A photovoltaic device comprised of an array of 20 nm wide, 32 nm pitch array of silicon nanowires is modeled as an optical material. The nanowire array (NWA) has characteristic device features that are deep in the subwavelength regime for light, which permits a number of simplifying approximations. Using photocurrent measurements as a probe of the absorptance, we show that the NWA optical properties can be accurately modeled with rigorous coupled-wave analysis. The densely structured NWAs behave as homogeneous birefringent materials into the ultraviolet with effective optical properties that are accurately modeled using the dielectric functions of bulk Si and SiO_2, coupled with a physical model for the NWA derived from ellipsometry and transmission electron microscopy

Heath, James R.

Tham, Douglas

English

Caltech Authors - Main

Supporting Information for “Ultra-dense, deep sub-wavelength 
nanowire array photovoltaics as engineered optical thin films” 
 
Ion implantation 
 The silicon-on-insulator (SOI) substrates (Soitec USA Inc., Peabody, MA) were 
implanted with dopant ions (CORE Systems, Sunnyvale, CA) through photoresist masks. 
Heavily-doped p-type (dose of 3.8×1014 cm-2 B+ at 2.5 keV) and n-type (dose of 3.2×1014 
cm-2 P+ at 6.5 keV) contact regions were used to promote the formation of ohmic 
contacts, while the device regions received a low- or high-dose p-type implant (dose of 
3.8×1010 cm-2 B+ or 3.8×1013 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 procedure in solutions 
of H2SO4:H2O2 (3:1 v/v, 90 °C, 10 min), HF:H2O (1:50 v/v, 15 s in dark), and 
H2O:HCl:H2O2 (6:1:1, 80 °C, 10 min). After each step, the substrate was rinsed 
thoroughly with de-ionized water and dried with dry N2. 
 
Superlattice nanowire pattern transfer 
Superlattice wafers (IQE Ltd., Cardiff, U.K.) of alternating layers of 
GaAs/AlxGa(1-x)As were cleaved into small pieces, and GaAs selectively etched away in 
NH4OH:H2O2:H2O (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 along 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 thin layer of thermally-
cured epoxy that had been previously spun onto the substrate. After curing, the entire 
assembly was placed gently in a H2O2:H3PO4:H2O (1:5:50 v/v) solution to dissolve the 
GaAs/AlGaAs superlattice chip, leaving the array of Pt nanowires immobilized on the 
substrate (Figure 1d). 
 
Contact metallization 
The chips were dipped into BOE:H2O (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 source coupled 
at f/4 through a home-built cut-on filter changer to an Oriel MS257 monochromator 
(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 silicon 
photodiode (Hamamatsu Corp., Bridgewater, NJ), calibrated between 250-1100 nm to 
NIST-traceable standards (Opto-Cal Inc., Lakeside, CA) and mounted behind a 500 µm 
diameter precision pinhole (Edmund Optics, Barrington, NJ). The wavelength-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 spectrum with an 
uncoated Glan-Thompson linear polarizer (Thorlabs Inc., Newton, NJ) mounted just 
before the detector and find that there is only a slight polarization introduced by the 
illumination system. 
Wavelength calibrations were regularly performed, often before each 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 was 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 reproducible to ~0.1 
nm. At the end of each wavelength calibration, monochromator slit functions were also 
measured at 10 nm bandpass in steps of 0.1 nm to characterize the instrumental 
broadening of the illumination system. The slit functions were nearly perfectly triangular 
and identically wide for all gratings used, indicative of a well-aligned optical system. 
 
Rigorous coupled-wave analysis calculation 
 The rigorous coupled-wave analysis (RCWA) represents periodic surface features 
as a Fourier series and propagates the incident wave through the optical 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 layer-by-layer by assigning 
appropriate optical constants to each volume element. In each layer, the periodic pattern 
of optical constants is assumed to be constant throughout the entire layer 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 incident wave enters the 
structure from the superstrate and exits via the substrate. Special 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 multilayer 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 lower interface between the 
bottommost layer and the substrate. 
There is no general restriction on the grid resolution, uniformity or geometry, 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 µm thick silicon handle wafer) media are assumed to be continuous, isotropic 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 assumed to 
be infinite in extent, which is a reasonable approximation given that our arrays are ≥10 
µm long, more than 10 times longer than the wavelengths of interest. In 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 illumination. To 
calculate the absorptance A = 1 – R – T – S, we used the zero-order (specular) reflectance 
R0 and transmittance T0 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 higher 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 because they appeared, by light 
microscopy inspection, to be the most homogeneous. The devices chosen were selected 
for the absence of irregularities due to fabrication variability, so as to avoid artifacts in 
the measured optical data.  Dark I-V curves were also obtained for those (and other) 
devices with a Model 6430 sourcemeter (Keithley Instruments, Cleveland, 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 (3.8×1013 cm-2 B+) in the device regions. These higher-doped nanowire 
array devices generate Isc = 17 pA and Voc = 0.26 V with FF = 0.50, while the higher-
doped film devices develop Isc = 28 pA and Voc = 0.37 V with FF = 0.62. However, the 
higher-doped nanowire arrays were of poorer structural quality and were less amenable to 
optical modeling. Hence we have chosen to focus on the lower-doped (3.8×1010 cm-2 B+) 
principal device in the main text. 
In Table S1 we summarize additional measurements from other devices. We note 
that the nanowire array devices tend to exhibit more scatter in 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 lengths 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 photovoltaics in the 
literature. 
 
Minority carrier diffusion length 
 Minority carrier diffusion lengths were measured using a WITec AlphaSNOM 
(WITec Wissenschaftliche Instrumente und Technologie GmbH, Ulm, Germany) 
scanning near-field optical microscope (SNOM). Light from laser diodes at 405 nm 
(blue) or 650 nm (red) was chopped at 83 Hz and fiber-coupled into the microscope. An 
objective lens was used to focus the laser light onto the device (far-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 to 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 rastered across the device 
while recording the lock-in output as a function of probe position. During the 
measurement, the devices were weakly illuminated using the microscope lamp to remove 
artifacts arising from light absorption in the substrate wafer. The minimum illumination 
level was used to remove capacitance transients from the output photocurrent so as to 
obtain a square wave output.  
Scanning photocurrent images acquired with far-field illumination were 
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 only by the tip 
aperture size (Figure S2). Unfortunately, because the tip is dragged across the surface, the 
sample undergoes damage during the measurement and can typically only 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 lengths on either side 
of the junction. 
 
Cross-sectional transmission electron microscopy 
 Focused-ion beam (FIB) liftout of the cross-sectional sample was performed in a 
Nova 600 DualBeam FIB/SEM (FEI Company, Hillsboro, OR) equipped with an 
Autoprobe 200 micromanipulator system (Omniprobe Inc., Dallas, TX). Initial 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 ions 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 Tecnai TF20ST TEM 
(FEI Company, Hillsboro, OR) for imaging at 200 kV. Sometimes, the cross-sectional 
sample was too thick, and contained contrast contributions from inelastically 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 contrast (Figure 3a,b in 
main text). Convergent beam electron diffraction (CBED) was performed by focusing the 
beam to crossover over the device regions and capturing the diffraction patterns on a 
charge-coupled device at the camera plane (Figure S3a,b). With sufficiently thin sample 
regions, high-resolution transmission electron micrographs were acquired along the [011] 
zone of the sample and confirm that the high crystallinity of the devices 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 Jsc using the projected active area Y = L × W of the device. 
Ideality factors nlit and ndark were obtained by fitting lit and dark I-V measurements to the 
diode equation I = I0 [exp(qV/nkBT) – 1] in the low forward bias region (up to ~0.4 V).  
 
Sample Isc 
(pA) 
Jsc 
(mA/cm2) 
Voc 
(V) 
FF nlit ndark Description 
3.8×1013 cm-2 
B+ dose 
       
NWA 17  0.26 0.50 2.2 2.7 10 µm long 
NWA 17  0.34 0.60 1.8 1.8 10 µm long 
NWA 17  0.34 0.55 2.2 1.9 25 µm long 
Thin Film 28  0.37 0.62 1.5 1.9 10 µm long 
Thin Film 27  0.36 0.60 1.6 1.8 10 µm long 
Thin Film 27  0.37 0.62 1.8 1.7 25 µm long 
NWA 18  0.26    25 µm long 
NWA 19  0.38    50 µm long 
NWA 19  0.35    100 µm long 
Thin Film 29  0.40    25 µm long 
Thin Film 30  0.40    25 µm long 
Thin Film 29  0.39    100 µm long 
3.8×1010 cm-2 
B+ dose 
       
NWAa 26 2.6 0.37    10 µm long 
Filmb 60 3.0 0.46    10 µm 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 µm 
Ref. 4 31.1 3.5 0.29 0.51 1.28  Axial p-i-n, i=4 µm 
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 images (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
ph
o
to
cu
rr
e
n
t (A
)
distance from junction (µm)
Lh = 100 nm
L
e
 = 200 nm
 
Figure S2. Line profiles through near-field scanning photocurrent images obtained with a 
scanning near-field optical microscope (SNOM) in contact mode, taken along the dashed 
lines in Figure S1. An exponential fit on the left (right) side of the peak yields the 
minority carrier diffusion length Le (Lh), with measurement resolution determined by the 
finite size of the SNOM tip aperture (100 nm). This yields upper estimates for the total 
diffusion length Lmax ~ 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 Lmin ~ 200 nm and 100 nm. 
(a) (b)
(c) (d)
Si
SiO2
SiO2
Si
SiO2
SiSi Si
 
Figure S3. Convergent beam electron diffraction (CBED) patterns of (a) bulk film 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 electron 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. 
 


Ultradense, Deep Subwavelength Nanowire Array Photovoltaics As Engineered Optical Thin Films

Supporting Information for “Ultra-dense, deep sub-wavelength 
nanowire array photovoltaics as engineered optical thin films” 
 
Ion implantation 
 The silicon-on-insulator (SOI) substrates (Soitec USA Inc., Peabody, MA) were 
implanted with dopant ions (CORE Systems, Sunnyvale, CA) through photoresist masks. 
Heavily-doped p-type (dose of 3.8×1014 cm-2 B+ at 2.5 keV) and n-type (dose of 3.2×1014 
cm-2 P+ at 6.5 keV) contact regions were used to promote the formation of ohmic 
contacts, while the device regions received a low- or high-dose p-type implant (dose of 
3.8×1010 cm-2 B+ or 3.8×1013 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 procedure in solutions 
of H2SO4:H2O2 (3:1 v/v, 90 °C, 10 min), HF:H2O (1:50 v/v, 15 s in dark), and 
H2O:HCl:H2O2 (6:1:1, 80 °C, 10 min). After each step, the substrate was rinsed 
thoroughly with de-ionized water and dried with dry N2. 
 
Superlattice nanowire pattern transfer 
Superlattice wafers (IQE Ltd., Cardiff, U.K.) of alternating layers of 
GaAs/AlxGa(1-x)As were cleaved into small pieces, and GaAs selectively etched away in 
NH4OH:H2O2:H2O (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 along 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 thin layer of thermally-
cured epoxy that had been previously spun onto the substrate. After curing, the entire 
assembly was placed gently in a H2O2:H3PO4:H2O (1:5:50 v/v) solution to dissolve the 
GaAs/AlGaAs superlattice chip, leaving the array of Pt nanowires immobilized on the 
substrate (Figure 1d). 
 
Contact metallization 
The chips were dipped into BOE:H2O (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 source coupled 
at f/4 through a home-built cut-on filter changer to an Oriel MS257 monochromator 
(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 silicon 
photodiode (Hamamatsu Corp., Bridgewater, NJ), calibrated between 250-1100 nm to 
NIST-traceable standards (Opto-Cal Inc., Lakeside, CA) and mounted behind a 500 µm 
diameter precision pinhole (Edmund Optics, Barrington, NJ). The wavelength-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 spectrum with an 
uncoated Glan-Thompson linear polarizer (Thorlabs Inc., Newton, NJ) mounted just 
before the detector and find that there is only a slight polarization introduced by the 
illumination system. 
Wavelength calibrations were regularly performed, often before each 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 was 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 reproducible to ~0.1 
nm. At the end of each wavelength calibration, monochromator slit functions were also 
measured at 10 nm bandpass in steps of 0.1 nm to characterize the instrumental 
broadening of the illumination system. The slit functions were nearly perfectly triangular 
and identically wide for all gratings used, indicative of a well-aligned optical system. 
 
Rigorous coupled-wave analysis calculation 
 The rigorous coupled-wave analysis (RCWA) represents periodic surface features 
as a Fourier series and propagates the incident wave through the optical 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 layer-by-layer by assigning 
appropriate optical constants to each volume element. In each layer, the periodic pattern 
of optical constants is assumed to be constant throughout the entire layer 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 incident wave enters the 
structure from the superstrate and exits via the substrate. Special 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 multilayer 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 lower interface between the 
bottommost layer and the substrate. 
There is no general restriction on the grid resolution, uniformity or geometry, 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 µm thick silicon handle wafer) media are assumed to be continuous, isotropic 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 assumed to 
be infinite in extent, which is a reasonable approximation given that our arrays are ≥10 
µm long, more than 10 times longer than the wavelengths of interest. In 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 illumination. To 
calculate the absorptance A = 1 – R – T – S, we used the zero-order (specular) reflectance 
R0 and transmittance T0 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 higher 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 because they appeared, by light 
microscopy inspection, to be the most homogeneous. The devices chosen were selected 
for the absence of irregularities due to fabrication variability, so as to avoid artifacts in 
the measured optical data.  Dark I-V curves were also obtained for those (and other) 
devices with a Model 6430 sourcemeter (Keithley Instruments, Cleveland, 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 (3.8×1013 cm-2 B+) in the device regions. These higher-doped nanowire 
array devices generate Isc = 17 pA and Voc = 0.26 V with FF = 0.50, while the higher-
doped film devices develop Isc = 28 pA and Voc = 0.37 V with FF = 0.62. However, the 
higher-doped nanowire arrays were of poorer structural quality and were less amenable to 
optical modeling. Hence we have chosen to focus on the lower-doped (3.8×1010 cm-2 B+) 
principal device in the main text. 
In Table S1 we summarize additional measurements from other devices. We note 
that the nanowire array devices tend to exhibit more scatter in 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 lengths 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 photovoltaics in the 
literature. 
 
Minority carrier diffusion length 
 Minority carrier diffusion lengths were measured using a WITec AlphaSNOM 
(WITec Wissenschaftliche Instrumente und Technologie GmbH, Ulm, Germany) 
scanning near-field optical microscope (SNOM). Light from laser diodes at 405 nm 
(blue) or 650 nm (red) was chopped at 83 Hz and fiber-coupled into the microscope. An 
objective lens was used to focus the laser light onto the device (far-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 to 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 rastered across the device 
while recording the lock-in output as a function of probe position. During the 
measurement, the devices were weakly illuminated using the microscope lamp to remove 
artifacts arising from light absorption in the substrate wafer. The minimum illumination 
level was used to remove capacitance transients from the output photocurrent so as to 
obtain a square wave output.  
Scanning photocurrent images acquired with far-field illumination were 
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 only by the tip 
aperture size (Figure S2). Unfortunately, because the tip is dragged across the surface, the 
sample undergoes damage during the measurement and can typically only 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 lengths on either side 
of the junction. 
 
Cross-sectional transmission electron microscopy 
 Focused-ion beam (FIB) liftout of the cross-sectional sample was performed in a 
Nova 600 DualBeam FIB/SEM (FEI Company, Hillsboro, OR) equipped with an 
Autoprobe 200 micromanipulator system (Omniprobe Inc., Dallas, TX). Initial 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 ions 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 Tecnai TF20ST TEM 
(FEI Company, Hillsboro, OR) for imaging at 200 kV. Sometimes, the cross-sectional 
sample was too thick, and contained contrast contributions from inelastically 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 contrast (Figure 3a,b in 
main text). Convergent beam electron diffraction (CBED) was performed by focusing the 
beam to crossover over the device regions and capturing the diffraction patterns on a 
charge-coupled device at the camera plane (Figure S3a,b). With sufficiently thin sample 
regions, high-resolution transmission electron micrographs were acquired along the [011] 
zone of the sample and confirm that the high crystallinity of the devices are retained after 
processing (Figure S3c). By placing an objective aperture about the (1̄11̄)  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 Jsc using the projected active area Y = L × W of the device. 
Ideality factors nlit and ndark were obtained by fitting lit and dark I-V measurements to the 
diode equation I = I0 [exp(qV/nkBT) – 1] in the low forward bias region (up to ~0.4 V).  
 
Sample Isc 
(pA) 
Jsc 
(mA/cm
2
) 
Voc 
(V) 
FF nlit ndark Description 
3.8×10
13
 cm
-2
 
B
+
 dose 
       
NWA 17  0.26 0.50 2.2 2.7 10 µm long 
NWA 17  0.34 0.60 1.8 1.8 10 µm long 
NWA 17  0.34 0.55 2.2 1.9 25 µm long 
Thin Film 28  0.37 0.62 1.5 1.9 10 µm long 
Thin Film 27  0.36 0.60 1.6 1.8 10 µm long 
Thin Film 27  0.37 0.62 1.8 1.7 25 µm long 
NWA 18  0.26    25 µm long 
NWA 19  0.38    50 µm long 
NWA 19  0.35    100 µm long 
Thin Film 29  0.40    25 µm long 
Thin Film 30  0.40    25 µm long 
Thin Film 29  0.39    100 µm long 
3.8×10
10
 cm
-2
 
B
+
 dose 
       
NWA
a
 26 2.6 0.37    10 µm long 
Filmb 60 3.0 0.46    10 µm 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 µm 
Ref. 4 31.1 3.5 0.29 0.51 1.28  Axial p-i-n, i=4 µm 
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 images (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
p
h
o
to
c
u
rr
e
n
t 
(A
)
distance from junction (µm)
L
h
 = 100 nm
L
e
 = 200 nm
 
Figure S2. Line profiles through near-field scanning photocurrent images obtained with a 
scanning near-field optical microscope (SNOM) in contact mode, taken along the dashed 
lines in Figure S1. An exponential fit on the left (right) side of the peak yields the 
minority carrier diffusion length Le (Lh), with measurement resolution determined by the 
finite size of the SNOM tip aperture (100 nm). This yields upper estimates for the total 
diffusion length Lmax ~ 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 Lmin ~ 200 nm and 100 nm. 
(a) (b)
(c) (d)
Si
SiO2
SiO2
Si
SiO2
SiSi Si
 
Figure S3. Convergent beam electron diffraction (CBED) patterns of (a) bulk film 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 electron 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 (1̄11̄)  
spot. All nanowires within the field are crystalline. 
 


Express

Heat Transfer

MRCWA -Multilayer Rigorous CoupledWave Analysis Home Page.

Photovoltaics

Silicon Dioxide (SiO2) (Glass). InHandbook of Optical Constants of Solids; Palik,

https://authors.library.caltech.edu/21184/2/nl102199b_si_001.pdf

Ultradense, Deep Subwavelength Nanowire Array Photovoltaics As Engineered Optical Thin Films

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