ARTICLE
Received 14 Aug 2014
|
Accepted 26 Mar 2015
|
Published 7 May 2015
Electronic modulation of infrared radiation
in graphene plasmonic resonators
Victor W. Brar
1,2
, Michelle C. Sherrott
1,3
, Min Seok Jang
1,4
, Seyoon Kim
1
, Laura Kim
1
, Mansoo Choi
4,5
,
Luke A. Sweatlock
6
& Harry A. Atwater
1,3
All matter at finite temperatures emits electromagnetic radiation due to the thermally
induced motion of particles and quasiparticles. Dynamic control of this radiation could enable
the design of novel infrared sources; however, the spectral characteristics of the radiated
power are dictated by the electromagnetic energy density and emissivity, which are ordinarily
fixed properties of the material and temperature. Here we experimentally demonstrate
tunable electronic control of blackbody emission from graphene plasmonic resonators on a
silicon nitride substrate. It is shown that the graphene resonators produce antenna-coupled
blackbody radiation, which manifests as narrow spectral emission peaks in the mid-infrared.
By continuously varying the nanoresonator carrier density, the frequency and intensity of
these spectral features can be modulated via an electrostatic gate. This work opens the door
for future devices that may control blackbody radiation at timescales beyond the limits of
conventional thermo-optic modulation.
DOI: 10.1038/ncomms8032
1
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA.
2
Kavli Nanoscience Institute,
California Institute of Technology, Pasadena, California 91125, USA.
3
Resnick Sustainability Institute, California Institute of Technology, Pasadena, California
91125, USA.
4
Global Frontier Center for Multiscale Energy Systems, Seoul National University, Seoul 151-747, Republic of Korea.
5
Division of WCU Multiscale
Mechanical Design, School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Republic of Korea.
6
Nanophotonics and
Metamaterials Laboratory, Northrop Grumman Aerospace Systems, Redondo Beach, California 90250, USA. Correspondence and requests for materials
should be addressed to H.A.A.(email: haa@caltech.edu).
NATURE COMMUNICATIONS
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T
hermal radiation is commonly viewed to be broadband,
incoherent and isotropic, with a spectral profile and
intensity that are dependent on the emissivity of a
material, and that vary only with changes in temperature. Recent
experiments on nanoengineered structures, however, have begun
to challenge these notions, showing that blackbody emission can
be coherent and unidirectional, with narrow spectral features.
These structures have included patterned gratings on metal or
silicon carbide surfaces that can control the directionality and
coherence of thermal radiation
1,2
, as well as photonic crystals
3
,
size-tunable Mie resonances
4
and frequency-selective meta-
surfaces
5
, which can tune the spectral profile. Progress has also
been made in demonstrating dynamic control of thermal
radiation through
in situ
modification of material emissivity.
This has been achieved with devices that incorporate phase
change materials, which display temperature-dependent
emissivities
6
, as well as electronically controlled devices, where
injected charges are used to overdampen polariton modes in
quantum wells
7
. These results suggest that careful control of both
the photonic and electronic structure of metasurfaces could allow
for thermal emitters that have continuously variable frequency
and directionality control, and that can operate at speeds much
faster than typical thermal cycling times, potentially approaching
speeds of modern telecommunication devices.
Graphene provides a unique platform for studying and
controlling thermal radiation at infrared wavelengths. The optical
absorptivity/emissivity of graphene depends on two carrier
density-dependent terms: an intraband contribution that is
characterized by a large Drude-like peak in the DC to far-IR
range, and an interband contribution that manifests as a step-like
feature in the absorption in the far to near-IR
8–13
. In addition, the
linear bandstructure and two-dimensional nature of graphene
allow for it to support plasmonic modes that have a unique
dispersion relation
14–17
. These plasmonic modes have
been proposed as a means of efficiently coupling to THz
radiation
18–20
, and they have been shown to create strong
absorption pathways in the THz to mid-IR when the graphene is
patterned to form plasmonic Fabry-Perot resonances
21–24
. The
intensity and frequency of the plasmonic modes in graphene are
carrier density dependent, and they display extermely large mode
confinement, which allows them to efficiently couple to
excitations (for example, phonons) in their environment and to
create new optical modes
21,22,25,26
. As the graphene sheet is
heated up, these different infrared absorption pathways become
thermal emission sources, with contributions that vary with the
graphene carrier density and surface geometry. The graphene
plasmons are particularly interesting as thermal emitters because
their small mode volumes allow for extremely efficient thermal
energy transfer in the near field
27,28
, and also lead to large Purcell
factors that can enhance the emission rate of emitters within the
plasmon mode volume
29
. These large Purcell factors suggest that
electronic control of the graphene plasmonic modes could
potentially control thermal radiation at timescales much faster
than the spontaneous emission rate for conventional light
emitting diodes and classical blackbody emission sources.
In the present work, we experimentally demonstrate the
dynamic tuning of blackbody emission through electronic control
of graphene plasmonic nanoresonators on a silicon nitride
substrate at temperatures up to 250
°
C. Our device is based on
field effect tuning of the carrier density in nanoresonators, which
act as antennas to effectively outcouple thermal energy within the
resonator mode volume. We show that through this mechanism
the thermal radiation generated by substrate phonons and
inelastic electron scattering in graphene can be tuned on and
off. By varying the charge carrier density of the graphene from 0
to 1.2
10
13
cm
2
, with resonator widths from 20 to 60 nm, we
show that a narrow bandwidth emission feature may be tuned in
intensity and varied in frequency across the mid-IR, from
B
1,200–1,600 cm
1
.
Results
Mid-IR graphene nanoresonator device geometry
. A schematic
of the measurement apparatus and device geometry are shown in
Fig. 1a (see Methods). The device consists of 20–60 nm wide
graphene nanoresonators patterned into a graphene sheet on a
1
m
m SiN
x
layer with a gold back reflector that also serves as a
back gate electrode. This device geometry was previously 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 energy of the
l
/4
n
SiN
resonance condition in the 1
m
m SiN
x
layer, which occurred at
1,360 cm
1
(refs 30,31) In those experiments, the polarized
absorption in the graphene nanoresonators could be tuned from 0
to up to 24.5% for large carrier densities. In this work, a similar
sample displayed up to 3% total absorption when probed
using our apparatus. This smaller number reflects the use
of non-polarized light, the higher numerical aperture
objective of the apparatus, the effect of the window of the
vacuum stage and the lower carrier densities used due to the
onset of Poole-Frenkel tunnelling in the SiN
x
at higher
temperatures and high gate biases (see Supplementary
Note 1; Supplementary Figs 1, 2 and 3 for details)
30,32
.
Tunable emission measurements on graphene nanoresonators
.
Figure 2 (left axis) shows the emitted radiation at 250
°
C from a
black soot reference sample and from a 40 nm graphene nanor-
esonator array at 250
°
C under doped (1.2
10
13
cm
2
) and
undoped conditions. On the right axis of Fig. 2, we plot the
change in emissivity corresponding to the observed change in
emitted light from the undoped to doped graphene resonators.
This change in emissivity is calculated assuming unity emissivity
at all frequencies for the black soot reference and normalizing
accordingly. As can be seen in the figure, increasing the carrier
density of the graphene nanoresonators leads to increases in
emissivity near 730 and 1,400 cm
1
.
To explore these gate-tunable emissivity features, we
investigate their behaviour as the nanoresonator doping and
width is varied, as shown in Fig. 3a,b, as well as their polarization
dependence (Fig. 3c). These results indicate that the intensity,
width and energetic position of the thermal radiation feature
near 1,360 cm
1
are widely tunable, and that this feature is
strongly polarized. The energy of this feature increases as the
nanoresonator width is decreased and as the carrier density is
increased, while the intensity of this feature increases with carrier
density, and is the largest in 40 nm resonators, when it occurs
closest to the
l
/4
n
SiN
resonance condition of the SiN
x
at
1,360 cm
1
. As Kirchoff’s Law dictates that thermal emissivity
is equal to absorptivity, these observations are consistent
with previously reported absorption measurements performed
on identical samples that showed a narrow absorption
feature near 1,360 cm
130
(see also Supplementary Note 2;
Supplementary Fig. 4).
Low-energy emission feature
. The lower-energy emissivity
modulation feature near 730 cm
1
shows different behaviour
than the higher-energy peak. Namely, the low-energy feature
shows an extremely weak polarization dependence and also shows
no noticeable dependence on graphene nanoresonator width. As
the carrier density is increased, there is a small, non-monotonic
increase in intensity for this feature, but it shows no spectral shift.
Finally, unlike the higher-energy peak, the lower-energy peak is
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also observed in the bare, unpatterned graphene, where it appears
as a slightly narrower feature. The absorption properties of this
device near the energy range of the lower-energy feature were not
discussed in previously reported work due to the low-energy
cutoff of the detector used in that work.
Discussion
We explain the above phenomena as electronic control of thermal
radiation due to a combination of plasmon–phonon and
plasmon–electron interactions, Pauli-blocking of interband tran-
sitions, and non-radiative transfer processes between the SiN
x
and the graphene sheet. While Kirchoff’s law dictates that the
thermal equilibrium emissivity must be equal to the absorptivity
for any material, the precise, microscopic mechanisms of thermal
emission are markedly modified in inhomogeneous artificial
photonic materials with highly confined optical modes relative to
homogeneous materials.
We attribute the prominent spectral feature at 1,360 cm
1
to a
Fabry-Perot plasmonic resonance from the patterned graphene.
The width and doping dependence of the 1,360 cm
1
feature follows the behaviour expected for graphene plasmonic
modes, and is consistent with reflection measurements
30
.
Specifically, the graphene plasmon resonant frequency should
vary as
o
p
p
n
1/4
W
1/2
, where
n
is the carrier density and
W
refers to the resonator width. This behaviour is in accord
with the emission spectra in which we observe a blue shift of the
plasmonic resonance at increased doping and decreased graphene
nanoresonator width. The intensity of the higher-energy
peak increases with graphene carrier density, an effect that
results from the increased polarizability of the resonant
plasmonic modes. Finally, this feature is strongly polarization
dependent, as we would expect for laterally confined graphene
plasmonic resonant modes, and vanishes quickly as we rotate the
polarization of the probing radiation from 90
°
to 0
°
relative to the
nanoresonator axis.
To understand the source of thermally excited plasmons in
graphene nanoresonators, we note that the microscopic processes
that lead to plasmonic loss in graphene should by reciprocity
correspond to plasmon-generating processes when the sample is
heated. For the case of the 1,360 cm
1
feature we observe here,
LN2 cooled
MCT detector
FTIR
1 mtorr
V
SD
V
G
A
Graphene nanoresonators
1
μ
m SiN
x
200
μ
m Si
200 nm Au
10
0
μ
m sapphire
2mm copper
Heated Ag block
2.0
1.5
1.0
Resistance (k
Ω
)
0.5
–100 –50
0
50 100
Gate voltage (V)
Δ
x
400 nm
Figure 1 | Device and experimental set-up.
(
a
) Schematic of experimental apparatus. The 70
70
m
m
2
graphene nanoresonator arrays are placed on a
1
m
m thick SiN
x
membrane with 200 nm Au backreflector. The graphene was grounded through Au(100 nm)/Cr(3 nm) electrodes that also served as
source-drain contacts. A gate bias was applied through the SiN
x
membrane between the underlying Si frame and graphene sheet. The temperature-
controlled stage contains a feedback controlled, heated silver block that held a 2 mm thick copper sample carrier, with a 100
m
m thick sapphire layer used
for electrical isolation. The temperature was monitored with a thermocouple in the block, and the stage was held at a vacuum of 1 mtorr. A 1 mm thick
potassium bromide (KBr) window was used to pass thermal radiation out of the stage, which was collected with a Cassegrain objective and passed into an
FTIR with an MCT detector. (
b
) A representative SEM image of 30 nm graphene nanoresonators on a 1
m
m thick SiN
x
membrane. (
c
) Source-drain
resistance versus gate voltage curve of the device. The peak in the resistance occurs at the charge neutral point (CNP), when the Fermi level (
E
F
) is aligned
with the Dirac point.
14
40 nm resonators
250° C
Carrier density
Soot
1.2 x 10
13
cm
–2
CNP
12
10
8
Emitted intensity (a.u.)
6
4
2
0
1,000
1,500
Wavenumbers (cm
–1
)
2,000
2,500
–0.01
0.00
0.01
0.02
Δ
Emissivity
Δ
Emissivity
0.03
0.04
0.05
Figure 2 | Experimental emission results.
(Left axis) Emitted thermal
radiation at 250
°
C from soot (black dotted line) and 40 nm graphene
nanoresonators at zero (red) and 1.2
10
13
cm
2
(green) carrier density.
(right axis, blue line) Change in emissivity of 40 nm nanoresonators due to
increase in carrier density. Soot reference is assumed to have emissivity
equal to unity.
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the plasmonic loss (and corresponding plasmon generating)
processes are attributed to the factors that limit the electron
mobility of the graphene, such as defect scattering, impurity
scattering, and inelastic electron–electron and electron–phonon
interactions
15,22,25,30,33
. In addition, plasmons have been shown
to decay via loss channels associated with the edges of graphene
nanostructures and by coupling to substrate phonons
22,25
. 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 serve as antennas that out-couple radiation, and the
plasmon decay processes give rise to free-space thermal emission
by exciting resonant plasmonic modes that then radiate.
The resonant enhancement of emission from plasmon
generating processes is in competition with the blocking of
interband transitions that act as thermal emitters in the undoped
graphene, but are forbidden due to Pauli blocking when the sheet
is doped
9,10
. The role of interband transitions can be seen most
clearly in the bare graphene emissivity spectra in Fig. 3b where
there is a broad decrease in emissivity near 1,360 cm
1
at higher
carrier densities. While interband transitions should occur across
a wide range of frequencies, in the back reflector geometry we use
here, thermal emission from the surface can either constructively
or destructively interfere with itself and is thus most prominent at
1,360 cm
1
, the
l
/4
n
SiN
frequency of the SiN
x
layer. For
patterned graphene areas, however, we find that doping the
graphene allows for the resonant plasmonic modes to create an
emission enhancement that outweighs the decrease in emission
due to Pauli blocking, and thus we get a net increase in emission
near 1,360 cm
1
.
As mentioned above, in addition to out-coupling of radiation
due to plasmon loss mechanisms in the graphene, the plasmonic
resonators 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 known
34–36
, and is attributed to
increasing the probability of radiative emission by modification of
the photonic mode density
37
. The rate enhancement is correlated
to the strong polarizability of the graphene at its plasmonic
resonance that enhances the outcoupling of thermal radiation
from the SiN
x
. In particular, the radiative rate is expected to
be most strongly amplified within the mode volume of the
resonant graphene plasmon, which for 40 nm resonators at
1.2
10
13
cm
2
roughly corresponds to the area within 10 nm of
the resonator (see Fig. 4a). We therefore assign the net increase of
thermal emission near 1,360 cm
1
to a combination of thermal
excitations in the graphene as well as thermal phonons in the
SiN
x
that is out-coupled through the confined plasmonic modes
in the graphene nanoresonators.
In contrast to the high-energy feature, which is due to
plasmons in the graphene, the low-energy feature at 730 cm
1
is related to an optically active phonon in the SiN
x
substrate. This
phonon mode is strongly absorbing (emitting) and is typically
located near 850 cm
1
. The large divergence in the SiN
x
permittivity due to this phonon, however, creates an additional
l
/4
n
SiN
condition in the structure that leads to a destructive
interference effect, resulting in an absorption (emission) max-
imum at 730 cm
1
. When graphene is placed on top of the SiN
x
,
the intraband and interband transitions in the graphene act to
modify the surface impedance of the device. The result is that
increasing the doping in the graphene leads to a stronger
destructive interference effect, which manifests as larger emission
from the SiN
x
layer (see Fig. 4b). In addition to direct emission
from the SiN
x
phonon, the graphene plasmons can couple to the
SiN
x
phonons to create new surface phonon plasmon polariton
modes
21,22,25,38
. The formation of these modes leads to a
modification of the plasmonic dispersion relation, and
additional absorption (emission) pathways near and below the
energy of the SiN
x
phonon (see Supplementary Note 3,
Supplementary Fig. 5). Emission from the SPPP modes,
however, should display some polarization dependence, which
was not observed in Fig. 3b; thus, an increase in direct emission
from the SiN
x
layer likely plays the dominant role in creating the
feature at 730 cm
1
.
To better understand and quantify the emission features
observed in the graphene-SiN
x
structure, we used a finite element
method to calculate the electromagnetic power density
r
S
ðÞ
0.03
40 nm resonators
250° C
Carrier density
0.1 x 10
13
cm
–2
1.2 x 10
13
cm
–2
1.2 x 10
13
cm
–2
40 nm resonators
250° C
Polarization angle
90 deg
45 deg
0 deg
Resonator width
20 nm
30 nm
40 nm
50 nm
60 nm
Bare
0.3
250° C
0.5
0.8
1.2
0.02
0.02
Δ
Emissivity
Δ
Emissivity
Δ
Emissivity
0.01
0.04
0.06
0.04
0.02
0.00
–0.02
0.00
0.00
–0.01
1,000
1,500
2,000
2,500
Wavenumbers (cm
–1
)
1,000
1,500
2,000
2,500
Wavenumbers (cm
–1
)
1,000
1,500
2,000
2,500
Wavenumbers (cm
–1
)
Figure 3 | Emissivity tunability.
(
a
) Carrier density dependence of change
in emissivity with respect to the CNP for 40 nm graphene nanoresonators
at 250
°
C. (
b
) Width dependence of change in emissivity for 20, 30, 40, 50
and 60 nm wide nanoresonators at 250
°
C and for a carrier density of
1.2
10
13
cm
2
. (black line) Emissivity change for a nearby region of bare,
unpatterned graphene at the same carrier density and temperature. (
c
)
Polarization dependence of the emissivity change for 40 nm graphene
nanoresonators at 250
°
C, for a carrier density of 1.2
10
13
cm
2
.
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associated with plane waves incident on 40 nm graphene
nanoresonators on an SiN
x
/Au substrate. The parameters for
our computational model were equivalent to those described in
our previous work, where the optical absorption of the device
was modelled
30
.As
r
S
reveals where power is absorbed, it
therefore also indicates where far-field thermal emission
originates, and an increase in
r
S
indicates an enhancement
of the spontaneous emission intensity of the thermally excited
dipoles
30
. The results of these simulations are shown in Fig. 4a
at 1,357 cm
1
, corresponding to the resonant energy of the
graphene plasmon mode when the carrier density is set to
1.2
10
13
cm
2
. It can be seen in this figure that there is a
marked increase in the amplitude of
r
S
near the graphene
nanoresonator. On resonance, there is a significant amount of
power absorbed directly into the graphene, and it can also be
seen that there is a large amount of absorption in the SiN
x
in
the immediate vicinity of the nanoresonator, where the fields
of the graphene plasmon mode extend. To further distinguish
the relative contributions to thermal emission, we integrate
the power densities at 1,357 cm
1
over the graphene, the SiN
x
within the plasmon mode volume and the remaining SiN
x
.
We calculate the mode volume of our structure as
V
eff
¼
R
udV
=
u
0
where the numerator is the total stored
energy and
u
0
is the electromagnetic-energy density at the
emitter position, chosen to be sitting directly atop the resonator.
We define the boundary of the mode to be centred about the
graphene resonator along a contour of constant electric field (
E
x
).
In Fig. 4b, we show results for undoped and doped
nanoresonators. For undoped graphene, we observe weak power
absorption in the SiN
x
near the graphene nanoresonator, and we
see only interband transitions contributing to absorption in the
graphene itself. As the carrier density is increased to
1.2
10
13
cm
2
, absorption in the graphene and the nearby
SiN
x
increases due to excitation of the confined plasmonic mode.
The absorption in the bulk of the SiN
x
layer shows little
dependence on graphene carrier density, except at low
frequencies, near 730 cm
1
, where absorption decreases with
carrier density due to changes in the reflection coefficient at the
surface, as described above. We note that our finite element
model does not account for the non-radiative processes discussed
in other work
39
. Our model indicates how graphene plasmons
interact with a homogenous, lossy medium but not the manner in
which individual dipoles interact with the graphene sheet, which
is another source of non-radiative quenching.
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
E
¼
1, and including our 50
50
m
m
2
collection
area and the 1.51 steradians covered by the 0.65 NA objective.
This calculation yields a maximum thermal power modulation of
50 pW cm
1
at 1,360 cm
1
(7.1
m
m) for 40 nm resonators at
250
°
C doped to a carrier density of 1.2
10
13
cm
2
(see
Supplementary Fig. 3). These calculations indicate that a
1
1mm
2
device could act as an electronically controllable
mid-IR source that would modulate 2
m
W of power over
100 cm
1
of bandwidth. This compares favourably with
commercial mid-IR LEDs at 7
m
m, which emit 1.25
m
W over
similar bandwidths (IoffeLED, OPLED70Sr). The percent change
in emitted power at the resonant plasmonic frequency is 7.5%, a
value that reflects the large background contribution due to SiN
x
phonons as well as the low mobility of the graphene sheet, the
polarization of the plasmon-assisted radiation and the low
dielectric strength of the SiN
x
at elevated temperatures (see also
Supplementary Note 2; Supplementary Fig. 4). Figure 4 shows
that while the SiN
x
phonons play some role in contributing to the
plasmon-assisted radiation, the majority originates in the
graphene sheet itself. Thus, by choosing a substrate with a low
optical phonon density at the resonant plasmon frequency, such
as diamond-like carbon
22
, the background signal could be
reduced without significantly suppressing the plasmon-assisted
radiation, leading to a larger modulation depth of the emitted
power. We also note that the maximum temperature and gate
bias applied in these experiments was not limited by the graphene
but by the SiN
x
dielectric, which is known to exhibit Poole-
Frenkel tunnelling at high temperatures
32
. By choosing a
dielectric that can withstand higher temperatures, such as SiO
2
or diamond-like carbon, devices displaying larger power
modulation could be fabricated. Finally, devices fabricated
with higher mobility graphene, less edge roughness and
with circular resonator geometries (that is, non-polarized) have
been predicted theoretically
31
to exhibit tunable absorptivity/
emissivity that can vary from 0 to 1 (that is, zero to total
absorption) within a narrow frequency range. Such devices would
display changes in absorbtivity that equal or exceed those
provided by electrochromic devices
40
, while also providing
potential for more operation cycles, and higher temperature
and higher speeds of operation.
In addition to providing utility as a tunable mid-IR source, the
physics by which this device operates is distinctly different from
n
= 1.2 x 10
13
cm
–2
n
= 1.2 x 10
13
cm
–2
n
≈
0 cm
–2
(CNP)
Top SiN
x
Top SiN
x
Bulk SiN
x
Bulk SiN
x
Graphene
Graphene
∇•
S (a.u.)
2
1
0
0
1,000
1,500
2,000
2,500
Wavenumbers (cm
–1
)
0.05
0.1
0.15
0.2
1
4
x
Power absorbed (W)
= 1,357 cm
–1
10 nm
2 nm
Figure 4 | Finite element power density simulations.
(
a
) Finite element electromagnetic simulation of
r
S
(electromagnetic power density) in
graphene/SiN
x
structure for 40 nm graphene nanoresonators on 1
m
m SiN
x
with a gold backreflector . The simulation is performed at 1,357 cm
1
(on plasmon resonance) at a carrier density of 1.2
10
13
cm
2
. Dotted white line indicates the mode volume of the plasmon resonance. (
b
) Integrated
power density absorbed in the 40 nm graphene nanoresonator, the SiN
x
within the plasmon mode volume (Top SiN
x
), and the remaining bulk of the SiN
x
(Bulk SiN
x
) for carrier densities of 1.2
10
13
cm
2
and
B
0cm
2
(the charge neutral point).
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8032
ARTICLE
NATURE COMMUNICATIONS
| 6:7032 | DOI: 10.1038/ncomms8032 | www.nature.com/naturecommunications
5
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2015
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