of 2
1
Three
-
D
imensional
S
ingle
G
yroid
P
hotonic
C
rystals with a
M
id
-
I
nfrared
B
andgap
(Supporting Information)
1
Siying Peng,
2
Runyu Zhang,
1
Valerian H. Chen,
1
Emil
T.
Khabibo
ul
line,
2
Paul Braun,
1
Harry A.
Atwater
1.
Applied Physics, California Institute of
Technology
2.
Department of Materials Science and Engineering,
University of Illinois at Urbana
-
Champaign
Optical constants of deposited materials
Figure
S
1
Optical constants at Mid
-
infrared wavelength
.
(a)
measured
real
part of refractive
index
of a
-
Si
(black solid line) and Palik’s real par
t of refractive index of a
-
Si (blue
dotted line)
(b)
measured
imaginary part of refractive index of a
-
Si
(red solid line) Palik’s imaginary part of
refractive index of a
-
Si (
blue
dotte
d line)
(c)
measured
real part of refractive index of Al
2
O
3
(black solid line) and Palik’s real part of refractive index of
Al
2
O
3
(
blue
dotted line)
(d)
measured
imaginary part of refractive index of
Al
2
O
3
and Palik’s real part of refractive index of
(
blue
dotted line)
Al
2
O
3
2
Psi (
Ψ
) and delta (
Δ
)
data
were measured using
IR
-
VASE Mark II
i
nfrared
v
ariable
a
ngle
s
pectroscopic
e
llipsometer
, from a
-
Si/Al
2
O
3
films
deposited on a
n
intrinsic silicon substrate.
Optical constants n and k
were then obtained from
p
si (Ψ) and delta (Δ) using a three layer
fitting
model.
Fill fraction
and discontinuity
u(x,y,z)
1.0
1.05
1.1
1.2
1.3
1.35
1.37
1.4
1.45
f
ill fraction
0.155
0.141
0.127
0.077
0.060
0.023
0.021
0.018
0.004
Table
S
1
u(x,y,z)
versus
fill fraction
for
a
solid
single gyroid
.
Figure
S
2
Single gyroid
with
different u(x,y,z)
.
(a) u(x,y,z) versus fill fraction for a solid
single gyroid
(b)
single gyroid with u(x,y,z)=1.00, 1.35, 1.40, 1.41 and 1.42 respectively
Fill fractions
are calculated in correspondence to u(x,y,z) for a solid single gyroid structure. Our
fabricated
structure
consists of a
-
Si
(100nm)
/Al
2
O
3
(40nm)
/a
-
Si
(100nm)
is a hollow single
gyroid structure with fill fraction of 0.1
04
.
The
a
-
Si (100nm) /Al
2
O
3
(40nm)
/a
-
Si (100nm)
layers
have u(x,y,z) values of 1.1, 1.2 and
1.25 respectively
.
The inner hollow part corresponds to a
connected
air
gyroid with u(x,y,z)=1.35
, shown in Fig.
S2b
.
For hollow single gyroid consists of
a
-
Si (150nm) /Al
2
O
3
(40nm)
/a
-
Si (150nm),
the fill fraction is 0.12
. The a
-
Si (150nm) /Al
2
O
3
(40nm)
/a
-
Si (150nm) layers have u(x,y,z) values of 1.05, 1.2 and
1.25 respectively
, and an inner
air gyroid with u(x,y,z)=1.37
.
For u(x,y,z)<
1.41, a
solid gyroid
structure is a connected network
.
T
he
surface becomes disco
nnected
at u(x,y,z)=1.41
, as shown in Fig. S2b.