Supporting Information
Additive Manufacturing of High Refractive Index, Nano-architected
Titanium Dioxide for 3D Dielectric Photonic Crystals
Andrey Vyatskikh
1
, Ryan C. Ng
2
, Bryce Edwards
1
, Ryan M. Briggs
3
, and Julia R. Greer
1,*
1
Division of Engineering and Applied Science, California Institute of Technology, 1200 E.
California Blvd., Pasadena, CA 91125, USA
2
Division of Chemistry and Chemical Engineering, California Institute of Technology, 1200
E. California Blvd., Pasadena, CA 91125, USA
3
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr,
Pasadena, CA 91109
*Correspondence to: jrgreer@caltech.edu
Materials and Methods
Hybrid photoresist
Titanium (IV) ethoxide (>97%), acrylic acid (anhydrous, 99%), 2-methoxyethanol (anhydrous,
99.8%), pentaerythritol triacrylate (technical grade), dichloromethane (DCM) (anhydrous,
≥99.8%),
and propylene glycol monomethyl ether acetate (PGMEA) (>99.5%) were
purchased from Sigma Aldrich. 7-diethylamino-3-thenoylcoumarin was purchased from
Exciton.
Hybrid photoresist preparation approach was adapted from refs.
19,32
576.5 mg of acrylic acid
was slowly added to 456.2 mg of titanium (IV) ethoxide in a glovebox and manually agitated.
The solution was then placed in a vacuum antechamber of the glovebox for 30 min to
remove ethanol produced as the result of the ligand exchange reaction. The resulting
solution was then taken out of the glovebox, mixed with 300 mg of 2-methoxyethanol and
1.2 g of pentaerythritol triacrylate, agitated for 30 s using a vortex mixer, and moved to a
yellow-light area. 30 mg of 7-diethylamino-3-thenoylcoumarin was then dissolved in 150 mg
of DCM and added to the mixture, followed by another agitation in the vortex mixer for 30
s. The resulting resist was then let to rest for 5 min to release air bubbles trapped as the
result of the agitation. Photopolymers to fabricate woodpile structures with lateral periods
of 1.12, 1.03, and 0.84
μm
shown in Fig. 4C were formulated for increased shrinkage by
reducing the wt% of a TiO
2
precursor in the described formulation by a factor of 2, 4, and 6,
correspondingly.
Fabrication
Titania pre-ceramic photoresist was drop cast on a round glass slide (170 micron thick)
between two strips of 100 micron-thick Kapton tape spaced at 3 mm. The glass was then
covered by a 10 x 10 mm silicon chip that served as a substrate. A commercially available
two-photon lithography system (Photonic Professional GT, Nanoscribe GmbH) was then
used to fabricate pre-ceramic architectures. Laser power was set at 22.5 mW and the laser
speed was 2.7 mm s
-1
. The samples were developed in 2-methoxyethanol overnight,
followed by 15 min in PGMEA and 3 min in filtered IPA. The samples were then transferred
to a critical point dryer (Autosamdri-931). The samples were then pyrolyzed in air in a tube
furnace using an open-ended 2” OD quartz tube. The temperature was ramped up to 900°C
at 3°C/min, kept at 900°C for 1 hour, and then the furnace was let to cool down at a natural
rate. Woodpiles with lateral periods of 1.12, 1.03, and 0.84
μm
shown in Fig. 4C were
fabricated using the same starting geometry as in Fig. 1E and higher shrinkage resists and
were calcinated using the same ramp-up rate at a maximum temperature of 750°C for 1
hour.
Material characterization
FEI Versa 3D DualBeam was used for SEM imaging. SEM Energy-Dispersive X-Ray
Spectroscopy (EDS) was conducted using Zeiss 1550VP FESEM equipped with Oxford X-Max
SDD. Raman spectra were collected using Renishaw M1000 MicroRaman Spectrometer
(514.5 nm laser). Samples of rutile and anatase titanium dioxide for reference Raman
spectra were provided by Prof. George Rossman (Caltech).
FTIR characterization
Reflectance and transmittance spectra were collected using Nicolet iS50 FT-IR spectrometer
equipped with a Nicolet Continuum Infrared Microscope, a calcium fluoride beam splitter,
and an infrared light source. The angle range for the Cassegrain objective used in the
microscope was between 16° and 35.5° relative to the normal. Background signal was
collected from double-sided polished silicon that served as a substrate for the samples.
Reflectance spectrum in Fig. 3B was normalized by the maximum value of reflectance within
the high reflectance band.
TEM and particle sizes
Transmission Electron Microscopy (TEM) was performed using FEI Tecnai F30ST (300kV)
transmission electron microscope. Samples for TEM analysis (~100 nm thickness) were
prepared using a lift out procedure in FEI Versa 3D DualBeam microscope. Particle sizes
were measured from SEM images using ImageJ. Confidence interval on the mean particle
size was calculated assuming normal distribution of the particle sizes and unknown variance
using t-distribution (n=100,
α=0.05).
Confidence interval on the variance of the particle size
was calculated using
distribution (n=100,
α=0.05).
휒
2
Ellipsometry
A 2 x 2 mm thin film of titanium dioxide with approximately 100 nm thickness for
ellipsometry measurements was fabricated on silicon using the method described above.
Ellipsometry data was collected at wavelengths between 275 nm and 2
μm
with a 0.5 mm
spot size. The n, k data was fitted using Forouhi-Bloomer model
43
with
ε
∞
=4.2344, A =
0.06053, B = 7.6778, C = 15.8439, and Eg = 0.09476
(χ
2
=39.1).
Plane Wave Expansion simulations
The photonic band structure of the 3D woodpile photonic crystals were calculated using a
plane wave expansion method with the commercially available software package RSoft
BandSOLVE, which rigorously solves Maxwell’s equations by forming a linear set of
eigenvalue equations and finding functions that minimize the E-field, allowing successive
modes to be found. The simulated structures have face centered tetragonal crystal structure
and individual lattice beams comprised of a single material with constant refractive index of
2.3, based on ellipsometry measurements on a thin film of as-fabricated titania. These
calculated photonic band structures guided the fabrication of physically realizable woodpile
structures that exhibit a full photonic band gap in the near infrared, and several sets of
geometric parameters for woodpiles that exhibit a full photonic band gap were generated.
Upon fabricating these structures, the band structure simulations were rerun in an iterative
process to ensure that the experimentally fabricated structures exhibit a full photonic band
gap.
Voxel shape model
To be able to predict and reliably control the feature size for 3D photonic crystal fabrication,
we adopted a simplified model by Serbin et al. that links the voxel dimensions to the
exposure parameters. Voxel height and voxel width can then be expressed as
퐿
푑
퐿
=
2
푧
푅
퐹
―
1
,
푑
=
푤
0
log
퐹,
where
is the Rayleigh distance [nm],
is the laser beam waist [nm], and non-
푧
푅
푤
0
dimensional factor is
퐹
퐹
=
휈
푁
2
0
휎
2
푡
휏
퐿
퐶
is the laser pulse repetition rate [Hz] ,
is the photon flux during the laser pulse,
is
휈
푁
0
휎
2
the effective two-photon cross-section [cm
4
s], is the exposure time [s], is the laser
푡
휏
퐿
pulse duration [s], and
, where
is the photoinitiator density [wt%], and
퐶
=
log
휌
0
휌
0
―
휌
푡ℎ
휌
0
휌
푡ℎ
is the threshold density of radicals required for polymerization [wt%].
The photon flux
can be expressed as
푁
0
푁
0
=
2(푃
Γ
)
(휋
푤
0
2
휏
퐿
)(휈ℏ
휔
퐿
)
,
where is the laser power, is the fraction of light reaching the photoresist, and
is the
푃
Γ
휔
퐿
laser frequency.
This means that the voxel height and the voxel width can be ultimately expressed as a
퐿
푑
function of the laser power and the exposure time as
푃
푡
퐿
=
2
푧
푅
훼푡
푃
2
―
1
,
푑
=
푤
0
log
[훼푡
푃
2
],
where
.
훼
=
휈
휎
2
퐶
휏
퐿
[
2
Γ
(휋
푤
0
2
)(휈ℏ
휔
퐿
)
]
2
Based on the experimental hardware, we set
,
,
and
휏
퐿
=
80
푓푠
휆
=
780
푛푚
휈
=
80
푀퐻푧,
assume
. The fit parameters for the model shown
Γ
=
0.15, and
휎
2
퐶
=
2.76
∗
10
―
54
푐푚
4
푠
in Fig. S1 were
,
.
푧
푅
=
430
푛푚
푤
0
=
245
푛푚
Figure S1. Predicted and measured voxel dimensions for the hybrid titania resist for a
constant laser power of 20 mW as a function of the exposure time.
Figure S2. Beam widths and lateral periods in the axial direction of as-fabricated titania
woodpile as measured by SEM
Figure S3. SEM image taken from the side of a woodpile architecture with with 960 x 150
nm elliptical cross-sections used to evaluate the crystal size distribution
Figure S4. Bright-field and dark-field TEM images of a 100 nm-thick cross-section of a
woodpile architecture with with 960 x 150 nm elliptical cross-sections showing fully dense
features consisting of nanocrystalline TiO
2
Figure S5. SEM image of a 100 nm-thick film of TiO
2
on Si prepared for ellipsometry
measurements
Figure S6. Band diagram from PWE showing the emergence of a full photonic bandgap in a
simulated woodpile tetragonal architecture
Table S1. Nested variance analysis of the lateral period in the top layer of as-fabricated
woodpile structure
Table S2. Full and partial photonic bandgap edges (nm) for woodpile structures with lateral
periods between 840 nm and 1470 nm
Woodpile lateral period, nm
Direction
Angle
Frequency
1470
1120
1030
840
0.544
2700
2054
1883
1545
16
0.457
3215
2445
2242
1839
0.492
2986
2271
2082
1708
X’-U’-L
35.5
0.418
3521
2678
2455
2014
0.543
2708
2060
1888
1549
16
0.451
3260
2479
2273
1865
0.530
2771
2108
1933
1586
X’-W’-K’
35.5
0.457
3217
2446
2243
1840
0.465
3161
2404
2204
1809
Full bandgap
0.474
3101
2359
2162
1774
Table S3. Comparison between fabrication methods for 3D photonic crystals in the infrared
and visible
Reference
Process
Materials
Key aspects
[28]
Micromanipulation
and stacking
GaAs
Manual stacking of individually
fabricated 2D layers; high
refractive index material (n~3.7 at
700 nm)
[10, 23]
Single- and Double-
inversion
Si, TiO
2
TPL of a polymer template
followed by a multi-step inversion
procedure; complex 3D structures;
up to 16% porosity
[13-16]
Two-photon
lithography
Polymers,
Silica with Zr,
Zn, and Ge
heteroatoms
Siloxane-based chemistry of the
photoresist; low refractive index
(n<1.6)
[9]
Direct Laser Writing
of chalcogenide
glasses
As
2
S
3
Direct writing using photo-induced
metastability; challenging control
of feature sizes; high refractive
index material (n~2.5)
[8]
Direct Laser Writing
of metal oxides
ZnO
Aqueous metal-containing resin;
shrinkage up to 87%; refractive
index n~1.9
[30]
Direct Ink Writing
TiO
2
Sol-gel ink; sub-micron features
with 10% porosity; complex 3D
structures; half of a lower-index
anatase phase
[18]
Laser-induced
insolubility
TiO
2
Partial decomposition of a liquid
precursor; poor adhesion to the
substrate; loss of 3D structures
[31]
Laser-induced
decomposition
carbon/TiO
2
2D patterning; presence of lossy
carbon; 3 micron features for
crystalline TiO
2
This work
Nanoscale AM
TiO
2
TPL of organic-inorganic material
followed by calcination; complex
3D structures; <1%
porosity; refractive index n>2.3