Broadband electromagnetic response and ultrafast dynamics
of few-layer epitaxial graphene
H. Choi,1 F. Borondics,2 D. A. Siegel,1, 3 S. Y. Zhou,1, 3 M. C. Martin,2 A. Lanzara,1, 3 and R. A. Kaindl1
1Materials Sciences Division, E. O. Lawrence Berkeley National Laboratory, Berkeley, CA 94720
2Advanced Light Source, E. O. Lawrence Berkeley National Laboratory, Berkeley, CA 94720
3Department of Physics, University of California, Berkeley, CA 94720
We study the broadband optical conductivity and ultrafast carrier dynamics of epitaxial graphene
in the few-layer limit. Equilibrium spectra of nominally buer, monolayer, and multilayer graphene
exhibit signicant terahertz and near-infrared absorption, consistent with a model of intra- and
interband transitions in a dense Dirac electron plasma. Non-equilibrium terahertz transmission
changes after photoexcitation are shown to be dominated by excess hole carriers, with a 1.2-ps
mono-exponential decay that re
ects the minority-carrier recombination time.
PACS numbers: 78.30.-j, 78.47.J-, 81.05.Uw
The discovery of graphene { a carbon monolayer and
building block of graphite, fullerenes, and nanotubes {
provides unique opportunities to explore the properties
of two-dimensional Dirac fermions [1]. The electromag-
netic properties and ultrafast carrier dynamics, in par-
ticular, are important for applications of this new ma-
terial [2, 3, 4]. In exfoliated graphene, the infrared re-
sponse is characterized by a universal quantum conduc-
tivity Q = e2=2h, arising from interband transitions
whose onset energy follows the carrier density [5, 6, 7, 8].
A promising route towards large-scale device production
is epitaxial growth of graphene layers on SiC substrates
[9]. The optical response of epitaxial graphene is, how-
ever, much less explored. Recently, rst equilibrium
and time-resolved infrared and terahertz (THz) measure-
ments were reported on epitaxial graphene with a large
number (N = 6{37) of layers [10, 11, 12, 13]. In this
letter, we present a broadband infrared and ultrafast
THz study of few-layer epitaxial graphene. Systematic
thickness variation covers nominally buer, monolayer,
and multilayer graphene lms. We utilize equilibrium in-
frared spectroscopy to characterize the broadband con-
ductivity and transient THz measurements to monitor
the photoexcited carrier dynamics. This yields momen-
tum and population relaxation times, and provides in-
sight into graphene's unusual electrodynamics.
The samples studied here were grown via thermal de-
composition on the Si-terminated face of semi-insulating
6H-SiC(0001) wafers [14]. The lm thickness and mor-
phology was characterized in situ via low-energy electron
microscopy (LEEM), showing nanoribbon-like monolayer
terraces with widths of ' 60 to 250 nm. Angle-resolved
photoemission spectroscopy (ARPES) and scanning tun-
neling microscopy (STM) evidenced a single-crystalline
character of such domains interspersed with some defects
[15, 16].
Measurements of the equilibrium broadband infrared
response from 20{2500 meV were carried out with
Fourier-Transform Infrared (FTIR) spectroscopy, using a
Bruker IFS 66v spectrometer with four dierent source-
detector combinations. This was complemented with
time-domain THz spectroscopy in the low-energy (3{10
meV) range [17]. The small absorption of the atomically-
thin layers necessitates optimal suppression of systematic
errors. We used rectangular SiC wafers (5:5  12 mm),
with graphene growth limited to a central, 4-mm di-
ameter area via the heater and LEEM cap geometry.
The sample was then spatially modulated below a 2-
mm aperture in the spectrometer (inset, Fig. 1), alter-
nating between graphene (transmission T ) and the bare
substrate (T0). Systematic errors were thus reduced to
about 1% and 2% for FTIR and THz spectra, respec-
tively. Figure 1 shows the resulting relative transmission
spectra T (!)=T0(!) at room temperature, for nominally
buer, monolayer, and multilayer graphene. A strong,
systematic transmission decrease with increasing thick-
ness is apparent, and all spectra show near-IR absorption
above ' 4000 cm1. Moreover, monolayer and multilayer
graphene
SiC
THz/IR
FIG. 1: (Color online) Relative transmission of nominally
buer, monolayer, and multilayer graphene (top to bottom),
measured by FTIR (solid lines) and time-domain THz spec-
troscopy (dots). Dotted lines: guide to the eye. Undula-
tions in the THz data below 100 cm1 arise from laser drift.
Hatched: Reststrahlen region of SiC. Inset: sample modula-
tion scheme.
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2graphene feature far-IR absorption below ' 500 cm1,
with considerable strength given the atomic-scale thick-
ness.
More insight is obtained from the optical sheet conduc-
tivity (!). It relates to the thin-lm transmission via
T (!)=T0(!) = j1 + Z0(!)=(nS + 1)j2, where Z0 is the
vacuum impedance and nS ' 2.5{3.1 the SiC refractive
index [11, 18]. The in
uence of the imaginary part of con-
ductivity is negligible for the given parameters. Thus, we
can directly obtain the real part 1(!) from the above ex-
pression, taking into account a frequency-dependent nS
[19]. Figure 2 shows the resulting sheet conductivity,
normalized by Q. The buer layer response is insu-
lating (Fig. 2a), as expected from a lack of Fermi-level
electronic bands [9], with some absorption around 1 eV.
Figures 2(b) and 2(c) show the mono- and multilayer re-
sponse after subtracting the buer layer. It exhibits sig-
nicant broadband conductivity, with a strong frequency
dependence in multilayer graphene.
For further analysis, we calculate 1(!) for an n-doped
graphene layer, which at temperature T reads
1(!)
Q
=
8kBT
h
ln

e
EeF
2kBT + e
EeF
2kBT

1
!2 + 1=
(1)
+
1
2

tanh

h! + 2EeF
4kBT

+ tanh

h! 2EeF
4kBT

;
where  is the momentum scattering time and EeF the
electron Fermi energy [3, 20]. The rst term is the Drude-
like intraband conductivity, while the second arises from
interband transitions above ' 2EeF . For high doping i.e.
EeF  2kBT , the conductivity reduces to
1(!)
Q
'
4EeF
h
1
!2 + 1=
+

1 + e
2EFh!
2kBT
1
: (2)
Here, EeF ' hv(N)
1=2, where N is the electron density
and v ' 106 m/s is the Dirac fermion velocity. Thus,
unlike ordinary conductors, the Drude spectral weight is
a nonlinear function of N .
The above model, scaled by the number of layers nL,
is shown as solid lines in Figs. 2(b) and 2(c). It provides
for a faithful representation of the measured sheet con-
ductivity, with nL = 1:5, EeF = 0:45 eV, and  = 2 fs
for the nominally monolayer sample, and nL = 4:5,
EeF = 0:22 eV,  = 9:5 fs for multilayer graphene. This
model comparison shows a consistent scaling of the in-
traband spectral weight with the high-frequency, inter-
band response set by nLQ. The Fermi energy re
ects
the large substrate-induced doping of few-layer graphene,
corresponding to N = 0:4{1:5  1013 cm2, which com-
pares well to ARPES and STM studies [15, 16]. We also
calculated the conductivity with a model that includes
the gap 2
seen in ARPES [11, 15]. It is shown by the
dashed lines in Figs. 2(b) and 2(c), with 2
=250 meV
and 50 meV respectively. Clearly, at these doping levels
(a)
(b)
(c)
0 ML
1 ML
(d)
(e)
(f)
0 ML
1 ML
2 ML
1 ML
2 ML
3 ML
4 ML
FIG. 2: (Color online) Real part of the optical sheet con-
ductivity (gray), normalized by Q: (a) buer layer, (b-c)
monolayer and multilayer graphene, with the buer conduc-
tivity subtracted. Solid and dashed lines: model as explained
in the text. (d)-(f) 2:5 2:5 m2 LEEM images of nominally
buer, monolayer, and multilayer graphene.
the eect of the gap on 1(!) is negligible. Figures 2(d)-
(f) show LEEM images of all three samples, which un-
derscore their nanoscale inhomogeneity [15]. Analysis of
these images yields an average thickness of, respectively,
0.25, 1.1, and 3.3 ML. This agrees reasonably with the
ts to the infrared spectra, when considering the lim-
ited LEEM eld of view. The short scattering times
from the model correspond to a mean-free path vf = 2{
10 nm, well below the ' 100 nm graphene terrace size but
consistent with scattering from impurities and inherent
nanoscale ripples in graphene [16].
We now turn to the non-equilibrium THz dynam-
ics measured via optical-pump THz-probe spectroscopy.
The graphene layers are excited at room tempera-
ture with 1.53 eV femtosecond pulses from a 250-kHz
Ti:sapphire regenerative amplier and probed with ps
THz pulses detected via electro-optic sampling [17]. Fig-
ure 3(a) shows a typical electric eld trace E0(t) trans-
mitted through the unexcited sample, and the pump-
induced change
E(t) measured at a xed pump-probe
delay
t. The sign and negligible phase shift of
E(t)
indicate a transmission decrease, i.e. added THz con-
ductivity. Also,
E(t) decays in amplitude with increas-
ing
t but retains its shape (not shown), allowing us
to determine the overall eld change at a xed time-
point (arrow, Fig. 3a). The relative transmission change
is
T=T0 = 2
E=E0 + (
E=E0)2, which is plotted in
Fig. 3(b). The signals peak within the time resolution
after excitation, followed by a mono-exponential decay
within the measurable range.
The maximum incident
uence of 0:9 J/cm2 corre-
sponds to photoexcited electron and hole densities n0 =

3p
E
k
( )N+nE
e
F
(a)
(c)
(d)
monolayer
(b)
multilayer
FIG. 3: (Color online) Non-equilibrium THz response. (a)
Reference eld E0 (gray) and pump-induced change
E
(black) at
t = 0:4 ps. (b) Transmission changes (symbols)
at 0.9 J/cm2 pump
uence. Lines: model of Eq. 3, for elec-
tron (dashed) and hole contributions (dotted) at Tc = 300 K,
and the sum (solid lines) with time-dependent Tc. Inset: non-
equilibrium state. (c),(d) pump
uence dependence of ampli-
tude
T and recombination time R for mono- (squares) and
multilayer (circles).
p0 = 4:6  1010cm2layer1; given the graphene inter-
band absorption 2Z0Q=(nS + 1) ' 1:3%. After exci-
tation, the excess carriers thermalize with the existing
plasma on a fs timescale, forming a hot Fermi distribu-
tion with a temperature increased by
T above the lat-
tice temperature TL. We can estimate
T from energy
conservation, Ue(TL; N) +
Q = Ue(TL +
T;N + n) +
Uh(TL +
T; p), where Ue;h is the electron or hole gas in-
ternal energy and
Q is the absorbed pulse energy. For
Dirac fermions Ue;h = 4k3BT
3=(v2h2)F2(E
e;h
F =kBT ),
where F2 is the second-order Fermi integral. For the high-
est
uence, this yields
T = 86 K for the monolayer and
201 K for the multilayer sample. These are upper limits,
as part of the energy is shed by phonon emission. The
dense electron gas thus represents a heat bath, and the
THz response can re
ect changes of both majority and
minority carriers (inset, Fig. 3b). This scenario is dier-
ent from THz studies of thick multilayer graphene, dom-
inated by photoexcited carriers in undoped layers [13].
For quantitative comparison, we calculate the non-
equilibrium conductivity change

1(!)
Q
'

2v
p
N
n+
4kBTc
h
ln(1 + e
EhF (p)
kBT )

1
!2 + 1=
;
(3)
for weak excitation n  N and transient carrier tem-
perature Tc  EeF =2kB . This model is shown as lines
in Fig. 3(b), assuming exponential decay n = p =
p0 exp(t=R) with R =1.3 ps and 1.2 ps for mono- and
multilayer graphene. Equation 3 includes two parts: (i)
the conductivity of photoexcited electrons, which follows
from Eq. 2 with a non-equilibrium electron Fermi energy
EeF +
E
e
F . For weak excitation,
E
e
F ' (n=2N)E
e
F
which renders the electron contribution linear in n. How-
ever, the electron response { shown as dashed lines in Fig.
3(b) { is about an order of magnitude too small, and thus
fails to explain the observed signals. (ii) The conductiv-
ity of photoexcited holes forms the second term in Eq. 3,
which we derive from the full intraband expression using
a hole distribution conned to the valence band [11, 21].
It exhibits a generally non-linear dependence on the hole
Fermi energy EhF (p) and, likewise, on the hole density
p(EhF ; Tc) =
2k2BT
2
c
v2h2
Li2(e
EhF =kBTc); (4)
where Li2 is the dilogarithm. The non-equilibrium hole
response [dotted lines, Fig. 3(b)] by far supersedes the
electron contribution and yields a close description of the
THz transmission change. This stark dierence between
electron and hole conductivity, evident in our highly-
doped layers, re
ects graphene's unusual sensitivity of
the Drude spectral weight on the carrier distribution [13].
Three more aspects should be noted. First, the above
evaluation assumed Tc = TL. In contrast, the solid
lines in Fig. 3(b) show the sum of electron and hole
signals with a time-dependent carrier temperature Tc =
TL +
T exp(t=c), with a cooling time c = 1:4 ps as
per Ref. 12. Clearly, the in
uence of cooling on the sig-
nals is minor. Second, stimulated THz emission due to
interband transitions at the Dirac point has been pre-
dicted for photoexcited gapless graphene [2]. The lack
of this eect in our signals re
ects the presence of the
electronic gap. Finally, as shown by the intensity de-
pendence in Fig. 3(c), the response is nearly linear in p.
This is conrmed by the model, see e.g. Fig. 3(b) where
the hole response follows the electron curve. The linear
hole response arises at suciently small densities where
EhF (p) < kTc, corresponding to p < 4
10
10cm2 at
300 K. In this limit, p ' 2k2BT
2
c exp(E
h
F =kBTc)=(v
2h2)
which renders the hole contribution in Eq. 3 proportional
to (2v2h=kBTc) p.
The transmission changes in Fig. 3(b) thus repre-
sent the population dynamics of excess holes. Since
few-layer epitaxial graphene is highly n-doped, electron-
hole recombination is dominated by the interaction of
the pump-induced minority carriers (holes) with the
paramount electron plasma. This explains both the
mono-exponential kinetics of the transient THz signals
and the largely excitation-independent eective recombi-
nation time R ' 1:2 ps in Fig. 3(d). This value of R
is consistent (within a factor of ' 3) with calculations of
Auger and phonon-mediated recombination [4].
In summary, we studied the broadband equilibrium
conductivity of few-layer epitaxial graphene { consis-

4tent with intra- and interband transitions of a dense
Dirac electron plasma { and measured the ultrafast
minority-carrier recombination time via non-equilibrium
THz transmission changes. Despite a balance of electron
and hole excitations, the non-equilibrium THz response
in these highly n-doped layers is shown to be dominated
by holes, a conrmation of graphene's unusual electrody-
namics.
This work was supported by the DOE Oce of Basic
Energy Sciences, Contract DE-AC02-05CH11231. F. B.
acknowledges a scholarship of the Rosztoczy Foundation.
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