Supplementary Information
Supplementary Figures
Supplementary Figure 1
:
Temperature
-
Dependent Resistance
Temperature dependence of resistance (Ohm) vs. applied gate voltage (
V
G
) for the graphene/ (1 um)
SiN
x
/(200nm)Au
device studied in this work. Measurements were performed at 1 mtorr.
Supplementary Figure 2
:
Temperature
-
and Voltage
-
Dependent Capacitance
(red line) Capacitance of device as a function of temperature, taken with a 30V gate voltage. (
black line)
Capacitance as a function of applied gate voltage, taken at 200
C.
Both measurements were taken with a
1kHz, 250mV peak
-
to
-
peak applied bias.
Supplementary Figure 3:
Temperature Dependence of Emissivity and Emitted Intensity
Temperature dependence of change in (a) total emitted intensity and (b) emissivity for 40nm graphene
nanoresonators at a carrier density of 1.1 ×10
13
cm
-
2
.
In order to compensate for the temperature
dependent gating effects, the data at each temperature wa
s obtained using a different applied gate voltage,
such that the plasmon resonance occurred at the same frequency. The intensity o
f
modulated thermal
radiation increases as the temperature of the sample increases
, but the change in emissivity displays
no
temperature dependence.
Supplementary Figure 4
:
Absorption and Emissivity Comparison
Comparison between carrier density dependent change in emissivity (black line) and absorption (green
line) for the same device measured at comparable carrier densities.
Supplementary
Figure 5:
Plasmon Dispersion
Relation
Calculated change in absorption as carrier density is changed from zero to 1.2×10
13
cm
-
2
for graphene
nanoresonators on a 1
μ
m thick SiN
x
membrane with a gold back reflector.
The dashed white line
indicates the dispersio
n relations for the plasmon and SPPP modes of graphene on an SiN
x
substrate.
1
Supplementary Figure 6
:
kHz Modulated Signal
Temporal waveform of applied voltage signal (black line) and detector signal of emission from 50nm
ribbons at 250°C (green line).
A voltage of 60V corresponds to a doping level of 1.2 × 10
13
cm
-
2
, resulting
in a positive detector signal. A voltage of 0V corresponds to the charge neutral point of the graphene and
th
erefore the measurement of an
‘o
ff
’
signal.
Supplementary
Notes:
Supplementary Note 1.
Temperature dependence of electrostatic gating
The carrier densit
y
of our device was determined by fitting the measured plasmon peak energies
to the peak positions predicted using a finite element model
at different carr
ier densities. As
d
iscovered
in our previous work
s
2
,
the
extracted
carrier densities tended to be higher than those
predicted by a simple capacitor model
, and
in this work
we discovered that this discrepancy
increased as the sample was heated
.
In
our previous studies (performed at room temperature in
atmosphere)
, the discrepancy was determined to be
due to
a combinati
on of factors, including the
unknown DC dielectric constant,
κ
,
of the SiN
x
, the ef
fects of atmospheric impurities
3
-
6
,
the
effects of gate activated charge traps in the SiN
x
7
,
8
,
and the effect of the geometry of the device
on the charge density on th
e surface
9
. For this study, all the above effects still apply, with the
exception of the effect of atmospheric impurities, since the measurements here were performed
at 1 mtorr
on a sample that had been vacuum annealed.
For
this work
, however,
we must
consider the temperature dependent effects on the SiN
x
dielectric. In order to study those
potential effects, we measured the source
-
drain resistance in our device as the gate v
oltage was
varied at different temperatures. The results of those measurements are shown in
Supplementary
Fig. 1
. As can be seen in this figure, at all temperatures the charge neutral point (CNP) occurred
at low (
|
|
V) gate bias. This is in cont
rast to room temperature measurements performed in
atmosphere, where the samples were found to be heavily hole doped. Additionally, it can be
seen in this figure that the s
-
d resistance is more sharply dependent on the gate voltage at higher
temperatures.
We attribute this to mobile charge carriers in the SiN
x
which become more
mobile as the substrate is
10
.
In combination with the fixed charge in the dielectric, these mobile
charges add to the effective
κ
of the SiN
x
dielectric
, and they should make a large contribution at
higher temperatures
. In order to explore this possibility further, we performed tempe
rature
dependent
C
(
V
)
measurements on our device, as shown in
Supplementary Fig. 2
. This figure
shows that, indeed, the capacitance of the device increases as the temperature as raised, with a
~
30% increase in capacitance between
25
and 250
C, and a
~10% increase betwenn 150
and
250
C. For comparison, we note that a 66V gate offset at 250
C gave an equivalent carrier
density as a 106V gate offset at 150
C
, corresponding to a 60% increase in capacitance
-
larger
than the change observed
in our
C
(
V
) measurements. We note, however, that the
C
(
V
)
measurements were performed at 1kHz, which may be too fast for some the mobile charges in
the SiN
x
. Moreover, there may also be some additional gate
-
activated charge traps at high
temperatures t
hat become accessible. Regardless of the precise microscopic origin, the
measurements shown in
Supplementary Figure
s
1 and 2
agree with the temperature
-
dependent
trends we observed when fitting the carrier densities to the resonant plasmon
peak positions in
our device.
Supplementary Note
2
.
Comparison between absorption and emission
The device geometry that we use for blackbody emission measurements in this work was previously
studied in
terms of i
ts gate dependent optical absorption properties
.
2
In that study, it was shown that a
change of up to 24.5%
optical absorption could be obtained for polarized light at 1.42 × 10
13
cm
-
2
carrier
density. In the measurement apparatus we use here, there are a number of differences in the device
properties and measurement geometry that alter these absorption properties. First, for most of the
measurments performed in this work, we probed
non
-
polarized emission. Second, in t
his work we could
only achieve a carrier density of 1.17 × 10
13
c
m
-
2
due to
leakage
currents
that occurred through the SiN
x
when high gate biases were applied at high temperatures. Third, the objective used in this w
ork had an
NA of 0.65, while the previous absorption study was performed with a 0.55 NA objective. This decreases
the absorption (and emissivity) of the sample due to the non
-
isotropic angle dependence of the
nanoresonator absorptivity
11
. Fo
u
rth, the measurements here were performed through a 1 mm KBr
window on the vacuum stage. This window offsets the focal plane of the microscope, and also allows for
more efficient collection of high angle emitted light, while steering more low angle light into the back of
the center mirror of the Cassegrain objecti
ve. Finally, the emission and absorption measurements were
performed using different MCT detectors, with the detector used for emissivity measurements having a
larger spectral range and larger element size, which allowed for more collection of spu
rious ra
diation that
was not properly removed with the microscope aperture.
All of the above effects should act to
reduce
the measured absorption and emissivity changes in the
sample. Thus to find a true comparison between the change in emissivity that we measu
re here, and the
change in absorptivity of the sample, we performed absorption measurements on the same sample using
non
-
polarized light with the same objective, carrier density, and vacuum stage as was used for emissivity
measurements (the detectors were
still different). As described in our previous work, the absorption
measurements were obtained by comparing the reflectivity of the graphene nanoresonators at zero and
finite carrier densities to the reflectivity of a gold mirror evaporated onto the sampl
e. The result of those
measurements is shown in
Supplementary Fig. 4
. As can be seen in this figure, there is a strong
agreement between the change in absorption to the change in emissivity, with the maximum absorption
being 3.0%, and the maximum
change in emissivity being 2.4%. The difference is likely due to the
different detectors used for the measurements. The discrepancy at low frequencies (i.e. 730 cm
-
1
) is also
due to the different detectors, as the detector used for absorption measurement
s had almost no sensitivity
in that range.
Supplementary Note 3
.
Plasmonic dispersion of graphene on SiN
x
The dispersion relation for the plasmonic modes of graphene on SiN
x
deviates from the expected
square root dispersion for bare graphene due to graphene plasmon
–
SiN
x
phonon coupling,
which forms hybridized surface
phonon plasmon polariton (SPPP) modes. The result of this
coupling can be seen in
Supplementary Fig. 5,
where we plot the calculated dispersion relation
for graphene on SiN
x
, and also the inverse width dependent change in absorption
(∆
A
)
for
graphene nanoresonators as the carrier density is increased
from zero to 1.2×10
13
cm
-
2
.
Simulations
were performed by finite element methods within a local random phase approximation.
12
These
calculations consider a
scale
-
invariant plasmon phase shift upon edge reflection, as described in previous
works
.
1
As can be seen in this figure, the graphene plasmon/SPPP dispersion relation displays an anti
-
crossing near SiN
x
phonon energy, and contains three branches due to plasmon
-
phonon coupling. For
high frequencies, the
upper branch corresponds well to the energy of maximum
∆
A
for
the graphene
nanoresonators. At low frequencies, however, there is a discrepancy
between the
∆
A
maxima and the
plasmon/SPPP dispersion. As described in the text, this phenomen
on
is due to a destructive
interference effect, which drives a large amount of absorption into the SiN
x
membrane near
730cm
-
1
. As the graphene carrier density is varied, the reflection coefficient from the surface
changes, which amplifies (or de
-
amplifies)
the degree of destructive interference. Because this
process occurs at energies where the SiN
x
permittivity is sharply varying, this process changes
the amount of absorption into the graphene in non
-
trivial ways.
Supplementary Note
4
.
kHz
Speed Signal Modulation
To test our structure as
a
mid
-
IR source
at higher speeds
, we
performed time
-
resolved emission
measurement
s
on
50nm resonators
at 250°C
.
A 2kHz modulated square wave
signal
was applied
to the structure
,
with an
“
off
”
voltage of 0V
,
corresponding to the charge neutral point of
graphene
and
an
“
on
”
voltage of 60V,
corresponding to
a
graphene
carrier density
of
1.2 × 10
13
cm
-
2
. The emission modulation was measured as a raw voltage signal from an FTIR MCTA
detector
using
a
n
infrared
filter
with transmission peak
ed
at
1383cm
-
1
and central bandwidth of
approximately 30cm
-
1
. This filter was selected to match the resonance frequency of the 50nm
resonators at a doping of
1.2 × 10
13
cm
-
2
, therefore isolating the plasmonic signal.
Th
e
relatively
small
filter
bandwidth results in a weakened signal
and decreased signal:noise ratio
.
The
measurement
results
along
with
the
applied voltage
temporal waveform
are
shown
in
Supplementary Fig. 6
.
A clearly modulated emission signal is seen in response to the input
square wave.
In these
measurement
s, the maximum modulation frequency
was 2kHz
due to limitations in the
speed of the detector and the RC time constant of the
combined
graphene nanoreson
ator
device,
contact resistance and electrical leads.
This frequency
is not indicative of the
inherent
upper
limits
of the structure itself
.
The detector used
in this
experiment was optimized to match the
low modulation frequency
of an FTIR
moving mirror
, and so experienced signal decay
and non
-
linearities
outside
of
this frequency range.
One can see
in
Supplementary Fig. 6
that the applied
voltage
signal
exhibits a
sharp
rise time
, indicating that the primary limitations here are
from the
detector
response
.
Supplementary References
1
Brar, V. W., Jang, M. S., Sherrott, M., Lopez, J. J. & Atwater, H. A. Highly Confined Tunable Mid
-
Infrared Plasmonics in Graphene Nanoresonators.
Nano Letters
13
, 2541
-
2547, (2013).
2
Jang, M. S.
et al.
Tunable large resonant absorption in a midinfrared graphene Salisbury screen.
Physical Review B
90
, 165409, (2014).
3
Levesque, P. L.
et al.
Probing Charge Transfer at Surfaces Using Graphene Transistors.
Nano
Letters
11
, 132
-
137, (2010).
4
Ryu, S.
et al.
Atmospheric Oxygen Binding and Hole Doping in Deformed Graphene on a SiO2
Substrate.
Nano Letters
10
, 4944
-
4951, (2010).
5
Wang, H., Wu, Y., Cong, C., Shang, J. & Yu, T. Hysteresis of Electronic Transport in Graphene
Transistors.
ACS Nano
4
, 7221
-
7228, (2
010).
6
Xu, H., Chen, Y., Zhang, J. & Zhang, H. Investigating the Mechanism of Hysteresis Effect in
Graphene Electrical Field Device Fabricated on SiO2 Substrates using Raman Spectroscopy.
Small
8
, 2833
-
2840, (2012).
7
Brar, V. W.
et al.
Gate
-
controlled io
nization and screening of cobalt adatoms on a graphene
surface.
Nat Phys
7
, 43
-
47, (2011).
8
Pi, K.
et al.
Electronic doping and scattering by transition metals on graphene.
Physical Review B
80
, 075406, (2009).
9
Thongrattanasiri, S., Silveiro, I. & de Ab
ajo, F. J. G. Plasmons in electrostatically doped graphene.
Appl Phys Lett
100
, (2012).
10
Dogan, A.
The Reliability of the Silicon Nitride Dielectric in Capacitive MEMS Switches
M.Sc.
thesis, The Pennsylvania State University, (2005).
11
Thongrattanasiri
, S., Koppens, F. H. L. & García de Abajo, F. J. Complete Optical Absorption in
Periodically Patterned Graphene.
Physical Review Letters
108
, 047401, (2012).
12
Falkovsky, L. A. & Varlamov, A. A. Space
-
time dispersion of graphene conductivity.
Eur. Phys. J
. B
56
, 281
-
284, (2007).