# Plasmonically enhanced tunable spectrally selective NIR and SWIR
photodetector based on intercalation doped nanopatterned multilayer graphene

Muhammad Waqas Shabbir(1) Michael N. Leuenberger(1,2)
<EMAIL_ADDRESS>(1) NanoScience Technology Center and Department
of Physics, University of Central Florida, Orlando, FL 32826, USA.
(2) College of Optics and Photonics, University of Central Florida, Orlando,
FL 32826, USA.

###### Abstract

We present a proof of concept for a spectrally selective near-infrared (NIR)
and short-wavelength infrared (SWIR) photodetector based on nanopatterned
multilayer graphene intercalated with FeCl3 (NPMLG-FeCl3), enabling large
modulation p-doping of graphene. The localized surface plasmons (LSPs) on the
graphene sheets in NPMLG-FeCl3 allow for electrostatic tuning of the
photodetection in the NIR and SWIR regimes from $\lambda=1.3$ $\mu$m to 3
$\mu$m, which is out of range for nanopatterned monolayer graphene (NPG). Most
importantly, the LSPs along with an optical cavity increase the absorbance
from about $N\times 2.6$% for $N$-layer graphene-FeCl3 (without patterning) to
nearly 100% for NPMLG-FeCl3, where the strong absorbance occurs locally inside
the graphene sheets only. Our NIR and SWIR detection scheme relies on the
photo-thermoelectric effect induced by asymmetric patterning of the multi-
layer graphene (MLG) sheets. The LSPs on the nanopatterned side create hot
carriers that give rise to Seebeck photodetection at room temperature
achieving a responsivity of $\mathcal{R}=6.15\times 10^{3}$ V/W, a detectivity
of $D^{*}=2.3\times 10^{9}$ Jones, and an ultrafast response time of the order
of 100 ns. Our theoretical results pave the way to graphene-based
photodetection, optical IR communication, IR color displays, and IR
spectroscopy in the NIR, SWIR, mid-wavelength infrared (MWIR), and long-
wavelength infrared (LWIR) regimes.

KEYWORDS: Localized surface plasmons, graphene, light absorption, Seebeck
effect, infrared light detection.

Because of the weak absorbance of pristine graphene of around 2%, we created
nanopatterned CVD-grown single-layer graphene (NPG) that exhibits absorbance
exceeding 60% in the long-wavelength infrared (LWIR) regime between
$\lambda=8$ $\mu$m to 12 $\mu$m.[1, 2] Recently, we showed that NPG with
smaller sizes of hexagonally arranged holes and smaller lattice constants
exhibits absorbance of 80% in the mid-wavelength (MWIR) regime between
$\lambda=3$ $\mu$m and 8 $\mu$m. Due to the resolution limit of e-beam
lithogaphic systems it is currently impossible to create smaller nanopatterns
for increasing the absorbance of graphene using nanopatterning at shorter
wavelengths.

Here, we show that LSP resonances can be realized in the technologically
relevant NIR and SWIR regimes between $\lambda=1.3$ $\mu$m and 3 $\mu$m by
means of nanopatterned multilayer graphene (NPMLG) intercalated with FeCl3.
Multilayer graphene intercalated with ferric chloride FeCl3, dubbed
graphexeter, was created for realizing an all-graphene photodetector which
operates at around 6 $\mu$m.[3] The intriguing proximity effect of single
layers of FeCl3 between the graphene sheets is to p-dope the graphene sheets
to a Fermi energy of $E_{F}=-0.6$ eV due to the large work function of FeCl3
of $W_{{\rm FeCl}_{3}}=5.1$ eV and the resulting charge transfer between FeCl3
and graphene, which has a work function of around $W_{g}=4.6$ eV.[4, 5]
Remarkably, the bandstructures of graphene and FeCl3 remain completely
decoupled due to the incommensurate lattice structures, i.e. their lattice
constants are 2.46 Åand 6.06 Å, respectively.[6] According to Ref. 6, MLG-
FeCl3 has a gap of 1.2 eV, to which the Fermi energy can be tuned by n-doping,
corresponding to a wavelength of 1.03 $\mu$m, and is therefore transparent in
the NIR and SWIR regimes between $\lambda=1.3$ $\mu$m and 3 $\mu$m. The
refractive index of FeCl3 is $n=1.365$, which gives a dielectric constant of
$\varepsilon=n^{2}=1.86$. By creating a hexagonal nanopattern of holes inside
the multilayer graphene/FeCl3-intercalated heterostructure (NPMLG-FeCl3), we
show that it is possible to achieve LSP resonances in the NIR and SWIR regimes
between $\lambda=1.3$ $\mu$m to 3 $\mu$m with absorbances of nearly 100%. The
method to tune the spectrally selective absorbance in NPMLG by means of a gate
voltage $V_{g}$ is based on the fact that $V_{g}$ varies the Fermi energy
$E_{F}$ inside NPMLG, thereby varying the charge density and therefore
resonance wavelength of the LSPs around the circular holes in the wavelength
regime between 1.3 $\mu$m and 3 $\mu$m.

Figure 1: Schematic showing our proposed ultrafast NIR photodetector based on
suspended NPG intercalated with FeCl3 placed on top of a cavity, which can be
tuned by means of a gate voltage applied to the ITO layer. Here we show the
example using five graphene layers for MLG-FeCl3 for stage 1 intercalation.

Taking advantage of the special properties of FeCl3, we present the proof of
concept for a NIR photodetector based on NPMLG intercalated with FeCl3. Fig. 1
shows the schematic of our envisioned NPMLG-FeCl3 photodetector. When the
incident NIR or SWIR light field is maximized at the position of the NPMLG-
FeCl3 heterostructure by means of the Au mirror and also in resonance with the
LSPs around the holes of the NPMLG, the NIR or SWIR light gets strongly
absorbed with absorbance exceeding 95%, as shown in Fig. 2. Subsequently, the
LSPs decay by creating hot carriers inside the graphene sheets due to
boundary-assisted intraband Landau damping.[7] While it is possible to detect
the NIR or SWIR light by means of the bolometric effect relying on the change
in conductance through NPG, this method is relatively slow because the lattice
of NPG needs to be heated by means of the electron-phonon interaction before a
signal can be detected, which is typically of the order of 1 ms.[8] In order
to reduce the response time to about 100 ns, we choose to nanopattern only
about half of the area of each graphene sheet, as shown in Fig. 1. Due to the
asymmetric heating inside each partially nanopatterned graphene, a temperature
gradient is created, which leads to the diffusion of the hot carriers from the
nanopatterned side to the pristine side of the graphene sheet. This charge
motion yields a Seebeck voltage across the Au source-drain contacts, giving
rise to the plasmonically enhanced photothermoelectric effect inside each
partically nanopatterned graphene sheet. Due to the record-high temperature
difference $\Delta T=5$ K, our envisioned NPMLG-FeCl3 NIR and SWIR
photodetectors exhibit extraordinarily large responsivity of
$\mathcal{R}=6.15\times 10^{3}$ V/W and detectivity of $D^{*}=2.33\times
10^{9}$ Jones.

As mentioned above, due to limited resolution of e-beam lithography it is
currently impossible to realize LSP resonances in NPG in the NIR or SWIR. A
natural way to increase the plasmon frequency is to increase the charge
density of the material. In graphene this can be achieved by stacking several
graphene sheets on top of each other. While for small twist angles between
$\theta=0^{\circ}$ up to about $15^{\circ}$, twisted bilayer, trilayer, and
multilayer graphene exhibit interlayer coupling, resulting in e.g.
electrostatically tunable band gaps in bilayer graphene[9] at $\theta=0$ and
exotic many-body correlations, such as superconductivity, in twisted bilayer
graphene at magic angle $\theta=1.1^{\circ}$,[10] twist angles around
$\theta=30^{\circ}$ in twisted bilayer graphene suppress completely interlayer
coupling due to the mismatch of the k-space locations of the Dirac cones of
the two layers.[11] At first, such incommensurate stackings of graphene layers
might look like being ideal candidates for increasing the plasmon frequency of
the LSPs. However, the electrostatic doping of all the incommensurate graphene
layers is impossible due to screening and also due to electronic decoupling of
the layers.[12]

Figure 2: Absorbance $A(\lambda)$ of the NPMLG-FeCl3 heterostructure shown in
Figs. 1 with Fermi energy $E_{F}=-1.0$ eV, mobility $\mu=1500$ V/cm2s, hole
diameter of $a=40$ nm and period $\mathcal{P}=60$ nm at $T=300$ K. The results
are obtained by FDTD calculations. (a) For a single NPG sheet the LSP
resonance is at around 4.5 $\mu$m. At $N=5$, the LSP resonance is at $1.55$
$\mu$m. At $N=8$, the LSP resonance is at $1.30$ $\mu$m. (b) The LSP resonance
gets shorter and shorter with larger number $N$ of NPG layers. (c) The full
width at half maximum (FWHM) of the LSP resonance gets smaller and smaller for
larger $N$.

In the seminal paper by Withers et al.[3] the authors studied the
optoelectronic properties of graphene/FeCl3-intercalated few layer graphene,
which they called graphexeter. They demonstrated a photodetector based on the
photothermoelectric effect with a responsivitiy of $\mathcal{R}=0.1$ V/W at a
wavelength of around $\lambda=6$ $\mu$m. Interest in such intercalation doped
multilayer graphene heterostructures has been recently rekindled by the
realization of modulation doping of multilayer graphene by means of
$\alpha$-RuCl3.[13] Due to the large work function of $\alpha$-RuCl3,
$W_{\alpha-{\rm RuCl}_{3}}=6.1$ eV, substantial p-doping of all graphene
layers of around $E_{F}=-0.8$ eV can be achieved without electrostatic gating.
There are conflicting reports on the band gap of RuCl3. In Ref. 14 IR
reflectivity and transmission measurements reveal a band gap of 200 meV, which
agrees with the energies of spin-orbit excitons measured in Ref. 15. However,
photoemission and inverse photoemission spectroscopies find a much larger band
gap of 1.9 eV.[16]

Since RuCl3 has an optical band gap of the order of 200 meV,[14] it is
transparent only up to a wavelength of $\lambda=3$ $\mu$m. In contrast,
FeCl3-intercalated few layer graphene MLG-FeCl3 is transparent in the visible,
infrared, and THz regimes due to the large band gap of FeCl3.[17, 18] The
absorbance of MLG-FeCl3 is approximately $N\times 2.6$%, where $N$ is the
number of layers.[17] This is the reason why MLG-FeCl3 can be used as a
transparent electrode in the visible, infrared, and THz regimes. Taking
advantage of the LSP resonances in nanopatterned graphene, we can increase the
absorbance of NPMLG-FeCl3 in the NIR and SWIR regimes to nearly 100%, as shown
in Fig. 4. Therefore, we propose the novel heterostructure material NPMLG-
FeCl3 for creating a NIR and SWIR photodetectors based on the plasmonically
enhanced photothermoelectric effect, which is shown in Fig. 1. The MLG channel
length, which is the distance between the Au source and drain contacts, is
chosen to be $L=10$ $\mu$m, of the same order as the diffusion length of
charge carriers in graphene.[19] The MLG channel width is chosen to be $W=10$
$\mu$m as well because carrier collection does not need to be enhanced. The
optimized hexagonal nanopattern on about half of the MLG-FeCl3 heterostructure
(see Fig. 1) has a period of 60 nm and a hole diameter of 40 nm.

Figure 3: (a) Band structure of bulk FeCl3. (b) Band structure of MLG-FeCl3.
(c) Bloch states localized in FeCl3 in MLG-FeCl3 at M, K, and $\Gamma$ points.
(d) Bloch states localized in graphene in MLG-FeCl3 at M, K, and $\Gamma$
points.

For the subsequent finite-difference time domain (FDTD) calculations, we
perform first ab-initio density-functional theory (DFT) calculations to
determine the band structure of MLG-FeCl3. The generalized gradient
approximation (GGA) plus Hubbard-U parameter is used with the Perdew-Burke-
Ernzerhof (PBE) parametrization[20] of the correlation energy. The
calculations are implemented within the Synopsis Atomistix Toolkit (ATK)
2019.12.[21] As shown in Fig. 1, we consider MLG-FeCl3 with stage 1
intercalation, where single graphene layers are sandwiched by single FeCl3
layers. We consider AB stacking between adjacent graphene layers, similar to
pristine graphite, and ABC stacking between adjacent FeCl3 layers, similar to
pristine bulk FeCl3.[22] The translational shifts between graphene layers and
also between FeCl3 layers ensures complete decoupling of the electron states
between the graphene-graphene, graphene-FeCl3, and FeCl3-FeCl3 layers.
Following Ref. 23, we reduce the lattice mismatch by using a supercell with
2x2 periods of FeCl3 and 5x5 periods of graphene. The results of the DFT GGA+U
band structure calculation are shown in Fig. 3, which are similar to the
results obtained in Ref. 23. A choice of $U=6$ eV results in a FeCl3 band gap
of around 4.5 eV [see Fig. 3(a)], which agrees well with experiments.[17, 18]
The difference is that by incorporating a relative translational shift between
each pair of adjacent layers, we achieve complete decoupling between the
electron states of each layer. This is clearly visible for Bloch states
localized in FeCl3 in MLG-FeCl3 [see Fig. 3(c)] and Bloch states localized in
graphene in MLG-FeCl3 [see Fig. 3(d)]. The band structure of MLG-FeCl3 shown
in Fig. 3(b) shows clearly strong p-doping by shifting the Fermi energy to
$E_{F}=-1.0$ eV relative to the graphene Dirac point.

In order to perform the FDTD, we use the linear dispersion relation of
graphene, which gives rise to the intraband optical conductivity[1, 24]

$\sigma_{\rm
intra}(\omega)=\frac{e^{2}}{\pi\hbar^{2}}\frac{2k_{B}T}{\tau^{-1}-i\omega}\ln\left[2\cosh\left(\frac{\varepsilon_{F}}{2k_{B}T}\right)\right],$
(1)

which in the case of ${\varepsilon_{F}}\gg{k_{B}}T$ is reduced to

$\sigma_{\rm
intra}(\omega)=\frac{e^{2}}{\pi\hbar^{2}}\frac{E_{F}}{\tau^{-1}-i\omega}=\frac{2\varepsilon_{m}\omega_{p}^{2}}{\pi\hbar^{2}(\tau^{-1}-i\omega)},$
(2)

where $\tau$ is determined by impurity scattering and electron-phonon
interaction ${\tau^{-1}}=\tau_{imp}^{-1}+\tau_{e-ph}^{-1}$ . Using the
mobility $\mu$ of the NPG sheet, it can be presented in the form
$\tau^{-1}=ev_{F}^{2}/(\mu E_{F})$, where $v_{F}=10^{6}$ m/s is the Fermi
velocity in graphene. $\omega_{p}=\sqrt{e^{2}E_{F}/2\varepsilon_{m}}$ is the
bulk graphene plasma frequency. Since the graphene sheets are electronically
decoupled from each other by the insulating FeCl3 layers (see above
discussion), the optical conductivity of MLG-FeCl3 is given by

$\sigma_{\rm intra}^{\rm MLG-
FeCl_{3}}(\omega)=N\frac{e^{2}}{\pi\hbar^{2}}\frac{E_{F}}{\tau^{-1}-i\omega},$
(3)

where $N$ is the number of graphene layers. This formula is only valid for
excitation energies below the band gap $E_{g}=1$ eV of FeCl3. Since the LSP
resonances occur at energies between 250 meV and 950 meV, we can safely
neglect the optical phonons in graphene at 200 meV and the optical phonons in
FeCl3 at 2.7 meV, 7 meV

Figure 4: Absorbance as a function of Fermi energy $E_{F}$. (a) For NPMLG-
FeCl3 containing 5 layers of graphene the LSP resonance occurs at
$\lambda=1.55$ $\mu$m. (b) The LSP resonance of the 5-graphene layer structure
can be tuned from $\lambda=2.5$ $\mu$m to 1.55 $\mu$m by varying the Fermi
energy between $E_{F}=-0.5$ eV and -1.0 eV. (c) For NPMLG-FeCl3 containing 8
layers of graphene the LSP resonance occurs at $\lambda=1.30$ $\mu$m. (d) The
LSP resonance of the 8-graphene layer structure can be tuned from
$\lambda=2.0$ $\mu$m to 1.30 $\mu$m by varying the Fermi energy between
$E_{F}=-0.5$ eV and -1.0 eV.

We use FDTD to calculate the absorbance as a function of Fermi energy $E_{F}$
for NPMLG-FeCl3 containing $N=5$ and $N=8$ layers of graphene, as shown in
Fig. 4. The LSP resonances for the 5-graphene layer and 8-graphene layer
structures exhibit wide tunability as a function of the Fermi energy $E_{F}$.
Compared to our previous results on NPG, the absorbance remains above 80% even
for lower Fermi energies of $E_{F}=-0.5$ eV. This large absorbance gives rise
to strong heating of the nanopatterned side of the NPMLG structure.

Figure 5: COMSOL simulated temperature gradient and Seebeck voltage generated
by the plasmonically enhanced photothermoelectric effect in NPMLG-FeCl3
heterostructure containing $N=5$ graphene layers for the LSP resonance at
$\lambda=1.55$ $\mu$m. The channel length and width are both 10 $\mu$m. For an
IR light incident power of $P_{\rm inc}=120$ nW a temperature difference of
$\Delta T=5.09$ K (a,b) and a Seebeck voltage of $\Delta V=0.74$ mV (c,d) are
achieved.

Using COMSOL, we obtain the temperature distribution inside the NPMLG-FeCl3
heterostructure, as shown in Fig. 5. The photothermoelectric effect in the
NPMLG-FeCl3 heterostructure relies on large difference in absorbance between
the patterned and the unpatterned side, i.e. the patterned side exhibits a
plasmonically enhanced absorbance of nearly 100% while the unpatterned side
absorbs only about 2% of the incident IR light. This results in a temperature
gradient across the channel length $\Delta X=X_{L}-X_{R}$, where $X_{L}$ and
$X_{R}$ are the edge positions of the left and right Au contacts,
respectively. The hot carriers created on the patterned side due to Landau
damping diffuse to the unpatterned side, resulting in a charge separation and
Seebeck voltage

$V_{S}=\int\limits_{X_{L}}^{X_{R}}S(x)\frac{\partial T_{e}(x)}{\partial x}dx,$
(4)

where $S(x)$ is the Seebeck coefficient, which has two values $S_{\rm pat}$
and $S_{\rm unpat}$ on the patterned and unpatterned side, respectively.
$T_{e}(x)$ is the temperature profile of the charge carriers across the
channel length, as shown in Fig. 5 (b). The Seebeck coefficient is
approximated well by Mott’s formula

$S=\frac{\pi^{2}k_{B}^{2}T}{3e}\frac{\partial{\rm ln}\sigma}{\partial E_{F}},$
(5)

where $\sigma$, $k_{B}$, and $e$ are the electrical conductivity, Boltzmann
constant, and elementary charge, respectively. $\sigma$ and $S$ depend on the
$E_{F}$.

Starting from room temperature at $T=300$ K and an incident power of the IR
light of $P_{\rm inc}=120$ nW we obtain a temperature difference of $\Delta
T=5.09$ K and a Seebeck voltage of $V_{S}=0.74$ mV. The Fermi energy of the
graphene layers is kept at $E_{F}=-1.0$ eV, close to the intrinsic p-doping
level due to the intercalation with FeCl3. A bias voltage of $V_{b}=\pm 0.6$ V
is applied for measuring the photocurrents in both directions. Owing to the
bias voltage, both plasmonically enhanced photothermoelectric and bolometric
effects contribute. In order to remove the bolometric effect for the
measurements, the dark and light Seebeck voltages $V_{S,d}$ and $V_{S,l}$ are
calculated in the absence and presence of the incident IR light, respectively.
The Seebeck voltage is then calculated by $V_{S}=V_{S,d}-V_{S,l}$. For a
constant Fermi energy $E_{F}$, a DC bias voltages $+V_{b}$ and $-V_{b}$ are
applied for two separate simulations across the channel width, which yields
the currents $I_{>}=I+I_{S}$ and $I_{<}=-I+I_{S}$, respectively. $I$ is the
current driven by the bias voltage and $I_{S}=(I_{>}+I_{<})/2$ is the Seebeck
current, which is captured in the absence ($I_{S,d}$) and presence ($I_{S,l}$)
of the incident IR light. Since the holes are circularly symmetric, $I_{S}$ is
independent of the polarization of the IR light. The Seebeck current and
voltage are then calculated by $I_{S}=I_{S,l}-I_{S,d}$ and $V_{S}=RI_{S}$,
respectively, where $R$ is the resistance of the NPMLG-FeCl3 heterostructure.
For the incident IR light, we assume a Gaussian beam with spot size radius of
$R_{\rm spot}=2$ mm, a focus size radius of
$R_{f}=\sqrt{(x-x_{f})^{2}+(y-y_{f})^{2}}$, and an incident power of $P_{\rm
inc}=120$ nW. The heat flux through the edges of the holes in the nanopattern
is then

$q_{0}=\frac{2P_{\rm inc}}{\pi R_{\rm spot}^{2}}e^{-2R_{f}^{2}/R_{\rm
spot}^{2}}.$ (6)

For an absorbance $A$ obtained from FDTD, the absorbed heat flux is determined
by $q_{A}=Aq_{0}$.

Figure 6: A maximum responsivity of $\mathcal{R}=6.15\times 10^{3}$ V/W is
achieved at a Fermi energy of $E_{F}=-0.8$ eV for an incident power of $P_{\rm
inc}=120$ nW and a bias voltage of $V_{b}=0.6$ V.

The responsivity is obtained by

$\mathcal{R}=\frac{V_{S}}{P_{\rm inc}}.$ (7)

The responsivity as a function of Fermi energy $E_{F}$ is shown in Fig. 6.
$\mathcal{R}$ ranges from a minimum of about $2.49\times 10^{3}$ V/W for
$E_{F}=-0.5$ eV to a maximum of about $6.15\times 10^{3}$ V/W for $E_{F}=-0.8$
eV. Assuming a typical noise equivalent power of ${\rm NEP}=7$ pW/Hz1/2 for
CVD graphene,[25] we obtain a maximum detectivity of $D^{*}=\sqrt{LW}/{\rm
NEP}=0.74\times 10^{9}$ Jones. If we scale the channel width to $W=200$
$\mu$m, it is possible to achieve $D^{*}=2.33\times 10^{9}$ Jones.

##  I Conclusion

In conclusion, we have demonstrated in our theoretical study that NPMLG-FeCl3
can be used to develop a plasmonically enhanced NIR and SWIR photodetector
with spectrally tunable selective light absorption. Most importantly, the LSPs
along with an optical cavity increase the absorbance from about $N\times 2.6$%
for multilayer graphene-FeCl3 (without patterning) to nearly 100% for NPMLG-
FeCl3, where the strong absorbance occurs locally inside the graphene sheets
only, thereby outperforming state-of-the-art graphene-based photodetectors.
Remarkably, by taking advantage of NPMLG-FeCl3 with a number of graphene
layers $1\leq N\sim 8$ it is possible to develop photodetectors that operate
over a wide wavelength range from $\lambda=1.3$ $\mu$m down to $\lambda=12$
$\mu$m and beyond, covering the NIR, SWIR, MWIR, and LWIR regimes. In the
future it would be interesting to study LSPs in NPG also in the THz regime.
Our proposed IR photodetector can be used to develop an IR spectroscopy and
detection platform based on NPMLG that will be able to detect a variety of
molecules that have IR vibrational resonances, such as CO, CO2, NO, NO2, CH4,
TNT, H2O2, acetone, TATP, Sarin, VX, viruses, etc.

###### Acknowledgements.

We thank Dirk Englund for useful discussions.

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