Two-probe study of hot carriers in reduced graphene oxide
Brian A. Ruzicka1, Nardeep Kumar1, Shuai Wang2, Kian Ping Loh2, and Hui Zhao1, a)
1Department of Physics and Astronomy, The University of Kansas, Lawrence, Kansas 66045,
2Department of Chemistry, National University of Singapore, 3 Science Drive 3,
The energy relaxation of carriers in reduced graphene oxide thin films is studied using optical pump-probe
spectroscopy with two probes of different colors. We measure the time difference between peaks of the carrier
density at each probing energy by measuring a time-resolved differential transmission and find that the carrier
density at the lower probing energy peaks later than that at the higher probing energy. Also, we find that
the peak time for the lower probing energy shifts from about 92 to 37 fs after the higher probing energy peak
as the carrier density is increased from 1.5 × 1012to 3 × 1013/cm2, while no noticeable shift is observed in
that for the higher probing energy. Assuming the carriers rapidly thermalize after excitation, this indicates
that the optical phonon emission time decreases from about 50 to about 20 fs and the energy relaxation rate
increases from 4 to 10 meV/fs. The observed density dependence is inconsistent with the phonon bottleneck
Graphene, a single layer of carbon atoms, is a
very attractive material for many applications in-
resonators,4, ultracapacitors,5and composite materials.6
Charge carriers play a central role in most of these ap-
plications.In particular, it has been shown that the
mean-free path of carriers in graphene is several hundred
nanometers even at room temperature.1,7Hence, even in
micrometer-sized devices, carriers injected with a high
kinetic energy only undergo few or even no phonon scat-
tering events during the transport through the device,
maintaining a temperature much higher than the lattice
temperature. Since the device is dominated by the hot
carriers, it is important to understand and control the
dynamics of hot carriers in graphene.
Over the past two years, significant progress has been
made on using ultrafast laser techniques to study hot car-
riers in graphene.8–19Most studies so far have focused on
measuring the energy relaxation of the carriers by fitting
the decay of a differential transmission signal. This tool
can be very valuable as it can give much insight into
the time scales and mechanisms behind the relaxation
of carriers, but it also has its limitations. First, the de-
cay time is often comparable to the temporal width of
the probe pulse. Second, a slow decay component re-
lated to carrier recombination is often seen, making the
decay multiple exponential. Both of these factors limit
the accuracy of such measurements in determining the
energy relaxation time of excited carriers. Furthermore,
previous studies have mainly been limited to graphene
samples fabricated by thermal reduction of silicon car-
bide substrates,8–16mechanically exfoliated graphene on
Si/SiO2 substrates17and graphene thin films grown by
chemical vapor deposition.14While studies of reduced
graphene oxide are relatively rare,16,18,19it can be ar-
gued that reduced graphene oxide may be one of the most
promising type of graphene for use in industry, as it can
a)Electronic mail: firstname.lastname@example.org
scheme (right panel).
Experimental setup (left panel) and pump/probe
be produced at low cost20and is favorable for large-scale
production of graphene-based electronics.21
Here we report a study of hot carriers in reduced
graphene oxide thin films using ultrafast optical pump-
probe spectroscopy with two probes of different colors.
First, carriers are injected by a pump pulse. By precisely
overlapping the two probes in time, and measuring the
time between which the differential transmission signals
peak with each probe, we are able to monitor the den-
sity of carriers at two different energies for various times
after excitation. From these measurements, we observe
that the peak carrier density at the lower energy probe
occurs about 92 fs later than the higher energy probe,
and this decreases to about 37 fs, as the carrier density
is increased from 1.5 × 1012to 3 × 1013/cm2. Under the
assumption that the carrier thermalization is much faster
than the time scales of the study, we can deduce energy
relaxation rates on the order of several meV/fs, and opti-
cal phonon emission times on the order of several tens of
fs. Furthermore, the observed increase in energy relax-
ation rate with increasing carrier density is in opposition
to what one would expect from a phonon bottleneck ef-
The reduced graphene oxide samples are fabricated by
spin coating graphene oxide flakes on quartz substrates.
The formed films are then transformed to graphene
films by thermal reduction at 1000◦C.21The number of
graphene layers is determined to be about 50 by using an
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FIG. 2. Cross correlation measurement of the 1714- and 857-
nm probe pulses using sum-frequency generation in a 
atomic force microscope. The absorption of the samples
at 800 nm is measured to be about 50%.
Figure 1 summarizes the experimental setup (left
panel) and pump/probe scheme (right panel).
ers are first excited with an 800-nm, 100-fs pump pulse,
which is focused to a size of approximately 2.3 µm at full
width at half maximum (FWHM). The pump pulse is ob-
tained from a Ti:sapphire laser (Ti:Sa) with a repetition
rate of about 80 MHz. To detect the carriers, we use
one of two different probe pulses of central wavelengths
1714 and 857 nm, respectively. The 1714-nm probe is
produced from the idler output of an optical parametric
oscillator (OPO), which is pumped by the Ti:Sa, and the
857-nm probe is obtained from second-harmonic gener-
ation of the 1714-nm probe using a beta barium borate
(BBO) crystal. The pulse width of each is 80 fs and 150
fs, respectively, and both are focused to a spot size of
approximately 1.5 µm (FWHM). The differential trans-
mission of the probe pulse, ∆T/T0≡ [T(n)−T0]/T0, i.e.
the normalized difference in transmission with [T(n)] and
without (T0) carriers, is measured by modulating the in-
tensity of the pump pulse with a mechanical chopper with
a frequency of about 2 kHz and using a lock-in amplifier.
For our experiment, it is crucial to precisely control the
time of each probe pulse so that the two probes arrive at
the sample at the same time. To do that, we use sum-
frequency generation in a GaAs sample grown along 
direction, which is mounted directly next to the graphene
sample. The squares in Fig. 2 show the intensity of the
sum-frequency signal with a central wavelength of 571
nm as a function of the time delay between the two probe
pulses. From a Gaussian fit to the data (solid line), we de-
termine the FWHM of this cross-correlation is about 180
fs. By repeatedly obtaining the maximum sum-frequency
generation, we conclude that we are able to consistently
overlap the two probe pulses in time with an error smaller
than 5 fs.
We measure the differential transmission with each
FIG. 3. The differential transmission for both the 857-nm
(squares) and the 1714-nm (circles) probes with an average
areal carrier density of 2.3×1013/cm2. A slight displacement
between the two peaks can be seen. The inset shows another
scan around the peaks, and from this we are able to determine
that the differential transmission measured with the 1714-nm
probe peaks approximately 47 fs later than the 857-nm probe.
probe as a function of time by changing the delay be-
tween the probe and pump pulses with an average areal
carrier density of 2.3×1013/cm2, as shown in Fig. 3. The
0-ps probe delay is defined arbitrarily here, as we are only
interested in the difference in time between the peaks of
the two curves. In fact, the 0-ps probe delay is expected
to be very close to the peak of the 857-nm probe since
the photon energies of the pump and the 857-nm probe
are close. The inset of Fig. 3 shows another scan around
the peaks. The peak of the differential transmission with
the 1714-nm probe occurs approximately 47 fs after the
peak of the 857-nm probe.
One of the difficulties in studies of hot carrier dynamics
in graphene is that the dynamics are often too short to
resolve. When the decay time of the signal is comparable
to the temporal width of the pulses used, the result can
be severely influenced by the convolution of the pulses. In
our two-color scheme, however, we can accurately deter-
mine the time delay between the two peaks even though
it is shorter than the pulses: The convolution of the finite
probe pulse with the actual signal only shifts the time of
the peak of both probes; the relative time delay between
the two peak is not changed. Therefore, it is sufficient to
consider only the convoluted pump-probe measurements
when determining the relative position of the two peaks.
In order to investigate the dependence of the relative
peak times on the carrier density, we repeat the mea-
surement with various carrier densities by changing the
energy fluence of the pump pulse. The results are sum-
marized in the left panel of Fig. 4. We see a systematical
change of the peak time of the 1714-nm probe with the
carrier density, while the peak time of the 857-nm probe
remains unchanged. At a density of 1.5 × 1012/cm2, the
FIG. 4. Left panel: The normalized differential transmission
measured with the 857-nm (squares) and the 1714-nm (cir-
cles) probes with average areal carrier densities of (from top
to bottom) 1.5, 2.9, 11.7, 17.6, and 30 × 1012/cm2, respec-
tively. Right panel: Deduced energy relaxation rate (right
axis) and optical phonon emission time (left axis) of hot car-
1714-nm probe peak occurs about 92 fs later than the
857-nm probe peak. When the density is increased to
3 × 1013/cm2, the 1714-nm peak shifts earlier, occurring
about 37 fs after the 857-nm peak.
It has been shown by previous ultrafast pump-
density carriers in graphene is extremely fast due to
the enhanced carrier-carrier scattering rate by the
unique linear energy dispersion.
shown that the carrier-carrier scattering time can be as
short as 10 fs.25Therefore, it is reasonable to assume
that the carriers injected by the pump pulse rapidly
reach a Fermi-Dirac distribution, with a temperature
determined by the pump photon energy.
present the following possible interpretation of the data:
Due to state filling effects, the differential transmission
of each probe pulse is proportional to the density of
carriers at each probing energy. So, when the differential
transmission (and therefore the density of carriers seen
by the probe) peaks for the 857-nm (1714-nm) probe,
the average energy of the carriers is approximately equal
to the central probing energy of 0.72 eV (0.36 eV), which
is half of the probe photon energy (right panel of Fig. 1).
The difference in the peak times gives the time it takes
for the average carrier energy to decrease by 0.36 eV
(from 0.72 to 0.36 eV). The dynamics of the holes in the
valence band is equally probed, and is expected to be the
same as the dynamics of the electrons in the conduction
band since the two bands have the same dispersion.
For example, we see from the measurement in Fig. 3
that the energy relaxation of 0.36 eV takes 47 fs. This
corresponds to an energy relaxation rate of about 8
meV/fs. We can extend this analysis even further, since
Recent studies have
it is known that the dominant energy relaxation channel
is the emission of G-mode optical phonons with an energy
0.195 eV.26Therefore, under the previous assumptions,
we deduce that at this carrier density, the optical phonon
emission time is 47 × (0.195/0.36) = 25 fs.
We can also perform this analysis on our study of the
power dependence of the relative peak times. These re-
sults are summarized in the right panel of Fig. 4. At a
density of 1.5 × 1012/cm2, the optical phonon emission
time is about 50 fs, corresponding to an energy relaxation
rate of about 4 meV/fs. When the density is increased
to 3 × 1013/cm2, the optical phonon emission time de-
creases to about 20 fs, corresponding to an energy relax-
ation rate of about 10 meV/fs. We note that the values
of the optical phonon emission time as well as the den-
sity dependence determined in this way are reasonably
consistent with recently theoretical calculations.27,28
To examine the validity of such an analysis, we con-
sider three different situations after excitation. The first
is the one we have just discussed – after excitation, the
electrons rapidly thermalize, then cool on a much slower
time scale. In this case we are able to obtain our con-
clusions about the optical phonon emission time and en-
ergy relaxation rate. The next situation is one in which
the thermalization is slow, and the energy relaxation is
even slower, so that during the duration of the differ-
ential transmission signals, we are observing only the
thermalization process. This situation can immediately
be eliminated as a possibility, due to the fact that we
are probing at energies below our excitation energy, and
therefore both probes will see the carrier density con-
tinually increase as the carriers equilibrate to attain a
Fermi-Dirac distribution. We verified this by simulation
using the Boltzmann equation, starting with a gaussian
distribution of carriers and ending with a Fermi-Dirac
distribution. The last situation is one in which both ther-
malization and energy relaxation occur at comparable
rates, i.e. both occur during the duration of the differ-
ential transmission signals. In this case, we are not able
to determine the average energy of the carriers when the
density of carriers at each probe reaches its peak value.
However, since we would not see any change in the rel-
ative peak times of the carrier density at each probing
energy without energy relaxation, we are still obtaining
some measure of the energy relaxation. So, while this sit-
uation may cause the magnitude of the deduced optical
phonon emission times to change, we expect the overall
behavior of the optical phonon emission time with carrier
density to remain the same.
Finally, it is interesting to note that our experimen-
tal results are in opposition to the phonon bottleneck
effect. Recently, a phonon bottleneck effect on the en-
ergy relaxation of hot carriers in graphene samples fab-
ricated by thermal reduction of silicon carbide has been
proposed.14,15In these studies, the decay time of the dif-
ferential transmission, on the order of 1 ps, was found to
increase with the carrier density. Under the assumption
that the carrier recombination time is much longer than
the measured decay time, the decay time was attributed
to the energy relaxation time. The increase of the energy
relaxation time with the carrier density was attributed
to the effect of a nonequilibrium distribution of optical
phonons emitted by the hot carriers. However, more re-
cent experiments indicated that the carrier recombina-
tion time can be as short as sub-ps.22–24Our experimen-
tal results are in opposition to the phonon bottleneck ef-
fect and can be well explained by the density-dependent
optical phonon emission time. Furthermore, the energy
relaxation times we measured by the two-probe technique
are significantly shorter than those deduced from these
studies. However, it is possible that the phonon dynam-
ics in the reduced graphene oxides are different from the
graphene samples fabricated from silicon carbide. Our
results suggest the more studies are needed on this inter-
We have studied photoexcited carriers in reduced
graphene oxide samples using a two-color probe tech-
nique. By overlapping the two probes in time, and mea-
suring the time at which the differential transmission sig-
nal peaks for each probe, we are able to directly measure
the time at which the carrier density peaks at the two
probing energies. Under the assumption that the carri-
ers rapidly thermalize after excitation, this can be inter-
preted as an average carrier energy decrease from 0.72
to 0.36 eV in approximately 47 fs with a carrier den-
sity of 2.3 × 1013/cm2. This corresponds to an energy
relaxation rate of about 8 meV/fs. Since the energy re-
laxation of carriers is mainly caused by the emission of
195 meV G-mode optical phonons, we deduce an optical
phonon emission time of about 25 fs. Furthermore, we
found that the optical phonon emission time decreases
from about 50 to about 20 fs, and the energy relaxation
rate increases from 4 to 10 meV/fs, as the carrier den-
sity is increased from 1.5 × 1012to 3 × 1013/cm2. The
observed density dependence in our graphene samples is
inconsistent with the phonon bottleneck effect that was
observed in graphene samples fabricated on silicon car-
We thank Wang-Kong Tse for useful discussions on
optical phonon scattering in graphene. We acknowledge
support from the US National Science Foundation un-
der Awards No. DMR-0954486 and No. EPS-0903806,
and matching support from the State of Kansas through
Kansas Technology Enterprise Corporation. We thank
the support of NRF-CRP ”Graphene Related Materials
and Devices” (Grant No. R-143-000-360-281). Acknowl-
edgment is also made to the Donors of the American
Chemical Society Petroleum Research Fund for support
of this research.
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