1
Electronic modulation of infrared
emissivity in graphene plasmonic
resonators
Victor W. Brar *&, Michelle C. Sh
errott *#, Luke A. Sweatlock ~#,
Min Seok Jang *%, Laura Kim*, Mansoo Choi %^ and Harry A. Atwater *
*
Thomas J. Watson Laboratory of Applied P
hysics, California Inst
itute of Technology,
Pasadena California 91125, United States
~
Nanophotonics and Metamaterials Laborator
y, Northrop Grumman Aerospace Systems,
Redondo Beach California 90250, United States
& Kavli Nanoscience Institute,
California Institute of T
echnology, Pasadena, California
91125, United States
#
Resnick Sustainability Institute, Californi
a Institute of Technology, Pasadena California
91125, United States
%
Global Frontier Center for Multiscale Ener
gy Systems, Seoul National University, Seoul
151-747, Republic of Korea
^
Division of WCU Multiscale Mechanical De
sign, School of Mechanical and Aerospace
Engineering, Seoul National Univers
ity, Seoul 151-742, Republic of Korea
Abstract
Electronic control of blackbody emission from
graphene plasmonic resonators on a silicon
nitride substrate is demonstrat
ed at temperatures up to 250
̊
C. It is shown that the
graphene resonators produce antenna-coupled
blackbody radiation, manifest as narrow
spectral emission peaks in the mid-IR.
By continuously varying the nanoresonators
carrier density, the frequency and intensity of
these spectral features can be modulated via
an electrostatic gate. We describe these
phenomena as plasmonically enhanced radiative
emission originating both fr
om loss channels associated with plasmon decay in the
graphene sheet and from vibrational modes in the SiN.
2
All matter at finite temperatures emits elec
tromagnetic radiation due to the thermally
induced motion of particles and quasiparticles. The emitted spectrum is characterized as:
ܫ
ሺ
ܶ,߱
ሻ
ൌ
߱
ଷ
ߨ4
ଷ
ܿ
ଶ
1
݁
ఠ
್
்
െ1
ሻܶ,߱ሺ߳
where I is the spectral radiant ener
gy density (spectral radiance), T the absolute temperature in
Kelvin,
reduced Planck’s constant,
߱
angular frequency, c the sp
eed of light in vacuum, k
b
the
Boltzmann constant, and
߳
the material spectral emissivity. While infrared thermal radiation
typically can be assumed to be broadband, inco
herent, and isotropic,
recent experiments on
engineered materials have shown the blackbody
emission can be coherent, unidirectional and
have narrow spectral features. Th
ese structures have included the
patterned gratings on metal or
silicon carbide surfaces,[1, 2] size-tunable Mi
e resonances,[3] and frequency selective
surfaces.[4] Negative differential thermal emittan
ce has also been explored in materials with
strongly temperature dependent
emissivity, such as VO
x
in the vicinity of its solid state phase
transition[5]. In the near-field, where the pow
er of blackbody radiation can exceed the Stefan-
Boltzmann limit for far field emission,[6-10] ther
mal devices have been proposed that display
unidirectional flow of heat
through control of the blackbody spectrum (i.e. thermal diodes)[11,
12], and that show large amounts of heat tran
sfer between nearby surf
aces for solar thermal
conversion devices.[13-16] Elect
ronically tunable emissivity has
also been demonstrated in the
THz regime, where injected charges were used to overdampen a surface phonon polariton mode
in a single quantum well.[17]
In this paper, we experimentally demonstrat
e active electronic control of infrared thermal
emission through antenna-mediated modulation of
the coupling strength
between the thermal
emitters and the photonic modes. Our structure is
based on field effect tuning of carrier density
in graphene plasmonic resonators, which act as
antennae to effectively enhance thermal radiative
emission within the resonator mode volume. We
show that through this mechanism the thermal
radiation generated by substrate phonons and inelas
tic electron scattering
in graphene can be
enhanced or attenuated and can be fixed within
a narrow bandwidth in the mid-IR. The large
Purcell factors associated with
these plasmonic antennas suggest that this device could
3
potentially control thermal radiat
ion at time scales much faster
than the spontaneous emission
rate for conventional light emitting diodes
and classical blackbody emission sources.
A schematic of our experimental setup is
shown in Figure 1a. Our measurements were
performed on graphene grown on 25
μ
m thick copper foils using established chemical vapor
deposition growth techniques.[18, 19]
The graphene was transferred to a 1
μ
m thick low stress
silicon nitride (SiN
x
) membrane with 200nm of Au deposited
on the opposite side that is used as
both a reflector and a backgate electrode. Nanor
esonators with widths ranging from 20-70nm
were then patterned over 60×60
μ
m
2
areas into the graphene
using 100keV electron beam
lithography (see Methods). A
typical gate-dependent resistance cu
rve for one of our structures is
shown in Figure 1. The peak in resistance corres
ponds to the charge neutral point (CNP) of the
graphene, where the Fermi level is aligned with
the Dirac point and th
e carrier density is
minimized. After the CNP for each structure was
measured, a capacitor m
odel[20] was used to
determine the carrier density
corresponding to each applie
d gate voltage (see Supporting
Information).
The device geometry described above was previo
usly used as a gate-tunable absorber in
the mid-IR, where a large enhancement in absorption was observed when the graphene
plasmonic resonance was matched to the same energy as the
ߣ
݊4
ௌே
ൗ
resonance condition in the
1
μ
m SiN
x
layer, which occurred at 1400cm
-1
.[21] In those experiment
s it was shown that the
total absorption in the graphene
nanoresonators could be tuned
from 0 to up to 24.5% for large
carrier densities, and up to ~10% for the carrier
densities used in this work, where the maximum
applied field is limited by Poole-Frenkel tunneling in the SiN
x
(See Supporting Information).[21,
22] For blackbody emission measurements, th
e device was connected to a temperature-
controlled stage consisting of a 100
μ
m thick layer of sapphire on 2m
m copper on a heated silver
block that can vary in temperat
ure from room temperature to 250
̊
C. The device and stage were
held at a pressure of 1-2 mT
orr during emission measurements.
Gate-dependent emission spectra
were measured using a Fourier transform infrared
(FTIR) microscope operating such that emitted
light from the heated device passes through a
KBr window and is collected in a Cassegrain
objective, collimated and passed through the interferometer in the FTIR before being focused on
a liquid nitrogen-cooled HgCdTe de
tector. For polarization depende
nt measurements a wire grid
polarizer was placed in the collimated beam pa
th. As a reference a SiN/Au membrane was
4
coated with an optically thick laye
r of black soot deposited using a
candle. Soot is known to be a
thermal emitter that approximates an ideal black
body with emissivity approaching unity across
the mid-IR.[5]
Figure 2 (left axis) shows the emitted radiation at 250
̊
C from the black
soot reference, a
bare SiN
x
/Au membrane, and from a 40nm graphene nanoresonator array at 250
̊
C under doped
(4.9 × 10
12
/ cm
2
) and undoped conditions. On the right ax
is of Fig. 2 we plot the change in
emissivity corresponding to the observed cha
nge in emitted light from the undoped to doped
graphene resonators. This change in emissivity
is calculated assuming un
ity emissivity at all
frequencies for the black soot reference and nor
malizing accordingly. As can be seen in the
figure, increasing the carrier de
nsity of the graphene nanoresona
tors leads to increases in
emissivity near 750cm
-1
and 1400cm
-1
.
In order to explore these gate
-tunable emissivity features fu
rther, we investigate their
polarization dependence (Fig. 3(c
)), as well as their behavior as the nanoresonator doping and
width is varied, as shown in Fig 3 (a,b). Thes
e results indicate that
the intensity, width and
energetic position of
the thermal radiation feature near 1400cm
-1
is strongly polarization
dependent and is widely tunable. The energy of
this feature increases as the nanoresonator width
is decreased and as the carrier density is increas
ed, while the intensity of this feature increases
with carrier density, and is
largest in 40nm resonators, wh
en it occurs closest to the
ߣ
݊4
ௌே
ൗ
resonance condition of the SiN at 1400cm
-1
. Because Kirchoff’s Law dictates that thermal
emissivity is equal to absorptivity, these observa
tions are consistent w
ith previously reported
absorption measurements performed on identical
samples that showed a narrow absorption
feature near 1400cm
-1
.[21] The lower energy emissivi
ty modulation feature near 750cm
-1
shows
different behavior than the
higher energy peak. Namely, th
e low energy feature shows an
extremely weak polarization dependence, and al
so shows no noticeable dependence on graphene
nanoresonator width. As the carrier
density is increased, there is an increase in intensity for this
feature, but it shows no spectral shift. Finall
y, unlike the higher energy peak, the lower energy
peak is also observed in the bare, unpatterned gr
aphene, where it appears as a slightly narrower
feature. The absorption properties of this de
vice near the energy range of the lower energy
feature was not discussed in pr
eviously reported work due to the low energy cutoff of the
detector used in that work.
5
We explain the above phenomena as electr
onic control of therma
l radiation due to a
combination of plasmon-phonon and plasmon-electr
on interactions, Pauli-
blocking effects, and
non-radiative transfer pr
ocesses between the SiN
x
and the graphene sheet. While Kirchoff’s law
dictates that the thermal equilibrium emissiv
ity must be equal to the absorbtivity for any
material, the precise, microscopic mechanism of th
ermal emission is interesting when the system
includes highly confined optical modes, as is
the case here. We now
describe in detail the
interplay of these microscopic processes fo
r both the high energy a
nd low energy features.
We first explain the pr
ominent feature at 1400cm
-1
as being due to a Fabry-Perot type
plasmonic resonance from the patterned gra
phene. The width and doping dependence of the
1400cm
-1
feature follows the behavior
expected for graphene plasmoni
c modes, and is consistent
with reflection measurements.[
21] Specifically, the graphene
plasmon resonant frequency
should vary as
ω
p
∝
n
1/4
W
−
1/2
and this behavior is reflected in
the emission spectra in which we
observe a blue-shift of the plasmonic resonance
as we increase doping and decrease the width of
the graphene nanoresonators. Furthermore, the
intensity of this higher energy feature increases
with graphene carrier density, an
effect that results from the
increased polarizability of the
resonant plasmonic modes. Finally, this f
eature is strongly polarizat
ion dependent - as we
would expect laterally bound graphene plasmonic re
sonances to be - and vanishes quickly as we
transition from probing radiation 90° to
0° relative to the
nanoresonator axis.
In order to understand the s
ource of the thermally excited
plasmons in the graphene
nanoresonators, we note that the mi
croscopic processes that lead
to plasmonic loss in graphene
should become plasmon-generating processes when th
e sample is heated. For the case of the
1400cm
-1
feature we observe here, the plasmon
decay (and therefore plasmon generating)
processes are mediated by the same pathways th
at limit the electron mobility of the graphene,
such as defect scattering, im
purity scattering, and inelastic el
ectron-electron and electron-phonon
interactions.[23-27] Additionally, plasmons ha
ve been shown to decay via loss channels
associated with the edges of graphene nanostr
uctures, and by coupling
to substrate phonons.[23,
27] For a bare graphene sheet, the plasmons
generated by thermal emission do not couple well
to free space and are thus non-radiative. Upon
patterning the graphene, however, the plasmonic
resonances can effectively out-couple radiation,
and the plasmon decay processes become free-
space thermal emission sources by exciting resonant
plasmonic modes which then radiate.
The resonant enhancement of emission from plasmon generating processes is in
6
competition with the blocking of interband tran
sitions which act as thermal emitters in the
undoped graphene, but are forbidden due to Pauli
blocking when the sheet is doped.[28, 29] The
role of interband transitions can be seen most cl
early in the bare graphene emissivity spectra in
Fig. 3b where there is a broad decrease in emissivity near 1400cm
-1
at higher carrier densities.
While interband transitions should
occur across a wide range of fre
quencies, in the backreflector
geometry we use here, thermal emission from the surface can either constructively or
destructively interfere w
ith itself and is thus most prominent at 1400cm
-1
, the
ߣ
݊4
ௌே
ൗ
frequency of the SiN
x
layer. For patterned graphene ar
eas, however, we find that doping the
graphene allows for the resonant plasmonic m
odes to create and emission enhancement that
outweighs the decrease in emission due Pauli
blocking, and thus we get a net increase in
emission near 1400cm
-1
.
As mentioned above, in addition to out-c
oupling of radiation due to plasmon loss
mechanisms in the graphene, the plasmonic resonato
rs also interact with
vibrations in the SiN
x
substrate. When the SiN
x
is heated, the plasmonic modes act as antennae to enhance the
spontaneous thermal radiation from the nearby SiN
x
. The enhancement of the spontaneous
emission radiative rate and of the quantum efficiency arising from dipole emitters’ proximity to a
dipole optical antenna is well know
n,[30-32] and is attributed to
increasing the probability of
radiation by modification of the photonic mode de
nsity.[33] The rate enhancement is correlated
to the strong polarizability of the graphene
at its plasmonic resonance which enhances the
outcoupling of thermal radiation from the SiN
x
. In particular, the radiativ
e rate is expected to be
most strongly amplified in the top 10nm of the SiN
x
in accordance with the approximate
effective mode volume of the resonant graphene pl
asmon. However, we also expect that thermal
emitters in the SiN
x
near the graphene surface should experience non-radiative decay which
competes with this enhacement effect.[34]
We therefore assign the net increase of thermal
emission as a combination of the confined
plasmonic modes out-coupling energy from thermal
excitations in the graphene as
well as thermal phonons in the SiN
x
. These processes exceed the
decrease in emission associated
with non-radiative quenching e
ffects of the graphene on the
nearby SiN
x
, as well as the blocking of interba
nd transitions in the graphene sheet.
We next consider the feature at 730cm
-1
which is located at the energy of a strongly
absorbing phonon in the SiN
x
that creates an emission peak at raised temperatures, as observed in
7
Fig. 2. This emission peak is influenced in a nu
mber of ways by the presence of the graphene.
First we note that, as shown in Fig. 2, emission from 720 to 1100cm
-1
is decreased for both
doped and undoped graphene ribbons on SiN
x
in comparison to the bare membrane. We attribute
this to non-radiative energy tr
ansfer processes from the SiN
x
thermal excitations to the graphene
sheet.[34] For undoped graphene, th
ese processes are represented by
interband transitions in the
graphene sheet that have been
predicted and shown to drama
tically quench the emission of
nearby dye molecules.[35] As the graphene
becomes doped, interband transitions are blocked,
but new non-radiative pathways are introduced in
the form of propagating plasmons in the
graphene sheet.[34]
The SiN
x
phonon at 730cm
-1
can also couple to the plasmons in the graphene to create a
new surface phonon plasmon polariton (SPPP) mode,
similar to what has been observed for
graphene on SiO
2
and h-BN.[23, 27, 36] Similar to the
resonant plasmonic modes described
earlier, this mode can also enhance the ther
mal emission into free space, and this emission
should increase with the carrier de
nsity of the graphene sheet. In
order to calculate the possible
contribution of this mode we performed full-wave
finite element electromagnetic simulations to
calculate the full plasmonic bands
tructure for the graphene/SiN
x
system, as shown in Fig. 6.
This figure shows, indeed, that the graphene
plasmon spectrum has been perturbed by the SiN
x
phonons, and that a new SPPP mode exists as
a flat band is introduced near 650cm
-1
along with a
fainter, also flat band at 750cm
-1
. While the lower branch of
SPPP mode is expected to show
gate tunable effects on the graphene nanori
bbon emissivity, it should also show a strong
polarization dependence, which is not observed in
Fig 3c. Additionally, this low energy feature is
observed in the emissivity modulation of the
bare graphene sheet where the SPPP mode should
show weak out-coupling behavior. In cont
rast, the weaker phonon branch near 750cm
-1
crosses
the lightline, and thus does not require patterni
ng to couple to freespace, and should not display
an intensity dependent polarization dependence.
Due to these observations, we determine that
the feature near 730cm
-1
is created by both non-radi
ative processes between SiN
x
phonons and
the nearby graphene sheet, as well as
by the weaker branch of the graphene/SiN
x
SPPP mode.
To better understand and qua
ntify our emission features from the graphene-SiN
x
interactions, we used a finite element method
to calculate the electromagnetic power density
(
ܵ∙
റ
) associated with the absorption of plane wa
ves incident on 40nm graphene nanoresonator
8
on a SiN
x
/Au substrate at 4.9×10
12
cm
-2
carrier density using parameters
described in our previous
works.[21] The electromagnetic power density
models where power is absorbed, and therefore
also indicates where far field thermal emission or
iginates. The results of these simulations are
shown in Fig. 4(a) at 1413cm
-1
, corresponding to the graphene plasmon mode. We observe a
strong enhancement of the density of electro
magnetic power absorpti
on near the graphene
resonators. On this resonance,
there is a significant amount of
power being absorbed into the
graphene; however, it can clearly be seen that
in the region in which the graphene plasmon
extends into the SiN
x
, there is an enhancement of power
absorption, which would translate into
an increased rate of spontaneous emission from th
is part of the substrate. To further quantify
this, we integrate the power
densities over each material
for undoped and doped graphene and
see that, the power absorbed into the top 10nm of the SiN
x
increases with the increased graphene
nanoresonator doping as shown in Fig. 4(b). At ~1400cm
-1
, it is observed that there is weak
power absorption in the top layer of SiN
x
for undoped graphene, and we see only the interband
transitions contributing in th
e graphene itself. Then as the doping is increased to E
F
=0.25eV, the
graphene plasmon can be excited and so abso
rption in the graphene and top 10nm of SiN
x
increases due to the effects de
scribed above. For comparison we show the absorption features
from the remaining bottom 990nm of SiN
x
. It is important to note that this finite element model
does not account for the non-radiat
ive processes discussed above.
This model only indicates
how graphene plasmons interact with a homoge
nous, lossy medium and not for the way that
localized dipole moments interact with the gr
aphene sheet which is the origin of the non-
radiative quenching effects.
In order to quantify the thermally radiated power
of this structure,
we consider Planck’s
law for spectral radiance using the black soot as a reference with
ɛ
=1, and including our 50x50
μ
m
2
collection area and the 1.51 steradians covere
d by the 0.65 NA objective. We plot these
results for different temperatures
in Fig. 5, showing an increase
in the thermally radiated power
that is modulated by the graphene sheet,
and a maximum thermal power modulation of
200pW/cm
-1
at 1400cm
-1
(7.1
μ
m). These calculations indicate that a 1x1 mm
2
device patterned
with 40nm resonators held at 250
̊
C could act as an electronically
controllable mid-IR source that
would emit 8
μ
W over 100 cm
-1
of bandwidth. This compares favorably to commercial mid-IR
LEDs at 7
μ
m, which emit 2
μ
W over similar bandwidths.[37]
We also note that the maximum
temperature and gate bias applied in these ex
periments was not limited by the graphene but by
9
the SiN
x
dielectric, which is known to exhibit Poole-
Frenkel tunneling at hi
gh temperatures.[22]
By choosing a dielectric that can withst
and higher temperatures, such as SiO
2
, larger powers
could be achieved in such devices.
In conclusion, we have demonstrated the di
rect electronic control of Mid-IR thermal
radiation using graphene plasmonic nanoresonato
rs. We show that the graphene plasmonic
modes can act to enhace the thermal radiation from the SiN
x
membrane as well as excitations in
the graphene sheet. We have developed a struct
ure with tunable narrow
band emission at a range
of frequencies in the mid-IR due to graphene na
nostructure resonances, and we have shown that
this emission can be changed statically with
resonator dimensions, and actively with charge
carrier density via the application of a gate bias
. We estimate that the power emitted from this
structure with a 1mm
2
areal coverage could exceed that of mid-IR LEDs.
Acknowledgements:
This work was supported by the Department of En
ergy Office of Science, Basic Energy Sciences
under Contract No. DE-FG02-07ER
46405 (M.C.S.,V.W.B. and H.A.A.). M. S. J. and M. C.
acknowledge support from the Global Frontier R&
D Program on Center for Multiscale Energy
Systems funded by the National Research Foun
dation under the Ministry of Science, ITC &
Future Planning, Korea (2011-0031561, 2011-0031577).
M.C.S. acknowledges support from a
Resnick Institute Graduate Fellowship. M.S. J.
acknowledges a post-doctora
l fellowship from the
POSCO TJ Park Foundation. V.W.B. acknow
ledges support from a Kavli Nanoscience
Postdoctoral Fellowship, and use of facilties of the Kavli Nanoscience Institute.
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, 2030 (2013).
[36] V. W. Brar, M. S. Jang, S. Kim, M. Sherrott, L. K. Kim, J.
J. Lopez, M. Choi, and H. A.
Atwater, in
2014
MRS
Spring
Meeting
&
Exhibit
(Materials Research Society, San Francisco,
2014).
[37]
http://www.mirdog.spb.ru/Specifications/Specifications%202012/O
PLED70Su.pdf
.
12
Figures
Figure 1:
Schematic of experimental setup.
(a)
Graphene structure on temperature-controlled
stage with FTIR emission measur
ement configuration. Graphene
structure consists of 80 × 80
μ
m
2
nanoresonator arrays on a 1
μ
m thick SiN
x
membrane with 200nm Au backreflector. The
graphene was grounded through Au(100nm)/Cr(3nm) el
ectrodes that also se
rved as source-drain
contacts. A gate bias was applied through the SiN
x
membrane between the underlying Si frame
and graphene sheet. Temperature controlled stage consists of 100
μ
m thick sapphire on 2mm Cu
on an Ag block. Emission measurements were take
n at different temperatures via FTIR using a
LN
2
cooled MCT detector.
(b)
A resistance vs gate voltage cu
rve of the graphene sheet showing a peak in the resistance at
the charge neutral point (CNP), when the Fermi level (E
F
) is aligned with the Dirac point.
(c)
A representative SEM image of 30nm graphene nanoresonators.
13
Figure 2:
Normalization scheme adopted for this e
xperiment including reference soot emission
spectrum (left axis) taken to have emissivity of unity. Emitted intensity at a given temperature
for bare SiN
x
, graphene at charge neutra
l point (CNP) and increased car
rier density (left axis).
Change in emissivity of structure from
CNP to doped graphene, normalized to emission
spectrum of soot (right axis).
Enhancement of emissivity is ob
served due to increased charge
carrier density in graphene.
14
Figure 3:
Modulation of emissivity and thermal emi
ssion. Emissivity calculated using a unity
emissivity soot reference at the same temperature.
(a)
Carrier density dependence of emissivity
modulation for a fixed temperat
ure and nanoresonator width.
(b)
Emissivity modulation for
different nanoresonator geometries as well as un
patterned graphene at a fixed temperature and
carrier density.
(c)
Emissivity change for different polarizat
ions of light for a fixed temperature,
resonator width, a
nd carrier density.
15
16
Figure 4:
(a)
Calculated 2D plot of
electromagnetic power density in graphene/SiN
x
structure with vacuum above obtained from finite
element electromagnetic simulation. Plotted at
1413cm
-1
(graphene plasmon peak) at E
F
=0.25eV. Enhancement of pow
er density noted closest
to graphene surface then decaying into SiN
x
substrate.
(b)
Integrated power density in 40nm width
graphene resonator, the top 10nm of SiN
x
(Top
SiN
x
), and the remaining 990nm of SiN
x
(Bulk SiN
x
) at E
F
= 0eV and E
F
= 0.25eV.
Figure 5:
Thermally radiated power from Graphene/SiN
x
/Au structure at varying temperatures
for a nanoresonator width of 40nm and carrier density of 4.9x10
12
/cm
2
. Calculated using black
soot reference, based on
a 0.65 NA objective and a 50x50
μ
m
2
collection area. A maximum
modulation of 200pW/cm
-1
is calculated.
17
Figure 6:
Theoretical change in absorption (
∆
A
) as a function of inverse ribbon width at
E
F
=0.25eV. Numerical full-field electromagnetic
simulation has been performed using a finite
element method under the assumption
of normal light incidence.