S
1
Supp
lementary
Information for:
I
NCLINATION OF
P
OLARIZED
I
LLUMINATION
I
NCREASES
S
YMMETRY
OF
S
TRUCTURES
G
ROWN
V
IA
I
NORGANIC
P
HOTOTROPISM
M
ADELINE
C.
M
EIER
,
a
N
ATHAN
S.
L
EWIS
,
*
a
b
A
ZHAR
I.
C
ARIM
*
a
b
a
Division of Chemistry and Chemical Engineering
b
Beckman Institute
California Institute of Technology
Pasadena, CA 91125
*E
-
mail:
nslewis@caltech.edu
,
aic@caltech.edu
Electronic
Supplementary
Material
(ESI)
for
Materials
Horizons.
This
journal
is
©
The
Royal
Society
of
Chemistry
2023
S
2
S1.
Contents
Th
is
document
contains
a description of the
experimental
and
modeling/simulation
methods
utilized in this
work
(Section
s
S
2
and S3
)
,
Fourier spectra fit data (Section S4),
and a list
of associated references (Section S
5
).
S
3
S2.
Experimental
Methods
Materials and Chemicals
H
2
SO
4
(ACS Reagent, J. T. Baker),
buffered
HF
improved
etchant
(
Transene
), 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.
Au
-
coated
n
+
-
S
i(1
00
) (
< 0.005
Ω
cm, As
-
doped,
525 ± 2
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 electrodes.
Substrate Preparation
n
+
-
Si wafers were etched with buffered HF for 30 s, rinsed with
H
2
O,
dried under a stream of N
2
(g), and then immediately transferred to an electron
-
beam metal
evaporator with a base pressure < 10
-
6
torr. Using an accelerating voltage of 10 kV, a 10 nm Ti
adh
esion layer was deposited on the polished side of the wafer u
sing a
4
0 mA
deposition current
,
and
50 nm of Au
was
then
deposited on top
of the Ti using a
1
5
0 mA deposition current
.
20
nm
of
Ti was deposited on the unpolished side of the wafer to serve as a
back
-
contact. The Au
-
topped Si
sections were then cut into square
0.
5
0
c
m by
0.50
c
m sections for use a
s
deposition substrates.
Electrode Preparation
Electrode assemblies were prepared by applying epoxy to the flat
sides of each of two Al half
-
round bars
(0.25 in diameter). The two bars were then joined together,
with an ~ 10 mm offset in the axial dimension to form a cylinder with two half
-
round ends.
Polytetrafluoroethylene heat
-
shrink tubing was used to insulate the cylindrical section and epoxy
was use
d to insulate the rounded side of one of the half
-
round ends.
Ag paint was applied to the
Ti
-
coated b
ack surfaces of the Au
-
topped Si sections
and the sections were
affixed to the flat
surface of the epoxied half
-
round end. Nail polish was used to insulate the remaining uncovered
area on the flat surface that surrounded the Au
-
topped Si section. Figure S1 presents a schematic
S
4
of an electrode assembly with an attached
Au
-
topped Si section. Immediately before deposition,
the surface of each electrode was briefly cleaned using a stream of N
2
(g).
Figure S1.
Schematic of an electrode assembly with an attached Au
-
topped Si section.
Electrode Illumination
Illumination for
photoelectrochemical
growth
was
generated using
a
narrowband diode (LED) source
with
an
intensity
-
weighted
average wavelength,
λ
avg
,
value
of
626
nm
and
a spectral bandwidth (FWHM) of
17
nm
(Thorlabs, SOLIS
-
62
3
C)
.
The
LED
output
was collected,
condensed and collimated
using
an aspheric lens (Ø25.4 mm, f = 1
6 mm
) followed
by
a
bi
-
convex lenses (Ø50.8 mm, f = 60
mm
)
and another aspheric lens (Ø50.8 mm, f = 32
mm
)
.
A
broadband
film polarizer (LPNIRE200
-
B) was
inserted
before the final lens to effect linear
polarization
.
A 1500 grit ground
-
glass (
UV Fused Silica
) diffuser was placed immediately in front
of the photoelectrochemical cell to ensure spatial homogeneity of the illumi
nation.
The light
intensity incident on the electrode was measured by placing a calibrated Si photodiode (Thorlabs
FDS100)
,
instead
of
an electrode
assembly
,
in the
photoelectrochemical cell with electrolyte
,
and
the stea
dy
-
state current response of that
S
i photo
diode
was measured
.
Depositions
with normally
-
incident illumination were
performed with
a
light
intensity
of
I
=
30
mW cm
-
2
.
For depositions
S
5
with
off
-
normal
incidence, the
illumination
was inclined
from the
substrate normal
in the plane of
the polarization
by
an angle
β
,
and the
intensities were increased by a factor of cos
-
1
(
β
)
relative to
the intensities used at normal incidence.
Photoelectrochemical Deposition
P
hotoelectrochemical deposition was
performed
using
a
Bio
-
Logi
c SP
-
200 potentiostat.
Deposition was performed in a two
-
compartment glass cell
with
a
quartz
window.
A three
-
electrode configuration was utilized with a
n
Ir wire
counter electrode
(99.999 %, Sigma
-
Aldrich)
isolated behind a porous glass frit
and a Ag/AgCl
reference electrode
(3
.00
M KCl
,
Bioanalytical Systems). Films were deposited from an aqueous solution of 0.0
2
00
M SeO
2
, 0.0
10
0 M
TeO
2
,
and
2.00
M
H
2
S
O
4
.
Photoelectrodeposition on isotropic substrates was
effected by biasing the Au
-
coated electrode, illuminated as detailed under the above subheading
(Electrode Illumination), potentiostatically at
-
0.15 V vs. Ag/AgCl for
4.00 min
at room
temperature.
After d
eposition, 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
Au
-
coated
substrate with
top
-
facing
Se
-
Te
film
was
mechanically
separated from the
rest of the electrode assembly.
The nitrocellulose
-
based
insulation
and
the majority of the
Ag
paint
were
then removed mechanically.
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
.0
mm and an in
-
lens secondary electron detector. Micrographs obtained for quantitative analysis were acquired
with a resolution of 172 pixels μm
-
1
over
~
120 μm
2
areas. Micrographs
that were used
to produce
display figures were
acquired with a resolution of 344 pixels μm
-
1
over
~
2
μm
2
areas.
S
6
S
3
.
Modeling and Simulation
Methods
Simulation of
Deposit
Morphology
Light
-
directed electrochemical growth was
simulated
with an iterative
growth
model
in which electromagnetic simulations were first used to calculate
the local
light absorption profile at the growth interface
. Then, mass addition was simulated via a
Monte Carlo method wherein the local
absorption
weighted the local rate of mass add
ition along
the film surface.
Three
-
dimensional simulations were discretize
d
using
a
cubic mesh with a lattice constant
of 10 nm. Growth
began
with a bare, semi
-
infinite planar
substrate.
In the first step, the light
-
absorption
profile under a
linearly polarized, plane
-
wave illumination
source
with
λ
avg
= 6
26
nm
was calculated using
full
-
wave finite
-
difference time
-
domain (FDTD) simulations
(“FDTD
Solutions” software package, Lumerical)
.
Perfectly matched layer boundary conditio
ns were
used
in the direction normal to the substrate. For simulations using normally
incident illumination,
periodic boundary conditions were used for the two orthogonal
directions
in the plane of the
substrate. For simulations using inclined illumination
, periodic and Bloch boundary conditions
were
used
in the directions in the plane of the substrate orthogonal
to,
and parallel to
,
the plane of
illumination inclination, respectively.
Previously measured values of the wavelength
-
dependent
complex refractiv
e index of Se
-
Te were
used, and a
value of
n
= 1.33 was used as the refractive
index of the electrolyte.
1
In the second step, a Monte Carlo simulation
was
perfor
med in which an amount of mass,
equaling that of a
15
nm planar layer covering the simulation area, was
added to the upper surface
of the structure with
a probability
F
:
퐹
(
퐴
)
=
퐴
∏
푥
푖
푟
푖
3
푖
=
1
(Equation
1)
where
A
is the
spatially dependent
absorption
at the deposit/solution interface
,
x
i
is the fraction of
S
7
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 definition of this probability (Equation 1) serves to reduce
the surface
roughness of the film to mimic the experimenta
lly observed surface roughness.
After
the initial Monte Carlo simulation, t
he absor
ption
of the new, struc
tured 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.
Th
is process of
absorbance calculation
and mass
addition
was
repeated
until the
simulated
morphologie
s
had
heights equivalent to
those
exhibited
by the experimentally generated
deposits.
Dipole Simulations
FDTD simulations of dipole emission were used to model the effect of
illumination inclination on the optical field profile generated by light scatteri
ng at the growth
interface. A two
-
dimensional simulation plane
was
discretized using a square mesh with a lattice
constant of 1 nm and
the
background
refractive
index
was
set to
1.33.
Perfectly matched boundary
conditions were
used
in both directions.
Dipo
le emission with a free space wavelength of λ =
626
nm was simulated. The dipoles
were
separated by one wavelength in the medium. Simulations
were performed with
the dipole oscillation axis along the vertical and
the separation axis along the
horizontal
,
and
were
then repeated with the dipole oscillation axis inclined 40° into the
simulation
plane.
Analogous
simulations were also performed for dipoles separate
d along a diagonal axis 30°
from the horizontal.
For the simulation with the dipole os
cillation axis inclined and
the dipoles
s
eparat
ed
along the diagon
al
,
a
phase angle between the emission from each dipole was introduced
to model the delay between stimulation of adjacent scattering sites.
S
8
S
4
.
Representative
Fourier Spectra Fit Data
Figure S
2
.
(a) and (b)
Fourier spectr
um
and associated fit curve
of the intensity along the vertical centerline of the
positive fundamental mode in the 2D FT
depicted
in
Figure 2a
,
and c, respectively.
S
9
S
5
.
References
1.
G. M. Hale and M. R. Querry,
Appl. Opt.
, 1973,
12
, 555
-
563.