Sub-50-nm self-assembled nanotextures for enhanced broadband antireflection in silicon solar cells

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Materials providing broadband light antireflection have applications as highly transparent window coatings, military camouflage, and coatings for efficiently coupling light into solar cells and out of light-emitting diodes. In this work, densely packed silicon nanotextures with feature sizes smaller than 50 nm enhance the broadband antireflection compared with that predicted by their geometry alone. A significant fraction of the nanotexture volume comprises a surface layer whose optical properties differ substantially from those of the bulk, providing the key to improved performance. The nanotexture reflectivity is quantitatively well-modelled after accounting for both its profile and changes in refractive index at the surface. We employ block copolymer self-assembly for precise and tunable nanotexture design in the range of ~10–70 nm across macroscopic solar cell areas. Implementing this efficient antireflection approach in crystalline silicon solar cells significantly betters the performance gain compared with an optimized, planar antireflection coating. Broadband light antireflection materials have numerous applications as highly transparent window, for broadband applications thin-film multilayers have been considered. Here, Rahman et al. demonstrate broadband antireflection enhancement in silicon solar cells using a self-assembled, nanostructured copolymer.

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### ARTICLE

Received 22 Jul 2014 | Accepted 26 Nov 2014 | Published 21 Jan 2015 DOI: 10.1038/ncomms6963
## Sub-50-nm self-assembled nanotextures for enhanced broadband antireflection in silicon solar cells

Atikur Rahman 1, Ahsan Ashraf 2,3, Huolin Xin 1, Xiao Tong 1, Peter Sutter 1, Matthew D. Eisaman 2,3,4

& Charles T. Black 1

Materials providing broadband light antireflection have applications as highly transparent

window coatings, military camouflage, and coatings for efficiently coupling light into solar

cells and out of light-emitting diodes. In this work, densely packed silicon nanotextures with

feature sizes smaller than 50 nm enhance the broadband antireflection compared with that

predicted by their geometry alone. A significant fraction of the nanotexture volume comprises

a surface layer whose optical properties differ substantially from those of the bulk, providing

the key to improved performance. The nanotexture reflectivity is quantitatively well-modelled

after accounting for both its profile and changes in refractive index at the surface. We employ

block copolymer self-assembly for precise and tunable nanotexture design in the range of
B10–70 nm across macroscopic solar cell areas. Implementing this efficient antireflection

approach in crystalline silicon solar cells significantly betters the performance gain compared

with an optimized, planar antireflection coating.

1 Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA. 2 Sustainable Energy Technologies Department,
Brookhaven National Laboratory, Upton, New York 11973, USA. 3 Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York
11794, USA. 4 Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, New York 11794, USA. Correspondence and requests
for materials should be addressed to C.T.B. (email: [ctblack@bnl.gov).](mailto:ctblack@bnl.gov)

roper design of an antireflection coating involves managing
the refractive index mismatch at the abrupt optical
interface 1 . The most straightforward approach places a
# P
single layer of intermediate optical index at the interface to create
destructive interference in the reflected light, providing full
antireflection at a single wavelength,plf f i f ¼ f i f f i f 4 f i fn f i f f i ffii � t, with material
thickness (t) and refractive index ni ¼ nS � nA, where nS and nA
are the refractive indices of the substrate and air, respectively.
Increasing broadband coverage, for application in transparent
window coatings 2–5, military camouflage 6 or solar cells 7–15, is
possible using thin-film multilayer schemes 16 . An alternative to
thin-film-coating strategies instead patterns the interface at
subwavelength dimensions, creating an effective medium
between the substrate and air, with ni changing gradually from
nA to nS 10,11,17 . Such structures, often called moth eyes because of
their biomimicry, provide broadband antireflection over a wide
range of incident light angles when subwavelength textures are
taller than tB0.4 � l and spaced closer than cBl/2ns 12,14,18–20 .

In this work, we enhance the broadband antireflection
properties of a nanofabricated moth eye structure through
simultaneous control of both the geometry and optical properties,
by designing nanotextures sufficiently small to take advantage of a
beneficial material surface layer only a few nm thick.

Results
Nanotexture fabrication. We leverage block copolymer selfassembly and plasma etching to fabricate highly regular surface
nanotextures, with precise control over the texture’s lateral feature
size in the range of 10–70 nm, vertical profile and feature density.
Self-assembly based nanofabrication provides a scalable approach
to creating deeply subwavelength moth eye structures (schematics
in Fig. 1a). We pattern surface nanotextures on polished (100)
silicon by first self-assembling a cylindrical phase polystyreneblock-poly(methyl methacrylate) (PS-b-PMMA) block copolymer

thin film (Mw ¼ 99 kg mol � 1, PS:PMMA B7:3) by spin-coating
and thermal annealing. Appropriate surface pretreatment facilitates perpendicular orientation of uniformly sized 25-nm-diameter PMMA cylindrical microdomains within a PS matrix,
locally hexagonally arranged with a separation c ¼ 52 ± 6 nm 21 .
We systematically vary c in the nanotexture from 40 ± 3 to
67 ± 13 nm using block copolymers with total molecular weight
ranging between 67 and 177 kg mol � 1 . Exposing assembled
copolymer films to three sequential cycles of tri(methyl
aluminium) and water vapour selectively loads PMMA microdomains with alumina by sequential infiltration synthesis (Fig. 1b;
Supplementary Fig. 1) 22 .

The self-assembled alumina pattern provides a rugged template
for creating surface nanotextures using plasma etching. We
anisotropically etch the underlying silicon by inductively coupled
plasma-reactive ion etching using a gas chemistry of hydrogen
bromide, chlorine and oxygen, which produces a sidewall angle of
480� (Fig. 1c,d). The gas mixture and etch parameters control
the nanotexture profile, with t increasing with etch time and taller
nanotextures tapering to smaller sizes at their tops (Fig. 1c,d).
Block copolymer self-assembly provides a scalable method for
producing these controlled nanotextures over arbitrarily large
areas, evidenced by its successful prior integration into 300-mmdiameter semiconductor wafer-processing facilities 23 . Previous
investigations have used different block copolymer phases 5,24 and
micelles 25 with larger length scales (4100 nm) as templates for
nanotextures imparting antireflection to glass and silicon
surfaces, which are too large to observe the enhancements
described here.

Nanotexture reflectance. The average reflectance of the nanotextured silicon surface decreases with increasing feature height
(t) in the l range of 400 nm to 1 m, from 35% on a flat surface to
o1% for tapered nanotextures with t ¼ 230 nm and c ¼ 52 nm

_n_ a

_n_ s

_n_ a

_n_ s

_n_ i

45° Flat s-pol
Flat p-pol
Nanotexture s-pol
Nanotexture p-pol

Flat
SiN 80 nm
SiN/inv pyramids
32 nm
65 nm
140 nm
230 nm

Flat s-pol _�_ = 650 nm

Flat p-pol
Nanotexture s-pol
Nanoteture p-pol

400 500 600 700 800 900

Wavelength (nm)

1,000

0 20

0
0 20 40 60 80

Angle of incidence (°)

1,000

400 500 600 700 800 900

Wavelength (nm)

Figure 1 | Silicon nanotexture fabrication and optical reflectance. (a) Schematic (i) tapered antireflection nanotexture and (ii) tapered nanotexture with
graded refractive index. (b) 70� Angle cross-sectional scanning electron microscope (SEM) image of close-packed alumina nanostructures formed by
infiltrating a 99 kg-mol � 1 cylindrical phase polystyrene-b-poly(methyl methacrylate) block copolymer. Scale bar, 20 nm. (c,d) 70� Angle cross-sectional
SEM images of nanotextures fabricated by (c) 60 s and (d) 100 s of plasma etch. Scale bar, 20 nm. (e) Measured reflectance versus l for a flat Si film, an
80-nm-thick silicon nitride film and nanotextures with c ¼ 52 nm and t ranging from 32 to 230 nm. Also shown is the simulated reflectance of an 80-nmthick silicon nitride film on chemically etched inverted pyramids. (f) Measured reflectance (at 650 nm) for s- and p-polarization versus incident angle for
flat silicon (black circles) and nanotextures with c ¼ 52 nm and t ¼ 230 nm (red triangles). (g) Measured reflectance of s- and p-polarization versus l (45�
incident angle) for nanotextures with c ¼ 52 nm and t ¼ 230 nm height.

(Fig. 1e). The nanotextured surface is significantly less reflective
than antireflection methods employed in commercial silicon solar
cells, including flat silicon coated with an 80-nm-thick silicon
nitride layer (Fig. 1e, green open circles) and chemically etched,
inverted pyramid coatings (Fig. 1e, green inverted triangles,
simulated using OPAL 2 (ref. 26)). This latter scheme requires
sacrificing B10 m of silicon at the device top surface, which may
have consequences for thin-film devices. In practice, all types of
silicon solar cells are bonded to a protective glass or plastic top
coating. In principle, block copolymer antireflection schemes can
be applied to glass surfaces as well. The tapered vertical profile
gradually changes ni from air (nA ¼ 1) to silicon (nS ¼ 5.6 at
400 nm; nS ¼ 3.6 at 1 mm). Shallower nanotextures preferentially
decrease the reflectance at shorter l (Fig. 1e, blue colour), consistent with the requirement of t/l40.4 for full antireflection in a
moth eye structure. Taller nanotextures extend the antireflection
to longer l (Fig. 1e, red colour). We estimate neff(z) for hexagonal
arrangements of cones with subwavelength dimensions that taper
to a point at their top (z ¼ 0) and join at their base (z ¼ t) using
the effective medium approximation (EMA) (q ¼ 0,
Supplementary Methods), valid for l4p � cB200 nm, by calculating the fractional areal coverage of silicon [pf f fS(z)] and air [fA(z)]
versus depth (z): fSðzÞ ¼ p=2 3 - ðz=tÞ 2 and fA(z) ¼ [1 � fS(z)].

pf f
3

f f

versus depth (z): fSðzÞ ¼ p=2 3 - ðz=tÞ 2 and fA(z) ¼ [1 � fS(z)].

Neglecting light absorption in air and silicon:

f f f f f f f f f f f f f f f f f f f f f f f f

pf f i f f i f f
neff ðzÞ ¼ Eeff ¼

f f f f f f i f i f i f i f i f f f f f f f f f f f f i f i f f

pf f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f
ES � fSðzÞ þ EA � ½1 � fSðzÞ�

f f f f f f i f i f i f i f i f f f f f f f f f f f f i f i f f

tB0.4 � lB400 nm to achieve average broadband reflectance of
o1%. The required nanotexture height decreases linearly with c
(Fig. 2c; Fig. 2d, red triangles), shrinking to only B165 nm for
c ¼ 40 nm. The largest textures we measured (c ¼ 67 nm) require
a height of t ¼ 440 nm (Fig. 2d, red triangles), similar to the value
of 430 nm for o1% average reflectance calculated using the

rf f i f f i f f i f f i f f i f f i f f i fp f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f� f i f f i fz f i�f f i f2 f i f ð1Þ

EA þ ~~pf~~ f ðES � EAÞ � ;

f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f f i f
p �z�2
EA þ ~~pf~~ f ðES � EAÞ � ;
2 3 t

with EA and ES are the frequency-dependent dielectric constants of
air and silicon, respectively.

The surface nanotexture provides broadband antireflection
over a wide range of incident light angles. The reflectance of a flat
silicon surface (at 650 nm) versus incident angle is markedly
different for s- and p-polarized light, while a nanotextured silicon
surface with t ¼ 230 nm and c ¼ 52 nm displays similar, reduced
reflectance for both polarizations (Fig. 1f). The texture’s deeply
subwavelength lateral separation (c) eliminates diffraction effects
(that is, col/2n for l4400 nm), such that the average
reflectance (R�(spol þ ppol)/2) remains o4% for angles as high
as 60� from normal. The nanotexture provides omnidirectional
antireflection across a broad l-range. For example, at a 45�
incident angle the average reflectance of s- and p-polarized light
between 400 nmolo1 mm is o1%, more than 10 � smaller
than that of flat silicon (Fig. 1g).

Reflectance dependence on nanotexture dimensions. Nanotextures made from self-assembled block copolymer templates
with different c have qualitatively similar vertical profiles and,
when sufficiently tall, also provide high antireflection across a
broad range of l. A powerful characteristic of block copolymers
as patterning materials is their lateral size tunability. For example,
a cylindrical phase PS-b-PMMA with Mw ¼ 67 kg mol � 1 generates surface textures with c ¼ 40 ± 3 nm (Fig. 2a), while
Mw ¼ 132 and 177 kg mol � 1 produce structures with c ¼ 60 ± 8
and 67 ± 13 nm, respectively (Fig. 2b; Supplementary Fig. 2).
Increasing the copolymer Mw broadens the distributions of
nearest neighbour separations (c) (Supplementary Fig. 3) and
decreases the degree of hexagonal ordering (Supplementary
Fig. 4), because of slower self-assembly kinetics. However, neither of these affects the general results of our experiments because
of the deeply subwavelength dimensions of our structures (c5l).

Discussion
Textures with smaller feature sizes outperform the geometric
model of equation (1), needing o50% of the minimum height

Flat
_l_ =40 nm, _t_ =165 nm

52 nm
60 nm
67 nm

0
400 500 600

225 nm
330 nm
440 nm

700 800

900 1,000

500

400

Wavelength (nm)

Expt.
Cone
Hourglass
Hourglass w/mod

300

200

100

30 40 50 60 70 80

Separation, _l_ (nm)

Figure 2 | Variation of antireflection performance with nanotexture
separation. Scanning electron microscope (SEM) images (70�) of
nanotextures made from (a) 67 kg mol � 1 polystyrene-b-poly(methyl
methacrylate), with t ¼ 155 nm and c ¼ 40 nm, and (b) 132 kg mol � 1, with
t ¼ 300 nm and c ¼ 60 nm. Scale bar, 20 nm. (c) Measured reflectance
versus l for nanotextures with c ranging from 40 to 67 nm, and
corresponding t from 165 to 440 nm. (d) Measured height for 1% average
broadband reflectance versus nanotexture separation, c (red triangles).
Transfer matrix calculations of the minimum height required for 1% average
reflectance from (grey line) cone, (open circles) hourglass and (open
triangles) hourglass with surface modification, versus nanotexture
separation. The optical constants in surface modification calculations used
values measured for c ¼ 52 nm. (Inset) schematic nanotexture profiles.

transfer matrix method (Fig. 2d, grey line; Supplementary
Methods) and consistent with the taller heights of other silicon
moth eye structures with larger lateral dimensions 12,14,27 .
Calculations of the reflectance of a silicon nanotexture with an
hourglass profile and alumina cap (Fig. 2d, inset) also fail to
capture the measured trend with decreasing c (Fig. 2d, open
circles). Reflectance values calculated using the actual nanotexture
refractive index profile measured by spectroscopic ellipsometry
(SE) (for c ¼ 52 nm) more accurately reproduce the measured
data at smaller c (Fig. 2d, open triangles). Because the refractive
index profile contains both shape- and material-dependent
properties, we conclude that the measured reflectance results
from combined effects of the geometry and modifications to the
silicon surface optical properties (Supplementary Fig. 9) 28 .

The chlorine, bromine and oxygen etch chemistries we use to
generate the nanotextures are known to modify the silicon within
B5–10 nm of the surface 28,29, including redeposition of silicon
oxychloride 30,31, creating a surface layer with substantially
different optical properties 32 and providing an additional
mechanism for grading ni between air and silicon. In nanotextures with larger dimensions, this surface layer is an
inconsequential fraction of the total volume. However, because
our nanotextures have lateral feature sizes on the scale of 10 nm,
even material modifications within a few nm of the surface
comprise a significant volume fraction, and can thus substantially
alter ni of the entire structure.

We visualize changes in the nanotexture surface by comparing
cross-sectional scanning electron microscope images before
(Fig. 3a) and after (Fig. 3b) treating with a dilute (50:1)
hydrofluoric acid:water mixture (buffered with NH4F), which
removes surface oxides. In addition to stripping the alumina caps,
the etch narrows the texture radius by several nm, consistent with
removal of a silicon oxide layer that has been previously observed
during studies of similar etch chemistries (Supplementary
Fig. 5) 30,31 . These results are consistent with transmission
electron microscopy images showing the etched silicon nanotextures coated with an amorphous material (Supplementary
Fig. 6). X-ray photoelectron spectra of the nanotexture’s Si 2p and
O 1s core levels display higher binding-energy peaks
(Supplementary Methods; Supplementary Fig. 7), consistent with
those of a material previously identified as a porous, anodic silicon
oxide 33 . SE measurements of the complex refractive index profile
(n þ ik) of nanotextures with c ¼ 52 nm and increasing t show
the effect of such a modification, most easily observed at the
nanotexture base, where ni increases abruptly from B2 to the bulk
silicon value (ns ¼ 3.7) (Fig. 3c). In a two-dimensional closepacked arrangement of nanotextures composed of silicon alone, we
would expect a ni reduced only slightly from that of silicon at the
base (niB3.5; equation (1) with z ¼ t). Transfer matrix reflectance
calculations of silicon nanotextures (c ¼ 52 nm) using optical
constants obtained from SE measurements accurately describe the
measured data for all nanotexture heights (Fig. 3d), capturing both
the reflectance magnitude and optical resonance positions. These
simulations provide a significantly improved description compared
with similar calculations using bulk silicon optical constants
(Supplementary Fig. 9).

Applying the block copolymer-based surface nanotexture to a
crystalline silicon solar cell improves the power conversion
efficiency under AM1.5G illumination from 8.7 to 13.1%
(Fig. 4a). The broadband antireflection improves the photocurrent (Jsc) from 22 to 33 mA cm � 2, a substantial increase of
50% that agrees well with the integrated (from 400 to 1,000 nm)
50% increase in solar power transmitted to the device
(Supplementary Methods; Supplementary Fig. 16). The photocurrent is significantly improved over that of similar planar
devices coated instead with an optimized 80-nm-thick silicon

400 500 600 700 800 900 1,000

Wavelength (nm)

Figure 3 | Influence of a nanotexture refractive index profile. (a,b) 70�
Angle scanning electron microscope (SEM) images of nanotextures (a)
before and (b) after removal of surface oxide. Scale bar, 20 nm.
(c) Spectroscopic ellipsometry measurements of the effective refractive
index profile (n þ ik) at 750 nm wavelength for nanotextures with
c ¼ 52 nm and different heights. Up and down arrows refer plotted data to
the appropriate horizontal axes. The procedure for obtaining these data is
described in the Supplementary Methods. (d) Reflectance measurements
(thick lines) and transfer matrix calculations (thin lines) (normalized to the
flat substrate reflectance) versus wavelength for surface nanotextures
with c ¼ 52 nm and different heights. Geometric parameters used in the
calculations are provided in Supplementary Table 1.

nitride antireflection coating (Fig. 4a, green open circles). The
surface nanotexture allows the device to maintain nearly 100% of
the Jsc at normal incidence, even at oblique light angles 60� from
normal (Fig. 4b). The performance of all three devices is limited
by charge recombination, which manifests in the device dark
current (J0) and diode ideality factor (ndiode), and reduces the
device open-circuit voltage (Voc). The silicon nitride antireflection
coating slightly reduces both J0 (to 10 � 3 mA cm � 2 ) and ndiode
(to B1.8) compared with both planar and nanotextured devices
(where J0B3 � 10 � 3 mA cm � 2 and ndiodeB2), which improves
the device fill factor from 70 to 71%. Our future studies will target
understanding the passivation effects of the nanotextured interface and integration with higher-performance devices.

_�_ _�_ _�_ _�_

0.0 0.4 0.0 0.4 0.0 0.4 0.0 0.4
0

–100

–200

100

1 2 3

4 1 2 3 4 1 2 3 4 1 2 3 4

_n_ _n_ _n_ _n_

Expt.

Calc.

32 nm

100 nm

160 nm

215 nm

–10

–20

–30

–40

10 0

10 –2

10 –4

Flat

SiN

Nanotexture

1 SUN

Unilluminated

0.0 0.2 0.4 0.6

Voltage (V)

5 30

0
0 20 40 60 80

Angle of incidence (°)

Figure 4 | Integration of nanotexture antireflection with silicon solar
cells. (a) Illuminated (1 SUN) and unilluminated current–voltage (J–V)
characteristics of (black) flat silicon solar cell and similar cells coated with
(green open circles) an 80-nm-thick silicon nitride antireflection coating
and (red) a surface nanotexture. (b) Angular dependence of device
photocurrent (solid red triangles) and reflectance (red open triangles) when
illuminated with 632-nm light. Left and right arrows refer plotted data to the
appropriate horizontal axes.

Methods
Sample fabrication. Our nanostructured samples included surface textures made
from PS-b-PMMA block copolymers (Polymer Source Inc.) with molecular weights
of MW ¼ 67 kg mol � 1 (PS:PMMA 46:21, polydispersity PD ¼ 1.09), 99 kg mol � 1

(PS:PMMA 64:35, PD ¼ 1.09), 132 kg mol � 1 (PS:PMMA 96.5:35.5, PD ¼ 1.11) and
177 kg mol � 1 (PS:PMMA 131:46, PD ¼ 1.10). We mixed solutions of all polymers
in toluene at concentrations of 1% by weight. Block copolymer films were spin cast
from solution onto silicon wafers at rates of 3K r.p.m. (67 K polymer), 2K r.p.m.
(99 K polymer) and 1.6K r.p.m. (132 and 177 K polymers) and then annealed at
o1 Torr at a temperature of 205 �C for 12 h. Prior to spin coating the block
copolymer, we coated with a PS-r-PMMA random copolymer brush
(MWC11 kg mol � 1, PS:PMMA 52:48) by spin casting (0.4 wt % in toluene,
600 r.p.m.), thermally annealing for 4 h and rinsing with toluene. We converted
self-assembled PS-b-PMMA templates to aluminium oxide nanostructures by
infiltration of the PMMA domains using three sequential exposures to tri-methyl
aluminium and water vapour (for 300 s each at 45 Torr and 85 �C) in a commercial atomic layer deposition system (Cambridge Nanotech Savannah S100). We
removed all remaining organic materials by oxygen plasma (20 W rf power,
100 mTorr O2, 2 min) using a March Plasma CS1701 etcher.
We generate nanotextures in silicon having a conical profile by inductively
coupled plasma-reactive ion etching using an Oxford Instrument Plasma Lab 100
with a 50:50:10 ratio of HBr, Cl2 and O2 gas (10 mTorr, 60 W rf power, 250 W
inductive plasma power) at room temperature. We measure a vertical silicon etch
rate of B2 nm s � 1 and a slower lateral etch rate of 0.07 nm s � 1 . The process
includes a 10-s breakthrough using BCl3 and Cl2 (20:5 standard cubic centimetre
per minute, 10 mTorr, 100 W rf power, 800 W inductive plasma power). Samples
were characterized by scanning electron microscopy (Hitachi S4800) operating at
20 kV.
We fabricated silicon solar cells from Czochralski p-type (100) single-sidepolished silicon wafers (550 mm thick, boron doped, 8 O cm). We used 4-cm 2

samples and are limited in our laboratory to 100-mm-diameter substrates. We
formed the device p–n junction by diffusing phosphorous dopants from a solid
source (ACCUSPIN, Honeywell P-8545) by first spin-coating at 3K r.p.m. for 30 s,
baking on a hotplate at 150 �C (1 min) and annealing at 1,050 �C (20 s) in Ar using
rapid thermal annealing processing. We removed the phosphosilicate glass from

the substrate top surface using 10:1 buffered hydrofluoric acid (10 m). We formed
the device back-contact by thermal evaporation of aluminium (100 nm) and
annealing at 600 �C (1 m). The front-side contact was made with a
photolithography-defined grid pattern and metal deposition of titanium (70 nm)
and silver (100 nm). The total device area including front-side grid contacts is
(0.5 cm) 2 . We deposited silicon nitride antireflection layers (80 nm) onto control
devices by plasma-enhanced chemical vapour deposition prior to front- and backcontact metallization. We also formed surface nanotextures by the block copolymer
process after p–n junction diffusion but prior to front- and back-contact metallization.

Ultraviolet–visible light spectroscopy and spectroscopic ellipsometry. We
performed hemispherical reflectance measurements using a PerkinElmer Lambda
950 spectrophotometer equipped with an integrating sphere detector. The samples
were placed at an 8� angle relative to the incident beam direction. Specular
reflectivity for varying angle of incidence was measured using a supercontinuum
laser at different wavelengths and angle of incidence ranging from 10� to 85�. We
crosschecked these data with measurements using a Woollam Ellipsometer for
angles of incidence 445�.

We performed spectroscopic ellipsometry measurements using a J. A. Woollam
Variable Angle Spectroscopic Ellipsometer M-2000, based on the diode array
rotating compensator ellipsometer technology. We made measurements in three
distinct spots on each sample in the wavelength range of 210–1,700 nm and at
angles varying between 45� and 75� in divisions of 7.5�. We analysed ellipsometric
data by simultaneously fitting identical models from each of the three spots, which
were defined with coupled complex refractive indices, using the WVASE32
software (version 3.770,
J. A. Woollam Co.). We determined the best fit for the optical constants by
minimizing the mean square error between the measured and the modelled curves
using the Levenberg–Marquardt multivariate regressions algorithm.

We described the silicon material using a Drude model with critical-pointparabolic-band oscillators at 3.34 and 4.31 eV. Nanotextured silicon films were
modelled using a graded EMA of optical constants of silicon and air/void, where
the volume fraction of air/void versus depth is geometrically calculated. In this
model, the optical constants determined from bare silicon were allowed to vary to
give modified silicon optical constants. We divided the EMA layer into 40 slices
and the modified silicon optical constants were held constant within each slice.
More details can be found in the Supplementary Methods.

X-ray photoelectron spectroscopy. X-ray photoelectron spectroscopy measurements were performed in an ultrahigh vacuum system equipped with a SPECS
Phoibos 100 hemispherical analyzer and a dual-anode X-ray source. All measurements were carried out with non-monochromatized Al Ka excitation. The
measured data are fit with a Gaussian–Lorentzian product analysis (60% Lorentzian) carried out using CasaXPS software (www.casaxps.com).

Optical modelling. We computationally model the light reflection, transmission
and absorption spectra by the different nanostructured surfaces using the
transfer matrix method. For these calculations, we use the software package
[http://sjbyrnes.com/fresnel-solver.nb](http://sjbyrnes.com/fresnel-solver.nb) with some modifications. More details are
provided in the Supplementary Methods.

Solar cell measurement. We measure the current–voltage characteristics of our
silicon solar cells in the dark and under simulated AM1.5G illumination (calibrated
using a certified silicon reference cell) at normal incidence using an HP4156B
Semiconductor Parameter Analyzer. We perform the single-wavelength angular
current–voltage measurements using a Thorlabs HNL150L EC, He Ne Laser at
632.8 nm. We mounted the sample on a Thorlabs CR1-Z7-motorized rotation stage
and rotated in steps of 5�. The angular reflection measurements under oblique light
incidence are carried out using a Fianium WL-Micro supercontinuum laser. The
polarization of the incident light is selected using a Thorlabs broadband-polarizing
beamsplitter cube and is adjusted using a half-wave plate. The incident/reflected
light is detected using a Thorlabs PM100A power meter with a SV120VC silicon
photo-detector.

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Acknowledgements
This research is supported by the US Department of Energy, Basic Energy Sciences at the
Center for Functional Nanomaterials (A.R., H.X., X.T., P.S. and C.B.) and the Sustainable
Energy Technologies Department (A.A. and M.E.) under Contract No. DE-AC0298CH10886. We thank Drs Eric Stach and Nanditha Dissanayake for helpful discussions.

Author contributions
A.R. and C.T.B. designed and performed experiments related to fabrication of the
antireflection structures and solar cells. A.A. and M.D.E. performed optical simulations
and analysis, and designed optical experiments. A.A. and A.R. performed optical measurements and photovoltaic measurements. X.T. and P.S. performed X-ray photoelectron
spectroscopy and analysis. X.L. performed transmission electron microscopy. C.T.B.
primarily wrote the paper with all authors contributing.

Additional information
Supplementary Information accompanies this paper at [http://www.nature.com/](http://www.nature.com/naturecommunications)
[naturecommunications](http://www.nature.com/naturecommunications)

Competing financial interests: The authors declare no competing financial interests.

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How to cite this article: Rahman, A. et al. Sub-50-nm self-assembled nanotextures
for enhanced broadband antireflection in silicon solar cells. Nat. Commun. 6:5963
doi: 10.1038/ncomms6963 (2015).

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