Working Title: Hysteretic Response of CVD Graphene on SiO2/SiC Substrates
Author Info:
Abstract:
Introduction:
The unique properties of single layer graphene, such as its high electrical conductivity, large
carrier mobility and ambipolar behavior make it a prime material of study for electrical device
applications1–3. The ambipolarity of response of graphene is manifested by maximum resistivity at a
given external electric field, known as the Dirac point4. Near the Dirac point, the resistance of graphene
is especially sensitive to local changes in electric field, enabling the development of graphene fieldeffect transistors (GFETs) with operational characteristics that are dependent on this unique ambipolar
response5,6.
Hysteretic effects have been widely observed in current-voltage (Isd-Vsg) transconductance
measurements of GFETs, causing the shape of the transconductance curve and the voltage of the Dirac
point to be dependent on direction, speed, and range with which gate voltage sweeps are performed 7–11.
The origin of this hysteresis has been shown to be caused by electrochemical doping of the substrate
material on which graphene is deposited12. The introduction of electrochemical p-type doping may
occur through device fabrication or after exposure to environment containing H2O and O2, or NO213–15.
Electrochemical doping involves electron transfer to or from graphene via a redox reaction:
O2 + 2H2O + 4e- (graphene) = 4OH-. The direction of the reaction is determined by the relative height
of Fermi energy levels of the graphene and the redox solution, the former being controlled by gate bias
and the latter by the density of redox states13,15.
Systematic studies have explored the hysteresis occurring in GFETs on Si/SiO2 substrates7–
by varying the Isd-Vsg sweep parameters. The time evolution of graphene resistance in the
presence of electrochemical species on SiO213,14,17,18, Si/SiO219, and in aqueous solution20 has also been
studied. While previous studies have already examined the hysteresis effect of CVD graphene on
Si/SiO221–23 and ferroelectric lead-zirconate-titanate (PZT)24 substrates, this Letter provides the first
insight into the hysteretic nature of GFETs fabricated by chemical vapor deposition (CVD) of graphene
on SiC/SiO2 substrates. This insight is developed by the use of a time-dependent characterization of
GFET. Additionally, a measurement technique is developed that measures the graphene
transconductance while being effectively kept at a fixed gate voltage. Such studies can provide
understanding into the operation of graphene-based devices with hysteretic behavior for memory
devices21,24–27, chemical sensing14,17,20,28–31, photodetectors[ref], and ionizing radiation detectors[ref].
11,15,16
Experiment:
Graphene is grown on a Cu foil through the decomposition of CH4 in a furnace at 1000 ˚C,
leading to carbon deposition and graphene formation. To transfer the graphene to other substrates, the
samples are spin-coated by PMMA (polymethyl methacrylate) and placed in an aqueous solution of
Fe(NO3)3 (iron nitrate) to etch off the Cu substrate. Afterwards, the graphene with PMMA coating is
retrieved from the solution by the transfer substrate. The PMMA is then removed by acetone and the
sample is rinsed several times by de-ionized water. Graphene field-effect devices are fabricated using
electron-beam lithography. The electrical contacts (5 nm-thick chromium and 35 nm-thick gold) are
fabricated by electron-beam evaporation.
GFET measurements have been conducted at room temperature by 2-point measurement, as
shown in Figure 1a. 4-point measurements of graphene reveal that contact resistance is negligible
compared to the resistance of graphene samples. An Ametek Model 7270 lock-in amplifier is used to
apply the source-drain voltage Vsd and measure the source-drain current Isd passing through graphene.
A Keithley Model 2400 source meter applies a voltage between the gold backgate and graphene and
measures the leakage current. The data acquisition system is controlled by a customized LabView code,
which also controls the instruments. The contact array and the active graphene region used during all
described experiments are shown in Figure 1b. Measurements are performed at room temperature in
ambient air.
Graphene’s physical and electrochemical properties are largely influenced by the underlying
substrate and have been previously studied for graphene deposited on a SiO2 layer37,38. In our GFET
design, shown in Figure 1a, the CVD graphene is also deposited on a SiO2 substrate, which is in turn
placed onto a SiC semiconducting substrate. In this design the electric field experienced by the
graphene is a function of the applied voltage to the backgate and the conductivity of SiC substrate. The
doping species located between graphene and SiO2 capacitively shield the electric field between the
backgate and graphene.
[Introduction to effects of light] In dark conditions, the SiC substrate is highly resistive, and a
large fraction of the applied backgate voltage, Vbg, drops across the substrate. The relatively large
thickness of the SiC substrate (in our design dSiC = 300 μm) results in a relatively small electric field (E
= Vbg/dSiC in a plate capacitor model). When exposed to broadband visible light, the SiC substrate
becomes partially conductive, increasing the electric field seen by graphene for the same Vbg.
Experiments show that the exposure to light can create electric fields strong enough to overcome the
capacitive shielding, as evidenced by the presence of Dirac peaks in Figure 2. In the absence of light
exposure the Dirac peaks are not visible for the same backgate voltage range used in lighted conditions.
The graphene resistance then becomes dominated by the electric field of the doping species, causing the
Dirac point to be at very high backgate voltages outside the range of experiment, as shown by the flat
curves of Figure 2. Thus, to effectively study hysteresis, the graphene is exposed to broadband visible
light, allowing the measurement of the Dirac peak within reasonable backgate voltage ranges. The
Dirac point voltage, Vd, is dependent on sweep direction, as evident in Fig. 2 and reported by other
studies8,11,35. The positive values of Vd indicate p-type doping of graphene, and the hysteretic and
doping characteristics in Figure 2 are consistent with electrochemical doping15,25. It would be expected
that for pristine, dopant free graphene with VD = 0 V, the exposure to light or dark would not affect the
voltage of the Dirac point. However, dark conditions would likely exhibit a substantial broadening of
the Dirac peak within the experimental backgate voltage range used in our experiments.
[ A comparison of the capacitance time constant (τrc) of the SiC GFET to a heavily p-doped Si
GFET shows that exposure to broadband visible light does not make the SiC fully conductive, allowing
it still be used in detection of greater than band-gap radiation. VD in the absence of light is estimated to
be ?V, as is evidenced by the slight upward trend with increasing positive backgate voltages of the flat
gm L
curves of Figure 2. The mobility of graphene was calculated by m =
, where L and W are the
CssVdsW
graphene channel length and width, gm is the transconductance (taken as the slope of the linear section
of the Dirac peak), Vds is the source-drain voltage, and Cbg is the capacitance of the GFET. ] <- perhaps
not needed.
There have been many studies characterizing hysteresis by sweep speed (V/s)8,9,21,23–25,35 with no
clear guide how to minimize measured hysteresis without annealing. Figure 3 illustrates the underlying
cause of this issue, which shows that graphene resistance fluctuates greatly with time when responding
to changes of backgate voltage. Instantaneously large voltage changes are utilized to better expose the
hysteretic behavior. For smaller monotonic changes in voltage, these hysteretic fluctuations are
partially concealed by graphene’s true field effect response to gate voltage, but never the less take place
during the course of an Isd-Vsg sweep. As observed in Figure 3, graphene resistance will eventually
become relatively time-independent, or stabilized. Stabilization (or relaxation) requires applying a
backgate voltage longer than the hysteresis time constant, τh. This time constant is a measure of the
period required for the density of redox states to come to equilibrium in response to a change in electric
field by a gate voltage12. By exponential fit of graphene resistance response to Vbg = -20 V in Figure 3,
τh = 67 s. This is the hysteretic time constant from one fully stabilized state (Vbg = 0 V) to another fully
stabilized state (Vbg = -20 V), and is comparable to previous studies21,25.
A Isd-Vsg measurement technique was developed to simultaneously address two issues: 1)
Minimization of measured hysteresis, and 2) Obtaining transconductance curves for any given
operating voltage in a hysteretic GFET. These were achieved through an Isd-Vsg measurement method
that stabilizes graphene resistance at a backgate voltage between voltage sweep steps. A voltage sweep
step time of 10 s was utilized. This was the amount of time generally required to reach resistance
minimums during a sweep voltage step, as shown in Figure 6 by the time to inflexion point ‘b’. This
point was selected as it straddled the time dependent features of a-b and c-d in Figure 6. A 20 s
stabilization time was selected, which proved sufficiently long except when sweep voltages were far
from the selected stabilization voltage. This is illustrated in the time dependent graphene response in
Figure 4, which shows that as sweep voltages become greater than 9 V (or after 890 s), the stabilization
resistance increases from the previously measured values around 5400 Ω. Fortunately, this does not
significantly affect the voltage of the Dirac points. The switching of the backgate voltage between
sweep and stabilization voltages causes the oscillating behavior in graphene resistance in Figure 4. A
guide to eye curve was traced over Figure 4, which transects the graphene resistance maximums (left of
Dirac point) and minimums (right of Dirac point) of the sweep voltages. This curve closely matches the
transconductance curve shown in Figure 5 (for -20 V, forward sweep).
Using the described Isd-Vsg measurement method results in transconductance curves for
backgate stabilization voltages of Vbg = -20, 0, and +20 V, shown in Figure 5. Measured Dirac point
hysteresis is reduced for all operational voltages compared to Figure 2. Transconductance curves
appear with the expected characteristics of electrochemical doping including the graphene maintaining
p-doping, and the Dirac point being pulled into the sweep direction15,25. Remaining hysteresis is due to
the selected voltage sweep step being comparable in time to τh. [Add more to time constant discussion
if add tc plots] The developed Isd-Vsg measurement technique can be used to evaluate signals that
modify the electric field experienced by hysteretic graphene so long as the sweep step time is equal to
the signal time. The sweep step time can be adjusted to equal an expected signal time, which will
modify the measured transconductance curves.
The features of graphene response in Figure 3 can now be explained with the aid of the Isd-Vsg
measurement method transconductance curves (Figure 5). An expanded view of time dependent
graphene resistance response with backgate voltage shift of Vbg = -20 V to 0 V is provided as an
example in Figure 6. The inset figure displays transconductance curves stabilized at Vbg = -20 V and 0
V (forward sweeps). There are two key features in time dependent graphene response to a change in
backgate voltage observed in our GFET. The first feature is dominated by the capacitance formed by
the backgate and graphene. The slow response speed of our GFET allowed time resolving of the Dirac
point after a change in backgate voltage, given as a to b in Figure 6. The time resolution of the Dirac
point is also observed by Ohno et al.30 As the Dirac peak is crossed, the graphene switches from h+ to
e- carrier type. In related experiments we conducted, the a to b Dirac point was not resolvable in
exfoliated graphene on doped Si due to the relatively small capacitance that enables fast device
response and are similar to observations by Martínez et al.20 and Wu et al.28 As evidenced in Figure 6,
the inflection point ‘b’ has a minimum resistance that roughly equals the resistance at V bg = 0 V in the
transconductance curve stabilized at Vbg = -20 V. The second feature, shown in c to d of Figure 6,
arises from electrons transferred from graphene to underlying dopant species through redox reactions
causing the eventual p-doping of graphene. During this time, the Dirac point slowly shifts from Vbg = 5 V to 7 V, corresponding to the Dirac points measured in transconductance curves stabilized at V bg = 20 V and 0 V, respectively, in Figure 5. Within this time, the graphene reverts back to h+ from ecarriers. Graphene resistance in Figure 6 eventually approaches the resistance at Vbg = 0 V for a
transconductance curve stabilized at Vbg = 0 V in Figure 5. In retrospect, each voltage sweep step of
Figure 4 can be explained similarly as is here.
Conclusion:
The hysteretic nature of CVD graphene on SiC/SiO2 substrate was explored and found to be
consistent with electrochemical doping of graphene through redox reaction. The GFET was also found
to be significantly sensitive to broadband visible light by induced SiC substrate conductivity and was
observed in measured transconductance curves in light vs. dark conditions. The hysteretic behavior was
studied with complimentary Isd-Vsg and Isd-t measurements, which reveal a relative fast/slow function
based on GFET capacitance (fast) and electron transfer through redox reaction (slow). Graphene carrier
type was discernibly observed to switch from h+ to e- back to h+ after a single relatively large change
in backgate voltage. To aid understanding and analysis of hysteretic Isd-t response, an Isd-Vsg
measurement technique was developed that reduces measured hysteresis and allows the measurement
of transconductance curves while stabilized at a backgate voltage. This technique will enable the
characterization of hysteretic GFET Dirac peaks while at a desired operating gate voltage, useful in
signal detection applications that rely on modifying the local electric field experienced by graphene.
Acknowledgements:
This work was funded by the Department of Homeland Security (DHS), Defense Threat
Reduction Agency (DTRA), and the National Science Foundation (NSF) through the Academic
Research Initiative (ARI) (2009-DN-077-ARI036-02).
Vsd
Isd
1 µm
Graphene
Insulator – SiO2
S
1 atom
150 nm
4 µm
Semiconductor – SiC
Backgate – Au
a)
300 µm
Vsg
40 nm
b)
D
Figure 1: a) Cross section of a GFET that consists of graphene on insulator (SiO2) on a semiconductor
(SiC) with ohmic electrodes and backgate. b) SiC GFET as viewed from top. Gold electrodes are
visible with source (S) and drain (D) indicated. Dotted box represents graphene area of 4 μm2.
Figure 2: Transconductance curves of SiC GFET in dark (dotted) and broadband visible light (solid)
conditions. The sweeps are done in ‘forward’ and ‘backward’ directions, which indicate the backgate
voltage change, which had a rate of |dVbg| = 1 V/s. Deviation of Dirac point by 9 V with sweep
direction indicates hysteresis.
Figure 3: Time dependent SiC GFET hysteretic graphene response from instantaneous change in
backgate voltage for Vbg = -20 V (red) to 0 V (black) to +20 V (blue). Graphene resistance is monitored
for five minutes at each voltage. Vbg = 0 V at the beginning of the test.
Backgate (V)
8500
−19−17−15−13−11 −9 −7 −5 −3 −1
1
3
5
7
9 11 13 15 17 19
Resistance ( )
8000
7500
7000
6500
6000
5500
5000
4500
0
200
400
600
Time (s)
800
1000
1200
Figure 4: Time dependent graphene resistance while conducting Isd-Vsg measurement for a stabilization
voltage of Vbg = -20 V in a forward sweep. Each grid spacing is composed of 30 s, the first 10 s is used
to apply the sweep voltage, while the last 20 s is used to allow stabilization at Vbg = -20 V. The
transconductance curve was traced in black where data points were recorded, matching the Dirac peak
given in Figure 5 for Vbg = -20 V (forward sweep).
Figure 5: Transconductance curves with stabilization at Vbg = -20 V (red), 0 V (black), and +20 V
(blue). The vertical dotted lines represent voltage of stabilization/operation respective to the same color
transconductance curve. The Dirac peaks are located above the stabilization/operation voltage (how
much?). The dot and stars data points represent forward and backward sweeps, respectively. Deviation
of the Dirac point with sweep direction is reduced to 1, 2, and 3 V for Vbg = -20 V, 0 V, and +20 V,
respectively.
8500
7500
c
7000
b
d
d
c
8500
8000
7500
Resistance ( )
Resistance ( )
8000
6500
6000
5500
7000
6500
6000
5500
a
300
5000
a
4500
−20 −16 −12
−8
b
−4
0
4
8
Backgate Voltage (V)
350
12
400
Time (s)
16
20
450
500
Figure 6: Expansion of Figure 3 time dependent graphene resistance response with backgate change of
Vbg = -20 V to 0 V. Inset graphically elaborates on the features observed in the time dependent response
and is composed of the transconductance curves stabilized at Vbg = -20 V and 0 V for left and right
Dirac peaks, respectively.
Bibliography:
1
K.S. Novoselov, a K. Geim, S. V Morozov, D. Jiang, M.I. Katsnelson, I. V Grigorieva, S. V
Dubonos, and a a Firsov, Nature 438, 197 (2005).
2
T.J. Echtermeyer, M.C. Lemme, J. Bolten, M. Baus, M. Ramsteiner, and H. Kurz, The European
Physical Journal Special Topics 148, 19 (2007).
3
S. V. Morozov, K.S. Novoselov, M.I. Katsnelson, F. Schedin, D.C. Elias, J.A. Jaszczak, and A.K.
Geim, Physical Review Letters 100, 4 (2008).
4
A.N. Grigorenko, M. Polini, and K.S. Novoselov, Nature Photonics 6, 749 (2012).
5
Z. Chen and J. Appenzeller, in Electron Devices Meeting, 2008. IEDM 2008. IEEE International
(2008), pp. 1–4.
6
F. Schwierz, Nature Nanotechnology 5, 487 (2010).
7
G. Kalon, Y. Jun Shin, V. Giang Truong, A. Kalitsov, and H. Yang, Applied Physics Letters 99,
083109 (2011).
8
Z.-M. Liao, B.-H. Han, Y.-B. Zhou, and D.-P. Yu, The Journal of Chemical Physics 133, 044703
(2010).
9
P. Joshi, H.E. Romero, a T. Neal, V.K. Toutam, and S. a Tadigadapa, Journal of Physics. Condensed
Matter : an Institute of Physics Journal 22, 334214 (2010).
10
J. Chen, J. Li, J. Yang, X. Yan, B.K. Tay, and Q. Xue, Applied Physics Letters 99, 173104 (2011).
11
P.J. Wessely, F. Wessely, E. Birinci, B. Riedinger, and U. Schwalke, Electrochemical and SolidState Letters 15, K31 (2012).
12
H. Pinto, R. Jones, J.P. Goss, and P.R. Briddon, Physica Status Solidi (a) 207, 2131 (2010).
13
P.L. Levesque, S.S. Sabri, C.M. Aguirre, J. Guillemette, M. Siaj, P. Desjardins, T. Szkopek, and R.
Martel, Nano Letters 11, 132 (2011).
14
F. Schedin, a. K. Geim, S. V. Morozov, E.W. Hill, P. Blake, M.I. Katsnelson, and K.S. Novoselov,
Nature Materials 6, 652 (2007).
15
H. Xu, Y. Chen, J. Zhang, and H. Zhang, Small (Weinheim an Der Bergstrasse, Germany) 8, 2833
(2012).
16
S. Unarunotai, Y. Murata, C.E. Chialvo, H. Kim, S. MacLaren, N. Mason, I. Petrov, and J.A. Rogers,
Applied Physics Letters 95, 202101 (2009).
17
R.S. Sundaram, C. Gómez-Navarro, K. Balasubramanian, M. Burghard, and K. Kern, Advanced
Materials 20, 3050 (2008).
18
Z. Liu, A.A. Bol, and W. Haensch, Nano Letters 11, 523 (2011).
19
a. a. Kaverzin, S.M. Strawbridge, a. S. Price, F. Withers, a. K. Savchenko, and D.W. Horsell, Carbon
49, 3829 (2011).
20
J.G. Martínez, T.F. Otero, C. Bosch-navarro, E. Coronado, C. Martí-gastaldo, and H. Prima-garcia,
Electrochimica Acta 81, 49 (2012).
21
G.R. Turpu, M.W. Iqbal, M.Z. Iqbal, and J. Eom, Thin Solid Films 522, 468 (2012).
22
J. Chan, A. Venugopal, A. Pirkle, S. McDonnell, D. Hinojos, C.W. Magnuson, R.S. Ruoff, L.
Colombo, R.M. Wallace, and E.M. Vogel, ACS Nano 6, 3224 (2012).
23
W. Li, C. Tan, M. Lowe, H. Abruña, and D. Ralph, ACS Nano 2264 (2011).
24
E.B. Song, B. Lian, S. Min Kim, S. Lee, T.-K. Chung, M. Wang, C. Zeng, G. Xu, K. Wong, Y.
Zhou, H.I. Rasool, D.H. Seo, H.-J. Chung, J. Heo, S. Seo, and K.L. Wang, Applied Physics Letters 99,
042109 (2011).
25
H. Wang, Y. Wu, C. Cong, J. Shang, and T. Yu, ACS Nano 4, 7221 (2010).
26
S.A. Imam, T. Deshpande, A. Guermoune, M. Siaj, and T. Szkopek, Applied Physics Letters 99,
082109 (2011).
27
S. Lee, E.B. Song, S. Kim, D.H. Seo, S. Seo, T. Won Kang, and K.L. Wang, Applied Physics Letters
100, 023109 (2012).
28
W. Wu, Z. Liu, L. a. Jauregui, Q. Yu, R. Pillai, H. Cao, J. Bao, Y.P. Chen, and S.-S. Pei, Sensors and
Actuators B: Chemical 150, 296 (2010).
29
Y. Lu, B.R. Goldsmith, N.J. Kybert, and a. T.C. Johnson, Applied Physics Letters 97, 083107
(2010).
30
Y. Ohno, K. Maehashi, and K. Matsumoto, Biosensors & Bioelectronics 26, 1727 (2010).
31
D. Chen, L. Tang, and J. Li, Chemical Society Reviews 39, 3157 (2010).
32
H.E. Romero, N. Shen, P. Joshi, H.R. Gutierrez, S.A. Tadigadapa, J.O. Sofo, and P.C. Eklund, ACS
Nano 2, 2037 (2008).
33
R. Yang, Q.S. Huang, X.L. Chen, G.Y. Zhang, and H.-J. Gao, Journal of Applied Physics 107,
034305 (2010).
34
J.-H. Chen, C. Jang, M. Ishigami, S. Xiao, W.G. Cullen, E.D. Williams, and M.S. Fuhrer, Solid State
Communications 149, 1080 (2009).
35
G. Kalon, Y. Jun Shin, V. Giang Truong, A. Kalitsov, and H. Yang, Applied Physics Letters 99,
083109 (2011).