IOP PUBLISHING
NANOTECHNOLOGY
Nanotechnology 20 (2009) 405704 (5pp)
doi:10.1088/0957-4484/20/40/405704
An electrical method for the measurement
of the thermal and electrical conductivity
of reduced graphene oxide nanostructures
Timo Schwamb, Brian R Burg, Niklas C Schirmer and
Dimos Poulikakos
Laboratory of Thermodynamics in Emerging Technologies, Institute of Energy Technology,
Department of Mechanical and Process Engineering, ETH Zurich, CH-8092 Zurich,
Switzerland
E-mail: dimos.poulikakos@ethz.ch
Received 25 June 2009, in final form 28 July 2009
Published 8 September 2009
Online at stacks.iop.org/Nano/20/405704
Abstract
This paper introduces an electrical four-point measurement method enabling thermal and
electrical conductivity measurements of nanoscale materials. The method was applied to
determine the thermal and electrical conductivity of reduced graphene oxide flakes. The
dielectrophoretically deposited samples exhibited thermal conductivities in the range of
0.14–2.87 W m−1 K−1 and electrical conductivities in the range of
6.2 × 102 –6.2 × 103 −1 m−1 . The measured properties of each flake were found to be
dependent on the duration of the thermal reduction and are in this sense controllable.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
2. Method description and experimental procedure
The emergence of engineered graphene and graphene oxide
(GOx) structures into nanotechnology research has sparked
related research activities worldwide [1–3]. A wide field
of possible application areas has been suggested so far,
e.g. membrane materials for fuel cells [4], transparent
electrodes [5], solar cells [6], transistors [3, 7], molecular
sensors [8] and composite materials [9]. Essential for the
development of applications and devices based on graphene
and GOx is an accurate knowledge of their material properties.
To date, results have been presented for the electrical properties
of graphene and GOx [1, 3, 5, 7, 10–12] and the thermal
properties of graphene films [13, 14]. A lack of knowledge
exists on the thermal properties of GOx films.
In this work, measurements of the electrical conductivity
σ and thermal conductivity κ of suspended, thermally reduced
graphene oxide (RGOx) flakes, deposited by dielectrophoresis
(DEP) are presented. The electrical measurements were
performed in the four-contact configuration, which enables the
determination of the intrinsic electrical sample resistance R .
The employed method to measure the thermal conductivity
differs from the electrical 1ω-/3ω-methods [15–18] and is
described in the following.
2.1. Measurement method
0957-4484/09/405704+05$30.00
The measurement method is a five-step process based on the
assumptions of diffusive heat transport in the sample and Joule
heating causing electrical resistance variations.
(1) In the first step, the electrical current limit causing no
detectable Joule heating, I0 , was determined by measuring
the intrinsic electrical resistance R as a function of the
electrical current I . This limit is identified by the intrinsic
electrical resistance R obeying R(I I0 ) = R0 =
constant. During the measurements the temperature inside
the vacuum chamber was kept at T = 20 ◦ C.
(2) In the second step, the sample was heated externally (not
electrically) by placing it in a temperature controlled oven,
to predefined temperatures. The temperature gradient of
the electrical resistance R was determined by applying
a current I0 to the sample to avoid Joule heating as
mentioned above. The equation for R reads
R = R(T =20 ◦ C) − R0 /T(=20 ◦ C) − T20 ◦ C I . (1)
0
In this equation, T(=20 ◦ C) represents the temperature
measurement points and R(T =20 ◦ C) the corresponding
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© 2009 IOP Publishing Ltd Printed in the UK
Nanotechnology 20 (2009) 405704
T Schwamb et al
Figure 1. Image (a) depicts a RGOx flake deposited across the electrode gap without touching the SiN substrate. The corresponding
schematic diagram of the electrical configuration is displayed in inset (c). In (b) the RGOx flake bridges four parallel electrodes touching the
substrate beneath it, which is schematically shown in inset (d).
measurement. Further, the temperature dependent Joule
heating term, Ts (x)R , was not taken into account in
equation (3). Neglecting this term was justified by
calculating the temperature rise of the heat conduction
equation with and without the temperature dependent
Joule heating term. The comparison of both solutions
resulted in an insignificant difference of ∼1% between the
two calculated temperature rises in the sample.
(5) In the final step, the thermal conductivity of the sample
was determined by substituting the measured temperature
(from step three) for the maximum temperature Ts (x =
0.5 L) = Ts,max in the parabolic temperature solution of
the heat conduction equation. This maximum temperature
substitution was performed supported by the fact that the
maximum temperature Ts,max corresponds to the measured
resistance of the sample, which was also supported by the
results of the platinum reference measurements.
measured electrical resistance. Since in this step the
sample was heated by the surrounding atmosphere and not
by Joule heating, it is crucial that the sample temperature
is in thermal equilibrium with the controlled temperature
of the surrounding atmosphere. This was achieved
by maintaining a long heating time and temperature
monitoring by a platinum (Pt) 100 resistance temperature
detector (RTD) unit, which was placed directly next to the
microchip. In order to assure a linear R(T ) relationship,
the variation of the chamber temperature was restricted to
only 5–10 K.
(3) The known power input by Joule heating was linked to the
unknown temperature rise in the sample by measurements
which were performed solely by Joule heating of the
sample by an electrical current chosen to be greater than
I0 . The atmosphere around the sample was kept at
constant temperature. The subsequent rise of the sample
temperature T was calculated by
T = [(R(I = I0 ) − R0 )/R ]Tatmosphere=const. .
2.2. Experimental procedure
(2)
In order to perform measurements with RGOx flakes, GOx
flakes were deposited onto MEMS (microelectro-mechanical
systems) structures on a silicon-based microchip. This was
achieved with a recently reported DEP technique [19, 20].
The used GOx flakes were prepared by a modified Hummers
method combining a long acid oxidation step with subsequent
thorough purification for highly exfoliated and pure GOx
dispersions [22]. The employed microchip design, described
in detail in [21], features four metal electrodes manufactured in
pairs with an insulating silicon nitride (SiN) layer in between
(figures 1(a) and (c)), or aligned in-plane (figures 1(b) and (d)).
The four-point contacted GOx flakes (figures 1(a) and (b)) were
reduced in a rapid thermal annealing device (J.I.P. Elec JetFirst
100) at 450 ◦ C in a N2 environment. The time of thermal
treatment τ was varied between 5 and 60 min reducing the
amount of oxygenated groups bound to the GOx flake [24].
(4) The one-dimensional heat conduction equation
−κ
d2 Ts (x)
I2R
,
=
dx 2
SL
(3)
was solved for the unknown temperature of the sample
Ts (x) with constant temperature boundary conditions. The
variable x points in the direction of the sample length
L connecting the electrodes. The right-hand side of the
heat conduction equation accounts for Joule heating and
S represents the cross section of the sample. For the
solution of the heat conduction equation it was assumed
that the thermal conductivity is not a function of the
temperature. This is a valid assumption for the small
temperature rise caused by the heating and the chosen
region (above the room temperature) for the temperature
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Nanotechnology 20 (2009) 405704
T Schwamb et al
Figure 2. Measurement results of the platinum microwire and the
RGOx flakes over the electrical current. The filled circles show the
reference measurements with the Pt microwire (left). The results of
the RGOx samples are represented by hollow circles for sample 1
(left), hollow triangles for sample 2 (right) and hollow squares for
sample 3 (right), respectively.
Figure 3. Measurement results of the platinum microwire and the
RGOx flakes over the temperature of the surrounding atmosphere.
The filled circles show the reference measurements with a Pt
microwire (left). The measurement results of the RGOx samples are
represented by hollow circles for sample 1 (left), hollow triangles for
sample 2 (right) and hollow squares for sample 3 (right),
respectively. The temperature coefficient of the electrical resistance
R was determined by a linear interpolation between the data points
for each sample.
All measurements were performed in vacuum
(<0.03 mbar) and in thermal equilibrium. A chip carrier holding the microchip itself and the Pt 100 RTD was placed inside
a two-part chip mount, equipped with two integrated heating
units including thermocouples. The heating units were used
to control the temperature in the vacuum chamber around the
microchip. The temperature of the microchip itself was monitored by the Pt 100 RTD. This RTD was placed directly next
to the microchip with the sample, allowing the sample temperature to be monitored accurately during the measurements.
Additionally, the mount served as a radiation shield and provided the electrical contacts to the measurement devices. The
measurement samples were connected to an electrical current
source (Keithley 6221), a lock-in amplifier (Stanford Research
System SR850) and a data acquisition unit. In order to perform
the measurements, an electrical current was passed through the
sample and, at the same time, a reference signal was fed to
the lock-in amplifier. The voltage drop across the sample was
measured by the lock-in amplifier. The data acquisition and the
temperature control were controlled and processed in a LabView environment.
measured at I > I0 and was compared to the analytical
solution of the 1d heat conduction equation, in order to validate
κ against literature values. The accuracy of the proposed
thermal conductivity measurement method depends on several
factors, namely, the accuracy of the electrical measurement,
the choice of the boundary conditions for the calculation of
the energy equation solution, the availability of information
about the sample geometry, heat loss caused by radiation,
and, for non-suspended samples, convection losses. For the
platinum wire a thermal conductivity of 66–67 W m−1 K−1
was measured. This yields an accuracy of ∼10 %, when
taking a heat loss of 6–7% due to radiation into account. The
impact of all possible error sources on the preciseness of the
GOx property measurements is discussed within the following
section.
Figures 2 and 3 also present the measurement results
for the RGOx flakes indicated by hollow circles (sample 1,
left graphs), hollow triangles (sample 2, right graphs) and
hollow squares (sample 3, right graphs). Figure 2 indicates
that detectable Joule heating occurred at an electrical input
current greater than 100 nA for samples 2 and 3 and greater
than 1 μA for sample 1, respectively. Figure 3 reports the
RGOx resistance as a function of the surrounding atmosphere
temperature. In order to elucidate the thermal and electrical
conductivities of the RGOx flakes, the data plotted in figures 2
and 3 were processed by the above explained method. I –V
curves of samples 1, 2 and 3 are displayed in figure 4. The
curves are plotted over the entire measurement range in which
the thermal conductivity measurements were carried out. The
first-order linearity of the I –V curves proves that the RGOx
flakes exhibited no apparent non-linearities in the measurement
range. Consequently, material effects can be excluded to be
at the origin of the second-order deviations of the electrical
sample resistance shown in figure 2. This exclusion allows
the attribution of the second-order deviations to Joule heating,
confirming the basic assumption of the herein presented model.
3. Results and discussion
A platinum microwire (diameter: 13 μm, length: 3.69 mm,
purity: 99.9%) served as the reference material for the applied
measurement method. This microwire was electrically fourpoint contacted to platinum electrodes resulting in a suspended
measurement section. The results of the Pt wire are illustrated
in figures 2 and 3 as filled circles. In the manner described
above, I0 was identified to be <1 mA from the data presented
in figure 2. Above 1 mA, the electrical resistance of the wire
increased due to Joule heating. The R0 value corresponding
to I0 was found to be 2.636 . Displaying the electrical
resistance as a function of the temperature of the surrounding
atmosphere (figure 3, left graph), R was calculated by linear
interpolation between the data points (filled circles). The
temperature rise in the sample caused by Joule heating was
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Nanotechnology 20 (2009) 405704
T Schwamb et al
Figure 4. Current–voltage plots of the RGOx samples. The curves
are by first order linear in the entire thermal conductivity
measurement range.
Figure 5. Atomic force microscope images of a deposited RGOx
flake. The scan allows the determination of the specimen height.
The RGOx samples 1 and 4 were not suspended. The
samples 2 and 3 were deposited suspended (not touching the
substrate underneath). As investigated by Burg et al [19],
the RGOx flakes deposited by the DEP method mentioned
above consist of a few layers with a total thickness of 5 nm,
i.e. approx. four layers [23]. For the present study an
additional height analysis of the deposited RGOx samples
was conducted in an atomic force microscope (AFM). The
results of the height analysis are depicted in figure 5. The
two upper images were both taken by the same scan over a
multi-layered chip, such as presented in figure 1(a), in the area
around the deposited sample. The upper left image visualizes
the deposited sample bridging the electrode gap by displaying
a broad z -axis range between 0 and −250 nm. Focusing
on the electrode surface by a narrower z -axis range (upper
right image), the surface roughness of the electrodes can be
measured. An average surface roughness of 3–5 nm was
estimated from the height curve recorded on the electrode
surface. The height curve is shown in the lower image of
figure 5. The RGOx flake touching the electrodes at the
scanned position cannot be distinguished in the height diagram
from the surface roughness. Consequently, the height of the
specimen was in the same range as the surface roughness.
The length of the samples was defined by the electrode
gap. The gap width varied between 0.5 and 3 μm.
The RGOx flakes exhibited an electrical conductivity σ0 at
T = 20 ◦ C in the range of 6.2 × 102 –6.2 × 103 −1 m−1 , which
is in good agreement with reported electrical conductivities of
reduced GOx [5, 7, 10, 26].
Analysing the data in table 1, sample 1 exhibited an
electrical conductivity which is an order of magnitude higher
than that of samples 2 and 3. This is explained by the longer
thermal treatment of sample 1 [11, 24]. As a result of the
thermal treatment and based on the results of Yang et al
[24], the atomic ratio of carbon to oxygen increases from
GOx to RGOx by a factor greater than 2. Nevertheless, the
electrical conductivities associated with pristine graphene films
are several orders of magnitude higher [10, 12].
Table 1. Measured electrical and thermal properties of RGOx. It
was observed that a longer thermal treatment time τ induces higher
electrical and thermal conductivities (σ0 , κ ).
Sample
1
2
3
4
κ (W mK−1 )
2.87
0.87
0.14
—
σ0 (−1 m−1 )
6.22 × 10
6.21 × 102
6.57 × 102
∼1.95 × 103
3
τ (min)
Rc (k)
60
5
5
20
120
2
130
300
In order to estimate the influence of Joule heating
at the contacts on the thermal conductivity measurements,
the electrical contact resistances Rc were determined by
subtracting the measured four-point electrical resistance from
the measured two-point electrical resistance of the graphene
oxide flakes, Rc = (R2pt − R4pt )/2 [25]. Table 1 summarizes
the results. The lowest electrical contact resistance of 2 k was
found to belong to sample 2. The Rc values of samples 1 and 3
were 120–130 k. Sample 4 showed the highest Rc of 300 k.
The results revealed no relation between Rc and the time of
thermal treatment. The I –V curves shown in figure 4 are linear
by first order, indicating the absence of Schottky barriers in
the contacts. Due to the significantly larger thermal mass, the
higher thermal conductivity of the electrodes compared to the
samples and the absence of Schottky barriers, the influence of
Joule heating in the electrical contacts was neglected. Thus,
for the boundary conditions of the heat conduction equation the
electrodes were modelled as infinite heat sinks, as mentioned
earlier.
The thermal conductivity of sample 1 was the highest with
κ = 2.87 W m−1 K−1 . Since sample 1 was not suspended, heat
loss to the substrate has to be taken into account. An estimate
according to [27] resulted in an uncertainty of 0.85 W m−1 K−1
due to heat loss to the substrate. This large uncertainty
underpins the need for suspended samples. The samples 2
and 3 did not have heat losses from heat conduction to the
substrate. These samples were not in contact with the substrate
due to their suspended deposition. They yielded values in
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Nanotechnology 20 (2009) 405704
T Schwamb et al
the range κ = 0.14–0.87 W m−1 K−1 (table 1). The thermal
conductivity of sample 4 could not be measured. It showed an
unstable behaviour which is possibly explained by low quality
contacts between the electrodes and the RGOx.
Comparing the results presented herein to the thermal
conductivity of pristine graphene, the still oxidized nature of
the RGOx flakes, even after thermal reduction, is revealed. The
oxidized chemical structure introduces lattice defects which
hinder the thermal transport and promote diffusion effects.
Hence, pristine graphene has a markedly higher thermal
conductivity by a factor of 103 –104 [13, 14].
As discussed in [11, 23] and [28], RGOx and GOx can
be described as a quasi-2d amorphous carbon with sp3 -similar,
distorted C–C bonds. Thus, the thermal properties of other
amorphous carbon materials serve as a benchmark for the
results reported herein. Indeed, a study by Shamsa et al
[29] reports that thermal conductivity values of diamond-like
carbon films mainly constituted by sp3 C–C bonds are in a
comparable range to the RGOx flakes of the present study.
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4. Conclusions
Concluding, a method which enables thermal and electrical
conductivity measurements of diffusive nanoscale materials
was presented and applied to the study of graphene oxide
structures deposited dielectrophoretically between electrodes.
The feasibility and expected accuracy of the method was
pursued and tested against a platinum microwire reference
sample. The thermal and electrical properties of few-layered,
reduced graphene oxide were found to be related to their level
of oxidation.
Acknowledgments
The experimental support of Julian Schneider, the technical
support of Jovo Vidic, the support of the EMEZ and FIRST
laboratory platforms of ETH, and the financial support of the
ETH Research Commission are greatly acknowledged.
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