S
1
Supp
orting
Information for:
ASSESSING EFFECTS OF NEAR
-
FIELD SYNERGISTIC
LIGHT ABSORPTION ON ORDERED INORGANIC
PHOTOTROPIC GROWTH
A
ZHAR
I.
C
ARIM
†
,
§
,
M
ADELINE
C.
M
EIER
†
,
§
,
K
ATHLEEN
M.
K
ENNEDY
‡
,
M
ATTHIAS
H.
R
ICHTER
‡
,
K
ATHRYN
R.
H
AMANN
†
AND
N
ATHAN
S.
L
EWIS
†
,
*
†
Division of Chemistry and Chemical Engineering
‡
Division of Engineering and Applied Sciences
California Institute of Technology
Pasadena, CA 91125
S
2
S1.
Contents
This document contains
a description of the
experimental
and
computational
methods
utilized in this work
(Section
s
S
2
and S3
)
,
additional computational data (Section S4),
and a list
of associated references (Section S
5
).
S
3
S2.
Experimental
Methods
Materials and Chemicals
Acetone
(
99.5 %
,
EMD
Millipore
), isopropanol (99.5 %, VWR),
methyl isobutyl ketone (9
0
-
100
%,
J.T.Baker
),
poly(methyl methacrylate) (PMMA, 495 A8,
Microchem),
b
uffered
oxide etchant
(
NH
4
F : HF
in a 6 : 1
volume
ratio
,
Transene)
,
In (99.999 %,
Alfa Aesar), Ga (99.999 %, Alfa
Aesar),
H
2
SO
4
(ACS Reagent, J.T.Baker),
SeO
2
(99.4 %, Alfa
Aesar), and TeO
2
(99+ %, Sigma
-
Aldrich) were used as received. H
2
O with a resistivity ≥ 18.2
M
Ω
cm (Barnstead Nanopure System) was used throughout.
n
+
-
Si(100) (
0.001
-
0.00
35
Ω
cm, As
-
doped, 525 ±
1
5 μm
thick
, single
-
side polished, Addison Engineering) was used as a substrate for
deposition. Flash
-
Dry Ag Paint (SPI Supplies), EP21ARHTND Epoxy (MasterBond) and
nitrocellulose
-
based nail polish were used to assemble the working el
ectrodes.
Substrate Preparation
n
+
-
Si wafers were
first
rinsed with acetone and isopropanol.
PMMA
resist
was
then
applied by spin
-
coating
for 1.0 min to
effect
a
0.8
μ
m thick layer and then cured
for 5.0 min at 1
80
°
C
.
Patterns consisting of circles
with
diameter
s of
0.2
,
0.4
,
0.8
,
1.2
, and
1.6
μ
m, on a square lattice with a pitch of 10 μm
,
were designed using AutoCAD (Autodesk) and
fractured using BEAMER (GenISys).
A
Raith
EBPG 5000+
electron
-
beam pattern generator
was
used
to write the
pattern
s
into the resist
with
a
100 kV accelerating voltage, 300 μm aperture, 5 nA
current, and a dose of 1000 μC cm
-
2
.
The pattern was then developed by immersing the
substrates
in
a
mixture
of
methyl
isobutyl ketone
: isopropanol
in
a
1 : 3 volume ratio
for
1.0 min
at room
temperatur
e
,
producing
an array of circular well structures
.
The patterned
wafers
, along with
additional unpatterned Si,
were then cut into square 0.
4
0 cm by 0.
4
0 cm
sections
using a Dynatex
GST
-
150 scriber
-
breaker system
; these
square pieces
were
then
used
a
s
substrates
for
the
photoelectro
chemical
growth
of Se
-
Te
.
S
4
Electrode Preparation
One end of a Sn
-
coated Cu wire (22 AWG) was bent to form a small,
flat coil and the wire was threaded through glass tubing (6 mm O. D.) such that the coil was just
outside the tubing. Epoxy was applied to seal the end of the tube from which the coil protru
ded. A
eutectic mixture of Ga and In was scratched with a carbide
-
tipped scribe into the unpolished back
surfaces of the Si sections. The wire coil was then contacted to the unpolished surface and affixed
with Ag paint. Nail polish was applied to insulate
the unpolished face, the wire
-
coil contact, and
the exposed wire between the coil and epoxy seal. Immediately before deposition, the Si
portion
of the electrode was immersed in buffered
oxide
etchant for ~ 45 s to remove surficial SiO
x
from
the Si. The ele
ctrode was then rinsed with H
2
O and dried under a stream of N
2
(g).
Electrode Illumination
P
hotoelectrochemical depositions
were performed using
a
narrow
-
band
light
-
emitting diode
(
LED
) source
(Thorlabs
SOLIS
-
940C
)
with an
intensity
-
weighted
average wavele
ngth,
λ
avg
,
of 934 nm
and
a
spectral bandwidth (FWHM) of
55
nm.
The output of
the
diode source
was
collected
, condensed,
and collimated
using
a series of three lenses: an
aspheric lens (Ø25.4 mm, f = 16 mm), followed by
a
bi
-
convex lens (Ø50.8 mm, f = 16 mm
),
and
last a plano
-
convex lens
(
Ø50.8 mm, f = 1
00
mm)
.
A film polarizer (Thorlabs LPNIRE200
-
B) was
inserted after the lenses to
produce
vertical linear polarization.
A
1
20
grit ground
-
glass (
N
-
BK7
)
diffuser was placed immediately in front of the photoelectrochemical cell to ensure spatial
homogeneity of the illumination
.
The light intensity incident on the electrode was measured by
placing a calibrated Si photodiode (Tho
rlabs FDS100)
,
instead of an electrode assembly
,
in the
photoelectrochemical cell with electrolyte, and the steady
-
state current response of
the
Si
photodiode was measured.
Depositions
were
performed with
a
light intens
i
ty
of
195
mW cm
-
2
.
Photoelectro
chemical
Deposition
P
hotoelectro
chemical deposition
was
performed
using
a
Bio
-
Logic SP
-
200 potentiostat
.
Deposition was performed in a glass cell with a
quartz
window. A
S
5
three
-
electrode, two
-
compartment cell was used with an Ir wire counter electrode (99.9
99 %,
Sigma
-
Aldrich) isolated behind a porous glass frit, and a Ag/AgCl reference electrode (3 M KCl,
Bioanalytical Systems).
Films were deposited from an aqueous solution of 0.0200 M SeO
2
, 0.0100
M TeO
2
,
and 2.00 M H
2
SO
4
.
D
eposition was effected by biasin
g the
patterned
Si
electrode
,
illuminated as
described
above (
Electrode Illumination
),
potentiostatically
at
-
0.
40
0
V vs.
Ag/AgCl for
3
.0
0
min at room temperature.
After deposition, the electrode was immed
iately
removed from the cell,
rinsed with H
2
O
, and then
dried under a stream of N
2
(g)
.
The
patterned
substrate with
the
top
-
facing
Se
-
Te
deposit
was
mechanically
separated from the
rest of the
electrode assembly.
The nitrocellulose
-
based insulation
and
the majority of the
Ag
paint and
In
-
Ga eutectic were then removed mechanically.
Patterned
substrate
s
w
ere
then immersed in
acetone
for ~ 5 min to remove the PMMA resist, rinsed with isopropanol, and then dried under a stream of
N
2
(g).
Microscopy
Scanning
-
electron micrographs (SEMs) were obtained with a FEI Nova
NanoSEM 450 at an accelerating voltage of 5.00 kV with a working distance of 5 mm and an in
-
lens secondary electron detector. Micrographs were acquired with a resolution of 688 pixels μm
-
1
over 2 μm
2
areas.
S
6
S3.
Computational Methods
Growth Modeling
The growths of the photoelectrochemically deposited films were
simulated with an iterative growth model in which electromagnetic simulations were first used to
calculate the local photocarrier
-
generation rates at the film surface. Then, mass addition was
simulated via a Monte Carlo method wherein the local photocarrier
-
generation rate weighted the
local rate of mass addition along the film surface.
Simulations of confined growth
began with a sem
i
-
infinite
Si
substrate
with an atop PMMA
layer with a single well structure
that had
the same dimensions as
the
wells
used in the experiments
described in Section S2
. In the first step, the light
-
absorption profile under a linearly polarized,
plane
-
wave i
llumination source was calculated using
full
-
wave finite
-
difference time
-
domain
(FDTD) simulations
. Perfectly matched layer boundary conditions
were utilized at the boundaries
of the
confined growth
FDTD simulations
. In the second step, a Monte Carlo simul
ation was
performed in which
mass
was added to the upper surface of the structure with a probability
F
:
=
3
1
=
)
(
i
r
x
G
G
F
i
i
(
Equation 1
)
where
G
is the spatially dependent photocarrier
-
generation rate at the deposit/solution interface,
x
i
is the fraction of
i
th
nearest neighbors occupied in the cubic lattice, and
r
i
is the distance to the
i
th
nearest neighbor. The multiplicative sum in the definiti
on of this probability (Equation 1) serves
to reduce th
e surface roughness of the film,
to mimic the experimentally observed surface
roughness.
After the initial Monte Carlo simulation, the absorbance of the new, structured film
was then calculated in the
same manner as for the initial planar film, and an additional Monte Carlo
simulation of mass addition was performed.
This process of absorbance calculation and mass
addition was repeated for a total of 30 iterations.
The amount of mass added in each Monte
Carlo
simulation equaled that of a 15 nm planar layer
covering
the projected well area, preventing
S
7
optically
-
large changes in the feature dimensions between iterations
and
thus
enabling a
discretized computational approximation of the continuous growth process
.
Optical Simulations of Simplified Morphologies
Three
-
dimensional FDTD simulations
were utilized to calculate the profiles of light absorption and the
time
-
average electric
-
field
magnitude for simplified lamellar structures.
A single plane
-
wave source polarized with the
electric field parallel to the lamellar long axis was considered.
P
eriodic boundary condit
ions
were
imposed
in the direction parallel to
the lamellar long axis whereas perfectly matched layer
boundary conditions were
imposed
in each of the perpendicular directions.
Dipole Emi
ssion
Simulations
FDTD simulation of dipole emission was utilized to
model
the interfacial optical modulation
at th
e onset of growth
.
A two
-
dimensional square simulation
plane was utilized
.
Dipoles were arranged with separation of twice the emission wavelength and
the oscillation axis was set perpendicular to the separation axis.
Perfectly matched layer boundary
condit
ions were imposed in
both
directions.
General Parameters
All FDTD simulations were performed with FDTD Solutions
(Lumerical).
Previously measured values of the complex refractive index of Se
-
Te were utilized.
V
alue
s
of
n
= 1.33
and 1.48
w
ere
used
for
the refractive index of the electrolyte
and the PMMA,
respectively
.
1
,
2
The simulations
utilized the intensity
-
weighted average wavelength, λ
avg
, of the
experimental source
described in Section S2
and were discretized using a
uniform
three
-
dimensional
cubic
mesh with lattice
constants of 10 nm and 2 nm for the growth modeling and
simplified simulations, respectively.
S
8
S4.
Additional Computational Data
Figure S1.
Origin of structure genesis via inorganic phototropic growth on a bare, isotropic substrate (a).
Electrochemical deposition produces a surface topology (b) that scatters the incident light beam (c).
Inorganic phototropic growth was effected by light
-
medi
ated electrochemical synthesis of
Se
-
Te using vertically polarized illumination with an intensity
-
weighted average wavelength (
λ
avg
)
of 934 nm from an incoherent, narrowband light
-
emitting diode source.
Light absorption in the
deposited Se
-
Te material acce
lerates the
rate of electrochemical
growth.
3
The surface topology
generated by the initial deposition results in scattering of the incident illumination
; t
h
is
initial
process is
graphic
ally
summarized in Figure S1.
This scattering in turn modulates the electric field
amplitude at the growth interface. The structure of the interfacial electric field
defined by scattering
of the vertically
polarized illumination
was calculated by modeling the scatterers as point dipole
emission sources.
Figure S2.
Normalized time
-
average of the E
-
field magnitude from two dipoles emitting radiation with a free space
wavelength of
λ
= 934 nm
in a medium of refractive index
n
= 1
.33. Dipoles separated by a distance of twice the
wavelength along the horizontal with the oscillation axis perpendicular to the axis of separation.
Figure S
2
presents a simulation of the normalized time
-
averaged electric field magnitude from two
dipoles emitting radiation with a free space wavelength of
λ
= 934 nm in a medium of refractive
index
n
= 1.33 (reflective of the growth solution) and separated by a d
istance of two wavelengths
S
9
perpendicular to the oscillation axis. Periodic bands of elevated field intensity were observed.
Light
-
driven electrochemical growth occurs preferentially in these areas of localized field
enhancement. Thus, the
se
data are consis
tent with the anisotropic, ordered morphology observed
experimentally (Figure 1a) a
nd present a
basis for inorganic phototropic growth.
Figure S3.
Simulated Se
-
Te deposit morphologies generated considering λ
avg
= 934 nm illumination with areal
constraint to the circular diameter
d
= 0.4 μm. Each panel presents the result of a fully independent set of growth
computations.
Figure S3 presents simulated morphologies of Se
-
Te deposits generated from independent
sets
of computations using the iterative, two
-
step growth model considering λ
avg
= 934 nm
illumination with areal constraint to the circular diameter
d
= 0.4 μm. The extremely close accord
between these mutually independent simulations of bottom
-
up mass additi
on
compellingly
indicates that the observed structures are a direct result of light
-
matter interactions between the
input illumination and the evolving Se
-
Te
deposits
.
S
10
S
5
.
References
(1) Hale, G. M.; Querry, M. R. Optical Constants of
Water in the 200
-
nm to 200
-
μm
Wavelength Region.
Appl. Opt.
1973
,
12
, 555
-
563.
(2) Zhang, X.; Qiu, J.; Li, X.; Zhao, J.; Liu, L. Complex refractive indices measurements of
polymers in visible and near
-
infrared bands.
Appl. Opt.
2020
,
59
, 2337
-
2344.
(3) Meier, M. C.; Cheng, W.
-
H.; Atwater, H. A.; Lewis, N. S.; Carim, A. I. Inorganic
Phototropism in Electrodeposition of Se
-
Te.
J. Am. Chem. Soc.
2019
,
141
, 18658
-
18661.