of 10
Operation of lightly doped Si microwires under
high-level injection conditions
Elizabeth A. Santori,
d
Nicholas C. Strandwitz,
d
Ronald L. Grimm,
d
Bruce S. Brunschwig,
a
Harry A. Atwater
*
bc
and Nathan S. Lewis
*
acd
The operation of lightly doped Si microwire arrays under high-level injection conditions was investigated by
measurement of the current-potential behavior and carrier-collection e
ffi
ciency of the wires in contact
with non-aqueous electrolytes, and through complementary device physics simulations. The current-
potential behavior of the lightly doped Si wire array photoelectrodes was dictated by both the radial
contact and the carrier-selective back contact. For example, the Si microwire arrays exhibited n-type
behavior when grown on a n
+
-doped substrate and placed in contact with the 1,1
0
-
dimethylferrocene
+/0
CH
3
OH redox system. The microwire arrays exhibited p-type behavior when
grown on a p
+
-doped substrate and measured in contact with a redox system with a su
ffi
ciently
negative Nernstian potential. The wire array photoelectrodes exhibited internal quantum yields of

0.8,
deviating from unity for these radial devices. Device physics simulations of lightly doped n-Si wires in
radial contact with the 1,1
0
-dimethylferrocene
+/0
CH
3
OH redox system showed that the carrier-
collection e
ffi
ciency should be a strong function of the wire diameter and the carrier lifetime within the
wire. Small diameter (
d
< 200 nm) wires exhibited low quantum yields for carrier collection, due to the
strong inversion of the wires throughout the wire volume. In contrast, larger diameter wires (
d
>
400 nm) exhibited higher carrier collection e
ffi
ciencies that were strongly dependent on the carrier
lifetime in the wire, and wires with carrier lifetimes exceeding 5
m
s were predicted to have near-unity
quantum yields. The simulations and experimental measurements collectively indicated that the Si
microwires possessed carrier lifetimes greater than 1
m
s, and showed that radial structures with micron
dimensions and high material quality can result in excellent device performance with lightly doped,
structured semiconductors.
Broader context
Structuring semiconductors on the nano- and microscale is a promising route to enable
exible, lightweight photovoltaics and e
ffi
cient solar fuels devices. Wire
devices with radial junctions should allow for both the e
ffi
cient absorption of light along the axial dimension of the wire and radial collection of excited
photocarriers, therefore enabling the fabrication of e
ffi
cient devices based on inexpensive materials with low electronic quality. Prior systematic experimental
and device physics modeling has largely focused on arrays of doped semiconductors, including Si radial p
n junction devices. The work described herein focuses
on the device performance and device physics of lightly doped Si microwires, to allow for new device architectures and increased understanding of dev
ices using
other semiconductor materials with less controllable doping.
I. Introduction
Si wire arrays grown by the vapor
liquid
solid (VLS) process
have emerged as a promising technology for the fabrication of
high e
ffi
ciency, scalable photovoltaics and arti
cial photosyn-
thetic devices.
1
6
The photovoltages of Si microwire arrays are
not yet comparable, however, to the highest values observed
from planar crystalline Si photovoltaics. By analogy to planar Si
systems, one approach to improve the photovoltage of the Si
microwire arrays would be to operate the system under high-
level injection conditions. For lightly doped Si under 1 Sun
illumination, the change in the concentration of photo-
generated electrons and holes (
D
n
and
D
p
, respectively) can
a
Beckman Institute, California Institute of Technology, 1200 E. California Blvd.,
Pasadena, CA 91125, USA. E-mail: nslewis@caltech.edu; Fax: +1 626 395-8867; Tel:
+1 626 395-6335
b
Thomas J. Watson Laboratories of Applied Physics, California Institute of Technology,
1200 E. California Blvd, Pasadena, CA, 91125, USA. E-mail: haa@caltech.edu; Fax: +1
626 844-9320; Tel: +1 626-395-2197
c
Member, Kavli Nanoscience Institute, California Institute of Technology, USA
d
Division of Chemistry and Chemical Engineering, California Institute of Technology,
1200 E. California Blvd, Pasadena, CA, 91125, USA
Electronic supplementary information (ESI) available: Additional information
regarding the VLS growth of Si microwire arrays, photoelectrochemical data
correction,
photoelectrochemical
performance
data,
and
the
chemical-mechanical polishing of Si microwire arrays. See DOI:
10.1039/c4ee00202d
Cite this:
Energy Environ. Sci.
,2014,
7
,
2329
Received 18th January 2014
Accepted 18th March 2014
DOI: 10.1039/c4ee00202d
www.rsc.org/ees
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greatly exceed the equilibrium carrier concentrations in the
dark (
n
0
and
p
0
, respectively). For such samples operated under
high-level injection conditions, the Shockley
Read
Hall
recombination rate is inversely proportional to the sum of both
the carrier lifetimes. The high-level lifetime is therefore longer
than the lifetime under low-level injection conditions for a
doped semiconductor, whose carrier lifetime is essentially
equal to the minority-carrier lifetime.
7,8
Planar devices operating under high-level injection condi-
tions, such as Si point-contact solar cells, have achieved the
highest e
ffi
ciencies for a single-junction Si photovoltaic cell,
with cell e
ffi
ciencies >27% under concentrated solar illumina-
tion.
9
11
These devices utilize lightly doped,
oat-zone Si, and
are fabricated with small interdigitated n
+
and p
+
back point-
contacts, to facilitate the selective collection of electrons and
holes, respectively. Such devices do not have signi
cant electric
elds in the bulk of the semiconductor, and the photogenerated
carriers are therefore driven by di
ff
usion, not dri
, within the
bulk of the material. Accordingly, the Si must possess an
extremely long (>1 ms) charge-carrier lifetime, and high-quality
surface passivation on both the front and back of the cell is
necessary to minimize recombination losses at the surfaces of
the device. The n
+
and p
+
point contacts generate strong electric
elds at the contacts, and thus facilitate the collection of pho-
togenerated carriers, in addition to creating low saturation
currents in the device. This highly optimized structure also
bene
ts from having a highly re
ective back surface, an anti-
re
ection coating on the front surface, and no shadowing due to
the lack of a top contact.
In this work, we describe the operation of Si microwire arrays
under high-level injection conditions. Non-aqueous redox
couples with varying electrochemical potentials, including the
1,1
0
-dimethylferrocene (Me
2
Fc)
+/0
CH
3
OH and cobaltocene
(CoCp
2
)
+/0
CH
3
CN redox systems, have been used to systemat-
ically probe the current density
vs.
potential,
J
E
, behavior of the
wire arrays and to compare their behavior with the
J
E
proper-
ties of point-contact planar Si systems operated under nomi-
nally the same conditions.
12,13
The Me
2
Fc
+/0
CH
3
OH and
CoCp
2
+/0
CH
3
CN systems have both been shown to generate an
inversion layer in contact with Si, resulting in semiconductor/
liquid interfaces that have a high selectivity for holes and
electrons, respectively, as well as low e
ff
ective surface recom-
bination velocities,
S
.
14
The lightly doped Si microwires are expected to be depleted
in contact with the chosen redox couples, given the acceptor
concentrations
N
A

1

10
13
1

10
14
cm

3
and diameters
d

2.5
3.0
m
m of the microwires. Previous device physics simula-
tions of doped Si microwires predicted that depleted wires (
i.e.
wires with small internal electric
elds, for which a fully
developed space-charge length would exceed the radius of the
wire) should have extremely low carrier-collection e
ffi
ciencies,
due to the absence of a signi
cant electric
eld within the wire
and the lack of majority carriers to facilitate axial carrier
transport.
15
17
These simulations exclusively examined the
performance of doped wires with radii on the order of
the depletion width of the wire,
i.e. r

100 nm for
N
A
¼
1

10
18
cm

3
. For Si microwires in contact with Me
2
Fc
+/0
CH
3
OH,
the near-surface region of the wire is expected to be strongly
inverted, as demonstrated previously for planar n-Si/Me
2
Fc
+/0
CH
3
OH junctions.
14,18,19
Although the lightly doped Si micro-
wires should be depleted, their radii are potentially large
enough such that the wires could still possess an electric
eld
due to the large concentration of holes at the surface relative to
the wire core, thereby allowing for selective carrier collection.
Thus, further quantitative modeling of lightly doped, structured
materials is required to fully understand the device properties
of these systems.
A focus of the work described herein was to experimentally
measure the external and internal quantum yields of such Si
microwires using non-aqueous photoelectrochemical redox
systems. Previous measurements of undoped Si microwire array
photoanodes in contact with Me
2
Fc
+/0
CH
3
OH have shown non-
unity carrier collection e
ffi
ciencies.
20
Some possible explana-
tions for this e
ff
ect include the presence of Cu silicide located at
the tops of the wires, as well as an inherently poor carrier
collection in lightly doped Si wires. To distinguish between
these possibilities, the Cu silicide located at the tops of the
wires was removed through chemical-mechanical polishing of
the wire arrays, and the internal quantum yield,
G
int
, of the wire
array photoelectrodes was subsequently measured.
In addition, device physics models were developed for the
operation of lightly doped Si wires with a selective n
+
back
contact, in radial contact with the Me
2
Fc
+/0
CH
3
OH electrolyte.
The internal quantum yield of a single wire has been simulated
as a function of: the distance,
d
T
, between the location of carrier
excitation and the top of the wire; the lifetime and carrier
concentration in the wire; and the wire diameter,
d
. This type of
scanning
simulation was preferred to a measurement of the
full spectral response or the
J
E
characteristics of a single wire,
because the actual excitation pro
le is not well known either for
wires with diameters on the microscale or for arrays of wires.
The absorption pro
le di
ff
ers signi
cantly from that of planar
Si, and should also vary considerably for wires with radial
dimensions ranging from nanometers to microns.
21
Hence, a
scanning illumination measurement e
ff
ectively removes the
unknown variable of the excitation pro
le within the wire, and
allows measurement of the e
ffi
ciency of carrier-collection at
each point along the axial direction of a single Si wire.
II. Experimental section
A. Reagents
Methanol (BakerDRY, Mallinckrodt Baker) and lithium
perchlorate (battery grade, Sigma-Aldrich) were used as
received. 1-1
0
-dimethylferrocene (Me
2
Fc, 95%, Sigma-Aldrich)
was puri
ed by sublimation at room temperature, and dime-
thylferrocenium tetra
uoroborate (Me
2
FcBF
4
) was synthesized
as described previously.
22
Acetonitrile (99.8% anhydrous,
Sigma-Aldrich) was puri
ed
rst by sparging with N
2
(g) for
15 min, and then passing the solvent, under pressure from
N
2
(g), through a column of activated A2 alumina (Zapp's).
Bis(cyclopentadienyl)cobalt(
II
) (CoCp
2
, 98%, Strem) was puri-
ed by vacuum sublimation at 65

C. Cobaltocenium hexa-
uorophosphate (Cp
2
CoPF
6
, 98%, Sigma-Aldrich) was
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recrystallized from an ethanol/acetonitrile mixture (ACS grade,
EMD) and dried under vacuum. VLS-catalyzed Si microwire
arrays were grown on both n
+
- and p
+
-doped (111)-oriented Si
substrates, using degenerately doped n
+
-Si substrates with a
resistivity
r

0.001
0.004
U
cm and 450 nm of thermal oxide
(University Wafer), or p
+
-Si substrates with
r

0.001
0.005
U
cm and 500 nm of thermal oxide (International Wafer Service).
B. VLS-catalyzed microwire growth
Arrays of square-packed Si microwires were grown on oxide-
coated, lithographically patterned, planar n
+
- and p
+
-Si(111)
substrates using the vapor
liquid
solid (VLS) growth method
with a Cu catalyst (99.9999%, ESPI) and without dopants (see
ESI
).
20
For photoelectrochemical measurements under 1 Sun
of light intensity, the resulting undoped wires grown on an n
+
-Si
substrate (n
+
/i-Si microwires) were 2.7
2.9
m
m in diameter and
67
80
m
m in height (Fig. 1). The p
+
/i-Si microwires were 1.65
1.75
m
m in diameter and 90
97
m
m in height. The n
+
/i-Si wires
that were measured for their spectral response and optical
properties were 2.1
2.3
m
m in diameter and 65
75
m
m in height.
A
er wire growth, the Cu VLS catalyst was removed by a 5 s
bu
ff
ered HF(aq) (BHF, Transene Inc.) etch, followed immedi-
ately by an etch in 6 : 1 : 1 (by volume) of H
2
O : HCl : H
2
O
2
at
70

C (RCA 2) for 15 min. This BHF/RCA2 procedure was then
repeated to ensure that all of the metal catalyst had been
removed.
Four-point resistance measurements on single wires were
performed as described previously, for wires grown on both n
+
-
and p
+
-Si substrates.
20,23
The undoped Si microwires had a
resistivity of 800

500
U
cm as grown on n
+
substrates and a
resistivity of 200

100
U
cm as grown on p
+
substrates. For
wires grown on either n
+
and p
+
-Si substrates, gate-dependent
conductance measurements indicated that the microwires were
slightly p-type, and showed an increase in conductivity with a
negative applied gate-bias. The as-grown microwires thus
possessed low electronically active acceptor concentrations,
N
A
,
of

1

10
13
1

10
14
cm

3
.
C. Electrode fabrication
To fabricate multiple electrodes for photoelectrochemical
measurements, arrays of Si microwires were cleaved into

4

4 mm samples. A SiC scribe was used to scratch Ga : In eutectic
into the backs of the samples, thereby producing an ohmic
contact to the Si substrate. Ag print (GC Electronics) was then
used to a
ffi
x the samples to a coiled wire that had been passed
through a glass tube, with the resulting electrode positioned in
a face-down con
guration. A low-creep epoxy (Loctite 9460 F)
was used to de
ne the active area of the electrode, and a higher
stability epoxy (Hysol 1C) was used to encapsulate the back
contact and wire coil. The electrodes were placed for 4 h in an
oven heated to 70

C, to further cure the epoxy, thereby
obtaining enhanced chemical stability in both the CH
3
OH and
CH
3
CN solutions. The electrode areas were

0.03 cm
2
,as
measured using a high-resolution scanner and analyzed by
Adobe Photoshop so
ware.
D. Photoelectrochemical Measurements
All non-aqueous photoelectrochemical
J
E
measurements were
performed with bottom illumination in air-tight,
at-bottomed
glass cells. The Me
2
Fc
+/0
CH
3
OH electrolyte solution consisted
of 200 mM of Me
2
Fc, 0.4 mM of Me
2
FcBF
4
, and 1.0 M LiClO
4
in
30 mL of methanol. The cell was assembled and sealed under an
inert atmosphere (<10 ppm O
2
), and subsequently was placed
under positive Ar(g) pressure on a gas manifold. A high surface-
area Pt mesh was used as the counter electrode, and the refer-
ence electrode was a Pt wire in a Luggin capillary that had been
lled with the same solution as that in the main cell compart-
ment. The di
ff
erence between the Nernstian potential of the
solution and the potential of the reference electrode was
recorded using a 4-digit voltmeter (Keithley), with the value
di
ff
ering from the reference electrode potential by <10 mV.
J
E
measurements were obtained at a scan rate of 5 mV s

1
.
The CoCp
2
+/0
CH
3
CN electrolyte solution consisted of
50 mM of CoCp
2
PF
6
, 5.0 mM of CoCp
2
, and 1.0 M LiClO
4
in
20 mL of acetonitrile. The cell was assembled and used under
an inert, dry atmosphere (<0.50 ppm O
2
; 0.5 ppm H
2
O). A high
surface-area Pt mesh was used as the counter electrode, and the
reference electrode was a Pt wire that was placed in the solution
in close proximity to the working electrode. A Luggin capillary
was not used as a reference electrode in this cell, due to the
instability and relatively low concentrations of CoCp
2
in the
electrolyte.
J
E
measurements were obtained at a scan rate of
Fig. 1
(A) Side view scanning electron microscopy image of a cleaved array of square-packed Si microwires. Scale bar
¼
30
m
m. (B) Top view of
the same Si microwire array. Scale bar
¼
20
m
m. (C) Energy
versus
position diagram for Si and two liquid electrolytes, Me
2
Fc
+/0
CH
3
OH and
CoCp
2
+/0
CH
3
CN, before contact.
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30 mV s

1
, to limit the solution optical absorption produced by
the generation of CoCp
2
at the working electrode.
A 300 W ELH-type tungsten-halogen bulb with a dichroic rear
re
ector and di
ff
user was used as the illumination source for
electrochemical measurements under simulated 1 Sun illumi-
nation in contact with Me
2
Fc
+/0
CH
3
OH or CoCp
2
+/0
CH
3
CN.
The incident light intensity was calibrated using a Si photo-
diode that was placed in the solution at the position of the
working electrode. The light intensity was adjusted until the
short-circuit photocurrent of the Si diode was the same as the
short-circuit photocurrent produced on the photodiode by 100
mW cm

2
of AM 1.5G illumination. The Si electrodes were
etched for 5 s in 5% HF(aq), rinsed with >18 M
U
cm resistivity
H
2
O, and dried thoroughly under a stream of N
2
(g) prior to
photoelectrochemical measurements. The electrochemical cell
solutions were vigorously stirred during the
J
E
measurements.
Data were collected and averaged for seven wire array samples
each, for wire array photoelectrodes tested in Me
2
Fc
+/0
and
CoCp
2
+/0
electrochemical cells.
To reduce the concentration overpotential losses within the
Me
2
Fc
+/0
CH
3
OH cell and to demonstrate the validity of the
corrections for these losses,
J
E
measurements were also per-
formed for electrolytes that had 40 mM Me
2
FcBF
4
added to the
cell (see ESI
for calculations). The cells were illuminated using
a 1 W 808 nm diode laser (Thorlabs), and
J
E
data were collected
by matching the short-circuit photocurrent density,
J
sc
, to the
value of
J
sc
that was obtained under 1 Sun ELH-type W-halogen
illumination for each electrode. This process required

55 mW
cm

2
of 808 nm illumination, as measured by a calibrated Si
photodiode (FDS-100, Thorlabs) placed in the electrochemical
cell at the position of the working electrode.
To determine the diode quality factor of the Si microwire
photoelectrodes in contact with Me
2
Fc
+/0
CH
3
OH, the
J
E
behavior was measured at a series of light intensities under 808
nm illumination. At each light intensity, the open-circuit pho-
tovoltage,
V
oc
, was initially measured using a Keithley 4-digit
voltmeter, and the
J
sc
was measured from the
J
E
behavior of the
electrode. The
V
oc
is expected to the have the general form:
V
oc
¼
nkT
q
ln

J
ph
J
0

(1)
where
n
is the diode quality factor,
k
is Boltzmann's constant,
T
is the absolute temperature,
q
is the unsigned charge on an
electron,
J
ph
is the photocurrent density, and
J
0
is the dark
saturation current density.
24
Therefore, a plot of
V
oc
versus
ln(
J
ph
) should be linear with a slope of
nkT
/
q
, allowing for the
determination of the value of
n
. To calculate the diode quality
factor, the behavior of the n
+
/i-Si microwire array photo-
electrodes was measured under 808 nm illumination ranging in
light intensity from

13 mW cm

2
to 165 mW cm

2
, corre-
sponding to

0.24
3.0 Suns of illumination.
E. Angle-resolved spectral response and optical
measurements
Angle-resolved spectral response and optical measurements of
Si microwire arrays were obtained as described previously,
using a chopped (
f
¼
30 Hz) Fianium supercontinuum laser
coupled to a monochromator, in conjunction with two rota-
tional stages that permitted rotation of the sample around both
the
q
x
and
q
y
axes.
20,25
The angle-resolved spectral response
measurements were obtained using side-facing electrodes of
high-
delity Si microwire arrays, with overall electrode dimen-
sions of

7mm

7 mm. The electrodes were fabricated so that
the Si microwire arrays would ultimately be eucentric with
respect to the rotational axes,
q
y
and
q
x
. The Me
2
Fc
+/0
CH
3
OH
electrochemical cell contained a solution of 10 mM of Me
2
Fc,
0.4 mM of Me
2
FcBF
4
, and 1.0 M LiClO
4
in 25 mL of methanol,
and was maintained under a positive pressure of Ar(g) during
the experiments. The photoelectrode was aligned in the cell by
utilizing the re
ected optical di
ff
raction pattern, and normal
incidence (
q
x
,
y
¼
0

) was determined by minimizing the
photocurrent of each electrode. A calibrated Si photodiode
(FDS-100, Thorlabs) that was positioned inside the cell was used
to calculate the external quantum yield,
G
ext
, of the Si microwire
array photoelectrodes.
An integrating sphere was used to perform optical trans-
mission and re
ection measurements as a function of the
wavelength (
l
) and incident angle of illumination on peeled-o
ff
lms of Si microwires embedded in polydimethylsiloxane
(PDMS; Sylgard 184, Dow Corning).
25
Optical measurements
were made on peeled arrays formed using pieces of the Si
microwire array that were adjacent to the pieces used for
measurement of the spectral response. Because the heights of
the wires can vary considerably across one growth chip, care was
taken to measure wires with the same heights for the optical
and photoelectrochemical measurements, by using adjacent
portions of the same array, with the samples located at equal
distances from the growth front on the chip. The optical
di
ff
raction patterns of the arrays were used to orient the
lms
relative to the rotational axes (
q
x
,
q
y
). The maximization of
transmission in the
lms was taken to indicate normal inci-
dence to the wire array.
To determine the e
ff
ect of the Cu silicide region on the carrier-
collection e
ffi
ciency of undoped Si microwires, the Cu-rich
region, located at the tops of the wires, was selectively removed
by chemical-mechanical polishing. Arrays of n
+
/i-Si microwires
were fully embedded with mounting wax and subsequently pol-
ished by hand using powder Al
2
O
3
and silica suspensions (see
ESI
). Half of each array was reserved as a control, to provide a
direct comparison for spectral response and optical measure-
ments, respectively, between the same wires in the measure-
ments of polished and unpolished electrodes and
lms.
F. Device physics simulations
Device physics simulations were performed using Sentaurus
Device so
ware (Synopsis Inc.). Wires were de
ned in two
dimensions (2D) using cylindrical coordinates. The contacts for
the wire included the high barrier-height contact, which was
applied radially to the wire, and an n
+
-doped back-surface
eld
that acted as an electron-selective contact. The wires were
n-type, with dopant densities
N
D
varying from
N
D
¼
1

10
11
to
N
D
¼
3

10
19
cm

3
. The radial liquid contact was simulated
2332
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using a Schottky-type contact that formed a high barrier-height
(
i.e.
, a Fermi level of
E
(A/A

)
¼
5.15 eV and an electron a
ffi
nity of
Si
E
ASi
¼
4.05 eV) with n-Si, with Si dopant densities as indi-
cated in the text. The surface recombination velocity for elec-
trons and holes was set to 100 cm s

1
at the radial contact, to
approximate a semiconductor/liquid contact using outer-sphere
redox couples.
16
The distance
d
T
¼
0
m
m was de
ned to be the
top of the wire (far from the n
+
back-surface
eld), and the wire
was 70
m
m in length. The n
+
back-surface
eld was de
ned from
d
T
¼
69.5
70
m
m, and consisted of an n
+
layer with a donor
concentration
N
D
¼
1

10
18
cm

3
. Electron and hole surface
recombination velocities at the back contact were set to 1

10
7
cm s

1
. The dopant density was uniform throughout the
wire, except at the base of the wire where the back-surface
eld
was present. Scanning photocurrent simulations were con-
ducted by scanning a simulated light beam (
l
¼
250 nm) axially
along a wire from
d
T
¼
0
70
m
m. The spot size was 100 nm and
the photon
ux was very low, having a value of 6.245

10
15
photons cm

2
s

1
. Because of the high barrier height and the
high concentration of holes, this photon
ux did not perturb
the hole concentration from the equilibrium value for undoped
wires. The quantum yield for carrier collection at zero applied
voltage was determined by integrating the total number of
excitations per unit time in the wire and dividing that quantity
into the number of electrons collected per unit time derived
from the current at the contacts. The simulation grid was set to
a minimum mesh size of 100 nm. The re
ned mesh was nar-
rowed linearly to 1 nm near the contacts as well as at the
interface between the wire bulk and the n
+
-doped back surface
eld. The carrier mobilities were taken to have bulk values
(1470 cm
2
V

1
s

1
and 470.5 cm
2
V

1
s

1
for electrons and
holes, respectively) that decreased with increasing dopant
densities according to empirically developed and well-estab-
lished relationships for Si.
26
Measurements of the Hall mobility
in single crystalline Si have shown no substantial change a
er
Cu incorporation.
27
The concentration of electronically active
interstitial Cu should be approximately 1

10
13
1

10
15
cm

3
a
er the growth period
27,28
and thus the present ionized impu-
rities should not have a substantial e
ff
ect on the carrier
mobility. A Shockley
Read
Hall lifetime was set for each
simulation (
s
n
¼
s
p
), and the value was adjusted based on the
empirical relationship with the dopant density given in eqn (2):
s
SRH
¼
s
n
1
þ
N
N
ref

(2)
where
N
is the dopant density,
N
ref
¼
1

10
16
cm

3
,
s
n
is the
initial value set for the carrier lifetime, and
s
SRH
is the
nal
value used in the computation of the recombination rates.
III. Results
A. Photoelectrochemical behavior of lightly doped Si
microwire arrays in contact with Me
2
Fc
+/0
CH
3
OH and
CoCp
2
+/0
CH
3
CN electrolytes
Fig. 2 shows the
J
E
behavior of the n
+
/i-Si and p
+
/i-Si microwire
array photoelectrodes in contact with Me
2
Fc
+/0
CH
3
OH under
1 Sun of simulated solar illumination. The n
+
/i-Si microwire
electrodes exhibited
V
oc
¼
445

13 mV,
J
sc
¼
12.8

2.1 mA
cm

2
,
ll factors
ff
of 0.41

0.03, and photoelectrode energy-
conversion e
ffi
ciencies
h
of 2.3

0.3%. In contrast, the p
+
/i-Si
microwire array photoelectrodes showed no photoresponse in
contact with this electrolyte. For all electrodes, the degenerately
doped growth substrates did not signi
cantly contribute to the
measured photoresponse of the wire arrays, as indicated by
measurement of the photoresponse of the electrodes with the
wires removed from the substrate through use of non-abrasive
mechanical force (see Table S1 in ESI
for all
gures of merit).
Fig. 3 shows the photoresponse of the same n
+
/i-Si and p
+
/i-Si
microwire array electrodes measured in contact with the
CoCp
2
+/0
CH
3
CN electrolyte. The p
+
/i-Si electrodes behaved as
photocathodes in contact with the CoCp
2
+/0
redox couple,
exhibiting
V
oc
¼
421

14 mV,
J
sc
¼
10.9

0.3 mA cm

2
,
ff
¼
0.32

0.02, and
h
¼
1.5

0.1%. Consistent with measurements
of p
+
/i-Si arrays in contact with Me
2
Fc
+/0
CH
3
OH, the n
+
/i-Si
arrays showed no photoresponse in contact with CoCp
2
+/0
CH
3
CN.
To reduce parasitic losses from concentration overpotential
e
ff
ects within the cell, the
J
E
response of the n
+
/i-Si microwire
electrodes was also measured in contact with Me
2
Fc
+/0
CH
3
OH
in the presence of a higher concentration of the oxidized form
of the redox couple, Me
2
Fc
+
. Under these conditions, the n
+
/i-Si
microwire photoelectrodes exhibited
ll factors of
ff
808 nm
¼
0.58

0.02 and an e
ffi
ciency
h
808 nm
¼
5.9

1.0% under 55 mW
cm

2
of 808 nm illumination, along with diode quality factors
of
n
¼
1.90

0.07 (Fig. 4). A
er correcting the
J
E
data for losses
due to concentration overpotential and uncompensated cell
Fig. 2
Uncorrected
J
E
behavior of (A) n
+
/i-Si and (B) p
+
/i-Si
microwire arrays in contact with Me
2
Fc
+/0
CH
3
OH under 100 mW
cm

2
of ELH-type W halogen illumination, and in the dark.
Fig. 3
Uncorrected
J
E
behavior of (A) n
+
/i-Si and (B) p
+
/i-Si
microwire arrays in contact with CoCp
2
+/0
CH
3
CN under 100 mW
cm

2
of ELH-type W halogen illumination, and in the dark.
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resistances, which contribute to the low
ll factors of the
measured wire arrays, the corrected
ll factor and photo-
electrode e
ffi
ciency values for electrodes measured under 1 Sun
of simulated solar illumination were
ff
corr
¼
0.62

0.04 and
h
corr
¼
3.5

0.6%, respectively (Fig. S1
).
To investigate the carrier-collection e
ffi
ciency of the lightly
doped Si microwire arrays, measurements of the external and
internal quantum yields were performed on n
+
/i-Si photo-
electrodes in contact with Me
2
Fc
+/0
CH
3
OH. Given the anisot-
ropy of light absorption within an array with respect to the angle
of incident illumination, the spectral response and optical
measurements were performed at normal incidence.
25
The
maximum external quantum yield of the n
+
/i-Si photoelectrodes
was
G
ext

0.23 under visible illumination. Measurements of the
external quantum yield with respect to wavelength displayed
oscillations, which have been previously attributed to whis-
pering-gallery modes within the cylindrical Si microwires.
20
The
maximum internal quantum yield was
G
int

0.79 (Fig. 5), in
good agreement with previous measurements on undoped Si
microwire array photoanodes.
20
Both
G
ext
and
G
int
showed no
change between as-grown wires that contained the Cu silicide
region near the top of the wires, and polished wires for which
the silicide had been removed. Thus, for the undoped Si
microwire arrays, the presence of the interfacial region at the
tops of the wires had no measurable e
ff
ect on the carrier-
collection e
ffi
ciency within the wires.
B. Device physics model of the photoelectrochemical
behavior of n
+
i-Si microwires in contact with Me
2
Fc
+/0
CH
3
OH
The carrier concentration within a single n
+
/i-Si microwire while
in contact with Me
2
Fc
+/0
CH
3
OH in the dark at zero applied bias
was simulated using Sentaurus Device. For either
d
¼
0.10
m
m
or
d
¼
2.4
m
m, the lightly doped n-Si wires with
N
D
¼
1

10
13
cm

3
had high concentrations of holes throughout the
volume of the wires (Fig. 6). The smaller diameter
d
¼
0.10
m
m
wire was simulated to be strongly inverted, with a background
concentration of holes exceeding 1

10
16
cm

3
within the core
and approaching 5

10
18
cm

3
at the surface of the wire. The
larger diameter
d
¼
2.4
m
m wire was simulated to be more
weakly inverted, but still possessed hole carrier concentrations
in the wire core that exceeded the background concentration of
carriers in the wire when not in contact with Me
2
Fc
CH
3
OH.
Within the simulations, the radial contact determined the
equilibrium concentration of carriers; thus, the results were
also directly applicable to the experimental system, in which the
wires are slightly p-type, with either n
+
or p
+
contacts.
The carrier-collection e
ffi
ciency within a single wire was
simulated for a wire with
d
¼
2.4
m
m, with the doping density
varying from
N
D
¼
1

10
11
to
N
D
¼
3

10
19
cm

3
(Fig. 7). The
Shockley
Read
Hall lifetime was
xed at a value of
s
SRH
¼
1
m
s,
which corresponds to an e
ff
ective di
ff
usion length,
L
e
ff
,
for electrons of

60
m
m, assuming an electron mobility of
m
e

1400 cm
2
V

1
s

1
. This lifetime was a realistic value for a
rst
simulation, given that
L
e
ff
values ranging from 10
m
m to >30
m
m
have been measured for single-wire Si p
n junctions under low-
level injection conditions.
3
The use of this particular lifetime
also assured that, for the
xed
d
employed, radial collection
would be unity for moderately doped wires, in agreement with
previous work on the behavior of radial p
n junctions.
29
However, for wires with
N
D
<1

10
15
cm

3
, the simulated
carrier-collection e
ffi
ciency deviated from unity, particularly for
Fig. 5
External quantum yield and internal quantum yields of as-
grown and polished n
+
/i-Si microwire array photoelectrodes,
measured in contact with Me
2
Fc
+/0
CH
3
OH.
Fig. 6
Concentration of holes within a single undoped Si wire in
contact with Me
2
Fc
+/0
CH
3
OH in the dark, as a function of the
distance radially within the wire, for two di
ff
erent wire diameters,
d
¼
0.10
m
m and
d
¼
2.4
m
m.
Fig. 4
Uncorrected
J
E
data as a function of illumination intensity
(labeled in units of mW cm

2
) at 808 nm for a representative n
+
/i-Si
microwire array photoelectrode in contact with 200 mM Me
2
Fc/40
mM Me
2
FcBF
4
in CH
3
OH.
2334
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,2014,
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carriers generated at the top of the wire. This result can be
understood in view of the carrier concentration within the wire;
under the simulation conditions, the n-type wires were fully
inverted, with a background concentration of holes greater than
the background concentration of electrons, resulting in an
increase in the recombination rate for electrons within the wire.
The photogenerated electrons must be transported down the
length of the wire to be collected at the back contact, but will
have a high probability of recombining with the large concen-
tration of holes throughout the wire. Thus, under these simu-
lation conditions, the performance of this device architecture
was limited by electron transport down the length of the wire.
Wires with
N
D

1

10
15
1

10
18
cm

3
were simulated to
exhibit
G
int
¼
1, in agreement with previous simulations for
wires with radii
R
<
L
e
ff
. For wires with
N
D
exceeding

5

10
18
cm

3
, other recombination mechanisms, such as Auger
recombination, began to dominate the carrier dynamics,
decreasing the overall lifetime and ultimately limiting the radial
collection of carriers.
The carrier-collection e
ffi
ciency within a single, lightly doped
wire was also simulated as a function of the radius of the wire
and the Shockley
Read
Hall lifetime of the Si (Fig. 8). Variation
of either parameter had a signi
cant e
ff
ect on the internal
quantum yield. For wires with
d
< 200 nm, the carrier-collection
e
ffi
ciency decreased precipitously relative to wires that had
larger diameters. This result is consistent with the expected
complete depletion of electrons within the wire at these diam-
eters, and with the presence of a hole-rich inversion layer in the
near-surface region that extended

100 nm in depth into the
wires. At such small radii, the wires are strongly inverted
throughout the radial dimension, resulting in high recombi-
nation rates for electrons traversing the length of the wire.
The internal quantum yield also exhibited a signi
cant
dependence on the carrier lifetime within the range of 1
10
m
s,
with
G
int
approaching values >0.9 in wires with
s
SRH
¼
10
m
s.
Assuming an electron mobility of
m
e

1400 cm
2
V

1
s

1
, this
range of lifetimes corresponds to
L
e
ff
¼
60
190
m
m. Thus, to
collect the majority of carriers in a 70
m
m long wire, the e
ff
ective
di
ff
usion length must be signi
cantly greater than the length of
the wire. Even though the device was structured to facilitate the
radial collection of carriers, the axial transport of electrons
Fig. 7
Variation of the carrier-collection e
ffi
ciency along the axial
direction of a single Si microwire with a dopant density
N
D
, with a
diameter
d
¼
2.4
m
m and a charge-carrier lifetime of 1
m
s. Included is a
schematic of the scanning internal quantum yield simulation for a
single Si wire, with the internal quantum yield simulated as a function
of the distance of the excitation from the top of the wire.
Fig. 8
Variation of the carrier-collection e
ffi
ciency along the axial
direction of a single wire with respect to the radius of the wire, for a
dopant density
N
D
¼
6.3

10
13
cm

3
and charge-carrier lifetimes of
(A) 1
m
s, (B) 5
m
s, and (C) 10
m
s.
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ultimately limits the carrier-collection within the device,
necessitating the use of a material with a large diameter as well
as a long carrier di
ff
usion length.
IV. Discussion
A. Current-potential behavior of Si microwire arrays under
high-level injection
Although the lightly doped Si microwires investigated herein
were expected to be depleted, the n
+
/i-Si wire arrays in contact
with Me
2
Fc
+/0
CH
3
OH yielded e
ffi
ciencies and
ll factors that
were very similar to those observed for optimally doped p-Si wire
array photocathodes in contact with MV
2+/+
(aq).
30,31
The
demonstrated photovoltages of the n
+
/i-Si wire arrays exceeded
the bulk recombination/di
ff
usion-limited
V
oc
under low-level
injection conditions of
V
oc
¼
392 mV, calculated from
eqn (3):
32,33
V
oc
¼
kT
q
ln

J
ph
L
n
N
A
qD
n
n
i
2

(3)
where
k
is Boltzmann's constant,
T
is the absolute temperature
(298 K),
q
is the unsigned elementary charge,
J
ph
is the light-
limited photocurrent density (12.8 mA cm

2
),
D
n
is the di
ff
usion
coe
ffi
cient of minority carriers (36 cm
2
s

1
),
L
n
is the minority-
carrier di
ff
usion length (
L
n
¼
13.4
m
m, where
L
n
¼
ffiffiffiffiffiffiffiffiffiffi
D
n
s
n
p
and
s
n
¼
5
m
s),
N
A
is the dopant density (3

10
13
cm

3
), and
n
i
is the
intrinsic carrier concentration (1.45

10
10
cm

3
) of the semi-
conductor. A
V
oc
exceeding the 392 mV value can only be ach-
ieved if the injected majority-carrier density exceeds the
equilibrium majority-carrier density, indicating that the wire
arrays were under high-level injection conditions under 1 Sun
illumination.
In addition, the arrays exhibited photoanodic behavior in
contact with Me
2
Fc
+/0
CH
3
OH even though the wires were
slightly p-type in doping. This behavior indicates that the
J
E
behavior of the arrays was not dominated by their background
doping levels, but instead was dominated by the formation of
carrier-selective contacts at the back of the wire through the n
+
substrate as well as through the conformal, high barrier-height
contact to the Me
2
Fc
+/0
electrolyte. The combinations of elec-
trochemical experiments and variation of the growth substrate
demonstrated that the back contact of the array, in addition to
the electrochemical junction, ultimately determined the pho-
toresponse of the wires. These kinetic asymmetries introduced
into the wires by the liquid junction and the back contact were
critical to achieving a photoresponse in the microwires. This
behavior is analogous to previous observations for p
i
n type Si
cells in contact with non-aqueous redox systems.
32
As predicted,
no photoresponse was observed for arrays with back contacts
that were selective for the same carrier type selected by the
radial solution contact (
e.g.
n
+
back contacted samples where
the electron was collected radially by an electrochemical contact
with a relatively negative Nernstian solution potential).
Photoelectrodes formed using n
+
/i-Si microwires in contact
with Me
2
Fc
+/0
CH
3
OH exhibited diode quality factors of
n

1.8
2.0, which is characteristic of devices operating under high-
level injection conditions. Diode quality factors of

2.0, ranging
from
n
¼
1.6
1.8, have been measured previously for planar p
i
n concentrator devices in contact with Me
2
Fc
+/0
CH
3
OH.
12,13
In
contrast, previous measurements of p-type Si microwire arrays
and of di
ff
used radial junction n
+
p-Si microwire arrays have
reported diode quality factors closer to 1.0. Arrays of p-Si
microwires in contact with the one-electron redox couple
methyl viologen, MV
2+/+
, have displayed
n
¼
1.5
1.6 whereas
Pt/n
+
p-Si wire arrays in contact with aq. 0.5 M H
2
SO
4
display
n
¼
1.10

0.04.
5,31
Single-wire radial p
n junctions have exhibited
n
values between 1.0 and 1.2, consistent with expectations for
high-quality, low-recombination p
n junctions operating under
low-level injection conditions.
34
B. Open-circuit photovoltages of n
+
/i-Si/Me
2
Fc
+/0
microwire
array contacts
vs.
p
+
/i-Si CoCp
2
+/0
CH
3
CN microwire array
contacts
The p
+
/i-Si microwires in contact with CoCp
2
+/0
CH
3
CN
typically produced lower
V
oc
values than their n
+
/i-Si/Me
2
Fc
+/0
counterparts. This slight di
ff
erence in the photoresponse was
consistent with di
ff
erences in the e
ff
ective surface recombina-
tion velocities for Si in contact with these redox couples.
Speci
cally
S

20 cm s

1
and
S

55 cm s

1
has been observed
for Si in contact with the Me
2
Fc
+/0
CH
3
OH and CoCp
2
+/0
CH
3
CN redox systems, respectively.
14
Even for planar n-type and
p-type Si photoelectrodes, the n-Si/Me
2
Fc
+/0
CH
3
OH contact
typically produces higher
V
oc
values than p-Si/CoCp
2
+/0
CH
3
CN
contacts.
35
37
p-Si with a resistivity of

0.24
U
cm in contact with
CoCp
2
+/0
CH
3
CN has produced
V
oc
values of

540 mV, while n-
Si with the same dopant density measured in contact with
Me
2
Fc
+/0
CH
3
OH has produced
V
oc
values of

635 mV. In
addition, redox couples with more negative electrochemical
potentials, such as 1,1
0
-dimethylcobaltocene
+/0
in acetonitrile,
have elicited higher
V
oc
values from p-Si, demonstrating that the
cobaltocene
+/0
redox system is not completely optimized to
produce the maximum photoresponse for photocathodes made
using Si/liquid contacts.
C. Carrier-collection e
ffi
ciency of n
+
/i-Si/Me
2
Fc
+/0
microwire
devices
The measured internal quantum yield of the wires deviated
from unity, consistent with device physics simulations of lightly
doped n-Si microwires in contact with Me
2
Fc
+/0
CH
3
OH. The
measured
G
int
showed no change between as-grown wires that
had the Cu/Si interfacial region present and polished Si
microwires for which this silicide had been removed. Deviations
from unity in the observed internal quantum yield can therefore
be attributed to the limiting axial transport of electrons in the
inverted microwires. The relatively high carrier-collection e
ffi
-
ciency of the n
+
/i-Si/Me
2
Fc
+/0
CH
3
OH system, with experimen-
tally measured peak
G
int
values of

0.8, con
rms that the Cu
VLS-grown Si microwires were of high electronic quality, with
lifetimes exceeding 1
m
s.
The device physics simulations provide insight into the
photoresponse of the n
+
/i- and p
+
/i-Si devices, given that the
wires should be depleted in contact with the electrolytes used in
this work. The simulations of lightly doped n-Si wires in radial
2336
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