Supplementary Information for
“
Highly Confined Tunable Mid-Infrared Plasmonics in
Graphene
Nanoresonators”
by Victor W. Brar, Min Seok Jang, Michelle Sherrott
, Josue J. Lopez and Harry Atwater
1 Approximating the Fermi Level Position
In order to determine the Fermi level position of o
ur devices, we first measured the resistance vs.
applied gate voltage dependence of the graphene she
et that contained the nanoresonators, as
shown in Fig. S1. From these measurements we were
able to determine the charge neutral point
(CNP) for each device, which corresponds to applied
gate voltage that aligns the Fermi level of
the graphene with the Dirac point, leading to a pea
k in the resistance curve. Once the CNP was
known, we used a simple capacitor model in order to
approximate the position of
E
F
for a given
gate voltage. For a 285nm SiO
2
layer, this relationship is given by
|
|
0.0319
|
|
.
For most devices,
V
G
could be varied from -100V to +200V without causin
g electric breakdown
of the SiO
2
layer.
We found that our as-prepared samples were hole dop
ed, and that the degree of hole doping was
dependent on the etchant we used to remove the copp
er foil that the graphene was grown on. As
shown in Fig. S1, when an Ammonium Persulfate (APS)
solution (2% by wt.) was used as the
etchant, the CNP typically occurred near
V
G
=50V. In contrast, when an Iron(III) Chloride(FeCl
)
solution (40% by wt.) was used as the etchant, the
CNP occurred at much higher gate biases,
typically with V
G
near +180V. This intrinsic hole doping allowed us
to electrostatically shift the
E
F
from 0 to -0.52 eV.
The above analysis applies to the bare graphene sur
face. However, it has been recently observed
by Thongrattanasiri,
et al
1
that the simple capacitance model typically used to
estimate the Fermi
level position of graphene devices may change when
the graphene is patterned in a nanoribbon
geometry. In particular, it was predicted by those
authors that the Fermi level position can
deviate strongly near the nanoribbon edges, and tha
t this deviation can affect the plasmonic
character of the graphene nanoresonators. In order
to see if such effects play a role in our
experiment, we compare in Fig. 2a the normalized tr
ansmission spectra of the bare graphene
surface to that of the nanoresonators, with light p
olarized parallel to the nanoresonators. These
data show the characteristic rise and drop in the n
ormalized transmission of doped graphene on
SiO
2
, with the drop in transmission roughly occurring a
t 2
E
F,
above which interband transitions
are no longer Pauli blocked
2
. It can be seen in these data that the drop in t
ransmission of the
nanoresonators occurs at similar energies to the ba
re graphene, and that the spectra evolve in a
similar fashion.
Although Figure S2 shows some deviations between th
e spectra taken on the bare graphene as
compared to the nanoresonators, it should be noted
that the transmission spectra on the
resonators can be influenced by a number of factors
other than those mentioned by Ref. [1]
.
First, the mobility of the graphene in the nanoreso
nators is likely to be much lower than the
mobility of the bare graphene due to the lithograph
ic processing that is used to pattern them, and
such a change in mobility can alter the normalized
transmission features. Second, charge traps
and edge states can be introduced on the nanoresona
tors as a result of the patterning, and those
can lead to a constant change in the background cha
rge density. Such edge effects may also play
a role in offsetting or moderating the effects pred
icted in Ref. [1].
2. Plasmon Lifetime
In Fig. S3 we plot the width,
∆
,
of the transmission peaks for graphene nanoresonat
ors of
different size and doping levels. A naïve estimati
on of the plasmon lifetime from the inverse
linewidth yields lifetimes of 5-50 fs based on thes
e data, with the lifetime decreasing as the
resonances move to higher frequencies. One explan
ation of this trend is that the graphene
plasmons should be damped as the plasmon energy mov
es above the in-plane optical phonon
energy of at 0.2eV.
3
Although this effect may play a role in increas
ing
∆
as the resonant
frequencies (
increase, it is important to note that the peak wi
dths that we experimentally
measure are due to multiple effects, many of which
are expected to show an energy dependence.
First, as the plasmons are confined into smaller gr
aphene nanoresonators (which exhibit higher
for the same carrier density), the edge roughness-
to-width ratio of the nanoresonators
becomes larger and thus the quality factor of the r
esonator worsens. Second, there is an
ensemble averaging effect that broadens the measure
d plasmon resonances due to the
±
2nm
deviations in the fabricated nanoresonator widths.
These small deviations in width will lead to a
spread of
values that will be larger for smaller lengthscale
nanoresonators, and will also
change as a function of doping. Finally, the permi
ttivity of the SiO
2
is dispersive under 0.25eV,
which distorts the shape of the resonance peaks and
thus leads to an energy-dependent
broadening effect on the transmission peaks that is
unrelated to the plasmon lifetime. These
effects make it difficult to estimate the true ener
gy- and doping-dependent plasmon lifetime
based on the experimentally measured
∆
.
Figure S1.
Resistance vs. Gate Voltage curves of graphene fie
ld effect transistor devices
containing nanoresonators. The red line correspond
s to a device that was prepared using
Iron(III) Chloride (40% by wt.) to etch away the co
pper foil, while the blue line indicates a
device that was prepared using Ammonium Persulfate
(2% by wt.) as the etchant. Source and
drain electrodes are typically separated by 0.5 – 5
.0 mm, and are placed on the bare graphene, at
least 200um from the nanoresonators
Figure S2.
Normalized transmission spectra obtained from grap
hene nanoresonators at different
gate voltages (black lines) compared to spectra obt
ained at identical gate voltages from the bare
graphene (green lines) adjacent to the nanoresonato
r patterns. Data was collected with light
aligned parallel to the graphene nanoresonators. S
ample A was prepared using an Iron(III)
Chrolide etch, and sample B was prepared using an A
mmonium Persulfate etch.
Figure S3.
Dependence of peak width
ω
on peak frequency of GP (open colored symbols) and
SPPP (filled colored symbols) resonances. The chara
cteristic width of nanoresonator varies from
15nm to 80nm. The dotted vertical line indicates th
e energy of in-plane optical phonons of
graphene.
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J. G.
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2012,
100, (20), 201105-
4.
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Nat
Phys
2008,
4, (7), 532.
3.
Jablan, M.; Buljan, H.; Soljacic, M.
Phys Rev B
2009,
80, (24), 245435.