of 10
1
Supplementary Figure
1 |
Characteristic of membrane
.
(
a
)
Transmission spectra for a single SiN
x
2μm membrane and a SiN
x
membrane with transparent back contact (ITO 4nm / a
-
Si 60nm). The solid
lines are simulation results, and the dotted
lines were obtained by a mid
-
infrared
transmission
measurement.
(
b
) Refractive index of SiN
x
measured by mid
-
infrared ellipsometry.
1000
1500
2000
2500
3000
3500
4000
T
(%)
0
20
40
60
80
100
Frequency (cm
-1
)
Simulation: SiN
x
Measurement: SiN
x
Simulation: SiN
x
/ITO/a-Si
Measurement: SiN
x
/ITO/a-Si
a
1000
1500
2000
2500
3000
3500
4000
Frequency (cm
-1
)
n
of SiN
x
k
of SiN
x
1
1.4
1.8
2.2
n
0
0.1
0.2
0.3
0.4
k
b
2
Supplementary
Figure
2 |
Modulation efficiency in transmission.
Comparison of modulation
efficiency in transmission
(
η
T
)
between the bare graphene plasmonic ribbons (GPRs)
device
and the
coupled structure (GPRs
-
EOT)
device
as a function of
graph
ene Fermi
level
(
E
F
)
with different
graphene carrier mobilities
(
μ
h
)
.
0
-0.2
-0.4
-0.6
-0.8
-1
E
F
(eV)
0
20
40
60
80
100
η
T
(%)
GPRs-EOT
μ
h
=15,000
μ
h
=3,000
μ
h
=1,000
(cm
2
V
-1
sec
-1
)
Bare GRPs
μ
h
=15,000
μ
h
=3,000
μ
h
=1,000
(cm
2
V
-1
sec
-1
)
@
λ
-1
=1340cm
-1
3
Supplementary
Figure 3
|
Anti
-
crossing behavior in the coupled structure.
(
a
) Absorption map of
the coupled structure
(GPRs
-
EOT)
as a function of frequency and
graphene Fermi level (
E
F
)
exhibiting
anti
-
crossing behavior. (
b
) Absorption spectra, (
c
) frequency splitting, and (
d
) transmission spectra as a
function of nu
mber of graphene plasmonic ribbon
s
(
N
GPRs
)
inside the subwavelength metallic slit. In (
b
)
and (
d
), the “EOT only”
indica
tes
the subwavelength metallic slit array w
ithout GPR
s.
50
1300
1400
1500
1600
-0
-0.2
-0.4
-0.6
-0.8
-1
A
(%)
Frequency (cm
-1
)
E
F
(eV)
40
30
20
10
a
Frequency (cm
-1
)
A
(%)
0
10
30
40
50
1250
1300
1350
1400
20
60
1450
Bare GPRs
EOT only
N
GPRs
=2
N
GPRs
=4
N
GPRs
=6
N
GPRs
=8
ΔΩ
b
Frequency splitting
N
GPRs
4
0
2
3
5
6
7
8
1
ΔΩ
(cm
-1
)
20
30
10
40
0
50
Fitting curve
c
Frequency (cm
-1
)
1250
1300
1350
1400
1450
T
(%)
0
10
30
20
40
d
EOT only
N
GPRs
=2
N
GPRs
=4
N
GPRs
=6
N
GPRs
=8
4
Supplementary
Figure 4
|
Anti
-
crossing behavior dependence
on graphene carrier mobility.
(
a
)
Absorption spectra and (
b
) absorption map of the bare
graphene plasmonic ribbons (
GPRs
)
device as a
function of graphene carrier mobility
(
μ
h
)
.
(
c
) Absorption spectra and (
d
) absorption map of the
coupled structure (
GPRs
-
EOT
)
device as a function of graphene carrier mobility
(
μ
h
)
. (
e
) Transmission
spectra and (
f
) transmission map of the
coup
led structure (
GPRs
-
EOT
)
device as a function of graphene
carrier mobility
(
μ
h
)
. In (
a
), (
c
), and (
e
), the “EOT only” indicates the subwavelength metallic slit array
without GPRs.
Frequency (cm
-1
)
1250
1300
1350
1400
1450
A
(%)
0
10
30
40
50
20
60
EOT only
μ
h
=15,000
μ
h
=5,000
μ
h
=1,000
μ
h
=450
a
Bare GPRs
(cm
2
V
-1
sec
-1
)
1250
1300
1350
1400
1450
Frequency (cm
-1
)
0.4
1
5
10
15
μ
h
(
1000 cm
2
V
-1
sec
-1
)
A
(%)
b
50
40
30
20
Bare GPRs
Frequency (cm
-1
)
1250
1300
1350
1400
1450
A
(%)
0
10
30
40
50
20
60
c
GPRs-EOT
EOT only
μ
h
=15,000
μ
h
=5,000
μ
h
=1,000
μ
h
=450
(cm
2
V
-1
sec
-1
)
10
20
30
40
50
1250
1300
1350
1400
1450
Frequency (cm
-1
)
0.4
1
5
10
15
μ
h
(
1000 cm
2
V
-1
sec
-1
)
A
(%)
d
GPRs-EOT
Frequency (cm
-1
)
1250
1300
1350
1400
1450
T
(%)
0
30
20
40
10
e
GPRs-EOT
EOT only
μ
h
=15,000
μ
h
=5,000
μ
h
=1,000
μ
h
=450
(cm
2
V
-1
sec
-1
)
1250
1300
1350
1400
1450
Frequency (cm
-1
)
μ
h
(
1000 cm
2
V
-1
sec
-1
)
5
10
15
20
25
T
(%)
f
0.4
1
5
10
15
GPRs-EOT
5
Supplementary
Figure 5
|
Characteristics of graphene.
(
a
) Raman
spectrum of graphene transferred
onto SiO
2
substrate, and (
b
) gate dependent resistance measurement of graphene on the SiN
x
substrate
showing the charge neutral point at
gating voltage
V
g
=430V. (
c
) Graphene plasmon resonance
frequency as a function of
graphene Fermi level (
E
F
)
for simulations and mid
-
infrared transmission
measurement.
Raman shift (cm
-1
)
1300
1700
2100
2500
2900
Intensity (
1000)
0
2
4
6
8
a
0
100
200
300
400
500
1
2
3
4
5
V
g
(V)
Resistance
(k
W
)
b
E
F
(eV)
-0.42
-0.46
-0.5
-0.54
-0.58
1250
1300
1350
1400
1450
1500
Resonance frequency (cm
-1
)
Simulation
Measurement
c
6
Supplementary Figure 6 |
Numerical fitting
.
(
a
) Calculated modulation efficiencies for bare
graphene
plasmonic ribbons (
GPRs
) device
varying the incident angle (
θ
in
) and the weighed sum. (
b
) Comparison
between the measurement result and the simulation result of bare GPRs with a broad angular distribution
of incoming light and a scaling factor of 0.633
to account for
degradation.
(
c
) Ca
lculated modulation
efficiencies for
coupled structure (
GPRs
-
EOT
) device
varying the incident angle
(
θ
in
)
and the weighed
sum. (
d
) Comparison between measurement and simulation result of GPRs
-
EOT
device
with a broad
angular distribution of incoming light and a scaling factor of 0.734
to account for
degradation.
0
4
8
12
16
20
1300
1400
1500
1600
Frequency (cm
-1
)
η
T
(%)
a
q
in
=0
q
in
=10
q
in
=20
q
in
=30
W eighted sum
0
2
4
6
8
10
12
1300
1400
1500
1600
Frequency (cm
-1
)
η
T
(%)
Simulation
Measurement
b
-20
-10
0
10
20
30
40
50
1300
1400
1500
1600
Frequency (cm
-1
)
η
T
(%)
c
q
in
=0
q
in
=10
q
in
=20
q
in
=30
W eighted sum
-5
0
5
10
15
20
25
30
1300
1400
1500
1600
Frequency (cm
-1
)
η
T
(%)
d
Simulation
Measurement