multiple wavelengths.
Note that the periodicity of the resonators along the ridges is smaller than the incident beam wavelength which
ensures efficient interaction of the Mie resonators with the incoming light, yielding a broadband absorption
enhancement. The phase plot of reflection from the Si trapezoid metasurface exhibits a large number of optical
resonances excited across the solar spectrum, and therefore reveals a broadband suppression of the reflection
26
and a broadband absorption enhancement in the Si layer (Fig. 1d).
To evaluate the proposed design experimentally, we fabricated two-dimensional periodic arrays of Si ridges
with trapezoid and rectangular patterns embedded in 210
nm thick Si-on-insulator (SOI) films. A crossed nano-
structure array was used to provide polarization independent response. Scanning electron microscopy images of
the fabricated arrays are shown in Fig. 1f. The design parameters are chosen to maximize integrated absorption
for AM 1.5
G illumination, determined using full-field electromagnetic simulations. For optimum absorption, a
periodicity of 450
nm is used for rectangular and trapezoid arrays. The width of the fabricated rectangular stripes
are 115
nm while the width of the trapezoid pattern varies from 40
nm to 220
nm, the resonator thickness is
125
nm. To verify our predictions, we performed spectral reflectivity and spectral response photocurrent meas-
urements and full-field simulations on planar and the nanoresonator-patterned silicon-on-insulator films of the
same thickness,
t
Si
=
210
nm, without antireflection coatings (Fig. 2).
The measured optical absorption spectra show excellent agreement with electromagnetic simulations
(Fig. 2a–c). The high reflection loss from the planar Si film, is partially mitigated by the crossed rectangular reso-
nators whereas over 90% absorption is achieved by the resonators with trapezoid shape at short wavelengths. We
note that in this case, the optical absorption measurement is not a direct measure of the absorption in the thin Si
slab as the underlying Si substrate also contributes to measured absorption. Nonetheless, absorption measure-
ments provide a useful method to characterize reflection losses and to indicate the close correspondence between
experimental measurements and simulations.
The absorption enhancement of nanostructured Si films can be directly determined by analyzing spectral
response photocurrent measurements (Fig. 2d–f ). The photocurrent spectral response of rectangular resona-
tors (Fig. 2e) shows a substantial overall enhancement compared to the bare film despite the sparse resonances.
However for rectangular resonators, the spectral response is relatively low at the 580
nm–670
nm spectral
region and the response is significantly reduced at wavelengths longer than 750
nm. By contrast, resonators
Figure 2.
(
a
c
) Spectral absorption measurements and simulations (
a
c
) comparison of bare Si slab (
a
) rectangular
(
b
) and cross-trapezoid (
c
) devices. Optical absorption is calculated as 1-Reflection. (
d
f
) Spectral photoresponse
comparison of (
d
) bare Si slab, (
e
) rectangular and (
f
) trapezoidal devices. We assumed unity internal photocarrier
collection efficiency for the simulations.
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RepoRts
| 6:31451 | DOI: 10.1038/srep31451
with trapezoidal shape exhibit a broadband increase in photocurrent spectral response, with additional reso
-
nances observable up to 950
nm (Fig. 2f ). The drop in the photocurrent density from 870
nm to 1000
nm is due
to decreased solar irradiation arising from water-related absorption when the measured spectral response is
weighted by the AM 1.5
G solar spectrum. The peak positions for simulated photocurrent spectra exhibit an excel-
lent match to those in experimental spectra and clearly demonstrate the presence of several coupled resonances
that enhance the photocurrent. The peak widths in the experimental photocurrent are found to be broader at long
wavelengths compared to those in electromagnetic simulations. We attribute this discrepancy to 1. our optical
measurement system which illuminates the sample with an angular distribution emerging from a 0.14 NA focus-
ing objective lens, and 2. deviations in the experimental fabrication parameters assumed in the simulations, e.g.,
slight rounding of the corners and edges of nanostructure sidewalls. Despite the discrepancy between simulations
and experiments, the integrated short circuit current doesn’t change significantly. Note that the underlying Si
substrate induces multiple Fabry-Perot resonances in the absorption and spectral response spectra for both bare
and nanostructured films, and it doesn’t contribute to the photocurrent enhancement.
Spectral contribution of resonant modes to absorption and carrier generation.
The integrated
short circuit current density (
J
SC
) for the rectangular and trapezoid patterns are 7.8
mA/cm
2
and 12.0
mA/cm
2
respectively, which are considerably higher than the bare film
J
SC
, 3.2 mA/cm
2
. To understand the photocurrent
enhancement mechanism, we calculated spatial absorption maps at several resonant frequencies for an incident
plane wave illumination polarized along the x-axis (Fig. 3). The maps at the same time provide the electric field
distribution, |
E
|
2
, therefore give us an idea about the resonant modes. The spatial absorption maps are shown for
different cross-sections at each wavelength, i.e. at the resonator- thin film interface, across the ridges, along the
ridges, and along the ridges with 100
nm displacement from the center of the ridges. From these maps, we can
identify three types of distinct resonant modes that account for photocurrent enhancement. Localized Mie reso-
nant modes are excited dominantly at shorter wavelengths. Figure 3c,d illustrates the excitation of Mie resonances
by plane wave illumination at 418
nm. At an excitation wavelength of 686
nm, the dominant absorption mecha-
nism is via waveguide modes of the trapezoid ridges propagating along the x-axis. As the Si absorption is reduced
at longer wavelengths, long-range interactions between trapezoidal unit cells get stronger, and the coupling effi-
ciency to the guided modes increases. At 934
nm illumination, waveguide modes of the thin film are excited. As
seen in Fig. 2, despite efficient coupling to waveguide modes and a high (~40
×
) observed absorption enhance-
ment compared to a bare Si film, the contribution of the waveguide modes to the short circuit current density is
negligible due to the smaller absorption coefficient of Si near its band edge and a reduced solar Irradiance at long
wavelengths. Thus in an optimization scheme for the overall performance solar cells, it is essential to consider
the contribution of resonant modes to carrier generation rather than enhancement factors relative to planar thin
films.
We integrated the charge carrier generation rate over all wavelengths at each point to determine the spatial dis
-
tribution of the resonance contribution to photocurrent generation. Figure 4c,d shows the spectrum-integrated
carrier generation map for a rectangular pattern. There is a pronounced pattern of modes for carrier gener
-
ation, a result of the finite number of resonant modes that have symmetric profiles within the rectangular
Figure 3.
Modal analysis of the enhanced absorption.
Depiction of planes (
a
,
b
) used for two-dimensional
representation of modes displayed at locations on cross sections in (
c
,
d
) respectively. (
c
) xy plane cross section
normalized absorption maps at various resonance wavelengths as indicated at the top. (
d
) yz plane cross section
normalized absorption maps. Map frame colors match the specified positions in (
b
). For each resonance, plane
intersecting the narrow tip, center and wide end of the trapezoid are presented in blue, red and green frames,
respectively.
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| 6:31451 | DOI: 10.1038/srep31451
resonator pattern. We also observe a strong polarization dependence of the carrier generation in the xz and
yz cross-sections. Note that although the spatial distribution of photocurrent density exhibits a local polariza-
tion dependent variation at different cross-sections, the spatially-integrated current density has no polarization
dependence. Figure 4g,h shows the carrier generation map for the trapezoid pattern. There is a high carrier gen-
eration rate within the trapezoids while the active layer has a uniform background generation throughout its
volume. The stronger contribution is attributed to the Mie resonances and ridge waveguide modes that are mainly
excited within the trapezoid while uniform background contribution is due to excitation of multiple waveguide
modes with spatially non-uniform mode profiles. An intriguing characteristic of the trapezoid pattern is the
polarization dependence of the generation rate observed at different cross-sections. The crossed trapezoid pattern
has similar carrier generation rates for both xz and yz cross-sections, which is a result of the broken symmetry
that facilitates the mode hybridization and conversion between different symmetries. Films with roughened sur
-
faces and randomly corrugated features exhibit similar light trapping effects
27
. However the trapezoidal design is
distinct from non-periodic and randomly distributed structures since the non-uniformity enabling broadband
absorption is implemented within a single subwavelength-scale structure.
Angular Dependence of Spectral Response.
An important parameter that determines the overall
energy output of a solar cell is its angular response, since solar modules with fixed axis experience a change of
sunlight incidence angle in the course of a day and throughout the year. We have measured the angular depend
-
ence of the spectral response for rectangular and trapezoid structures (Fig. 5). For both structures, the peak posi-
tions of the resonances are preserved with slight shifts at shorter wavelengths (400
nm–650
nm) while larger shifts
are observed at longer wavelengths (700
nm–1000
nm). The observed dependence of the peak shift on wavelength
is a consequence of Mie resonances mainly residing at short wavelengths with less angular dependence while
waveguide modes are excited at relatively longer resonant wavelengths via Bragg-scattering which has a signif-
icant angular dependence. Figure 5c shows the overall integrated short circuit current density for each system.
Same power density was assumed at each angle, excluding the cosine drop, to reveal the variation in the contri-
bution of resonant absorption to the short circuit current as a function of angle. Trapezoid and rectangular struc-
tures show a 9% and 4% decrease in current density at an incident angle of 60° while a bare film has a 8% decrease.
Optimizing structure design to give higher photocurrent density at larger incident angles can circumvent the
Figure 4.
Photo generated carrier density maps.
Depiction of locations for cross sections for (
a
,
b
) rectangular
and (
e
,
f
) trapezoidal resonator structures are displayed in (
c
,
d
) and (
g
,
h
) respectively. The cross sectional
carrier generation maps (
c
,
d
,
g
,
h
) are color framed to match specified planes indicated in (
a
,
b
,
e
,
f
). Plane wave
illumination was polarized along the x direction.
Figure 5.
(
a
,
b
) Maps of measured spectral response from Si devices with (
a
) rectangular and (
b
) trapezoidal
nanostructures versus incident angle and wavelength of the incoming light. (
c
) Angular dependence of
Integrated
J
SC
curves for bare (blue), rectangular (green), and trapezoid (red) devices.
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| 6:31451 | DOI: 10.1038/srep31451
small decrease in the photocurrent density, and thus a possible future research direction is to design structures
that compensate the geometrical cosine factor to achieve a flat photocurrent density response throughout the day.
Discussion
So far we have discussed the performance of a specific thin film absorber that incorporates trapezoidal shaped
nanoresonators optimized to maximize the overall photocurrent density in 210
nm Si thin films. The proposed
geometry could be optimized for a wide range of solar cell materials over a large thickness range. However the use
of brute-force full-field simulations to scan a vast design parameter space would be inefficient and computation-
ally intensive. It is preferable to use general principles that yield first order estimates for the design parameters.
The modal dispersion and the periodic length scale determine the spectral position of the waveguide resonances,
whereas Mie resonances can be tuned by changing the long and short cross-sections of the trapezoidal resonators.
In the present fabricated design, we have chosen a period of 450
nm, providing waveguide resonance response
function centered around 550
nm for 85
nm thick Si films, whereas the large variation in the trapezoid width
creates Mie resonances across a wide portion of the optical spectrum, but here mainly targeted at shorter wave-
lengths. The design parameters can be adjusted according to the material and the thickness. For instance for a
micron-scale Si thin film it would be more desirable to minimize reflection at short wavelengths and to shift the
coupling resonances to longer wavelengths. AR effect could be implemented by using trapezoid structures with
triangular cross-section in this case to enable an adiabatic index change and minimize the reflection loss, and the
resonances could be tuned by increasing the period and the trapezoid size parameters accordingly.
In conclusion, we have proposed a semiconductor metasurface design to realize broadband absorption
enhancement by efficient coupling into both broadband Mie resonators and guided mode resonances across
the solar spectrum. We have fabricated a prototype nanostructured thin film cell design on silicon-on-insulator
films with Schottky barrier collection of carriers, and achieving a 4-fold increase in the photocurrent compared
to unetched planar thin films. The present work provides a useful framework on how to identify and analyze the
resonant modes of Mie nanoresonators by generating spatial absorption maps and gives a general design strategy
for use of broadband subwavelength dielectric resonators to optimize photocurrent density.
Methods
Sample fabrication.
Schottky barrier photodetectors as shown on Fig. 1e were realized in the 210
nm
thick Si layer of a lightly doped (1
ohm cm) p-type silicon on insulator wafer using standard photolithography
techniques. The electrical contacts of the detector were spaced by 120
μ
m. We generated arrays of Si nanoreso-
nators between the contacts with rectangular and trapezoid shapes using standard electron-beam lithography,
Reactive Ion Etching, thermal oxidation and thermal diffusion doping techniques. Optical measurements were
carried out using an inverted microscope coupled with a spectrometer and an Electron Multiplication Charge
Coupled Device array. Samples were illuminated using a 2x objective with a numerical aperture of 0.06 to ensure
a near normal incidence. The reflected light is calibrated by a broadband dielectric mirror (Edmund Optics).
Photocurrent measurements were carried out using a Fianium supercontinuum white-light source coupled to a
Spectra Physics monochromator. The photocurrent signal was measured using a Keithley SourceMeter connected
to a SRS lock-in amplifier. The 50
×
50
μ
m
2
nanoresonator arrays were illuminated with a Gaussian beam using a
5x Mitutoyo objective providing a spot size of 5
μ
m in diameter.
Full-field simulations on non-periodic arrays.
Full-field electromagnetic wave calculations are per
-
formed using Lumerical, a commercially available Finite-Difference Time-Domain (FDTD) simulation software
package. The FDTD simulations utilized the resonator shapes that were obtained from digitized SEM images of a
2
×
2 unit cell of experimentally fabricated arrays using Lumerical’s digitization feature. For the material data of Si
and SiO2, tabulated data from Palik
28
and a constant refractive index of 1.45 were used, respectively. A mesh over
-
ride region of 2
×
2
×
2 nm
3
was defined over the structure to amply resolve fine features in digitized SEM images.
References
1.
Wang, K. X., Yu, Z., Liu, V., Cui, Y. & Fan, S. Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection
and light-trapping nanocone gratings.
Nano Letters
12,
1616–1619, doi: 10.1021/nl204550q (2012).
2.
Krogstrup, P.
et al.
Single-nanowire solar cells beyond the shockley-queisser limit.
Nat Photon
7,
306–310, doi: 10.1038/
nphoton.2013.32 (2013).
3.
Polman, A. & Atwater, H. A. Photonic design principles for ultrahigh-efficiency photovoltaics.
Nat Mater.
11,
174–177, doi: 10.1038/
nmat3263 (2012).
4.
Brongersma, M. L., Cui, Y. & Fan, S. Light management for photovoltaics using high-index nanostructures.
Nat Mater.
13,
451–460,
doi: 10.1038/nmat3921 (2014).
5.
Fan, Z.
et al.
Ordered arrays of dual-diameter nanopillars for maximized optical absorption.
Nano Letters
10,
3823–3827,
doi: 10.1021/nl1010788 (2010).
6.
Mariani, G., Scofield, A. C., Hung, C. H. & Huffaker, D. L. GaAs nanopillar-array solar cells employing
in situ
surface passivation.
Nat Commun.
4,
1497, doi: 10.1038/ncomms2509 (2013).
7.
Yablonovitch, E. Statistical ray optics.
Journal of the Optical Society of America
72,
899–907, doi: 10.1364/JOSA.72.000899 (1982).
8.
Yu, Z., Raman, A. & Fan, S. Fundamental limit of nanophotonic light trapping in solar cells.
Proceedings of the National Academy of
Sciences
107,
17491–17496, doi: 10.1073/pnas.1008296107 (2010).
9.
Schiff, E. A. Thermodynamic limit to photonic-plasmonic light-trapping in thin films on metals.
Journal of Applied Physics
110,
104501, doi: 10.1063/1.3658848 (2011).
10.
Callahan, D. M., Munday, J. N. & Atwater, H. A. Solar cell light trapping beyond the ray optic limit.
Nano Letters
12,
214–218,
doi: 10.1021/nl203351k (2011).
11.
Green, M. A. Enhanced evanescent mode light trapping in organic solar cells and other low index optoelectronic devices.
Progress
in Photovoltaics: Research and Applications
19,
473–477, doi: 10.1002/pip.1038 (2011).
12.
Biswas, R. & Xu, C. Nano-crystalline silicon solar cell architecture with absorption at the classical 4n2 limit.
Optics Express
19,
A664–A672, doi: 10.1364/OE.19.00A664 (2011).
www.nature.com/scientificreports/
7
SCIENTIFIC
RepoRts
| 6:31451 | DOI: 10.1038/srep31451
13.
Callahan, D. M., Horowitz, K. A. W. & Atwater, H. A. Light trapping in ultrathin silicon photonic crystal superlattices with
randomly-textured dielectric incouplers.
Optics Express
21,
30315–30326, doi: 10.1364/OE.21.030315 (2013).
14.
Zhou, D. & Biswas, R. Photonic crystal enhanced light-trapping in thin film solar cells.
Journal of Applied Physics
103,
093102,
doi: 10.1063/1.2908212 (2008).
15.
Kim, S.-K.
et al.
Tuning light absorption in core/shell silicon nanowire photovoltaic devices through morphological design.
Nano
Letters
12,
4971–4976, doi: 10.1021/nl302578z (2012).
16.
Pala, R. A.
et al.
Optimization of non-periodic plasmonic light-trapping layers for thin-film solar cells.
Nat Commun
4,
doi: 10.1038/
ncomms3095 (2013).
17.
Rockstuhl, C.
et al.
Comparison and optimization of randomly textured surfaces in thin-film solar cells.
Optics Express
18,
A335–A341, doi: 10.1364/OE.18.00A335 (2010).
18.
Burresi, M.
et al.
Two-dimensional disorder for broadband, omnidirectional and polarization-insensitive absorption.
Optics Express
21,
A268–A275, doi: 10.1364/OE.21.00A268 (2013).
19.
Cai, W. & Shalaev, V.
Optical Metamaterials
(Springer-Verlag New York, 2010).
20.
Yu, N. & Capasso, F. Flat optics with designer metasurfaces.
Nat Mater.
13,
139–150, doi: 10.1038/nmat3839 (2014).
21.
Yu, N.
et al.
Light propagation with phase discontinuities: Generalized laws of reflection and refraction.
Science
334,
333–337,
doi: 10.1126/science.1210713 (2011).
22.
Esfandyarpour, M.
et al.
Metamaterial mirrors in optoelectronic devices.
Nat Nanotech
9,
542–547, doi: 10.1038/nnano.2014.117
(2014).
23.
Arbabi, A.
et al.
Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and
high transmission.
Nat Commun.
10,
doi: 10.1038/nnano.2015.186 (2015).
24.
Kim, S. J., Fan, P., Kang, J. H. & Brongersma, M. L. Creating semiconductor metafilms with designer absorption spectra.
Nat
Commun.
6,
doi: 10.1038/ncomms8591 (2015).
25.
Aydin, K., Ferry, V. E., Briggs, R. M. & Atwater, H. A. Broadband polarization-independent resonant light absorption using ultrathin
plasmonic super absorbers.
Nat Commun.
2,
doi: 10.1038/ncomms1528 (2011).
26.
Spinelli, P., Verschuuren, M. A. & Polman, A. Broadband omnidirectional antireflection coating based on subwavelength surface
Mie resonators.
Nat Commun.
3,
doi: 10.1038/ncomms1691 (2012).
27.
Wiersma, D. S. Disordered photonics.
Nat Photon
7,
188–196, doi: 10.1038/nphoton.2013.29 (2013).
28.
Palik, E. D.
Handbook of Optical Constants of Solids
(Academic Press, New York, 1985).
Acknowledgements
This work was supported by the Multidisciplinary University Research Initiative Grant (Air Force Office of
Scientific Research, FA9550-12-1-0024) and used facilities supported by the DOE ‘Light-Material Interactions
in Energy Conversion’ Energy Frontier Research Center under grant DE-SC0001293 and the Kavli Nanoscience
Institute (KNI) at Caltech. We thank Dr. Dennis Callahan for helpful discussions.
Author Contributions
R.A.P., K.A. and H.A.A. designed and conceived the experiments. R.A.P. fabricated the samples. R.A.P. developed
the measurement setup. R.A.P. and S.B. performed the optical measurements. R.A.P. performed the photocurrent
measurements. R.A.P. and S.B. performed numerical simulations. R.A.P., S.B., K.A. and H.A.A. wrote the paper.
All authors discussed the results and commented on the manuscript.
Additional Information
Competing financial interests:
The authors declare no competing financial interests.
How to cite this article
: Pala, R. A.
et al.
Omnidirectional and broadband absorption enhancement from
trapezoidal Mie resonators in semiconductor metasurfaces.
Sci. Rep.
6
, 31451; doi: 10.1038/srep31451 (2016).
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