Supplementary information
Fabrication methods
The Si microwire arrays were grown by a
photolithographically patterned SiCl
4
VLS
process, as described previously, using BCl
3
for
p-type doping and 300 nm Cu as the catalyst.
1-3
Following growth, the Cu catalyst was removed
by etching the wire arrays for 30 s in 5% HF(aq),
for 20 min in 6:1:1 by volume H
2
O:H
2
O
2
(30% in
H
2
O):conc. HCl(aq) at 75 °C, and for 60 s in
20 wt % KOH(aq) at 20 °C. A conformal SiO
2
diffusion-barrier (~200 nm thick) was grown by
dry thermal oxidation for 2 hr at 1100 °C. The
wire arrays were then partially infilled with poly-
dimethylsiloxane (PDMS), as described
previously.
6
Briefly, wire array samples were
coated with a solution that contained 4.4 g
hexamethylcyclotrisiloxane (Sigma-Aldrich), 1 g
PDMS (Sylgard 184, Dow Corning), and 0.10 g
curing agent in 5 ml of dichloromethane; spun at
1000 RPM for 30 s; and cured for 30 min at
150 °C, producing a 10–15
μ
m thick PDMS layer
at the base of the wire a
rray (thicker infill layers
were achieved by repeating this process up to 4
times). The partially infilled arrays were etched
for 5 min in buffered HF (BHF) to remove the
exposed diffusion-barrier oxide, then the PDMS
was removed by etching for 30 min in a solution
of 1.0 M tetra-n-butylammonium fluoride made
using a 1:1 (vol) mixture of tetrahydrofuran and
dimethylformamide.
7
A 10 min piranha etch (3:1
aq. conc. H
2
SO
4
:30% H
2
O
2
) was also performed
to remove any residual organic contamination.
To form the radial p-n junctions, the wire arrays
were etched for 5 s in 10% HF(aq), then thermal
P diffusion was performed for 10 min at 850 °C
using CeP
5
O
14
source wafers (Saint-Gobain, PH-
900), followed by a 30 s deglaze in BHF.
Spreading resistance me
asurements (Solecon
Laboratories) on Si control wafers indicated a
junction depth of 100 nm and a surface dopant
concentration of 1×10
19
cm
-3
. Individual micro-
wires were removed from the array using a razor
blade, suspended in isoproponal, and dispersed
onto sapphire or SiN
x
/Ag-coated-Si wafers.
*
Ag-capped Al contacts
were photolitho-
graphically patterned as described previously.
4
*
The PECVD a-Si:H was deposited at 240 °C and
500 mTorr, using 5% SiH
4
in Ar at a total flow
rate of 100 sccm, and a 13.56 MHz plasma at
3 W forward power. A 30 min deposition time
was chosen to produce a ~10 nm-thick layer of
nominally intrinsic a-Si:H on the wire sidewalls.
After metallization, the a-Si:H-coated single-
wire devices required a 30 min anneal at 275 °C
in forming gas (5% H
2
in N
2
) to produce ohmic
contacts through the a-Si:H layer. The a-SiN
x
:H
was deposited at 350 °C and 1 Torr in a parallel-
plate reactor (Plasmalab System100, Oxford
Instruments), using a SiH
4
/NH
3
gas chemistry
whose ratio was chosen to produce films that
had a refractive index of ~2.0 (400 sccm 5%
SiH
4
in N
2
, 30 sccm NH
3
). In-situ stress control
was performed by alternating between a 3.56-
MHz and 50-kHz plasma frequency, both with
20 W of forward power (65% RF duty cycle).
Deposition was performed
for 25 min, producing
a coating that varied from ~60 nm thick at the
wire base to ~120 nm thick at the wire tip, as
observed by cross-sectional SEM (Fig. S3). Prior
to removing wires from the growth substrate, the
a-SiN
x
:H-coated arrays were partially infilled
with wax (Quickstick 135, South Bay Tech.) and
then etched for 10 s in 49% HF(aq) to remove
the a-SiN
x
:H from the uppermost ~10 μm of
each wire,
8
enabling the formation of single-wire
contacts.
I–V
measurements were performed with a four-
point source-measure unit (Keithley 238). Sim-
ulated sunlight was provided by a 1000 W Xe arc
lamp with AM 1.5G filters (Oriel) calibrated to 1-
sun illumination (100 mW•cm
-2
) by an NREL-
traceable Si reference cell (PV Measurements).
*
Sapphire substrates: 2”, 350 μm thick, double-side-polished
C-plane wafers. Ag substrates: 3” n
+
Si <100> wafers, top-
side-polished, coated with 100 nm Ag by thermal
evaporation (for reflectivity), then with 200–300 nm SiN
x
by
PECVD as described above (for insulation).
M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs, C. Baek, N. Lewis, and H. Atwater.
Supplementary information, "High-performa
nce Si microwire photovoltaics," 2010
1
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Characterization of PECVD films
Note: Some of the information and figures
regarding the a-SiN
x
:H films also appear as
supplementary information for reference (
5
).
The res
e
arch for both studies was carried out
concurrently using identical a-SiN
x
:H deposi-
tion conditions.
a
b
Figure S1.
Characterization of PECVD a-SiN
x
:H by
spectroscopic ellipsometry.
These plots also
appear as supplementary figure S2 in reference (
5
).
In this study, amorphous hydrogenated films of
silicon (a-Si:H) and silicon nitride (a-SiN
x
:H)
were deposited by plasma-enhanced chemical
vapor deposition (PECVD) onto Si wire-arrays to
serve as anti-reflective and/or surface-
passivation layers. The optical properties of
both film types were measured by depositing
them onto planar Si wafers and performing
multiple-angle spectroscopic ellipsometry.
Ψ
and
Δ
spectra, ranging from 350–2200 nm, were
measured at angles of 60°, 65°, and 70° (as
shown in Fig.
S1a
for an a-SiN
x
:H film). The
spectra were then fit to a Forouhi-Bloomer
model for amorphous dielectric materials.
9
The
real and imaginary parts of the index produced
by the fit are plotted in Figures
S1b
and
S2
for
a-SiN
x
:H and a-Si:H, respectively. These values
were used for the optical modeling of Si wire
solar cells presented elsewhere in this study.
Figure S2.
O
p
tical properties of PECVD a-Si:H as
determined by spectros
copic ellipsometry.
The thickness profile of the a-SiN
x
:H films
deposited onto the Si wires was measured by
SEM, using focused-ion beam (FIB) milling to
produce wire cross-sections (Fig.
S3
). Individual
wires were r
e
moved from the growth substrate
and deposited (horizontally) onto a Si wafer,
then blanket-coated by the same Al/Ag metal
layers used to form electrical contacts elsewhere
in this study (in this the metal served to facilitate
milling and imaging). The deposited nitride
thickness increased gradually along the length of
the wires, reaching ~2× the base thickness at the
top sidewall of the wire, and ~2.5× the base
thickness on the top surface of the wires.
Average sidewall deposition rates were ~4×
slower than those produced on planar
structures. For this study, the deposition was
performed for 25 min to target wire-sidewall
nitride-thicknesses ranging from ~60 nm at the
wire bases to ~120 nm at the wire tips. The
a-Si:H film thickness was not directly imaged on
Si wire surfaces. However, the deposition rate
was calibrated for planar control structures,
using ellipsometry to measure film thicknesses,
and the deposition time was extended by 4× to
produce the desired film thickness (~10 nm) on
the wire sidewalls.
Figure S3.
Cross-sectional SEM images of an
a-SiN
x
:H-coated wire, showing nitride thickness
variation along the length of the wire, as well as
the structure of the evaporated Al/Ag films used
for contact electrodes in th
is study. Partial false-
coloring added for clarity.
This image also appears
as supplementary figure S1 in reference (
5
).
M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs, C. Baek, N. Lewis, and H. Atwater.
Supplementary information, "High-performa
nce Si microwire photovoltaics," 2010
2
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Scanning photocurrent microscopy
Scanning photocurrent microscopy (SPCM)
measurements have been widely used to study
carrier transport within semiconductor nano-
wire and microwire structures.
1
,
4
,
10
-
13
In this
study, SPCM measurements were performed
using a confocal microscope in a light-beam-
induced current (LBIC) configuration as
described previously.
1
,
4
A chopped laser source
(
λ
= 650 nm for bulk excitation or
λ
= 405 nm
for surface excitation) was focused to a diffract-
tion-limited spot size through a 50×, N.A. = 0.95
microscope objective, and the induced specimen
photocurrent was record
ed using lock-in detec-
tion. SPCM images were formed by rastering the
single-wire devices beneath the beam.
Prior to each measurement, the incident beam
intensity was measured with a calibrated photo-
diode, allowing the specimen current to be
reported in terms of the external quantum
efficiency (E.Q.E.). A typical beam photocurrent
of 20–200 nA was used, which induced peak
specimen photocurrent values of the same
approximate magnitude as each device’s 1-sun
I
SC
. We note, however, that all devices exhibited
nominally identical SPCM profiles under
~2000× lower illumination levels (Fig.
S4
),
indi
cati
ng that the observed recombination rates
were not an effect of higher injection levels than
would be present within each wire under 1-sun
illumination. The SPCM profiles were found to
be insensitive to sample bias (ranging from
−
1 to
0.4 V), and were also not affected by the
application of broad-area illumination that was
previously shown to temporarily reduce surface
recombination in p-type VLS-grown Si micro-
wires with native-oxide-terminated surfaces.
1
Unless noted, all SPCM measurements reported
in this study were perf
ormed at short-circuit
(zero bias voltage) using
λ
= 650 nm excitation
under otherwise dark conditions.
Passivation with hydrofluoric acid
For this study, some SPCM measurements were
performed on single-wire devices that were fully
immersed in buffered hydrofluoric acid (BHF).
Hydrofluoric acid is known to effect unusually
low surface recombination velocities at Si
surfaces (
S
< 1 cm·s
-1
).
14
To enable these meas-
urements, single-wire devices were fabricated on
sapphire substrates to provide the necessary
stability under BHF immersion. (For consist-
ency, all other SPCM devices were also
fabricated on sapphire substrates.) The devices
were then covered with a positive photoresist
layer (S1813, Microchem) to protect the metal
contacts from corrosion. The photoresist was
patterned and developed to expose a well over
the central portion of each wire (Fig.
S5a
) and to
expose
th
e contact bond pads (located several
mm away). To extend the longevity of the
photoresist under BHF immersion, the devices
were baked at 115°C for ~2 min shortly before
beginning the measurements. Initial
I–V
behavior and SPCM profiles were recorded to
determine the properties and extent of the radial
p-n junction within each device (Figs.
S5b
and
S5d
). A droplet of pH = 5.0 BHF (Transene) was
then
plac
ed over the wire and covered by a small
plastic coverslip to prevent evaporation and
enable imaging through the liquid.
Figure S4.
SPCM profiles of an a-SiN
x
:H-coated
device measured under typical (
I
opt
= 200 nA) and
reduced (
I
opt
= 0.1 nA) excitation intensity. The
dashed white lines indicate the location of the
contacts, and the arrows
indicate start of radial
p-n junction.
For the first 1–3 min
of immersion
in BHF
(before the SiO
2
diffusion-barrier was etched
away), the wires exhibited no noticeable change
in SPCM behavior. Once the surface oxide had
M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs, C. Baek, N. Lewis, and H. Atwater.
Supplementary information, "High-performa
nce Si microwire photovoltaics," 2010
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been removed, collection was observed from
throughout the axial region of the wire (Fig.
S5c
). Because each SPCM image acquisition
required ~3
min to co
mplete, we were unable to
observe the dynamics of the transition. The
SPCM behavior indicated an effective carrier
collection length,
L
eff
, of >> 20
μ
m (the longest
axial wire length studied by this technique).
Light
I–V
measurements, performed under
broad-area illumination from the microscope’s
halogen lamp, showed an increase in
I
SC
that was
roughly commensurate with the increase in
active area observed by SPCM (Fig.
S5d
). The
SPCM
an
d
I–V
behavior of the BHF-immersed
devices remained essentially constant for
another 10–30 min, after which time the
contacts began to corrode (starting with the
evolution of bubbles beneath the photoresist
that quickly grew so as to preclude further SPCM
measurements). The devices were then rinsed
and dried, after which some exhibited open-
circuit behavior (due to the wire or contact
structure having been washed away), while
others exhibited SPCM profiles similar to that
observed prior to BHF immersion (i.e.,
L
eff
< 0.5
μ
m).
Prior to removal from the growth substrate,
some wires had also been etched in BHF to fully
remove the SiO
2
diffusion-barrier from the axial
region. These wires also showed
L
eff
< 0.5
μ
m
behavior under SPCM, confirming that a high
axial-region surface recombination velocity also
existed at native-oxide-terminated surfaces.
Determination of junction position and
minority-carrier collection length
Non-passivated wires:
SPCM measurements
on non-passivated wires indicated a very short
L
eff
within the axial portion of each wire. In fact,
the decay in carrier collection within these
regions could not be resolved by the ~0.5
μ
m-
diameter diffraction-limited spot size of the
illumination source. Figure
S6
shows the log-
scale SPCM
profile of a typical non-p
assivated
wire device, illustrating how the spatial decay in
photocurrent along the axial direction of the
wire occurred as abruptly at the end of the radial
junction as at it did at the edge of the metal
contacts. The abrupt transition from radial to
axial carrier collection clearly identified the
endpoint of the radial p-n junction within each
wire, and always occurred at the edge of the SiO
2
diffusion-barrier oxide (when such was present,
e.g., as shown in Figure 3a of the manuscript).
Figure S5.
SPCM measurements of single Si
wire device
s pass
ivated by buffered HF (BHF).
a,
Microscope image of the test structure.
b,c,
SPCM profiles of the exposed wire area before (b)
and after (c) immersion in BHF. Dashed lines
indicate the location of metal contacts. The
reduced spatial resolution of these SPCM profiles
was due to the use of a 20x, N.A. = 0.4 objective to
provide greater working distance.
d,
Light
I-
V
behavior under microsco
pe lamp illumination,
measured before and during immersion in BHF.
Figure S6.
Microscope image (top) and log-scale
SPCM image (bottom) of
a typical non-passivated
single-wire test structure.
M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs, C. Baek, N. Lewis, and H. Atwater.
Supplementary information, "High-performa
nce Si microwire photovoltaics," 2010
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Figure S8.
SPCM image (above) and linear-scale
cross-section (below) of
the wire shown in Fig.
S7
,
acquired using a
λ
= 405 nm illumination source.
a-Si:H-coated wires:
SPCM measurements
on a-Si:H-coated wires indicated exponentially-
decaying carrier collection along the axial length
of each wire, as expected for transport limited by
minority-carrier diffusion within the quasi-
neutral region of a p-n junction device. Figure
S7
plots linear- and log-scale cross-sections of
the SPCM p
r
ofile of the a-Si:H-coated device
from Fig. 3c. Approximately constant E.Q.E.
was observed throughout the radial portion of
the wire (
x
< 0
μ
m), while exponentially
decaying E.Q.E. was observed in the axial
portion of the wire (
x
> 0
μ
m). A fit to the
exponential decay indicated
L
eff
= 8.7
μ
m for this
device. Six a-Si:H-coated single-wire devices
were studied by SPCM, and
L
eff
values ranging
from 5.4–9.8
μ
m were observed.
Because the SiO
2
diffusion-barrier had been
removed from the a-Si:H-coated wires, the
spatial extent of the axial region could not be
directly observed by optical microscopy. Thus,
the endpoint of the radial p-n junction was
inferred from the SPCM pr
ofiles of each wire,
assumed to occur at the onset of exponentially
decaying E.Q.E. However, minor fluctuations in
E.Q.E. were also observed throughout the entire
wire, obfuscating the transition between radial
and axial collection. We believe that these
fluctuations arose from photonic effects rather
than from variations in
the carrier-collection-
efficiency along the wires. At the illumination
wavelength (
λ
= 650 nm), the optical absorption
properties of Si microwires are dominated by
scattering and dielectric resonance effects, which
depend strongly on the wire diameter.
15
The
diameters of our wires varied and generally
decreased slightly from base to tip, with a typical
taper of 10–20% observed by SEM (see Fig.
S3
).
To demons
tr
ate that the radial-region carrier-
collection-efficiency was approximately uniform,
we performed SPCM measurements with a
λ
= 405 nm illumination source, at which
wavelength the Si microwires were optically
opaque and thus less affected by dielectric
resonances. Figure
S8
shows the
λ
=
405
nm
SPCM image of the same a-Si:H-coated wire,
which exhibits a more-uni
form carrier-collection
efficiency within the radial
region of the wire, as
well as a more-pronounced transition to
exponentially decaying behavior within the axial
region of the wire.
a-SiN
x
:H-coated wires:
SPCM measurements
on a-SiN
x
:H-coated wires indicated relatively
constant E.Q.E. throughout the entire non-
Figure S7. Cross-sectional SPCM profile of an
a-Si:H-coated
single-
wire device.
Top: SPCM
image, with the metal contacts and the start o
f
the radial p-n junction indicated by the white
hashed areas and arrow, respectively. Below:
Linear-scale (center) and log-scale (bottom) cross-
sections of the above SP
CM data, taken along the
center of the wire, with dotted line indicating
exponential fit to data. Data is aligned so that the
axial region started at
x
> 0
μ
m.
M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs, C. Baek, N. Lewis, and H. Atwater.
Supplementary information, "High-performa
nce Si microwire photovoltaics," 2010
5
Supplementary Material (ESI) for Energy & Environmental Science
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shaded extent of each wire, indicative of large
values of
L
eff
. This behavior, combined with the
absence of the SiO
2
diffusion-barrier as a visual
aid, presented a challenge to the determination
of the junction position within the a-SiN
x
:H-
coated wires.
SPCM measurements performed at
λ
= 405 nm
and
λ
= 650 nm both showed mild variations in
E.Q.E. along the length of the a-SiN
x
:H-coated
wires (Fig.
S9
). However, the two measure-
me
nts showed no common trends that might
identify the start of the radial junction,
suggesting that the variations were due to optical
(rather than electrical) phenomena. In addition
to the effects of the tapering wire-diameter
described above (evident in
λ
= 650 nm SPCM
images), the a-SiN
x
:H-coated wires also
exhibited optical artifacts due to the varying
nitride thickness (evident at both SPCM
wavelengths). As shown in Figure
S3
, the
PECVD a-Si
N
x
:H films tapered from ~60 nm
sidewall thickness at the wire base to ~120 nm
sidewall thickness at the wire tip, which also led
to apparent variations in the color of the wires
under optical microscopy (Fig.
S10
).
Figure S9.
SPCM measuremen
ts of an a-SiN
x
:H-
coated single-wire device, measured with
λ
=
405 nm (upper) and
λ
= 650 nm (lower) illumina-
tion sources. Below: no
rmalized cross-sections o
f
the above profiles. The radial p-n junction
extends from beneath the left contact.
Figure S10.
Optical micrograph of two a-SiN
x
:H-
coated Si microwires lying on a Ag substrate,
showing coloration due to the variation in nitride
thickness along the length of the wires.
Figure S11.
a,
Optical microscope image,
b,
SEM
image, and
c-d,
SPCM images of an a-SiN
x
:H-
coated single-wire devi
ce. The SPCM images
were recorded before (c) and after (d) exposure to
30 keV electrons in the course of SEM imaging,
and reveal the extent of the radial p-n junction.
To determi
n
e the location of the radial p-n
junctions within the a-SiN
x
:H-coated wires, it
was found that irradiating them with 30 keV
electrons in the course of scanning electron
microscopy resulted in
L
eff
< 0.5
μ
m behavior
within their axial regions. Thus, immediately
following SEM imaging of the single-wire
devices, the junction position could be observed
by SPCM. Figure
S11
shows the SPCM profiles
for an a-SiN
x
:H-coated device observed before
(above) and after (below) SEM imaging,
revealing an axial wire length of ~30
μ
m.
Calculation of
τ
eff
and
S
Several previous studies have inferred effective
bulk minority-carrier lifetimes (
τ
eff
) and surface
recombination velocities (
S
) from minority-
carrier collection length (
L
eff
) measurements in
Si nano- and microwires.
1
,
4
,
16
The effective
minority-carrier lifetime is related to the
observed minority-carrier
collection length by
the standard relationship,
effn
eff
DL
,
where
D
n
is the minority-carrier (electron)
M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs, C. Baek, N. Lewis, and H. Atwater.
Supplementary information, "High-performa
nce Si microwire photovoltaics," 2010
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M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs
Supplementary information, "High-performa
nce Si microwire photov
diffusion coefficient. For cylindrical structures
such as Si wires, Allen et al. have provided
equations relating
τ
eff
to the bulk minority-
carrier lifetime,
τ
n
, the wire diameter,
d
Si
, and
the surface recombination velocity,
S
, in the
supplementary information of reference (
16
).
For each S
P
CM measurement, we solved these
equations numerically (ignoring bulk recombi
-
nation), using the measured diameter of each
wire (subtracting the estimated surface-coating
thickness from the apparent diameter when
appropriate), to obtain the value of
S
correspon-
ding to surface-recomb
ination-limited carrier
transport. Because all Si microwires in this
study were subject to identical high-temperature
processing steps, we assumed that all the devices
had identical bulk lifetimes (
L
n
>> 30
μ
m,
τ
n
>>
500 ns), and that variations in
L
eff
were due
solely to different
surface recombination
velocities.
Spectral response of single-wire test structures
Spec
tral r
esponse measurements were
performed on the champi
on single-wire test
structures of each surface-coating type. The
J-V
characteristics of these devices appear in Fig. 4.
Fi
gure S12.
Schematic illus-
tration of horizontal single-
wire test structures
and
definition of the active
device width,
d
. Substrates
had > 100 nm evaporated
Ag and ~300 nm PECVD SiN
x
.
Figure
S12
illustrates the cross-section of the
single
-wire devices in this configuration.
Because the optical absorption of horizontally
oriented microwires depends on the polarization
of the incident light, and because the
polarization state of our illumination source was
not known, the spectral response of each device
was measured twice, rotating the specimen 90°
between measurements. The two measurements
were then averaged to determine the spectral
response of each wire to
unpolarized light (such
as sunlight). The photoresponse of each device
was measured at short circuit (0 V) under
uniform, collimated monochromatic illumina-
tion (
λ
= 300–1100 nm) using lock-in detection,
and was normalized (by area) to that of a 3 mm
diameter calibrated photodiode to determine the
absolute external quantum efficiency (E.Q.E.) at
each wavelength (Fig.
S13a
).
Figure S13. a,
Measured spectral
response of the
champion single-wire devi
ce of each passivation
type. External quantum efficiency (E.Q.E.) was de-
termined based on the exposed physical area o
f
each wire.
b,
Simulated optical absorption of each
of the three devices plotted in (a).
c,
Simulated
photogeneration profiles within the non-coated
Si wire device at three
selected wavelengths.
, C. Baek, N. Lewis, and H. Atwater.
olt
aics," 2010
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Following the convention of prior single-wire
solar cell studies,
4
,
17-18
the exposed physical area
of each wire
*
(observed by SEM; excluding that
covered by the metal contacts) was used to
calculate the E.Q.E. Interestingly, this normal-
ization resulted in an apparent peak E.Q.E. of
~110% (near
λ
= 500 nm) for the a-SiN
x
:H-
coated single-wire device, warranting further
investigation of the optical absorption and the
effective area of these microstructures.
The observation of E.Q.E. > 100% can be
explained by the photonic dimensions of the Si
microwires (1.2–1.8
μ
m diameter). At this size
regime, scattering theory
predicts that particles
can exhibit effective absorption cross-sections
which exceed their physical cross-sections.
19
This enables Si microwires to interact with (and
potentially absorb) more sunlight than predicted
by physical area and conventional ray-
optics.
5
,
15
,
20-21
Combined with the anti-
reflectivity the a-SiN
x
:H coatings, the relatively
strong absorption of Si at
λ
~ 500 nm, and the
use of a back-reflecting substrate, this could lead
to an apparent E.Q.E. exceeding >100% when
the measured photocurrent is normalized to the
optical power incident upon the physical area of
the a-SiN
x
:H-coated wire structure.
To further investigate the interaction of light
with horizontal Si microwires, we simulated the
optical absorption of each of the studied single-
wire structures under the experimental
configuration of Figure
S12
. Two-dimensional
ele
c
tromagnetic simulations were performed at
40 discrete wavelengths spanning the measure-
ment range (
λ
= 310, 330, ... 1090 nm) using
finite-difference time-domain software (FDTD
Solutions, Lumerical). At each wavelength, the
results of independent tr
ansverse-electric (TE)
and transverse-magnetic (TM) simulations were
averaged, and partial spectral averaging was
*
For wires coated with SiO
2
, a-Si:H, or a-SiN
x
:H, the
outer diameter of the wire structure (
d
) , rather than
the diameter of the crystalline Si wire (
d
Si
), was used
to calculate device area (see Fig.
S12
).
For tapered
wir
es, the average diameter was used.
applied to emulate unpola
rized plane-wave illu-
mination at normal incidence.
†
22
Each simula-
tion took into account the measured wire diame-
ter, the estimated surface-coating thickness, and
the measured PECVD film optical properties
(see Figs.
S1
and
S2
), using tabulated optical
consta
nts
23
for Si and approximating the Ag
substrate as an ideal metal boundary condition.
Figure
S13c
shows the simulated absorption
profiles for t
h
e non-coated,
d
= 1.61
μ
m Si wire
device at three selected wavelengths. At short
wavelengths (
λ
< 450 nm), the absorption was
concentrated near the wire surface, whereas at
longer wavelengths (
λ
> 500 nm), the absorption
was concentrated near the center of the wire.
Following each simulation, the absolute
absorption was calculated by dividing the total
energy dissipated within the Si by the total
energy of the plane wave incident above the
cross-sectional width of the wire structure (
d
in
Fig.
S12
). For comparison with experimental
E.Q.E. measu
r
ements, the simulated absorption
of the non-coated wire was reduced by 23% to
account for the inactive (axial) portion of the
champion cell (determined by SPCM.)
The simulated absorption of the horizontal wire
structures (Fig.
S13b
) exhibited marked
qualitat
ive a
nd quantitative agreement with the
experimentally observed E.Q.E. of the single-
wire solar cells. This suggests that the internal
quantum efficiency (I.Q.E.) of the single-wire
solar cells was close to 100% at all wavelengths,
as previously predicted and measured for radial-
junction Si microwires.
5
,
24
Both the measured
E.Q.E. and simulated absorption of each device
also predict similar
J
SC
values (weighted across
the AM 1.5G spectrum) to those measured under
calibrated solar illumination (Table
S1
),
indi
cati
ng good agreement between simulations
and measurement techniques.
†
Partial spectral averaging
22
(PSA) suppressed reso-
nance effects that were not experimentally observed
due to mildly tapering wire diameter. The PSA width
(
Δ
f
) was calculated based on simulation frequency (
f
)
and Si refractive index (
n
Si
), as:
.
SiSi
ndff
1
M. Kelzenberg, D. Turner-Evans, S. Boettcher, M. Putnam, R. Briggs, C. Baek, N. Lewis, and H. Atwater.
Supplementary information, "High-performa
nce Si microwire photovoltaics," 2010
8
Supplementary Material (ESI) for Energy & Environmental Science
This journal is (c) The Royal Society of Chemistry 2011