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Complex Optical Conductivity of Graphene Measured by
Ultra-broadband THz Time-domain Spectroscopic Ellipsometry
Sho Ikeda1,2, Masatsugu Yamashita1, and Chiko Otani1,2
RIKEN Center for Advanced Photonics, 519-1399 Aoba, Aramaki, Aoba, Sendai, 980-0845, Japan
Grad. Sch. of Sci. Tohoku Univ., 6-3 Aoba, Aramaki, Aoba, Sendai, 980-0845, Japan
Abstract—Carrier dynamics in a single-layered graphene has
been studied by reflection-type THz time-domain spectroscopic
ellipsometric parameter ρ=rp/rs by measuring the p- and
s-polarized THz waveforms after the reflection form sample. We
successfully obtained the frequency-dependent complex sheet
conductivity of monolayer graphene from 0.3 to 20 THz. By fitting
with Drude model, the sheet resistance, sheet carrier density and
mobility of graphene were estimated. THz-TDSE can be a novel
tool for the non-contact and non-destructive characterization of
the carrier transport property in graphene samples.
ECENT progress of ultra-broadband THz time domain
spectroscopy (THz-TDS) has enabled to extend the phase
sensitive spectroscopic technology from THz to
mid-infrared (MIR) region [1,2], which is a powerful tool for
the study of the carrier dynamics and the determination of the
dielectric function. Monolayer graphene is a gapless
two-dimensional material with linear electron and hole bands.
The charge carriers in this system behave like massless Dirac
fermions and have high Fermi velocity and mobility. Because
of such unique properties, graphene has many possibilities of
application for electronic or optoelectronic devices. In order to
realize such high performance devices [3,4], non-contact and
non-destructive characterization method for carrier transport
property of graphene is necessary. Here, we report the direct
measurement of the frequency dependent optical conductivity
of a monolayer graphene by a reflection type ultra-broadband
THz time-domain spectroscopic ellipsometry (THz-TDSE)
utilizing GaP and GaSe crystals as THz emitters [1].
THz or MIR pulses reflected from the sample transmit the
free-standing WP(B) with the computer-controlled rotation
stage. The system detector is a low-temperature grown GaAs
(LT-GaAs) epitaxial
switch (ELT-PCS). The ELT-PCS detector has a LT-GaAs
epitaxial layer with a thickness of 2 μm which is bonded to a Si
substrate using epoxy-based adhesive. The transmission
angle of WP(C), which is fabricated on a high-density
polyethylene (HDPE) film, is set at a 45° angle against the
p- and s-polarized waves balancing the sensitivity of the
ELT-PCS between the p- and s-polarized THz or MIR
pulses. The extinction ratios of WP(A) and WP(B) are below 1
×10-4 in the 1.2–30 THz range, and the extinction ratio of
WP(C) is below 1×10-2 in the 0.3–30 THz range.
Figure 1 shows a schematic of the ultra-broadband
THz-TDSE system. We used a 200-μm thick GaP (110) crystal
and a 100-μm thick z-cut GaSe crystal as the THz and MIR
emitters, respectively. These emitters are excited by
femtosecond laser pulses (300 mW average power, 800-nm
center wave-length, 75-MHz repetition rate) with a 10-fs pulse
duration obtained by compensating the group velocity
dispersion(GVD) with negative GVD mirrors. The emitters
can be switched without requiring additional optical alignment
by moving the computer-controlled emitter stage. The
generated THz or MIR pulses transmit the ultra-broadband
free-standing wire-grid polarizer (WP) (A) fixing the
polarization angle at 45°and illuminate the sample at a
60° incident angle. To reduce the uncertainty of the incidence
angle due to the opening angle of the incident waves, the THz
or MIR pulses are loosely focused by a 2-in. off-axis parabolic
mirror (M 2) with a 6-in. focal length. The p- or s-polarized
FIG. 1. Schematic diagram of the ultra-broadband THz-TDSE. The
systemutilizes GaP and GaSe crystals for generating the THz and MIR
pulses,respectively, and an ELT-PCS detector. The measurable frequency
range can be switched between 0.5–7.8 THz and 7.8–30 THz by moving
the computer-controlled emitter stage.
A sample measured is a mono-layer polycrystalline graphene
on a polyethylene terephthalate (PET) substrate. The sheet
resistance is 800 Ω/sq. Figure 2(a) and (b) show the temporal
waveforms of the p- and s-polarized THz and MIR pulses after
the reflection off the graphene layer, respectively, and the
obtained ellipsometric parameter ρ (=rp/rs) are shown in Fig.
2(c). By using the thin film approximation, the complex
reflection coefficient of graphene for p- and s-polarized
electromagnetic pulses are given by the following formula
(CGS units) using optical conductivity of graphene[5].
⎜σ − c ⎜ ε 2 −
4π cos θ
ε 1 − ε 2 sin 2 θ
rp =
⎜σ + c ⎜ ε 2 −
4π cos θ
ε 1 − ε 2 sin 2 θ
⎜σ +
rs = −
⎜σ +
determination of the carrier transport property of graphene
samples on various substrates.
⎟ ⎟⎟
⎟ ⎟⎟
− ε 2 sin 2 θ − cos θ ε 2 ⎟
− ε 2 sin 2 θ + cos θ ε 2 ⎟
where, σ is the in-plain complex optical conductivity of
graphene, ε1 is the dielectric constant of PET substrate, ε2 is the
dielectric constant of air, and θ is the incident angle of THz and
MIR pulses. By using the eq.(1), the complex sheet
conductivity of graphene are obtained from the ellipsometric
parameter ρ=rp/rs as shown in Fig. 2(d). We performed the
fitting of the optical complex conductivity with the Drude
model for charge carriers in graphene.
σ (ω ) = 2
π= (Γ − iω )
where Γ is the average scattering rate for momentum changing
collisions of charge carriers, and EF is Fermi energy. By fitting
the data with the eq. (2), EF and Γ are determined as 0.35 eV
and 27 THz, respectively. The estimated sheet resistance is 740
Ω/sq. The sheet carrier density N and carrier mobility μ are
obtained as 7.48×1012 /cm2 and 1279 cm2/Vs, respectively.
The transmission measurements of thin film samples suffer
from the acquisition of the accurate phase information due to
the error of the substrate thickness. The THz-TDSE enables the
phase-sensitive reflection measurement and is useful to the
Fig. 2 The p- and s-polarized temporal waveforms of (a) THz and (b) MIR
pulses after the reflection off the graphene sample. (c) The ellipsometric
parameter ρ=rp/rs and (d) The complex optical conductivity σ(ω) of the
graphene obtained from ρ and the eq. (1).
We have successfully measure the frequency-dependent of
a single layer graphene by using ultra-broadband THz-TDSE.
Since graphene shows the Drude-like sheet conductivity, we
could estimate the sheet carrier density and carrier mobility by
analysis. The THz-TDSE enables the phase-sensitive reflection
measurement and can be applied to determine the carrier
transport property of graphene samples on various substrates
with no-contact and no-destructive.
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