of 15
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
1
Thomas J. Watson Laboratories of Applied Physics,
California Institute of Technology, United States
2
Kavli Nanoscience Institute, California In
stitute of Technology, United States
3
Department of Electrical Engineering and Computer Science, Northwestern University, United States
Abstract
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 d
esign could surpass this limit
by providi
ng broadband
increase in the local density of states in a subwavelengt
h volume and maintaining efficient coupling of light.
Here we report a broadband metasurface design, enab
ling efficient and broadband absorption enhancement
by direct coupling of incoming light to resonant m
odes of subwavelength-scale Mie nanoresonators defined
in the thin-film active layer. Ab
sorption was investigated both theo
retically 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 the visibl
e and near-IR spectra. Our numerical simulations,
optical absorption measurements and photocurrent
spectral response measureme
nts demonstrate that
crossed trapezoidal Mie resonant structures enable an
gle-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 futu
re ultrathin-film solar cell designs incorporating
nanostructured thin active layers.
Introduction
Optically engineered nanostructures have opened ne
w design paths for solar cells that feature light
management 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 be
en shown that the ray optical light trapping limit
7
can in
principle even be surpassed using ultrathin film ce
ll 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 acro
ss the solar spectrum and an optimal broadband light-coupling scheme.
Numerous solar cell designs have been proposed 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 dens
ity 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 compared to the solar
spectrum. Separate efforts have been made to devel
op optical coupler designs for broadband light coupling
using non-periodic
16
and disordered
17, 18
structures. However achieving an increase in the bandwidth of the
coupling via of disordered systems results in a signifi
cant 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
control the effective optical materials properties
19, 20
, phase
21
and amplitude and potentially realize effective
light trapping. Nonetheless these structures are composed
of resonators with a particular design frequency
22
,
limiting their performance to narrowband applications.
Metasurfaces with multiple r
esonant spectra can be
obtained by interlacing semiconductor nanostructu
res with distinct resonance frequencies
23
, 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, mu
lti-resonant Mie resonators that enhances light
trapping and increases absorption with a broadband sp
ectral 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 wa
velength and the bandwidth are simply determined by
the design parameters of the nanostructure. In ou
r prototype structures, we break symmetry in a
subwavelength volume by use of crossed trapezoids
24
with rectangular cross section as absorbers, which
enables formation and excitation of multiple Mie an
d guided mode resonances
and achieves broadband
light trapping across the visible spectrum.
Results
Light Trapping in Resonant Si nanostructures
To motivate the absorption enhancemen
t mechanism in trapezoidal Mie res
onator structures, we focus first
on a simple model system consisting of a structured Si thin film on an SiO
2
substrate patterned with a
periodic array of Si ridges with rectangular (Fig. 1a –
top) and trapezoidal shape (Fig. 1a - bottom). Such a
high-index dielectric ridge structure act as an array
of resonators, with increased absorption arising from
two distinct origins: 1) Mie resonances that locali
ze light intensity in indivi
dual high-index ridge regions,
with the resonant frequencies determined by the size
of the trapezoid or wire cross section, and 2)
delocalized resonant waveguide modes supported by the
entire periodic ridge array in the Si film, with
incoupled frequencies determined by the periodic a
rray properties. To investigate these two coupling
regimes, we performed full-field simulations and calcu
lated the Si slab absorption for normally incident
plane waves. In our simulations, we considered Si ridges of width
w
= 85 nm, thickness
t
= 100 nm, period
P
= 400 nm and a Si thickness of
t
Si
= 210 nm. Figure 1b shows the magnetic field profile for a transverse
magnetic (TM) polarized plane wave at free space wa
velengths of 575 nm and 620 nm respectively. At
575 nm, light is localized within the Si ridges by coup
ling into Mie resonances. On the other hand, at 620
nm Si ridges enable coupling into the waveguide m
odes of the Si slab. In both cases the local H-field
amplitudes are enhanced by more than an order of ma
gnitude 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 wa
velengths and rapidly decreases towards the Si bandgap.
The peaks seen for the bare film arise from Fabry-Pe
rot resonances in the Si layer. Several absorption
enhancement features can be identified in the ab
sorption spectrum of the stripe array (in green),
corresponding to different orders of the Mie and guide
d mode resonances, yielding in total a 50% overall
increase in photocurrent density. At each resonance, th
e 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 enhancement fro
m the rectangular stripe array, we observe that
these resonances are quite spar
se across the solar spectra.
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 th
e periodicity of the resonators along the ridges is
smaller than the incident beam wavelength which ensur
es efficient interaction of the Mie resonators with
the incoming light, yielding a broadband absorption e
nhancement. The phase plot of reflection from the Si
trapezoid metasurface reveals a broadband suppression of
reflection and excitation of multiple resonances
with broadband absorption enhancement
across the solar spectrum. (Fig. 1d).
To evaluate the proposed design experimentally, we fabr
icated two-dimensional periodic arrays of Si ridges
with trapezoid and rectangular patterns embedded in
210 nm thick Si-on-insulator (SOI) films. A crossed
nanostructure array was used to provide polarizati
on independent response. Sc
anning electron microscopy
images of the fabricated arrays are shown in Fig.
1f. The design parameters are chosen to maximize
integrated absorption for AM 1.5G illumination, de
termined 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 12
5 nm. To verify our predictions,
we performed spectral reflectivity
and spectral response photocurrent measurements
and full-field simulations on planar and the
nanoresonator-patterned silicon-on-insu
lator films of the same thickness,
t
Si
= 210 nm, without
antireflection coatings (Fig. 2).
The measured optical absorption spectra show excelle
nt agreement with electromagnetic simulations (Fig.
2a-c). The high reflection loss from the planar Si film, is partially mitigated by the crossed rectangular
resonators whereas over 90% absorption is achieved by
the resonators with trapezoid shape at short
wavelengths. We note that in this case, the optical ab
sorption measurement is not a direct measure of the
absorption in the thin Si
slab as the underlying Si substrate al
so contributes to measured absorption.
Nonetheless, absorption measurements provide a usef
ul method to characterize reflection losses and to
indicate the close correspondence between expe
rimental measurements and simulations.
The absorption enhancement of nanostructured Si films
can be directly determined by analyzing spectral
response photocurrent measurements (Fig. 2d-f). Note
that the underlying silicon dioxide layer induces
multiple Fabry-Perot resonances but do not contribute to
the overall photocurrent. The photocurrent spectral
response of rectangular resonators (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 - 670nm spectral region and the respon
se is significantly reduced at wavelengths longer
than 750 nm. By contrast, resonators with trapezoid
al shape exhibit a broadband
increase in photocurrent
spectral response, with additional resonances obser
vable 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 AM1.5G solar spectrum. The
peak positions for simulated photocurrent spectra exhi
bit an excellent 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 ar
e found to be broader at long wavelengths compared
to those in electromagnetic simulations. We attribute
this discrepancy to our optical measurement system
which excites the sample with illumination over the fi
nite angular distribution emerging from a 0.14 NA
focusing objective lens and also experimental deviations
from the rectangular cross sections assumed in the
simulations, e.g., due to slight rounding of the
corners and edges of nanostructure sidewalls.
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 considerab
ly higher than the bare film
J
sc
, 3.2 mA/cm
2
. To
understand the photocurrent enhancemen
t mechanism, we calculated spa
tial absorption maps at several
resonant frequencies for an incident pl
ane 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 differ
ent 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 ma
ps, we can identify three types of distinct resonant
modes that account for photocurrent enhancement.
Localized Mie resonant modes are excited by plane
wave illumination at 418 nm. At an excitation wavele
ngth of 686 nm, the dominant absorption mechanism
is via waveguide modes of the trapezoid ridges propaga
ting along the x-axis. As the Si absorption is reduced
at longer wavelengths, long-range inte
ractions between trapezoidal unit cells get stronger, and the coupling
efficiency to the guided modes increases. At 948 nm
illumination, waveguide modes of the thin film are
excited. As seen in Fig. 2, d
espite efficient coupling to wavegui
de modes and a high (~40x) observed
absorption enhancement 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 ge
neration rate over all wave
lengths at each point to determine the spatial
distribution of the resonance contribution to photocu
rrent generation. Figure 4e and 4f shows the spectrum-
integrated carrier generation map for a rectangular
pattern. There is a pronounced pattern of modes for
carrier generation, a result of the finite number of re
sonant modes that have symmetric profiles within the
rectangular resonator pattern. We also observe a st
rong 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 polarization dependent variation at different cr
oss-sections, the spatially-
integrated current density
has no polarization dependence. Figure 4g and 4h shows
the carrier generation map for the trapezoid pattern.
There is a high carrier generation rate within the tr
apezoids while the active laye
r 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 th
e 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 polari
zation 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 sy
mmetry that facilitates the mode hybridization and
conversion between different symmetries. Films with
roughened surfaces and randomly corrugated features
exhibit similar light trapping effects
25
. However the trapezoidal design is distinct from non-periodic and
randomly distributed structures since the non-uniform
ity enabling broadband absorption is implemented
within a single wavelength-scale structure.
Angular Dependence of Spectral Response
An important parameter that determin
es the overall energy output of a so
lar 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 angula
r dependence of the spectral response for rectangular
and trapezoid structures (Fig. 5). For both structures,
the peak positions of the resonances are preserved
with slight shifts at shorter wa
velengths (400 nm – 650 nm) while larg
er shifts are observed at longer
wavelengths (700 nm – 1000 nm). The observed de
pendence of the peak shift on wavelength is a
consequence of Mie resonances mainly residing at sh
ort wavelengths with less angular dependence while
waveguide modes are excited at relatively longer r
esonant wavelengths via Bragg-scattering which has a
significant angular dependence. Figure 5c shows the overa
ll integrated short circuit current density for each
system. Trapezoid and rectangular structures show a 9%
and 4% decrease in current density at an incident
angle of 60
o
while a bare film has a 8% decrease. Optimizi
ng structure design to give higher photocurrent
density at larger incident angles can circumvent the sm
all decrease in the photocurrent density, and thus a
possible future research direction is to design structur
es 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 computationally intensive. It is prefer
able 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 re
sponse function centered around 550 nm for 85 nm
thick Si films, whereas the large variation in th
e trapezoid width creates Mie resonances across a wide
portion of the optical spectrum, but here mainly target
ed at shorter wavelengths. The design parameters can
be adjusted according to the material and the thickne
ss. For instance for a micron-scale Si thin film it would
be more desirable to minimize reflection at short wave
lengths and to shift the coupling resonances to longer
wavelengths. AR effect could be im
plemented by using trapezoid struct
ures 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 me
tasurface design to realize broadband absorption
enhancement by efficient coupling in
to both broadband Mie resonators
and guided mode resonances across
the solar spectrum. We have fabricated a protot
ype 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 film
s. 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 silic
on on insulator wafer using
standard photolithography
techniques. The electrical contacts of the detector were spaced by 120
m. We generated arrays of Si
nanoresonators between the contacts with rectangular
and trapezoid shapes using standard electron-beam
lithography, Reactive Ion Etching, thermal oxidation a
nd thermal diffusion doping techniques. Optical
measurements were carried out usi
ng an inverted microscope coupled with a spectrometer and an Electron
Multiplication Charge Coupled Device array. Sampl
es were illuminated using a 2X objective with a
numerical aperture of 0.06 to ensure a near norma
l 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 Spec
tra Physics monochromator. The photocurrent signal
was measured using a Keithley SourceMeter conn
ected to a SRS lock-in amplifier. The 50x50
m
2
nanoresonator arrays were illuminated with a Gaussian
beam using a 5X Mitutoyo objective providing a
spot size of 5
m in diameter.
Full-field simulations on non-periodic arrays.
Full-field electromagnetic wave calculations are
performed 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 fabri
cated arrays using Lumerical's digitization feature.
For the material data of Si and SiO
2
, tabulated data from Palik
26
and a constant refractive index of 1.45 were
used, respectively. A mesh override region of 2×2×2 nm
3
was defined over the structure to amply resolve
fine features in digitized SEM images.
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Acknowledgements
This work was supported by the Multidisciplinary Un
iversity 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 Fron
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Kavli Nanoscience Institute (KNI) at Caltech. We
thank Dr. Dennis Callahan for helpful discussions.
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All authors contributed to all aspects of this work.
Figure Captions
Figure 1
Figure 1:
(a) A schematic representation of Si ridge grating
model structure with rectangular stripe (top)
and trapezoid (bottom) cross-section. (b) Simu
lated H-field intensity distribution maps in
xy
plane of the
rectangular stripe array for plane wave incidence
in TM-mode at 620 nm and 575 nm respectively. (c)
Simulated absorption spectrum for bare (blue) and nanost
ructured Si films with rectangular stripe (green)
and trapezoidal (red) ridges. (d) Calculated reflecti
on phase from Si metasurfaces with rectangular stripe
(green) and trapezoidal (red) ridges. (e) Schematic
of silicon-on-insulator late
ral 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 co
ntacts, respectively. (f) SEM images of fabricated
device featuring crossed rectangular (top) and trapezo
idal (bottom) nanostructures. Scale bar is 0.5
m.
Insets are the corresponding unit cells of the nanostructured patterns.
Wavelength (nm)
400
500
600
700
800
900
1000
Absorption
0
0.
2
0.
4
0.
6
0.
8
1
Wavelength (nm)
400
500
600
700
800
900
1000
Phase (radians)
0
1
2
3
4
x
y
z
0
200
400
600
800
0
200
400
0
200
400
x (nm)
z (nm)
H
y
/H
0
0
5
10
a
b
c
575 nm
620 nm
SiO
2
air
Si
SiO
2
Si
d
bare
stripe
trapezoid
stripe
trapezoid
e
f
SiO
2
Si
Si
Au
Ti
Ni
SiO
2
pattern
Figure 2
Figure 2:
(a-c) Spectral absorption measurements and simulati
ons (a-c); comparison of bare Si slab (a),
rectangular (b) and cross-trapezoid (c) devices. Op
tical 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 colle
ction efficiency for the simulations.
Wavelength (nm)
Wavelength (nm)
Spectral Current Density (mA/cm
2
/nm
)
Absorption
Absorption
Absorption
Wavelength (nm)
Wavelength (nm)
Wavelength (nm)
Wavelength (nm)
a
b
d
e
f
c
Figure 3
Figure 3:
Modal analysis of the enhanced absorption. Depi
ction of planes (a,b) used for two-dimensional
representation of modes displayed at locations on
cross-sections in (c) and (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 fra
me 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.
a
b
c
d
=418 nm
=686 nm
=934 nm
=418 nm
=686 nm
=934 nm
xy
z
x
y
z
x
y
z
y
Figure 4
Figure 4:
Photo-generated carrier density ma
ps. (a-d) Depiction of locations for cross-sections for (a-b)
rectangular and (c-d) trapezoidal resonator struct
ures displayed in (e-f) and (g-h) respectively. The
cross-sectional carrier generation maps (e-h) are color
framed to match specified planes indicated in (a-d).
Plane wave illumination was polarized along the
x
direction.
a
b
e
f
xy
z
x
y
z
x
y
z
y
z
x
x
y
z
y
z
x
xy
z
x
y
z
c
d
g
h
Charge Pairs/cm
3
/s
Charge Pairs/cm
3
/s