of 11
Supplementary Information:
Hybrid Surface-Phonon-Plasmon Polariton Modes in Gr
aphene /
Monolayer h-BN stacks
Victor W. Brar
1,2†
, Min Seok Jang
3,†
, Michelle Sherrott
1
, Seyoon Kim
1
, Josue J. Lopez
1
, Laura B.
Kim
1
, Mansoo Choi
3,4
, and Harry Atwater
1,2
† These authors contributed equally.
1) Thomas J. Watson Laboratory of Applied Physics,
California Institute of Technology,
Pasadena, CA 91125
2) Kavli Nanoscience Institute, California Institut
e of Technology, Pasadena, CA91125
3) Global Frontier Center for Multiscale Energy Sys
tems, Seoul National University, Seoul 1517
747, Republic of Korea
4) Division of WCU Multiscale Mechanical Design, Sc
hool of Mechanical and Aerospace
Engineering, Seoul National University, Seoul 15177
42
I. Electromagnetic Simulations
We solve classical electromagnetic equations by emp
loying the finite element method in order to
simulate the plasmon oscillation in graphene nanore
sonators. The sheet conductivity of graphene
σ
(
ω
) is evaluated within the local phase approximation
.
1




=
2
ℏ+Γ
log2cosh


2
+

4ℏ
[

2
+
4
!"
#
$


"

−

2


−4"
,
where


"

=
sinh

"/

cosh



/

+cosh

"/

.
Here, the temperature
is set as 300K. The carrier scattering rate Γ take
s into account scattering
by impurities with the carrier mobility of 500cm
2
/Vs, and by optical phonons estimated from
theoretically obtained self7energy.
2, 3
The in7plane and out7of7plane relative permittivit
y of
graphene are then separately assigned as
ε
=1+
/
ωδ
and 1, respectively. The thickness of
graphene(
δ
) and h7BN are both set as 0.34nm from the interlay
er spacing of bulk hBN and
graphite. An oscillator model is used to describe i
n7plane dielectric function of h7BN,
+
,-



= +
#
+.
/
0

0
−
+1
0
0
where
+
#
= 4.95 is the optical dielectric constant.
4
The parameters for strong in7plane phonon
mode at ω
1
=1370cm
71
are determined by fitting the theoretical extincti
on spectra to the measured
data as s
1
2
= 3.9×10
6
cm
72
, and γ
1
= 19cm
71
(Fig. S1). The complex dielectric function of SiO
2 is
adopted from Palik.
5
Figure S1:
h-BN optical phonon extinction spectra.
Extinction spectra of h7BN/SiO
2
/Si sample
normalized by transmission through bare SiO
2
/Si sample. Absorption peak at 1370cm
71
is due to
the h7BN in plane optical phonon oscillation. The m
easured data (black dashed) can be fitted
well with theoretical spectra assuming an oscillato
r model for h7BN dielectric function (red).
2. Carrier Density Dependence of Graphene/h-BN pla
smon and SPPP modes
Figure S2:
Experimental dependence of transmission modulation
on carrier density.
Measured transmission modulation spectrum at variou
s carrier densities for 30 (left), 60
(middle), and 100nm (right) graphene nanoresonators
. In all cases, the peaks are blue shifted and
becomes stronger with increasing doping concentrati
on.
Figure S3:
Carrier density dependence of plasmons in graphene/
h-BN.
Calculated change in
transmission for graphene/monolayer h7BN nanoresona
tors of varying width at low (
n
=
0.46×10
13
cm
72
) and (b) high (
n
= 1.8×10
13
cm
72
) carrier densities. The wavevector is determined
by considering the ribbon width,
W
, as well as the phase of the plasmon reflecting of
f the
graphene ribbon edge.
3. Characterization of h-BN in areas exposed to 10
0keV e-beam and O
2
plasma
Figure S4:
Optical characterization of graphene/h-BN areas exp
osed to lithography process.
Measured transmission modulation spectrum from a co
ntinuous 50x50
μ
m
2
region of graphene/h7
BN exposed to the 100keV in PMMA electron beam patt
erning process in PMMA, followed by
the O
2
plasma etch (red line). For comparison, the trans
mission spectrum from an untouched
region of graphene/h7BN is included (green line).
These spectra reveal that the optical
absorption peak at 1370cm
71
due to the in7plane optical phonon of h7BN is lost
in the lithography
process, indicating that the h7BN sheet has been de
graded.
4. Determination of carrier density of graphene sh
eet
Interband transitions occur in graphene when the in
cident photon energy is higher than two times
of the Fermi level (
E
F
) of the graphene, and thus it is possible to estim
ate the Fermi energy from
the transmission modulation due to the onset of int
erband transition.
6
As a reference signal, we
first took a near infrared transmission spectrum at
the charge neutral point (CNP). Here the
charge neutral condition was achieved by applying t
he gate voltage (
V
CNP
= 165V) which gave a
maximum in the resistance as shown in Fig. S5. The
near7IR transmission spectra at various gate
voltage values (
V
G
) were then taken, and normalized with respect to t
he reference spectrum in
order to see the difference. The resulting transmis
sion modulation spectra of an area patterned
with 80nm nanoresonators at
V
G
= −90V and
V
G
= 0V (background doping) are presented in
Fig.S6, and they both exhibit a downward slope whic
h is originated from the onset of the
interband transition. We observe that the 2
E
F
interband onset is considerably wider than the
theoretical estimate for thermal broadening of 2
E
F
at room temperature, which is consistent with
the observation by Li et al.
6
In order to determine the carrier densities at
each
V
G
values, we
obtained the theoretical transmission spectra which
give the best fit to the measured data by
using both the Fermi level position and broadening
as fitting parameters. As a result, the carrier
densities are determined to be
n
= 1.0×10
13
cm
72
(hole doped)
for the highest carrier density used
in this experiment, and
n
= 0.4×10
13
cm
72
(hole doped)
as the background doping. The theoretical
spectra were calculated by numerically solving clas
sical electromagnetic equations using finite
element method.
1, 7
The background doping observed in our samples has
been shown previously
to be mainly caused by the FeCl etchant that is use
d to remove the copper foil from the as7grown
CVD graphene,
7
although atmospheric impurities, and charge traps
in the substrate can also play
a role.
8, 9
Interband transition measurements and
E
F
fittings performed on bare graphene areas
showed a similar gate vs. carrier density dependenc
e to the patterned graphene areas, as was also
observed in previous works.
7
We note that the carrier density we extract by mon
itoring the interband transitions is
lower that what would be obtained from a simple par
allel plate capacitance calculation for our
device.
10, 11
We attribute this to two possible effects. Firs
t, our measurements were performed
under nitrogen purged conditions, where atmospheric
impurities were still, inevitably present.
These impurities cause hysteresis in our gate7depen
dent resistance curves, and have been shown
to change the gate voltage vs. carrier density rela
tionship in graphene devices.
12714
Second, it has
been shown that impurities on graphene that contain
states near the Dirac point can be charged
and discharged as the graphene Fermi level is varie
d via the applied gate bias.
15, 16
This charging
and discharging process cause the background doping
to have a gate dependence (as impurities
are turned ‘on’ and ‘off’) , and thus alter the exp
ected gate voltage vs. carrier density dependence.
Such impurity states could be intrinsic to the CVD
h7BN sheet, or could be introduced during the
fabrication process by either PMMA residue on top o
f the graphene, or impurities trapped
between the graphene and h7BN sheets. For these re
asons, we feel that fitting the high energy
transmission spectrum, where the interband transiti
ons occur, is the most direct and accurate way
to determine the graphene nanoresonator carrier den
sity.
Figure S5:
Resistance vs. applied gate voltage for graphene/h-
BN device.
Measured two7
probe resistance value of the graphene sheet on mon
olayer h7BN. The maximum in resistance
occurs at 165V, corresponding to the gate voltage t
hat removes all free carrier from the graphene
sheet and aligns the Fermi level with the Dirac poi
nt.
Figure S6:
Change in transmission due to blocking of interband
transitions.
(Solid lines)
Normalized near IR experimental spectra taken with
V
G
= − 90V
(∆V
G
= ─ 255V) and
V
G
= 0V
(
∆V
G
= − 165V) from an area of the graphene/h7BN sample
patterned with 80nm nanoresonators.
(Dashed lines) Fitted theoretical change in transmi
ssion giving
n
= 1.0×10
13
cm
72
for
V
gG
= − 90V
and
n
= 0.4×10
13
cm
72
for
V
G
= 0V (intrinsic doping).
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