Study of transport properties in graphene monolayer
flakes on SiO[sub 2] substrates
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Tirado, J. M., D. Nezich, X. Zhao, J. W. Chung, J. Kong, and T.
Palacios. “Study of Transport Properties in Graphene Monolayer
Flakes on SiO[sub 2] Substrates.” J. Vac. Sci. Technol. B 28, no.
6 (2010): C6D11.
As Published
http://dx.doi.org/10.1116/1.3516649
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American Institute of Physics/American Vacuum Society
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Study of transport properties in graphene monolayer flakes on SiO 2 substrates
J. M. Tirado, D. Nezich, X. Zhao, J. W. Chung, J. Kong, and T. Palacios
Citation: Journal of Vacuum Science & Technology B 28, C6D11 (2010); doi: 10.1116/1.3516649
View online: http://dx.doi.org/10.1116/1.3516649
View Table of Contents: http://scitation.aip.org/content/avs/journal/jvstb/28/6?ver=pdfcov
Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Study of transport properties in graphene monolayer flakes
on SiO2 substrates
J. M. Tiradoa兲
EII, University of Castilla La Mancha, 45071 Toledo, Spain
D. Nezich, X. Zhao, J. W. Chung, J. Kong, and T. Palacios
Department of Electrical Engineering and Computer Science and Microsystems Technology Laboratories,
Massachusetts Institute of Technology, 77 Massachusetts Ave., Massachusetts 02139
共Received 8 July 2010; accepted 18 October 2010; published 12 November 2010兲
This work studies the transport properties of field effect transistors fabricated on graphene single
monolayer flakes. In particular, carrier mobilities in graphene for electrons and holes as a function
of the vertical electric field are presented and compared with universal mobility curves in silicon.
The graphene device shows excellent transport properties, especially at low electric fields due to the
lack of Coulomb scattering. At higher electric fields, the phonon scattering dominates and makes the
electron mobility similar to the one in silicon. The effect of defects and traps by charged impurities
in the transport properties has also been studied, and it has been shown that an initial high
temperature annealing significantly improves the transport properties and stability of these
devices. © 2010 American Vacuum Society. 关DOI: 10.1116/1.3516649兴
I. INTRODUCTION
Materials based on carbon nanostructures are quickly becoming a feasible alternative to silicon technology in future
high speed electronics. Graphene, a single monolayer of
sp2-bonded carbon atoms, turns out to be an ideal candidate
for this application due to its excellent high mobility and
Fermi velocity. In spite of these very promising properties,1
the development of graphene devices is still in a very preliminary stage and there are many unknowns about the reproducibility and transport properties of these devices.2 Extrinsic scattering sources, many of which arise from the
surface morphology, chemistry, structural, and electronic
properties of the widely used SiO2 substrate, limit the mobility of graphene devices by as much as several orders of magnitude with respect to theoretical calculations.3 Great effort is
currently underway to increase the mobility beyond extrinsic
limits.
For example, the extrinsic mobility reported in graphene
devices varies widely across the literature. Mobility values
between 3000 and 40 000 cm2 V−1 s−1 have been
reported.1,4–7 In addition, the gate voltage required for minimum conduction in this ambipolar material is not centered at
0 V as is typical in other ambipolar semiconductors, but it is
shifted toward positive gate voltages.4,8 The origin of this
shift is still under study, although impurity density7 and
chemical doping4 are proposed to explain this phenomenon.
In this work, the transport properties of a field effect transistor fabricated on a graphene flake have been studied. In
particular, carrier mobilities in graphene for electrons and
holes as a function of the vertical electric field are presented
and compared with the universal mobility curves in silicon.
The effect of temperature on the electrical response of the
device and its influence on the mobility curves for electrons
a兲
Electronic mail: josemaria.tirado@uclm.es
C6D11 J. Vac. Sci. Technol. B 28„6…, Nov/Dec 2010
and holes have also been analyzed to understand the origin
of the shift in the gate voltage required for minimum conduction.
II. METHOD OF ANALYSIS AND DISCUSSION
p-type silicon wafers 共100兲 with a boron doping concentration of NA = 1015 cm−3 have been thermally oxidized to a
SiO2 thickness of tox = 300 nm. Then, graphene has been deposited onto the silicon dioxide by microcleaving according
to Reina et al.9 and visually inspected to identify a suitable
monolayer graphene flake. Optical lithography was used to
define the contact pads and a titanium 共50 nm兲/chrome 共5
nm兲 bilayer was used as the contact metal. The typical dimensions of the graphene flakes used in this work are 615
nm in length and 1450 nm in width.
The current-voltage 共I-V兲 characteristics of this device
were measured with an Agilent 4155A semiconductor parameter analyzer. In these measurements, the source-drain bias
was set to a very low value of 0.1 V to prevent device selfheating, while a back-gate step voltage was applied to the
conductive Si substrate with a bias sweep ranging from ⫺40
to 40 V and back again in steps of 0.5 V. No significant
hysteresis was found in the device. The same experiment was
repeated again with a negative source-drain voltage of ⫺0.1
V; similar results were found in both cases showing a clear
bidirectional behavior of the device. All the measurements
were performed under vacuum 共chamber pressure below 5
⫻ 10−6 Torr兲 to avoid the oxidation of the graphene layer.
The device temperature was varied from 300 to 425 K
through the use of a thermal chuck.
Figure 1 shows the drain current of the device as a function of the back-gate voltage at different chuck temperatures.
Initially, the starting temperature is 300 K, then the temperature is increased in steps of 25 K until it reaches a maximum
value of 425 K. Finally, the temperature is decreased again in
1071-1023/2010/28„6…/C6D11/4/$30.00
©2010 American Vacuum Society C6D11
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C6D12
Tirado et al.: Study of transport properties in graphene monolayer flakes
C6D12
FIG. 2. Effect of a temperature annealing cycle in the position of the minimum conductivity valley in Fig. 1. The cycle initially starts at a temperature
of 300 K. Then, the temperature is increased until it reaches 425 K, in steps
of 25 K, and then the temperature is decreased again to finally achieve
325 K.
FIG. 1. 共Color online兲 Drain current of a back-gated graphene field effect
transistor. The back-gate voltage is swept from VGS = −40 to 40 V in steps of
0.5 V. Drain-source voltage is set to 0.1 V to minimize self-heating. The
curves when the temperature is increased from 300 to 425 K are plotted in
solid lines, while dashed lines show the behavior of the device when the
temperature is decreased from 425 to 325 K.
steps of 25 K. The ambipolar nature of the graphene is
clearly revealed in Fig. 1. For negative gate voltages, the
conduction is mainly due to holes, and the current decreases
as the voltage becomes more positive. For a positive enough
gate voltage, the current reaches a minimum, where the conduction due to electrons and holes is equally important. For
even more positive voltages, the electron current dominates
as the Fermi level moves deeper into the conduction band.
Finally, for high enough gate voltages, the current decreases
again. The origin of this decrease in the conduction is still
under study but may be due to the effect of traps by charged
impurities in the graphene layer being the dominant scattering mechanism or carrier injection in low electron velocity
valleys of the band diagram.
Figure 1 also shows a shift in the gate bias required for
minimum conduction toward positive voltages. Some authors
attribute this behavior to unintentional chemical doping, impurity densities, or trapping by absorbed gas molecules or
defects during processing and handling of the sample.4,6,7 In
addition, the possible existence of zigzag edges in graphene
ribbons could lead to localized edge states at the Fermi
level.8 Other authors proposed that the band diagram of
graphene is better represented by a conduction model with an
overlap between conductance and valence bands,6 where a
mixed state of both electrons and holes would be present. To
clarify the main mechanism behind this shift in the minimum
current, in this article, we have studied the position of this
minimum as a function of temperature.
Figure 2 shows the gate voltage required to get minimum
current in the graphene device as a function of device temperature. Initially, at 300 K, the valley of minimum current is
located at a gate bias voltage near 29 V. As the temperature
increases, the minimum current valley shifts toward lower
voltages. This effect is more pronounced for temperatures
above 350 K. At a temperature of 425 K, the maximum
temperature allowed by our measurement setup, the valley
has shifted to 13.6 V. When the sample temperature is reduced, the voltage finally stabilizes at 8 V. For repeated temperature cycles, the voltage minimum remains constant at
8 V. This behavior supports the theory of unintentional acceptorlike doping of the graphene layer by adsorbed gas
molecules by explaining 72% of the shift. At high enough
temperatures 共i.e., 350 ° C兲, the gas molecules 共possibly hydrogen or oxygen兲 are desorbed and the conductivity of the
graphene layer becomes more intrinsic. The origin of the
remaining shift in the gate bias required for minimum conductivity could be due to undesorbed gas molecules or an
overlap between conduction and valence bands. Further experiments at higher temperatures are needed to understand
this phenomenon. Absorption/desorption of gas molecules
changes the local carrier concentration, which leads to
changes in resistance and conductivity.
Carrier mobilities in this device have been calculated as a
function of temperature using the following relation:
␮=
1
L
I
W QG共VG兲 VD
共cm2 V−1 s−1兲,
共1兲
where W and L are the width and length of the graphene
flake, respectively, and VD is the applied drain bias. QG共VG兲
is the accumulated charge in the graphene layer induced by
the voltage directly applied to the graphene layer 共VG兲,
QG共VG兲 = CG共VG兲 · VG ,
共2兲
where CG is the quantum capacitance of graphene; this
value has been extracted from Fang et al.10 CG共VG兲 = 25
⫻ 10−6 · 兩VG兩 共F cm−2兲. Using these expressions in Eq. 共1兲,
we obtain
␮=
1
L
I
.
−6
2
W 25 ⫻ 10 · 共VG兲 VD
共3兲
To determine the relation between the back-gated voltage
共VBG兲 and graphene voltage 共VG兲, we set the stored charge in
J. Vac. Sci. Technol. B, Vol. 28, No. 6, Nov/Dec 2010
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C6D13
Tirado et al.: Study of transport properties in graphene monolayer flakes
C6D13
FIG. 3. 共Color online兲 Electron universal mobility curves for graphene and
silicon.
FIG. 4. 共Color online兲 Hole universal mobility curves for graphene and
silicon.
the graphene quantum capacitance 共CG兲 equal to that in the
silicon dioxide capacitance 共Cox兲 as they are both connected
in series,
function of transversal electric field. In this figure, the electron mobility in graphene is also compared with the universal
mobility curve of electrons in silicon.11 Graphene shows
electron mobilities much higher than silicon at low electric
fields. For example, the mobility reaches values close to
6600 cm2 / V s for electric fields of 50 000 kV/cm. These
high mobilities are probably due to the reduced effect of
Coulomb scattering in graphene when compared with
silicon.12
However, at higher electric fields, phonon scattering significantly reduces the electron mobility, making it very similar to the mobility in Si devices. The important effect of the
transversal electric field in the carrier mobility emphasizes
the need of knowing the transversal electric field when
studying graphene mobilities. The change in mobility with
temperature has also been measured. As expected in a semimetal, the mobility increases when temperature increases
共not shown in the figure兲.
Hole mobility curves versus electric field are shown in
Fig. 4 for both the graphene flake reported in this article and
for silicon transistors as reported by Liang et al.13 The hole
mobility behaves in a very similar fashion to the electron
mobility: very high values at low electric fields due to the
lack of Coulomb scattering and a decrease at high electric
fields due to the effect of phonon scattering. A hole mobility
in excess of 6700 cm2 / V s is calculated in graphene at low
electric fields. As in the case of electrons, the hole mobility
increases when temperature increases.
共4兲
Cox · Vox = CG · VG .
In this expression, given an oxide thickness of 300 nm, Cox is
equal to
Cox =
␧ox 3.45 ⫻ 10−13
=
= 11.5 ⫻ 10−9 F cm−2
300 ⫻ 10−7
tox
共5兲
and
共6兲
Vox = VBG − VG .
By substituting Eqs. 共5兲 and 共6兲 in Eq. 共4兲 and using the
expression of the quantum capacitance, we can solve for the
voltage applied to the graphene layer, VG, as follows:
VG ⬵ ⫾ 21.4 ⫻ 10−3冑VBG ,
共7兲
where VBG is the applied back-gate voltage assuming that
VBG = 0 V happens at the point of minimum conductivity.
The mobility at each value of the gate voltage can be expressed as
␮=
1
L
I
.
−6
−3
2
W 25 ⫻ 10 共⫾21.447 ⫻ 10 冑VBG兲 VD
共8兲
To plot the universal mobility curves, an expression for the
transversal electric field in the graphene flake is needed. This
relation is obtained from the following expression:
QG = CG · VG = EG · ␧r,G · ␧0 ,
共9兲
where the value of relative permittivity for graphene is ␧r,G
= 2.4.4 Finally, using again the expression for the quantum
capacitance in graphene and substituting it in the expression
关Eq. 共9兲兴, we have
EG =
2
25VG
2
= 1.18 ⫻ 108 · VG
2.13 ⫻ 10−7
共V/cm兲.
共10兲
Figure 3 shows the electron mobility in graphene as a
III. CONCLUSIONS
In conclusion, in this article, we have studied the transport
properties of a field effect transistor based on a monolayer
graphene flake. Universal carrier mobilities for electrons and
holes have been extracted and compared with universal mobility curves for silicon. At low electric fields, the graphene
mobilities are much higher than in silicon due in part to the
lack of Coulomb scattering. At high electric fields, the effect
of phonon scattering significantly reduces the mobilities.
JVST B - Microelectronics and Nanometer Structures
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C6D14
Tirado et al.: Study of transport properties in graphene monolayer flakes
Temperature annealing effects have also been studied, revealing a clear influence on the transport properties of the
material, shifting the valley of minimum conductivity to gate
voltages closer to 0 V. The effect of temperature on the carrier mobilities has also been investigated, concluding that
mobilities are not very dependent on temperature, although a
light improvement with temperature has been observed.
ACKNOWLEDGMENTS
This work has been partially supported by Consejeria de
Educacion y Ciencia de la Junta de Comunidades de
Castilla-La Mancha and the European Social Fund. The MIT
team acknowledges the support of the Microsystems Technology Laboratories.
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