of 8
Supporting Information for “Ultra-dense, deep sub-w
avelength
nanowire array photovoltaics as engineered optical
thin films”
Ion implantation
The silicon-on-insulator (SOI) substrates (Soitec USA Inc., Peabod
y, MA) were
implanted with dopant ions (CORE Systems, Sunnyvale, CA) through photore
sist masks.
Heavily-doped
p
-type (dose of 3.8×10
14
cm
-2
B
+
at 2.5 keV) and
n
-type (dose of 3.2×10
14
cm
-2
P
+
at 6.5 keV) contact regions were used to promote the formation of ohmi
c
contacts, while the device regions received a low- or high-dose
p
-type implant (dose of
3.8×10
10
cm
-2
B
+
or 3.8×10
13
cm
-2
B
+
at 2.5 keV). All implants were performed at an off-
normal angle of 7° to mitigate implant profile broadening due to ion channeling.
Modified RCA clean
Our modified RCA cleaning recipe consists of a three-step proce
dure in solutions
of H
2
SO
4
:H
2
O
2
(3:1 v/v, 90 °C, 10 min), HF:H
2
O (1:50 v/v, 15 s in dark), and
H
2
O:HCl:H
2
O
2
(6:1:1, 80 °C, 10 min). After each step, the substrate was rinsed
thoroughly with de-ionized water and dried with dry N
2
.
Superlattice nanowire pattern transfer
Superlattice wafers (IQE Ltd., Cardiff, U.K.) of alternating
layers of
GaAs/Al
x
Ga
(1-
x
)
As were cleaved into small pieces, and GaAs selectively etche
d away in
NH
4
OH:H
2
O
2
:H
2
O (1:20:300 v/v) to expose a comb of parallel AlGaAs ridges running
along the cleaved edge. 100 Å of Pt was evaporated at a 45° angle to
coat just the tips of
the ridges, forming an array of parallel Pt nanowires running alon
g the edge. The
superlattice chip was then placed array-side down onto the doped SOI
substrate with a
home-built aligner system (Figure 1c), and held in place by a thi
n layer of thermally-
cured epoxy that had been previously spun onto the substrate. After curi
ng, the entire
assembly was placed gently in a H
2
O
2
:H
3
PO
4
:H
2
O (1:5:50 v/v) solution to dissolve the
GaAs/AlGaAs superlattice chip, leaving the array of Pt nanowi
res immobilized on the
substrate (Figure 1d).
Contact metallization
The chips were dipped into BOE:H
2
O (1:25 v/v, 10 s in dark) to remove oxides
over the contact regions before Ti/Pt/Au (100/100/1200 Å) contacts were evaporated onto
the devices (Figure 1d).
Irradiance and wavelength calibrations
Our illumination system consists of an Oriel 150 W Xe arc lamp s
ource coupled
at
f
/4 through a home-built cut-on filter changer to an Oriel MS257 monochrom
ator
(Newport Corp., Stratford, CT). The divergent output from the monochromator
was
collimated into a ~1 cm diameter spot at the sample plane using a
plano-convex
f
= 75
mm lens (Thorlabs Inc., Newton, NJ). We selected “UV-grade” fused
silica for all optical
elements to maximize transmission of the ultraviolet wavelengths.
The irradiance calibration reference is a Hamamatsu S1337-1010BQ s
ilicon
photodiode (Hamamatsu Corp., Bridgewater, NJ), calibrated between 250-1100 nm
to
NIST-traceable standards (Opto-Cal Inc., Lakeside, CA) and mounte
d behind a 500
μ
m
diameter precision pinhole (Edmund Optics, Barrington, NJ). The waveleng
th-dependent
irradiance was measured in the center of the collimated beam at
the sample plane using a
10 nm bandpass in steps of 1 nm. We have also measured the irradiance spect
rum with an
uncoated Glan-Thompson linear polarizer (Thorlabs Inc., Newton, NJ) m
ounted just
before the detector and find that there is only a slight polarizat
ion introduced by the
illumination system.
Wavelength calibrations were regularly performed, often before ea
ch set of
measurements, using the sharp emission lines from a Hg(Ar) pen
-style lamp (Newport
Corp., Stratford, CT) at the input of the monochromator and the reference
photodiode at
the sample plane. For each of the gratings used, the monochromator wa
s scanned in 0.1
nm steps in the vicinity of a strong emission line. The position of
the peak was used to
calibrate the monochromator wavelength readout, and was typically r
eproducible to ~0.1
nm. At the end of each wavelength calibration, monochromator slit funct
ions were also
measured at 10 nm bandpass in steps of 0.1 nm to characterize the instr
umental
broadening of the illumination system. The slit functions were nearl
y perfectly triangular
and identically wide for all gratings used, indicative of a well-aligned opti
cal system.
Rigorous coupled-wave analysis calculation
The rigorous coupled-wave analysis (RCWA) represents periodic s
urface features
as a Fourier series and propagates the incident wave through the opti
cal model by solving
Maxwell’s equations exactly. Essentially, a three-dimensional
grid is overlaid over a unit
cell of the periodic structure, and the optical model is built up laye
r-by-layer by assigning
appropriate optical constants to each volume element. In each layer, t
he periodic pattern
of optical constants is assumed to be constant throughout the entire lay
er thickness and is
approximated as a truncated Fourier series. The illumination conditions
are then defined
and the differential equations solved layer-by-layer as the inci
dent wave enters the
structure from the superstrate and exits via the substrate. Speci
al care is taken to match
the electromagnetic boundary conditions at each interface. In this
way, the reflected and
transmitted diffraction amplitudes are obtained for the entire mult
ilayer structure, from
which the reflectance and transmittance can be calculated for
any given diffracted order.
The reflectance is evaluated at the upper interface between
the superstrate and the
topmost layer, while the transmittance is evaluated at the lowe
r interface between the
bottommost layer and the substrate.
There is no general restriction on the grid resolution, uniformity or geom
etry, so
we have used a somewhat coarse (1 nm × 1 nm) uniform square grid to
discretize the
nanowire array for speed and simplicity. The superstrate (air
or vacuum) and substrate
(680
μ
m thick silicon handle wafer) media are assumed to be continuous, isotr
opic and
infinite. For a grating structure like our nanowire arrays with
features dependent on the
x
,
y
,
z
-space coordinates, the Fourier series is one-dimensional in
x
(normal to the
nanowires). In the
y
-direction (parallel to the nanowire axis) the features are as
sumed to
be infinite in extent, which is a reasonable approximation given that
our arrays are
10
μ
m long, more than 10 times longer than the wavelengths of interest. I
n the
z
-direction,
we used 3 layers to represent the bulk film device (see Figure
2a) and 17 layers to
represent the nanowire array structure (Figure 2b). A total of
65 Fourier modes were
included in the calculation assuming normal incidence plane-wave illumi
nation. To
calculate the absorptance
A
= 1 –
R
T
S
, we used the zero-order (specular) reflectance
R
0
and transmittance
T
0
and assume no scattering (
S
= 0). We have verified that the
reflectance and transmittance are identically zero for non-zero
diffraction orders; this
implies complete absorption and therefore evanescent diffracted waves for hi
gher orders.
Diode and photovoltaic characterization
A few sets of thin film and NWA devices were fabricated. The
devices described
in the main text were chosen for optical characterization beca
use they appeared, by light
microscopy inspection, to be the most homogeneous. The devices chosen we
re selected
for the absence of irregularities due to fabrication variabili
ty, so as to avoid artifacts in
the measured optical data. Dark I-V curves were also obtained fo
r those (and other)
devices with a Model 6430 sourcemeter (Keithley Instruments, Clevela
nd, OH) by
sourcing voltage and measuring current.
Figure 2 in the main text shows clear diode responses from a set
of devices with
high-dose doping (3.8×10
13
cm
-2
B
+
) in the device regions. These higher-doped nanowire
array devices generate
I
sc
= 17 pA and
V
oc
= 0.26 V with
FF
= 0.50, while the higher-
doped film devices develop
I
sc
= 28 pA and
V
oc
= 0.37 V with
FF
= 0.62. However, the
higher-doped nanowire arrays were of poorer structural quality and we
re less amenable to
optical modeling. Hence we have chosen to focus on the lower-doped (3.8
×10
10
cm
-2
B
+
)
principal device in the main text.
In Table S1 we summarize additional measurements from other device
s. We note
that the nanowire array devices tend to exhibit more scatter i
n their properties, while the
film devices are essentially homogeneous. The photovoltaic properties
do not exhibit any
dependence on device length as the minority carrier diffusion lengt
hs are far smaller than
the geometrical dimensions of the device. On the whole, our devices
are comparable in
performance to previously reported examples of silicon nanowire photovol
taics in the
literature.
Minority carrier diffusion length
Minority carrier diffusion lengths were measured using a WITe
c AlphaSNOM
(WITec Wissenschaftliche Instrumente und Technologie GmbH, Ulm, Ge
rmany)
scanning near-field optical microscope (SNOM). Light from laser di
odes at 405 nm
(blue) or 650 nm (red) was chopped at 83 Hz and fiber-coupled into the mic
roscope. An
objective lens was used to focus the laser light onto the device (f
ar-field illumination), or
onto the 100 nm aperture of a SNOM tip (near-field illumination). The
device was
mounted on a computer controlled stage under the objective lens, connected t
o a SR570
current-to-voltage preamplifier and the preamplifier output voltage
measured with a
SR830 lock-in amplifier (Stanford Research Systems Inc., Sunnyvale,
CA). To acquire
the scanning photocurrent images, the laser probe beam was raster
ed across the device
while recording the lock-in output as a function of probe position. Duri
ng the
measurement, the devices were weakly illuminated using the micros
cope lamp to remove
artifacts arising from light absorption in the substrate wafer. T
he minimum illumination
level was used to remove capacitance transients from the output photoc
urrent so as to
obtain a square wave output.
Scanning photocurrent images acquired with far-field illumination w
ere
resolution-limited by the quality of the focusing objective or by
focusing errors (Figure
S1). On the other hand, near-field illumination using the SNOM tip in
contact-mode
enabled high-resolution measurements of the diffusion length limited o
nly by the tip
aperture size (Figure S2). Unfortunately, because the tip is dragge
d across the surface, the
sample undergoes damage during the measurement and can typically onl
y tolerate a few
repeat measurements. After the measurement, line profiles were
taken along the device
axis and fitted to an exponential function to determine the diffusion l
engths on either side
of the junction.
Cross-sectional transmission electron microscopy
Focused-ion beam (FIB) liftout of the cross-sectional sample wa
s performed in a
Nova 600 DualBeam FIB/SEM (FEI Company, Hillsboro, OR) equipped with a
n
Autoprobe 200 micromanipulator system (Omniprobe Inc., Dallas, TX). Initia
l cuts were
made at a higher ion energy of 30 kV and high beam currents of >1000 pA
for increased
speed. Final thinning to electron transparency was performed with i
ons at 10 kV at
glancing incidence and lower beam currents of <100 pA to minimize sample damage.
After the cross-section was prepared, it was loaded into a Tec
nai TF20ST TEM
(FEI Company, Hillsboro, OR) for imaging at 200 kV. Sometimes, the c
ross-sectional
sample was too thick, and contained contrast contributions from inelasti
cally scattered
transmitted electrons. In that case, a Gatan Imaging Filter (
Gatan Inc., Pleasanton, CA)
was used to image the zero-loss electrons and provided improved contras
t (Figure 3a,b in
main text). Convergent beam electron diffraction (CBED) was pe
rformed by focusing the
beam to crossover over the device regions and capturing the diffracti
on patterns on a
charge-coupled device at the camera plane (Figure S3a,b). With suff
iciently thin sample
regions, high-resolution transmission electron micrographs were acquire
d along the [011]
zone of the sample and confirm that the high crystallinity of the de
vices are retained after
processing (Figure S3c). By placing an objective aperture about
the (1 ̄ 11 ̄ ) spot, tilted-
beam dark-field micrographs also show that the devices remain crystalline
(Figure S3d).
Table S1.
Measured parameters of some of our devices, compared to literature
reported
values for silicon nanowire photovoltaic devices. Where possible, we
have calculated the
short-circuit current density
J
sc
using the projected active area
Y
=
L
×
W
of the device.
Ideality factors
n
lit
and
n
dark
were obtained by fitting lit and dark I-V measurements to the
diode equation
I
=
I
0
[exp(
qV
/
nk
B
T
) – 1] in the low forward bias region (up to ~0.4 V).
Sample
I
sc
(pA)
J
sc
(mA/cm
2
)
V
oc
(V)
FF
n
lit
n
dark
Description
3.8×10
13
cm
-2
B
+
dose
NWA
17
0.26 0.50
2.2
2.7
10

m long
NWA
17
0.34 0.60
1.8
1.8
10

m long
NWA
17
0.34 0.55
2.2
1.9
25

m long
Thin Film
28
0.37 0.62
1.5
1.9
10

m long
Thin Film
27
0.36 0.60
1.6
1.8
10

m long
Thin Film
27
0.37 0.62
1.8
1.7
25

m long
NWA
18
0.26
25

m long
NWA
19
0.38
50

m long
NWA
19
0.35
100

m long
Thin Film
29
0.40
25

m long
Thin Film
30
0.40
25

m long
Thin Film
29
0.39
100

m long
3.8×10
10
cm
-2
B
+
dose
NWA
a
26
2.6
0.37
10

m long
Film
b
60
3.0
0.46
10

m long
Literature
values
Ref. 3
5.0
0.19 0.40
3.6
Axial Schottky
Ref. 4
3.5
0.12
1.78
Axial p-n
Ref. 4
14.0
0.24
Axial p-i-n, i=2

m
Ref. 4
31.1
3.5
0.29 0.51
1.28
Axial p-i-n, i=4

m
Ref. 5
4.28
0.29 0.33
2.1
Radial p-n
Ref. 2
503
23.9
0.26 0.55
1.86
1.96
Radial p-i-n
a) This device corresponds to the array device in Figures 3 and 4.
b) This device corresponds to the film device in Figures 3 and 4.
p+
n+
p
Figure S1.
Optical micrograph of bulk film (top) and nanowire array (bottom)
devices,
overlaid with far-field scanning photocurrent images obtained at 405 nm
(blue) and 650
nm (red). The excellent overlap between the red and blue photocurrent im
ages (purple)
indicates that there is no wavelength dependence for the minority
carrier diffusion length.
There is some spurious intensity in both blue and red photocurrent images even in regions
far away from the junction due to beam reflections and a poorly focused probe beam.
-1.0
-0.5
0.0
0.5
1.0
10
-13
10
-11
10
-9
film,
λ
= 405 nm
array,
λ
= 405 nm
L
e
= 300 nm
photocurrent (A)
distance from junction (

m)
L
h
= 100 nm
L
e
= 200 nm
Figure S2.
Line profiles through near-field scanning photocurrent images obtained w
ith a
scanning near-field optical microscope (SNOM) in contact mode, take
n along the dashed
lines in Figure S1. An exponential fit on the left (right) side of
the peak yields the
minority carrier diffusion length
L
e
(
L
h
), with measurement resolution determined by the
finite size of the SNOM tip aperture (100 nm). This yields upper es
timates for the total
diffusion length
L
max
~ 400 nm and 300 nm respectively for the bulk film and nanowire
array devices. Accounting for the broadening due to the tip aperture,
the respective lower
estimates are
L
min
~ 200 nm and 100 nm.
(a)
(b)
(c)
(d)
Si
SiO
2
SiO
2
Si
SiO
2
Si
Si
Si
Figure S3.
Convergent beam electron diffraction (CBED) patterns of (a) bulk f
ilm and
(b) nanowire devices, taken along the B = [011] zone (parallel to the
nanowire axis). As
expected, the CBED patterns are identical since both devices are
fabricated from the
same starting substrate. (c) Cross-sectional transmission ele
ctron microscope (XTEM)
image of bulk film device down B = [011], showing high crystallinity
of the film. (d)
Tilted-beam dark-field XTEM image of the nanowire array device
formed with the (1 ̄ 11 ̄ )
spot. All nanowires within the field are crystalline.