1
Probing
the b
and
structure
of topological
silicon
photonic
lattices
in the visible
Siying Peng
(
彭斯颖
)
,
1
Nick
J.
Schilder,
2
Xiang Ni,
3
Jorik van de Groep,
4
Mark
L.
Brongersma,
4
Andrea
Al
ù
,
5
,6,3
Alexander
B.
Khanikaev,
3
,6
Harry A. Atwater
1
, and Albert
Polman
2
1
Applied Physics, California Institute of Technology
Pasadena, California 91125, United States
2
Center for Nanophotonics, AMOLF
Science Park 104, 1098 XG, Amsterdam, the Netherlands
3
Department of Electrical Engineering,
City College of
City
University of New York, NY
10031
, USA
4
Geballe Laboratory for Advanced Materials, S
tanford University
476 Lomita Mall,
Stanford,
California 94305,
USA
5
Photonics
Initiative
,
Advanced Science Research Center, City University of New York, 85 St. Nicholas
Ter
race, New York, NY 10031 USA
6
Physics
Program
,
The Graduate Center, City University of New York, 365 Fifth Avenue, New York, NY
10016 USA
SUPPLEMENTAL INFORMATION
Sample fabrication
Silicon nanopillars were fabricated on 10
-
nm
-
thick free standing Si
3
N
4
membranes (Norcada, Fig
. S1
). We
start with epitaxial liftoff of a
2
00
-
nm
-
thick single
-
crystalline
intrinsic
Si film from a
silicon
-
on
-
insulator
(
SOI
)
wafer in 52% HF solution
1
,
2
,
3
. The SiO
2
layer was etched (lateral etching rate ~ 300 nm/s), leaving the
silicon film floating on top of the HF solution. The Si film is then transferred from the HF solution to water
(this process was repeated until the HF was cleaned away) and subsequently place
d onto a 10
-
nm
-
thick
Si
3
N
4
membrane, which was surface
-
cleaned by a Nanostrip solution (90% sulfuric acid, 5%
peroxymonosulfuric acid, <1% hydrogen peroxide, 5% water). The wet transferred film and the membrane
substrate were then left to dry at an incline
d angle, followed by Nanostrip cleaning of the Si film surface.
A 100
-
nm
-
thick layer of electron beam resist (Diluted ZEP
-
520A; Zeon chemicals; anisole:ZEP520 volume
ratio 1.3:1) was then spin
-
coated on the Si film (4000 rpm) to produce a 100
-
nm
-
thick film
.
Deleted:
,
4
2
Figure
S
1.
Schematic of p
reparation of
photonic lattices composed of Si nanopillars
on a 10
-
nm
-
thick free
-
standing Si
3
N
4
membrane
.
After lithographically defining a pattern using a 100 k
e
V electron beam
(Raith EBPG5200)
, the electron
beam resist was
developed (ZED
-
N50, Zeon Chemicals); the remaining resist was treated by electron beam
irradiation at 2 keV with a dose of 500 C/m
2
. This step is essential for high
-
quality pattern transfer during
reactive ion etching, since cross
-
linking of the resist on
the pattern edge is significantly improved
.
Then
the pattern was transferred into the Si layer via reactive ion etching (
Oxford Instruments System 100 ICP
380,
mixture of C
4
F
8
and SF
6
gases
;
23 W RF generator forward power, 1200 W ICP generator forward
pow
er, 27 sccm SF
6
, 52 sccm C
4
F
8
) and the remaining etch mask was removed by O
2
plasma cleaning.
SEM
images of
the fabricated structure are shown in Fig. 1c,d. Since we are using a positive resist, an inverse
pattern with hole diameter of 118 nm was written.
The final pillars dimensions are 90 nm in diameter and
200 nm in height for electron beam dose of 260
μC/cm
2
. For electron beam dose of 250
μC/cm
2
, the pillars
are 85 nm in diameter and 200 nm in height.
There are several advantages of our fabrication met
hod. Firstly, a 10
-
nm
-
thick
membrane has minimal
influence on the dielectric environment of the dielectric resonator, preserving its intrinsic
optical
properties. Secondly, the
free standing 10
-
nm
-
thick
Si
3
N
4
membrane is almost transparent for the electron
beam, therefore reducing both charging and
incoherent defect
luminescence compared to a thick
substrate, making it an ideal platform to study subtle photonic features
by
electron
excitation
.
Band structure d
ispersion
In Fig. S2a the dispersion data derived from Fig. 2b are overlaid with the simulations and show good
agreement. A broad collection of low
-
Q
guided modes is observed with high
-
Q
flat bands within the Dirac
cone representing the Mie resonances.
In
Fig.
S2
b we plot the (zone
-
folded
) dispersion bands of TM
3
surface modes with an effective mode index
n
=1.05
(obtained by fitting Fig. 2b with
k=nk
0
)
; they
correspond well to the simulated data.
Figure S2. Band structure dispersion.
(a) Experimental
angle
-
resolved CL data
.
(b) Same as
(a), overlaid with n
umerically simulated band diagram for the photonic lattice with two
hexagonal pillars for the unit cell in Fig. 2 (colored dots). The quality factor Q of the modes is
indicated by the color scale.
(
c
)
Same simulated data as in (b) with f
it to experimental data
from diffractive outcoupling model using a TM surface mode with mode index
n
=1.05 (black
lines).
Cathodoluminescence
Cathodoluminescence spectroscopy was carried out using a 30 keV electron beam in
a ThermoFisher
Scientific/FEI Quanta 650 SEM
equipped with a Delmic SARC system for cathodoluminescence collection
and analysis. Light emitted by the sample was collected by a
half
-
parabolic mirror placed between the
sample and the electron column, with a focus on the sample of
~
20
μ
m. Collected light was either guided
to a spectrometer for spectral analysis to make spatial maps, or projected onto a CCD imaging camera for
angul
ar analysis (see Fig. 1b). The parabolic mirror contains a hole for the electrons to go through. This
hole spans an angle of 6.9°. For a horizontally placed sample, this hole hinders collection of light emitted
along the Γ
-
point. To probe the bandgap of th
e topological photonic crystals at the Γ
-
point, we put the
sample under an angle of 7.5° for the data presented in Fig. 4 of the main text. Light emitted normal to
the sample can then be collected. To avoid electron
-
induced background CL from the sample ho
lder, we
drilled a hole through the sample holder underneath the sample.
Confocal microscopy measurements
Confocal transmission measurements were performed using a WiTec
a
300 confocal microscope. A fiber
-
coupled tungsten broadband light source (Thorlabs
SLS202L) was used to illuminate the sample from the
bottom. A 10
́
objective (Zeiss, numerical aperture: 0.2) was used to weakly focus the light into a
Deleted:
N
Deleted:
(a
) Experimental angle
-
resolved CL data
overlaid.
Deleted:
b
Deleted:
F
Deleted:
4
homogeneous spot larger than the patterned area. Light transmitted by the sample was collected with a
50
́
objective (Zeiss, numerical aperture: 0.7) and coupled into a 25
μ
m core collection fiber that
functioned as the confocal pinhole, and analyzed using a spectrometer (300 lines/mm, spectral resolution
of 0.27 nm). The signal was normalized to the transmiss
ion of an uncovered Si
3
N
4
membrane.
Numerical simulations
First
-
principle simulations were performed
using
full
-
wave finite
-
element
-
solver COMSOL Multiphysics
(RF Module)
. For bulk band structure calculations
in Figs. 3
, the
periodic boundary conditions were
imposed along the
boundaries
of the unit cell
, and
perfectly matched layer (PML) boundary conditions
were applied perpendicular to the surface of the sample
.
Dimensional sizes of the structure are the same
as the ones used
for the fabricated sample.
Opti
cal constants for Si were taken from Ref.
5
.
R
eferences
1
W. Chang, C.P. Kao, G.A. Pike, J.A. Slone, and E. Yablonovitch, Sol. En. Mat. Sol Cells
58
, 141 (1999).
2
A. Tilke, M. Rotter, R.H. Blick, H. Lorenz, and J.P. Kotthaus, Appl.
Phys. Lett.
77
, 558 (2000).
3
M. Cho, J.
-
H.
Seo, J. Lee, D. Zhao, H. Mi, X. Yin, M. Kim, X. Wang, W. Zhou, and Z. Ma, Appl. Phys. Lett.
106
,
181107 (2015).
5
D
. E. Aspnes and A. A. Studna, Phys.
Rev. B
27
, 985 (1983)