Gate tunable non-linear currents in bilayer graphene diodes
ABSTRACT Electric transport of double gated bilayer graphene devices is studied as a
function of charge density and bandgap. A top gate electrode can be used to
control locally the Fermi level to create a pn junction between the
double-gated and single-gated region. These bilayer graphene pn diodes are
characterized by non-linear currents and directional current rectification, and
we show the rectified direction of the source-drain voltage can be controlled
by using gate voltages. A systematic study of the pn junction characteristics
allows to extract a gate-dependent bandgap value which ranges from 0 meV to 130
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ABSTRACT: Conducting steady-states of doped bilayer graphene have a non-zero sublattice pseudospin polarization. Electron-electron interactions renormalize this polarization even at zero temperature, when the phase space for electron-electron scattering vanishes. We show that because of the strength of interlayer tunneling, electron-electron interactions nevertheless have a negligible influence on the conductivity which vanishes as the carrier number density goes to zero. The influence of interactions is qualitatively weaker than in the comparable cases of single-layer graphene or topological insulators, because the momentum-space layer pseudospin vorticity is 2 rather than 1. Our study relies on the quantum Liouville equation in the first Born approximation with respect to the scattering potential, with electron-electron interactions taken into account self-consistently in the Hartree-Fock approximation and screening in the random phase approximation. Within this framework the result we obtain is exact.Phys. Rev. B 87. 12/2013;
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ABSTRACT: We investigate the electronic structure of graphene ribbons under the competition between lateral electric and normal magnetic fields. The squeezing of quantum level spacings caused by either field is studied. Based on the knowledge of the dispersion under both fields, we analyze the electronic trajectories near the junctions of different electric and magnetic fields configurations. The junctions can split and join electron beams, and the conductance is quite robust against disorder near the junction interfaces. These junction devices can be used as bricks for building more complicated interference devices.Physics Letters A 03/2012; 376(14):1215–1218. · 1.63 Impact Factor
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ABSTRACT: We propose using disorder to produce a field effect transistor (FET) in biased bilayer and trilayer graphene. Modulation of the bias voltage can produce large variations in the conductance when the effects of disorder are confined to only one of the graphene layers. This effect is based on the ability of the bias voltage to select which of the graphene layers carries current, and is not tied to the presence of a gap in the density of states. In particular, we demonstrate this effect in models of gapless ABA-stacked trilayer graphene, gapped ABC-stacked trilayer graphene and gapped bilayer graphene.Journal of Physics Condensed Matter 02/2013; 25(10):105303. · 2.22 Impact Factor
arXiv:1201.1105v1 [cond-mat.mes-hall] 5 Jan 2012
Gate tunable non-linear currents in bilayer graphene diodes
Hiroki Shioya,1, a)Michihisa Yamamoto,1Saverio Russo,2Monica F. Craciun,2and Seigo Tarucha1
1)Department of Applied physics, University of Tokyo, Japan.
2)Centre for Graphene Science, CEMPS, University of Exeter, United Kingdom.
(Dated: 6 January 2012)
Electric transport of double gated bilayer graphene devices is studied as a function of charge density and
bandgap. A top gate electrode can be used to control locally the Fermi level to create a pn junction between
the double-gated and single-gated region. These bilayer graphene pn diodes are characterized by non-linear
currents and directional current rectification, and we show the rectified direction of the source-drain voltage
can be controlled by using gate voltages. A systematic study of the pn junction characteristics allows to
extract a gate-dependent bandgap value which ranges from 0 meV to 130 meV.
PACS numbers: Valid PACS appear here
Graphene -a single layer of carbon atoms- is the
thinnest known conductor1,2with a room temperature
charge carrier mobility considerably higher than silicon
(i.e. more than 100,000cm2/V s). One of the major chal-
lenges in graphene-based electronics is that charge car-
rier conduction cannot be simply switched off by means
of gate voltages because of the lack of a bandgap3.
While chemical functionalization constitutes a valuable
approach to engineer a bandgap4, bilayer graphene of-
fers an alternative solution to this problem with a gate
tunable bandgap5,6. Indeed, bilayers can be continuously
driven from the semimetal to insulator state simply by
means of gate voltages. This remarkable property paves
the way towards bilayer-based transistor and diode ap-
plications with large on/off ratio of the current.
The observation of an electric field tunable bandgap
in bilayer graphene was reported in infrared optical
spectroscopy7,8and a method, which is different from
that9. However, a direct measure of this energy-gap in
electrical transport experiments has so far been elusive
due to the presence of disorder induced sub-gap states
dominating the low energy transport properties.
deed, systematic electrical transport experiments demon-
strated that the temperature dependence of the bilayer
graphene resistance for sub-gap energies is successfully
described by mainly two parallel electrical transport
channels10–14. They are caused by variable range hop-
ping (and by nearest neighbor hopping especially in the
lower temperature region than variable range hopping12)
and by thermally activated transport over the bandgap,
respectively. The formation of bilayer graphene pn junc-
tions has attracted considerable theoretical interest15–17
and it is a key element in graphene-based electronics.
Though up to date there is only one experimental report
on pn-junction devices, no evidence for a rectified current
has yet been reported leaving graphene-based electronics
still a pure academic exercise18.
In this letter we show that the current-voltage (I-V)
characteristics of the pn junction devices exhibit a recti-
a)Electronic mail: firstname.lastname@example.org
FIG. 1. (Color online) (a) Optical micrograph of a measured
device: Black lines show the edge of bilayer graphene flake.
(b) Schematic diagram of our measurement system.
fying behavior with the threshold given by the bandgap
rather than the disorder induced sub-gap states.Then we
analyze the I-V characteristics to derive the electric field
tunable bandgap of bilayer graphene. We finally extract
a gate-dependent bandgap value ranging from 0 meV to
130 meV in our double gated bilayer graphene devices.
The graphene devices are fabricated by mechanical ex-
foliation of Kish graphite on p-doped Si wafer coated by
285nm SiO2, which acts as a uniform back gate. We
have selected bilayer graphene flakes by analyzing the in-
tensity of the green light of optical micrograph pictures
of different flakes19. Subsequently, we fabricated elec-
trodes and local top gates by electron beam (EB) lithog-
raphy, evaporation and lift-off process of respectively
Ti/Au (25 nm/65 nm) for the electrodes and SiO2/Ti/Au
(150 nm/25 nm/32 nm) for the top gates. Figure 1(a)
shows an optical micrograph of a typical double gated
The double-gated geometry allows us to independently
control the Fermi level and the perpendicular electric
field through the bilayer graphene. The polarity of the
charge carriers -i.e. electrons (n) or holes (p)- can be
controlled by tuning the Fermi level position via both
top gate and back gate voltages. This property is used
to create controllable pn-junctions. On the other hand,
the external perpendicular electric field breaks the ener-
getical symmetry between the two planes of the bilayer
graphene resulting in the opening of a bandgap5.
Here we use more than 5 different double gated pn-
junction devices to the study of the electrical properties
in a voltage-bias configuration (see Figure 1(b)) with top
FIG. 2. (Color online) (a) Color coded plot of Isd versus Vtg and Vbg at T=4.2K. I-V characteristic of the Nn junction with
Vtg = −35V andVbg= 80V (b), Np junction with Vtg = −45V andVbg= 55V (c), Pn junction with Vtg = 20V andVbg = −93.45V
(d), respectively. (e) Differential conductance vs. Vsd plotted for a range of back gate voltages with Vtg = 40V . The back gate
voltages correspond to measurements at points on the dotted line in (a). Minimum points are shifted indicating the shift of
the quasi-Fermi level. The number attached to each curve shows the applied Vbg value.
and back gate voltages as parameters and at a tempera-
ture of 4.2K. In all these bilayer pn-junction devices we
observed similar I-V characteristics. Here we discuss the
representative data obtained from one of them. To esti-
mate the mobility (µ) of the charge carriers, we use the
value of the conductance per square measured at high
gate voltage i.e., G?= neµ, from which we have sub-
tracted the contact resistance between bilayer graphene
and Ti/Au20. The density of charge carriers is given
by the known capacitance to the gate, and using the
known planar capacitance in the device channel we ob-
tain µ = 650cm2/V s at 4.2K. Thus the typical electron
mean free path in our devices is about 16.5 nm, which
is much shorter than the device channel. Therefore, the
electron transport in our devices is diffusive.
Figure 2(a) shows a color coded plot of source-drain
current (Isd) measured for a constant source-drain volt-
age Vsd= 1mV as a function of top- and back-gate volt-
ages, Vtg and Vbg, respectively. The Isdshows two min-
ima, one corresponding to the charge neutrality point of
the double gated region -which depends on both Vtgand
Vbg- and the other corresponding to that of the region not
covered by the top-gate -i.e. independent of Vtg. These
two minima cross at Vtg= 8V and Vbg= −64V which is
the global neutrality point for the whole device. There-
fore, by adjusting the gate voltages we can prepare four
different polarity regions, i.e. Pp, Pn, Np and Nn as in-
dicated in Figure 2(a). For instance, for Vbg≤ − 64V in
the region of the flake without top-gate the Fermi level
is in the valence band (P-doping). By application of the
specific top-gated voltages the Fermi level of the double
gated region can be brought from the valence (p-doping )
to the conduction band (n-doping) realizing a transition
of a Pp to Pn-junction.
The I-V characteristics of double gated bilayer
graphene devices measured for the Nn, Np and Pn con-
ditions are shown in Fig.
tively. For the Pp (or Nn) junction we observe linear I-
V characteristics, whereas for the Pn (or Np) junctions,
which are realized by the gate voltages near charge neu-
tral points we consistently observe nonlinear I-V char-
acteristics. This nonlinearity becomes more pronounced
when the Fermi level is set in the opened bandgap of the
p-region. Correspondingly, the non-linear I-V character-
istic is also reflected in the dIsd/dVsdvs. Vsdcharacter-
istics (see Fig 2. (c) and (d)). The dIsd/dVsd starts to
increase progressively when Vsd is tuned outside of the
region, indicated with two arrows in Fig 2. (c) and (d):
The dIsd/Vsdvalue is apparently reduced in the positive
Vsd(0mV ≤Vsd≤70mV ) in Fig. 2 (c) and in the negative
Vsd(0mV ≥Vsd≥−80mV ) in Fig.2 (d), respectively. That
is the rectified direction in the Vsd axis, which changes
with the polarities in the channel of the device, e.g. nega-
tive Vsdfor Pn and positive Vsdfor Np. This observation
implies that in our devices the rectification direction of
Vsd can be controlled by selecting the appropriate gate
voltage configuration. In addition, in a higher electric
field -i.e. wider bandgap- we observed an even more pro-
nounced non-linearity in the I-V characteristics(see Fig.
3 (c)). The zero-bias dip in conductance, see Fig. 2c
and d, is likely to originate from both contact resistance
and disorder induced sub-gap states. The energy range
associated with this zero-bias dip is much smaller than
the estimated energy gap, see Figs. 2(c)-2(e), highlight-
2 (b), (c) and (d), respec-
FIG. 3. (Color online) (a) Schematic of band structure at an
interface when the Fermi level is set in the opened bandgap:
The differential conductance would show different slopes out-
side of the gap in the differential conductance curves when
carriers are driven by the Vsd voltage. Carrier conduction
would be suppressed when carriers experience the opened
bandgap.(b) Analysis of a differential conductance curve
(Vtg = −40V,Vbg = 37.5V ): The point at which the slope
of derivative conductance starts to change corresponds to the
edge of the opened bandgap. The product of difference be-
tween 2 inflection points of Vsd and e of elementary charge
corresponds to the opened bandgap value.
bandgap values vs. the applied electric fields. Circles are
the evaluated values of our analysis. Squares are the values
of previous optical measurements(see Ref. 7) and continuous
curve is the theoretical calculation in the previous work(see
ing a non-leading role of the contact resistance in these
Contrary to conventional semiconductor pn-junctions,
there is no so-called built in potential at a bilayer
graphene pn interface. In the bilayer graphene devices
the fringing field from the side edge of the top gate smears
out the pn interface. Figure 3 (a) shows a simplified
schematic of the band-bending at a pn bilayer interface.
Here the bandgap is assumed to act as a potential bar-
rier for carriers and to generate non-linear currents. We
confirmed the validity of this model from measurements
of the Vbgdependence of the differential conductance, see
figure 2 (e). In this figure the Fermi level is tuned from
below to above the bandgap by changing Vbgfrom -72.5V
to -57.5V. The position and the width in Vsdof the dif-
ferential conductance depend on Vbg. This observation
suggests that the non-linear current is a consequence of
transport through a Pn interface where the gap acts as a
potential barrier for charge carriers.
Within the proposed band-bending model we estimate
the value of the electric field induced bandgap opened in
bilayer graphene. A typical dIsd/dVsd vs. Vsdis shown
in figure 3 (b). We start by analyzing the differential
conductance curves with the quasi-Fermi level set as de-
picted in figure 3 (a), i.e.
top gate (left region) and in the conduction band out-
side the top gate (right region). When the quasi-Fermi
in the bandgap under the
level reaches the bottom (top) of the conduction (valence)
band under application of Vsdan inflection point appears
in the dIsd/dVsdvs. Vsdcurves (see figure 3 (b) caption).
For the forward Vsd, the carrier conduction will increase
when the incident energy of carriers overcome the energy
of the potential barrier. For the backward Vsd, the carrier
conduction will increase when the carriers in the valence
band in the P-region start to flow. Therefore, the two
inflection points correspond to the situations where the
quasi-Fermi level is located at the upper edge and the
lower edge of the gap, respectively. The Vsd range be-
tween the two inflection points in figure 3 (b) is 110mV,
we can therefore infer that the opened bandgap value is
110meV for Vtg = −40V and Vbg = 37.5V . We apply
this analysis for the data with combinations of gate volt-
ages and derive the bandgap value ranging from 0meV
to 130meV, see blue circles in figure 3 (c). Furthermore,
we compare our estimates to those previously obtained
from infrared optical spectroscopy7, see red squares in
figure 3 (c). The magnitude and the overall electric field
dependence of the bandgap obtained from our electrical
transport experiments are both in good agreement with
those of the previous work7.
In conclusion, we demonstrated that local electrostatic
doping of bilayer graphene can be used to form pn diodes
with nonlinear rectified current-voltage characteristics.
The rectification behavior can be continuously tuned by
means of gate voltages. From the analysis of the pn junc-
tion current-voltage characteristics we estimate a gate-
dependent bandgap as large as 130mV, which is in agree-
ment with previous optical studies. Our experimental
findings demonstrate a step forward to future bilayer
graphene diode applications.
(Acknowledgement) H.S. acknowledges financial sup-
port from GCOE for Phys.
Project for Developing Innovation Systems, MEXT,
Japan. M.Y. acknowledges financial support from Grant-
in-Aid for Young Scientists A (no. 20684011). S.T. ac-
knowledges financial support from JST Strategic Inter-
national Cooperative Program (GFG-JST and EPSRC-
JST). S.R. and M.F.C. acknowledge financial support
from EPSRC (Grant No.
EP/J000396/1) and from the Royal Society Research
Grant 2010/R2 (Grant no.
(Grant No. SH-05323).
Sci.Frontier and from
EP/G036101/1 and no.
SH-05052) and 2011/R1
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