SUPPLEMENTARY INFORMATION
doi: 10.1038/nmat2635
nature materials
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1
M. Kelzenberg, S. Boettcher, J. Petykiewicz, D. Turner-Evans, M.
Putnam, E. Warren, J. Spurgeon, R. Briggs, N. Lewis, and H. At
water.
"Enhanced
Absorption and Carrier Collection in Si Wire
Arrays for Photovoltaic Applications," 2009
1
Supplementary information
Device fabrication
Silicon nitride deposition
Silicon nitride antireflective (AR) coatings were
deposited onto Si wire arrays using an Oxford
Instruments Plasmalab System100 plasma-
enhanced chemical vapor deposition (PECVD)
tool. Silane and ammonia gas chemistry was
used at 350 °C and 1 torr, and the gas ratio was
adjusted to produce films with a refractive index
near 2. The PECVD process was performed with
in-situ stress control by
alternately pulsing a
13.56-MHz radio-frequency generator and a
50-kHz low-frequency generator, both with
20 W of forward power. Due to the large surface
area and aspect ratio of the arrays, the coating
required a much longer deposition time than
would be required for a pl
anar film of the same
thickness.
The nitride final film thickness was measured by
SEM, using focused-ion beam (FIB) milling to
produce wire cross-sections (Fig. S1). Individual
wires were removed from the growth substrate,
and deposited (horizontally) onto a Si wafer that
was coated with 80 nm SiN
x
(for contrast
reference). This was coated with various layers
of metal (Ag, Al) to facilitate milling and
imaging. The deposited nitride thickness was
observed to increase gradually along the length
of the wires, reaching ~2x the base thickness at
the top sidewall of the wire, and ~2.5x the base
thickness on the top surface of the wires (Fig.
S1a). Thickness appeared uniform around the
diameter of the wires (Fig. S1b). The nitride
thickness of the actual wire array whose
absorbance is plotted in Fig. 3 was verified by
milling a cross section of a single wire within the
center of the array, at approx. half the height of
the adjacent wires (Fig. S1c).
Multiple-angle spectroscopic ellipsometry was
used to measure the optical properties of a
planar film of PECVD silicon nitride.
Ψ
and
Δ
spectra, ranging from 350–2200 nm, were
measured at angles of 60°, 65°, and 70°, as
shown in Fig. S2a. The spectra were then fit to a
Forouhi-Bloomer
model
for
amorphous
dielectric materials.
1
The real and imaginary
parts of the index produced by the fit are plotted
in Fig. S2b. Based on these values, the
absorption of an 80-nm nitride film is negligible
(<2%) throughout most of the measurement
range in this study (
λ
> 500 nm).
a
b
Figure S2.
Spectroscopic ellip
sometry characteri-
zation of silicon
nitride film.
c
Figure S1. Determination of nitride thickness.
a,b,
cross-sectional SEM im
ages of nitride-coated
wires removed from growth substrate. Partial
false-coloring adde
d for clarity.
c,
cross-sectional
SEM image of nitride-coated wire from center o
f
wire array, with inset showing milling area.
a
b
2
nature materials
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SUPPLEMENTARY INFORMATION
doi: 10.1038/nmat2635
M. Kelzenberg, S. Boettcher, J. Petykiewicz, D. Turner-Evans, M.
Putnam, E. Warren, J. Spurgeon, R. Briggs, N. Lewis, and H. At
water.
"Enhanced
Absorption and Carrier Collection in Si Wire
Arrays for Photovoltaic Applications," 2009
2
Al
2
O
3
light-scattering particles
Alumina particles were embedded within the
PDMS infill of selected wire arrays, to scatter the
light that might otherwise pass between the
wires without being absorbed. Al
2
O
3
particles
(< 0.9
μ
m
nominal
particle
size)
were
hydrophobicized via surface functionalization
(> 1 hr in 10
l/ml trimethylchlorosilane in
CH
2
CL
2
). After washing several times to
removed excess trimethylchlorosilane, the parti-
cles were suspended in CH
2
CL
2
by sonication.
This suspension was mixed with uncured PDMS
to yield a ratio of 1:10:10 Al2O3:CH2Cl2:PDMS
by weight. The suspension was drop cast onto
the wire arrays and spun at speeds of 1500–
3000 RPM (depending on de
vice area). Prior to
curing, the arrays were
centrifuged for several
minutes to drive the Al
2
O
3
particles towards the
bottom of the PDMS layer. Wire array films
were cured and peeled-off as described in the
Methods
section.
Following characterization of the optical absorp-
tion, a wire array with the SiN
x
AR-coating and
embedded Al
2
O
3
particles was sliced in half with
a razor blade for cross-sect
ional imaging. Due to
the insulating nature of the PDMS, an
environmental SEM was employed, using H
2
O
vapor at 2–4 mbar to mitigate charging effects.
Fig. S3a shows the cross-section of the wire
array whose absorption is plotted in Fig. 3.
Alumina particles were
observed between the
wires, distributed within the lower half of the
PDMS film. Near the edge of this specimen,
larger agglomerates of alumina particles were
also observed above the top of the wire array
(Fig. S3b), although these areas were not
illuminated during optical measurements. Some
wires were inadvertentl
y severed during the
cross-sectioning process, allowing the ~80 nm
SiN
x
AR-coating to be observed (Fig. S3b, inset).
The optical properties of the PDMS-embedded
Al
2
O
3
particles were also measured, to ensure
that they did not contribute to parasitic
absorption within the Si wire arrays. A drop of
the PDMS with suspended Al
2
O
3
particles was
cured on a quartz slide without spinning or
centrifuging,
to
yield
a
film
thickness
comparable to that of the wire arrays (est.
300
μ
m). The absorption of this film is shown in
Fig. S4, indicating absorption was less than 2%
throughout the spectral range of this study.
a
b
Figure S3.
SEM images of the polymer-
embedded Si wire array
that was measured in
Fig. 3.
a,
cross-section of central area of array
showing distribution of Al
2
O
3
particles.
b,
view o
f
edge of array, with inset showing the ~80 nm SiN
x
AR-coating visible on wire sidewall.
Figure S4.
Integrated normal-incidence absorp-
tion of ~300
μ
m-thick film of Al
2
O
3
particles
embedded within PDMS. Inset: Digital photo-
graph of this
specimen.
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SUPPLEMENTARY INFORMATION
doi: 10.1038/nmat2635
M. Kelzenberg, S. Boettcher, J. Petykiewicz, D. Turner-Evans, M.
Putnam, E. Warren, J. Spurgeon, R. Briggs, N. Lewis, and H. At
water.
"Enhanced
Absorption and Carrier Collection in Si Wire
Arrays for Photovoltaic Applications," 2009
3
Integrating sphere measurements
Experimental apparatus
Integrated
reflection
and
transmission
measurements were performed with a custom-
built 4” integrating sphere apparatus, as shown
in Figure S5. The internal surfaces of the sphere,
baffles, port apertures, and stages were
sandblasted, then cleaned and coated with a
BaSO
4
integrating sphere coating (LabSphere,
Inc) to achieve nearly ideal Lambertian
reflectivity. Illumination was provided by a
chopped supercontinuum laser source (Fianium)
coupled to a 0.25 m monochromator, allowing
tunable excitation from 400 nm to > 1600 nm
with a typical passband of < 0.5 nm. The illumi-
nation beam was focused to produce a 1 mm spot
size (FWHM) with < 0.1
of beam divergence. A
pair of calibrated Si (400–1150 nm) or Ge
(1000–1600 nm) photodiodes was used to
simultaneously monitor the light intensity of the
incident beam (referenced via a quartz beam-
splitter) and the light intensity internal to the
sphere. Measurements were typically performed
from 400–1150 nm in 2 nm increments, except
between 1058 and 1070 nm where the reported
values were interpolated from measurements at
either endpoint due to an unstable peak in the
illumination intensity at 1064 nm.
In transmission mode, each specimen was
placed over a 10 mm-diameter entrance port of
the integrating sphere (Fig. S5a). Motorized
operation permitted eu
centric rotation and
translation in two dimensions with 0.1
and
100 μm resolution, respectively. The wire array
transmission was normalized to the previously
measured transmission of the quartz slides
which was accessed by motorized translation of
the sphere at the beginning of the measurement
sequence. In reflection mode, each specimen
was placed at the center of the sphere over a 5
mm-diameter light trap that absorbed any light
transmitted through the specimen (Fig. S5b).
Motorized
operation
permitted
eucentric
rotation in one dimension (
θ
x
) with 0.1
resolu-
tion. The tilt in the second (
θ
y
) dimension was
typically fixed at ~0.5°, to prevent the specular
reflection from escaping the sphere through the
1 mm-diameter illumination port aperture. The
wire array reflection
was normalized to a
Figure S5. Illustration of integrating sphere measurements.
a,
configuration for transmission
measurements. The incidenc
e beam angle variation was achieved by
the eucentric tilt of the entire sphere
apparatus.
b,
configuration for reflection measurements.
The incidence beam angl
e variation was achieved
by rotation of the reflection stage within the sphere.
b
a
4
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SUPPLEMENTARY INFORMATION
doi: 10.1038/nmat2635
M. Kelzenberg, S. Boettcher, J. Petykiewicz, D. Turner-Evans, M.
Putnam, E. Warren, J. Spurgeon, R. Briggs, N. Lewis, and H. At
water.
"Enhanced
Absorption and Carrier Collection in Si Wire
Arrays for Photovoltaic Applications," 2009
4
reflectance standard (Lab
Sphere, Inc) within the
sphere, which was accessed by motorized
translation and rotation of the specimen stage
and sphere assembly. For the measurements
performed on specular back-reflectors, each wire
array film was removed from the transparent
quartz slide and placed onto a slide which had
been coated with >100 nm of evaporated Ag.
For the Lambertian back reflector studies, each
wire array film was removed from the
transparent quartz slide and placed onto a sheet
of Al, that had been cleaned, roughened, and
coated with BaSO
4
like the other internal
surfaces of the integrating sphere. The
reflectivity of such surfaces exceeded 97%
throughout most of the measurement range (see
Fig. S6).
Determination of absorption
The
absorption
of
each
specimen
was
determined from the wavelength- and angle-
resolved integrated tran
smission and reflection
measurements. For non-opaque specimens (e.g.
wire arrays placed upon quartz slides),
absorption was calculated as:
)
,
(
)
,
(
1
)
,
(
T
R
A
(1)
For opaque specimens (e.g. the commercial Si
solar cell) or those placed on opaque back-
reflectors, absorption
was calculated from
reflectivity measurements only:
)
,
(
1
)
,
(
R
A
(2)
Example transmission, reflection, and resulting
absorption measurements of a triangular-tiled
array (
η
f
= 8.8%, 68
μ
m wire length) are shown
in Fig. S7. Similar measurements were
performed on all wire arrays in this study.
In Eqns. (1) and (2),
θ
represents the direction of
tilt during measurements, which was usually
θ
x
as defined in Fig. 1. Due to the angularly
anisotropic optical properties of the periodic
(e.g. square-tiled) wire arrays (see Fig. 2), it was
important that each array be tilted in the same
direction with respect to the lattice pattern of the
wires—especially
when
combining
angle-
resolved reflection and transmission measure-
ments to calculate absorption. Fiducial
markings at the corner of each array provided
approximate alignment marks; however to
ensure reproducible orie
ntation of the periodic
arrays within the tilt plane, their transmitted (or
reflected) diffraction patt
erns were used to align
Figure S6.
Integrated reflection measurements o
f
the back-reflectors used in these studies.
Figure S7. Example absorption measurements.
Schematic (top row) and measurements of reflec-
tion (second row), transm
ission (third row), and
absorption (bottom row) of a triangular-tiled wire
array (
η
f
= 8.8%), placed on a quartz slide (left
column) or a Lambertian back-reflector (right).
N/A
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SUPPLEMENTARY INFORMATION
doi: 10.1038/nmat2635
M. Kelzenberg, S. Boettcher, J. Petykiewicz, D. Turner-Evans, M.
Putnam, E. Warren, J. Spurgeon, R. Briggs, N. Lewis, and H. At
water.
"Enhanced
Absorption and Carrier Collection in Si Wire
Arrays for Photovoltaic Applications," 2009
5
each array’s lattice pattern orientation to the
match the convention depicted in Fig. 2.
Furthermore, the specular reflection from each
specimen was used to align the equipment to
normal-incidence illumination conditions prior
to each measurement.
Sub-bandgap absorption
Spectrally resolved measurements of the wire
arrays were also performed at wavelengths
exceeding the Si band edge (1150–1200 nm),
where no band-to-band absorption is expected.
In the absence of a back-reflector, the observed
sub-bandgap absorption did not exceed -4% to
+12%, and was typically below 5%. Some
deviation from zero absorption (negative values
in particular) can be attributed to an
experimental artifact ar
ising from the spatial
variation in the array’s optical density, because
the transmission and reflection measurements
were not necessarily performed at the same
location
on
each
wire
array
specimen.
Variations of up to 0.08 in absolute transmis-
sion were observed ac
ross the wire arrays;
however this artifact alone could not account for
the larger instances of sub-bandgap absorption,
nor that observed when
the arrays were placed
on the back-reflector (1–16%). Thus, this sub-
bandgap absorption may be due to parasitic
(non-photovoltaically useful) absorption proc-
esses. Parasitic absorption at above-bandgap
wavelengths would be detrimental to any photo-
voltaic device, and must be addressed in this
absorption study.
Free-carrier absorption is an intrinsic source of
parasitic absorption within Si solar cells.
2
However the absorption due to free-carrier pro-
cesses was likely negligible at these wavelengths,
because most wires were nominally undoped,
and the illumination levels were low (<< 1-sun
equivalent intensity). Absorption due to the
PDMS was also negligible: A relatively thick
(est. 1 mm thick) film of cured PDMS exhibited
absorption
below
~0.02
throughout
the
measurement range (Fig. S8).
Others have reported su
b-bandgap absorption in
Au-catalyzed, VLS-grown Si wire arrays (up to
~0.6 at these wavelengths), and this has been
primarily attributed to the presence of surface
states, defects, or catalyst metal particles
3-5
. It is
well-known that certain defects or impurities
introduce energy levels or bands within a
semiconductor’s bandgap, and can give rise to
extrinsic (trap-assisted) sub-bandgap absorp-
tion.
6
Known as the impurity photovoltaic (IPV)
effect, this theoretically useful sub-bandgap
absorption mechanism has been proposed and
studied as route to exceed the efficiency limit of
a single-junction solar cell,
7-9
particularly in non-
planar junction geometries.
10-11
The IPV effect has been experimentally observed
at roughened Si surfaces
12
and for Au traps in
bulk Si,
13-14
both of which may be present in Au-
catalyzed, VLS-grown Si wires. However, IPV
absorption has not yet been shown to produce
an overall increase in e
fficiency vs. comparable
conventional Si solar ce
lls. Moreover, no sub-
bandgap photogeneration has been reported for
either surface-state-induced or Au-trap-induced
IPV absorption within a purely photovoltaic
device. Because of this, and the well-known
deleterious properties of surface damage and
deep-level traps within Si solar cells, we
conclude that IPV absorption, if present, should
not presently be considered useful for the
purpose of estimating photovoltaic performance
limits from absorption measurements.
Figure S8.
Integrated normal-incidence
absorption of ~1-mm-thick PDMS film.