Graphene Field Effect Transistor

IH2654 NANOELECTRONICS 1
Graphene Field Effect Transistor
Sumit Mohanty, Mohamed Atwa, Ahmed Al-Askalany, Faraz Khavari
I. INTRODUCTION
It was around fifty years ago that for the first time Graphene
was theoretically predicted [1], but for scientists and re-
searchers to succeed in its isolation, it took until Nosolov and
Geim micro exfoliated the first graphene sheets in 2004 at
the University of Manchester. [2] Since its isolation in 2005,
numerous groups have worked in uncovering the exceptional
properties of this material. It is at once, the thinnest, most
flexible and strongest material known. The amazing properties
of graphene have sparked an immense research following in
a host of fields, ranging from electronics, to chemistry, to
biotechnology and beyond. Table I summarizes the maximum
values of various physical properties of graphene.
TABLE I: Graphene properties
Property Details
Optical transparency 97.7%
Electron Mobility 200,000 cm2 (V.s)-1
Thermal Conductivity 5,000 Wm-1 K-1
Specific Surface Area 2,630 m2 g-1
Breaking strength 42 N m-1
Elastic Modulus 0.25 TPa
Potential applications harnessing the properties of graphene
range from the enhancement of organic and CdTe based
solar cells, to transparent electrodes in touch screens, to logic
devices such as FET switches and tunneling FETs, to ultra-
high density storage media, such as flash memory devices.
Niche applications of graphene that are also being pursued
include chip interconnects and ultra-thin graphene aerogels
that are extremely heat-resistant. [3]
II. THEORY OF GRAPHENE
A. Graphene Synthesis Techniques
Methods used to synthesize graphene can be organized
according to the number of resulting graphene layers. The
term graphene here is used liberally, as the products of
many of these synthesis techniques may be (unavoidably)
functionalized with hydrogen, oxygen or other radical groups.
[4]
1) Highlighted Technique: Chemical reduction of exfoliated
graphene oxide: Chemical reduction of exfoliated graphene
oxide for the production of bilayer graphene (BLG) is fo-
cused upon as an example, given that BLGs show the most
promise for electronic applications due to the tunability of their
bandgap, as will be discussed later in the report. Graphene
Oxide as an Exampl. (1) Graphene oxide is prepared by
the Hummers method involving the oxidation of graphite
with strong oxidizing agents such as KMnO4 and NaNO3 in
Advisor: Jan Linnros, KTH
H2SO4 /H3PO4. Oxygen atoms interleave between the layers
increasing the atomic spacing from 3.7 to 9.5 . (2) Reduction
and ultrasonication in dimethyl fluoride or water yields bilayer
graphene. [4]
Fig. 1: Hummer’s method and subsequent sonication for the
production of graphene from graphene oxide. [5]
B. Structure of Monolayer Graphene
Monolayer graphene consists of carbon atoms arranged
with a two-dimensional honeycomb crystal structure. It has a
hexagonal Bravis lattice with a two-atom basis. Its reciprocal
lattice is also hexagonal. The real (a1 and a2) and reciprocal
(b1 and b2) lattice parameters of monolayer graphene are listed
below. [6]
a = 2.46 ˚A
acc = a √
3 = 1.42 ˚A
a1 = a
2 ,
√
3a
2
a2 = a
2 , −
√
3a
2
b1 = 2π
a , 2π√
3a
b2 = 2π
a , − 2π√
3a
C. Electronic Structure and The Tight Binding Approximation
Carbon atoms each possess six electrons, two of which
are the 1s core electrons and the other four of which are
valance electrons divided one each between the 2s, 2px,
2py, and 2pz orbitals. In graphene, the 2s and planar 2px
and 2py orbitals undergo sp2
hybridization producing three
sp2
hybridized orbitals. These sp2
-hybridized orbitals are
oriented 120◦
relative to one another and are also in-plane.
The remaining 2pz orbital for each atom lies perpendicular
to the plane, and, when combined with the 2pz orbitals on
adjacent atoms in graphene, form orbitals. Electronic states
close to the Fermi level in graphene can be modeled by only

Fig. 2: Top-view of single-layer graphene depicting bravis
lattice. [6]
taking into account the orbitals, which arise from the single
electron per atomic site in the 2pz orbital. This approximation
in monolayer graphene yields a transfer integral matrix H:
H1 =
ε2p −γ0f(k)
−γ0f ∗ (k) ε2p
And an overlap integral matrix S:
S1 =
1 s0f(k)
s0f ∗ (k) 1
γ0 is the nearest-neighbor hopping energy. The π-orbital
energy, ε2p, is normally taken at a datum value of zero. s0
is a factor accounting for the non-orthogonality of orbitals
on adjacent atomic sites. and are the structure factor and its
complex conjugate describing nearest neighbor hopping:
f(k) =
3
l=1
eik.δl
δ1 = 0, a√
3
δ2 = a
2 , − a
2
√
3
δ3 = −a
2 , − a
2
√
3
|δ1| = |δ2| = |δ3| = a √
3
H and S are related as:
Hψj = EjSψj
Ej is the band energy, which can be determined by solving
the secular equation:
det (H − EjS) = 0
Fig. 3: Depiction of the bonding orbitals of a single carbon
atom in graphene. [7]
D. Low-Energy Dirac-Like Hamiltonian
Solving the secular equation for monolayer graphene at low
energies yields the energy band description:
E± =
2p ± γ0 |f(k)|
1 s0 |f(k)|
Around the Brillouin zone edges K+ and K-, this reduces to
the linear relation:
E± = ±υp
Where is the mean electron velocity:
υ =
√
3aγ0
(2¯h)
And p is the canonical momentum described as:
p = ¯hk − ¯hKξ
is an index taking either +1 or -1 indicating for K+ and K-
respectively.
io
Fig. 4: Band Diagram along the Kx axis in a single Brillouin
zone for monolayer graphene. [6]

E. Chirality and pseudospin
The effective Hamiltonian and eigenstates near each K point
have two components, reminiscent of the components of spin-
1/2. This is not the physical spin of the electron, but rather,
a degree of freedom related to the relative amplitude of the
Bloch function on the A or B sublattice called pseudospin..
If all the electronic density was located on the A sublattice,
this would corresponds to a pseudospin up state. Similarly, if
all electron density were confined solely on the B sublattice,
this would correspond to a pseudospin down state. The actual
pseudospin in monolayer graphene is a linear interpolation
of the up and down states. The conduction band pseudospin
is parallel to the momentum, whereas the pseudospin in the
valence band is antiparallel to it.
1) Wave function Angular dependency and chirality: Ro-
tations of the pseudospin degree of freedom change the
amplitudes on the A or B sublattice of the eigenstate depend on
the polar angle . This angular dependence of the pseudospin
component of the wave function relative to the momentum
results in the anisotropic scattering of chiral electrons in
monolayer graphene. When an A-B symmetric potential is
applied to monolayer graphene the scattering probability has
an angular dependence of:
w(ϕ) = cos2
(ϕ/2)
This anisotropic scattering probability is one of the physical
manifestations of the chirality of electrons in monolayer
graphene. The probability of backscattering in monolayer
graphene is zero, as
w(π) = 0
. This 0-π range of the chiral wave function is called the Berrys
phase, which is in monolayer graphene. Scattering into a state
with opposite momentum is prohibited because it requires a
reversal of the pseudospin. Another manifestation of electron
chirality in monolayer graphene is Klein tunneling, anisotropic
scattering at potential barriers in graphene monolayers.
Fig. 5: Depiction of pseudospin in monolayer graphene. [6]
Fig. 6: Scattering probability versus angular momentum rota-
tion angle in single-layer. [6]
F. Bilayer Graphene
1) Bernal Stacking: Two parallel layers of carbon atoms are
arranged with a honeycomb arrangement as in a monolayer,
but are coupled together so that two atoms, B1 and A2, are
directly below or above each other, whereas the other two
atoms, A1 and B2, do not have a counterpart in the other
layer. There are four atoms in the each unit cell: a pair A1,
B1, from the lower layer and a pair A2, B2, from the upper
layer.
2) Electronic structure: Four atoms per unit cell, with one
pz orbital accounted for in the tight binding model per atomic
site means there are a total of 4 bands near zero energy in
bilayer graphene. This simplified low-energy electronic band
model for bilayer graphene accounts for the nearest-neighbor
intralayer coupling between A1 and B1, and A2 and B2.
The model also accounts for the nearest-neighbor interlayer
coupling between B1 and A2 atoms that are directly below
or above each other. The interlayer-coupled A1-B2 and A2-
B1 pairs form a bonding and anti-bonding pair of bands and
are called dimer states, split away from zero energy. This
interlayer coupling is of critical importance for electronic
applications, as it defines the maximum achievable bandgap
in bilayer graphene, to be defined in later sections.
γ0 = 3.033eV
γ1 = 0.39eV
3) Low Energy Massive Chiral Hamiltonian: Solving the
secular equation for the resulting overlap and transfer integral
matrices from applying the tight binding model to bilayer
graphene near the K points yields the following band energy
description:
E
(−1)
± ≈ ±
γ1
2
1 +
4υ2p2
γ2
1
− 1
At low energies, this reduces to:
E
(−1)
± ≈
4υ2
p2
γ1
≈ ±
p2
2m

Fig. 7: Real-space structure of single-layer graphene depicting
Bernal stacking. [6]
This indicates that the dispersion relation in bilayer graphene is
quadratic and describes massive chiral fermions. The resulting
band structure is shown in figure 8. Electrons in bilayer
graphene also exhibit chirality. Pseudospin is divided in to up
and down states based on the upper and lower sublattices. If
the electronic density were solely on the A1 sublattice of the
lower layer, a pseudospin up state would result. Meanwhile,
if the density were solely on the B2 sublattice of the upper
layer, this would result in a pseudospin down state. The actual
pseudospin is a linear interpolation between the two states, as
before.
Fig. 8: Resulting band diagram from the solution of the secular
equation at low energies for bilayer graphene. [6]
4) Chirality: In bilayer graphene, the angular dependence
of the scattering probability is:
w(ϕ) = cos2
(ϕ)
This indicates that while electrons are chiral in bilayer
graphene, they are not incapable of backward scattering as
is the case in monolayer graphene.
Fig. 9: Depiction of electron pseudospin in bilayer graphene.
[6]
Fig. 10: Bilayer graphene scattering probability versus angular
momentum angle. [6]
III. GRAPHENE NANORIBBON FIELD EFFECT TRANSISTOR
A. Band structure and dispersion characteristics
Traditionally, a band-gap could be opened up in a mono-
layer Graphene either by laterally confining the electrons
to a dimension or by externally inducing it by means of
external voltage or strain [6]. Following the former approach,
confining electrons in a certain direction results into formation
of Graphene Nanoribbons (GNR) [12]. One could confine the
electrons along possible reciprocal lattice vectors, forming the
respective electron transport direction, discussed above leading
to two configurations as shown in fig 11. The zig-zag config-
uration is found to have metallic properties due to formation
of edge states of electron confinement whereas the armchair
configuration maybe metallic or semiconductor, depending
upon the width of nanoribbon [13]. Based on the tight binding
theory discussed above, the dirac like hamiltonian results into
a linear energy dispersion relation, which can be rephrased for

Fig. 11: Energy sub-bands near dirac points for different
configurations of graphene, namely (a) armchair and (b)zig-
zag with edge states along x-direction seen in the latter [13].
wavevectors q very close to the dirac points (K+, K−) as,
H = −i¯hυF σ (1)
where υF is the fermi velocity, σ is the Pauli’s matrix for
momentum [12]. Thereby based on this dispersion relation,
density of states (DOS) (at low energies) for a unit cell A,
upon approximation for wavevectors very close to dirac points
takes the form,
ρ(E) =
2A|E|
πυ2
F
(2)
where E being the energy, taking into account the degeneracy
of monolayer graphene to be 4 at the dirac point [14]. This
clearly abides with the hackneyed DOS for two dimensional
systems. However, upon confining the electrons along the
direction perpendicular to the length of GNR, leads to a
singularities of the form 1/
√
E suggestive of 1-D like electronic
spectrum, fairly similar to carbon nanotubes in nature [14].
Hence, the overall density of states resembles the traditional
step like (2-D) characteristics with 1-D singularities as shown
in the fig 5a. Fig 12a is suggestive of a bandgap occurring in
graphene which increases as the number of atoms decrease i.e.
the width of GNR (W) decreases. Further, the energy of indi-
vidual 1-D like sub-bands appearing in the spectrum decreases
in energy steps with the width as well. Quantum mechanically
this influence of width W, and energy of individual sub-bands
En, can be expressed as,
ρ(E) =
2|E|
π¯hυ2
F E2 − E2
n
(3)
where En attributes to the width dependent nanoribbon con-
finement [16]. It has been found that GNR could be patterned
Fig. 12: (a) DOS simulated for hydrogen terminated armchair
configuration GNRs of varying widths, indicated by number of
graphene atoms N, w.r.t. conduction (E≤0) and valence bands
(E≥0) [15] (b) GNR based FET device with Al contacts acting
as source and drain and silica as the oxide material on a Si
substrate [17].
in widths upto several nm, resulting into energy gaps of upto
several hundreds of meV. This width of nanoribbon, W is
termed as the lithographic parameter from the point of view
of fabrication. Experimentally, it has been demonstrated that
reducing this width, not only opens up the bandgap but also
favors device characteristics like a higher ION /IOF F ratio and
switching speed at low temperatures of operation [12] [15]
[16]. Thus, band gap tuning achieved by crafting the GNR
width can be formulated as,
EG =
2πhυF
3W
(4)
Moreover, the net carrier concentration summing up all the
sub bands was derived to be [16],
n =
2kT
π¯hυF
Σ
∞
n
kT
u
u2 − ( n/kT)
2
du
1 + eu−EF /kT
(5)
B. Transmission characteristics
The quasi-one dimensional confinements cause the transport
carriers to occupy these energy sub-bands as the voltage
increases thereby giving birth to quantized conductance [17].
A simple GNR based FET device (as shown in fig 12b)
was taken into consideration in order to understand this
phenomenon. Ideally, Landaeur formula is used to determine
the conductance at a finite temperature given by,
G =
2e2
h
Σt(E) −
∂f(E)
∂E
dE (6)
where t(E) is the transmission probability and f(E) is the
fermi dirac statistics [19]. Experimentally obtained quantized
conductance shows a step like progression w.r.t. gate voltage,
in coherence with the Landauer theory, as shown in fig 13a.
In order to estimate t, its essential to correlate the gate
voltage with fermi energy EF , facilitated by the use of above
mentioned equation and experimental results. Analysis of this
conductance could be done by relating the charge density (Eq.
5) on both the sides of GNR with the back gate voltage applied
(VBG) and the effective gate capacitance per unit area (Cg),
Cg(VBG − VDirac) =
E2
π¯h2
υ2
F
(7)

Where, VDirac represents bias in undoped condition at min-
imum current through the channel (analogous to VF B for
Si MOS). For the give device of 20nm width, sub-band
energy was δE=32eV and having known other parameters
such as oxide capacitance, the transmission coefficient found
was t=0.02. This suppression of t value was attributed to
scattering at the GNR edges [17]. This scattering occurring
at the boundary of GNRs are even more pronounced as the
width decreases, an anomaly known as edge roughness [18].
This not only leads to a leaky OFF current, aiding static power
consumption, but also severely reduced ON current thereby
killing the operating conditions of the device. Following the
inception of using high-κ materials in conjunction with native
gate oxide, analogous fabrication design have been reported.
A thin layer of HfO2 has been implemented with GNRs
with promising ION /IOF F ratio, without ameliorating the ION
selectively [20].
Fig. 13: (a) Experimental vs simulated comparison of Quan-
tized Conductance and (b) high field I-V characteristics at 77K
and 4.2K (inset) [17].
C. Transfer characteristics
Investigating the I-V characteristics of this device (at low
temperature) at high fields i.e. VDS to go upto 6V (field across
the channel length to be 30kV/cm), it was found that I-V curve
was symmetric as shown in fig 13b. This was a problem
in conventional III-V semiconductor FETs where the carrier
transport velocities depreciate at high fields across the channel
[20]. Intuitively, unlike traditional MOSFETs, the gate in this
case controlled the whole channel uniformly. Moreover, the
enormously high current density at such a high field (fig 13b
inset) suggestive of its high current drive capacity [17].
IV. BILAYER GRAPHENE FIELD EFFECT TRANSISTOR
Pristine bilayer graphene (BLG) is a gapless semiconductor,
with inversion symmetry between the two layers maintaining
such nature at the K point. This symmetry leads to a degen-
eracy of states at the K point. [6] Breaking the symmetry
between the upper layer (B2 sublattice) and the lower layer
(A1 sublattice) in a bilayer graphene allows for the existence
of a bandgap, which is essentially tunable. Figure14 [21]
[22] An external perpendicular electrical field achieves such
asymmetry between the layers, with the interlayer coupling as
the upper limit for the achievable bandgap. Some experiments
show a bandgap up to mid-infrared. The unbiased graphene
has a two parallel conduction and two parallel valence band
structure, with the lower conduction and upper valence touch-
ing at the valleys, leading to gapless nature.Figure 15 shows
the gapless unbiased BLG, and the bandgap induced by the
perpendicular electrical field. [21] An asymmetry parameter
Fig. 14: A perpindecular electric field can create a bandgap in
BLG by breaking the symmetry between the A1 sublattice in
the lower layer and the B2 equivalent sublattice in the upper
layer. [22]
Fig. 15: non-gated and gated bilayer graphene band structure
[21]
between the layers can be described as ∆ = 2 − 1,
and it relates to the electronic density distribution when an
external field is applied. However, determining the induced
bandgap ∆g under applied field requires knowing the the
asymmetry parameter and the electronic distribution, and both
are related. This called for a self-consistent solution of both.
A self-consistent model of screening in BLG was presented
in [6], and it was developed by the following assumptions.
In figure 16, the two graphene layers are located at c0/2
and −c0/2; at co spacing from each other of permitivity εr.
The layers support electronic desities n1 and n2, respectively.
Which leads to charge densities σ1 = −en1 and σ2 = en2. For
a dual-gate biased BLG, the bottom and top gates are located
at −Lb and Lt, with potentials Vb and Vt, and separated from
the layers by dielectrics of constants εb and εt, respectively.
Additional background charge is accounted for as σb0 and σt0.

Hence, the electrical fields at the bottom and top layers are,
Eb =
Vb
Lb
, Et =
Vt
Lt
(8)
E =
(V1 − V2)
C0
=
∆
ec0
(9)
Considering both layers of area A, and applying Gauss’s law
to both layers yields the following,
−ε0εbEbA + ε0εtEtA = −e(n1 + n2 − nb0 − nt0)A (10)
While solving it for only one of the layer yields,
−ε0εrEA + ε0εtEtA = −e(n2 − nt0)A (11)
Substituting equations (8) and (9) in (10) and (11), and solving
for the asymmetry parameter ∆ and the electronic distribution
n gives,
n = n1 + n2 =
ε0εbVb
eLb
+
ε0εtVt
eLt
+ nb0 + nt0 (12)
which relates the π-electrons total density to the bottom and
top gate potentials, and the asymmetry parameter as
∆ = −
εt
εt
c0
Lt
eVt +
e2
c0
ε0εr
(n2 − n0) (13)
Which can be rewritten as follows,
∆ = ∆ext + Λγ1
(n2 − n1)
n⊥
(14)
where ∆ext is the asymmetry parameter at low screening, and
is given by
∆ext =
1
2
εb
εr
c0
Lb
eVb −
1
2
εt
εr
c0
Lt
eVt + Λγ1
(n2 − n1)
n⊥
(15)
where n⊥ is the characteristic density scale of the layers’
electronic densities causing the screening, and is given by,
n⊥ =
γ2
1
π¯h2
ν2
(16)
and Λ is a dimensionless parameter indicating the strength of
such screening, and is given by,
Λ =
c0e2
n⊥
2γ1ε0εr
(17)
The layer electronic densities in the presence of the asymme-
Fig. 16: A perpendicular electric field can create a bandgap in
BLG by breaking the symmetry between the A1 sublattice in
the lower layer and the B2 equivalent sublattice in the upper
layer. [6]
try parameter caused by the electric field is give by,
n1(2) = nCB
1(2) + nV B
1(2) (18)
n1(2) =
n
2
n⊥∆
4γ1
ln

 |n|
2n⊥
+
1
2
n
n⊥
2
+
∆
2γ1
2


(19)
For a backgated BLG (Vt = 0), figure ?? shows the electronic
density dependence on the screening parameter and ∆ext =
Λγ1/n⊥, which is described by the following,
∆(n) ≈
Λγ1n
n⊥
(20)
and the actual bandgap is given by,
∆g =
|∆|γ1
∆2 + γ2
(21)
A novel device structure, shown in figure 18, utilizes two
Fig. 17: Electronic density dependence on the bandgap and
the screening parameter in back-gated BLG. [6]
gates for breaking the symmetry between the layers; top
gate and bottom gate. The effect of such dual gating shifts
the Fermi level, effectively doping the BLG due to the
difference between electrical displacement fields at the top
and at the bottom, and breaks the symmetry leading to a
bandgap between the lower conduction band and the upper
valence band, which is induced by the average of the electricl
displacement fields. [22] A charge neutrality point is where
the minimum conductance occurs for the BLG, such point
corresponds to a zero difference between the top and bottom
electrical displacement fields. Varying both Dt and Db, while
maintaining a zero difference, allows for tuning the bandgap
and changing the position of the charge neutrality or Dirac
point. Then, varying the difference allows for injection of
electrons or holes, while maintaining the bandgap. Dt and
Db are given by,
Dt =
εt(Vt − V 0
t )
dt
(22)
Db = −
εb(Vb − V 0
b )
db
(23)

Fig. 18: Dual-gated bilayer graphene FET structure [22]
where Vt and vb are the top and bottom gate voltages, respec-
tively. And V 0
is an offset for the shift in charge neutrality
due to environment, and ε and d are the dielectric constant
and the thickness of the top and bottom gates dielectrics. The
difference and the average of the top and bottom electrical
displacement fields is given by the following equations re-
spectively,
δD = Db − Dt (24)
¯D =
(Db + Dt)
2
(25)
Infrared spectroscopy is used to determine the dual-gate in-
duced bandgap, figure 21 shows a comparison between the
absorption spectra of the BLG at charge neutrality point, for
different average electrical displacement fields (different top
and bottom voltages), and the theoretical absorption spectra for
the different induced bandgaps. The substrate absorption has
been subtracted to allow for correct determination of bandgap
in the BLG. The peaks at about 300meV correspond to the
actual induced bandgap for each biasing condition, while the
dips at about 400meV correspond to the transitions to and
from the other two parallel conduction and valence bands as
shown in figure A BLGFET was fabricated by sandwitching
Fig. 19: Drain current relation with top and bottom gate
voltages, the inset shows the tunability of the bandgap at
different average electrical displacement top and bottom fields
[22]
Fig. 20: Drain current relation with top and bottom gate
voltages, the inset shows the tunability of the bandgap at
different average electrical displacement top and bottom fields
[21]
Fig. 21: Optical transitions in BLG under different top and
bottom gate bias conditions, at charge neutrality point. (I)
induced band gap transition, other transitions are due to the
existence of the other two parallel conduction and valence
bands in BLG. [21]
the BLG between two gates, with an organic seed layer ( 9
nm) and ALD grown HfO2 (10 nm) as top gate dielectric,
and SiO2 (300 nm) as bottom gate dielectric. The seed layer
enhances the growth conditions for HfO2, and maintains high
carrier mobility in the BLG. Figure 23 [22] The fabricated
device was able to achieve an Ion/Ioff ration of 100 at room
temperature, which is an important parameter for logic devices
insuring very low current consumption in their off state. The
device was fabricated with a channel of 1.6µm and 3µm width
and length, respectively. Grounding the source and holding the
drain at 1mV, the transfer characteristics for different fixed
bottom gate voltages and sweeps of top gate voltages are
shown in figure 19. It is clear that certain bias conditions lead
to better on/off current ratio. The output characteristics of the
devices were extracted by fixing the bottom gate at -100V,
sweeping the drain voltage from 0 to 50 mV, and plotted for
different top gate voltages. Figure 21

Fig. 22: BLGFET fabricated and characterized [22]
Fig. 23: Output characteristics for the fabricated BLGFET in
[22]
V. CONCLUSION
By scaling down device dimensions every 18 months in
CMOS technology towards 7.4nm (based on the ITRS), some
limitations are arising faster such as increase of static power
dissipation (as number of transistors increases), leakage cur-
rent, production costs and power density. Thus there is a need
to find a new material such as Graphene to replace Si in
semiconductor technology in order to maintain these trends
Figure4 (upper left), [23]. Potential of Graphene in not clear
for transistors yet. However based on some important features
e.g. possibility of creating very thin channels, extremely
high mobility and high heat conductivity it is an appropriate
material for scaling down which can control short channel
effect, [23]. There are still some difficulties in transistor
application compare to Si technology as following that must
be overcome, [6]; (1)Very low Ion/Ioff ratio in GFETs (static
current of 270uA/um at VDD=2.5 compare to silicon with
100nA/um at 0.75v) as Graphene is a zero band gap material,
(2)Very high static power dissipation, (3)Band gap engineering
without losing great properties such as mobility and high field
transport.
Using the tight binding approximation, we showed how
Dirac-like Hamiltonians depict the electrons in monolayer and
bilayer graphene as massless and massive chiral fermions
respectively. The resulting dispersion relations near the K
points were linear with a single electron and valance band
for monolayer graphene and quadratic, with two valance and
conductance bands for bilayer graphene. This chirality was
shown to have a Berrys phase of in monolayer graphene,
illustrating how backscattering is not possible in this structure.
Meanwhile, bilayer graphene was shown to have a Berrys
phase of 2, indicating that while there is an angular de-
pendency to scattering in this structure, both forward and
backwards scattering were possible.
In few years Graphene interconnects will be fabricated.
In order to GFETs can be used for CMOS logic, threshold
voltage must be controlled for both p-type and n-type.
Working on controlling contact resistance for other areas of
electronic such as (E-paper, folded OLEDs and touch screen)
is in advanced based on the diagram in Figure4 (bottom
left, right) [23]. Over 20 years the most important plan is
to replace silicon technology with Graphene technology. In
Figure5 we can follow the Graphene Moors law, [23]. As it
illustrates, every 8 months the number of GFETs on the chip
get doubled but it will be changed in the near future.
The ability of lithographically patterned GNRs to tune
the bandgap of monolayer graphene has benchmarked its
possibility of implementation as a pragmatic solution to Si
MOSFETs further complemented by its compatibility with
planar IC manufacturing [16]. However, geometrical limita-
tions such as edge termination, lack of non-classical switching
mechanisms and compatibility with traditional CMOS shadow
its candidature [15].
Bilayer graphene can have a bandgap by applying an electric
field, which creates asymmetry between the two layers. The
relation between the top and bottom voltages in a dual gated
bilayer graphene FET controls the conduction in the bilayer
graphen channel. A thorough review was made discussing
how both voltages affect the I-V characteristics of the device.
One major problem of BLGFET is the ION /IOF F ratio,
which must be very high to allow for low power consumption
operation when the device is in the off state.
Although the obstacles in the way to introduction of
graphene to the market as a strong candidate replacing CMOS
devices, the ongoing research activities by many research
group shows good progress which hints to a great potential
in the foreseeable future. Many research topics and challenges
need to be tackled, and a lot of studies need to be conducted to
ensure an economically viable industry for carbon electronics.
REFERENCES
[1] S. Ijima, K. Tanaka., Carbon Nanotubes and Graphene 2e,Amsterdam:
Elsevier, 2014 .
[2] Jamie H. Warner, Fransizka Schaffel, Mark Rummeli, Alicja Bachmatiuk.,
raphene: Fundamentals and Emergent Applications.,Elsevier, 2013.
[3] Wolf, Edward L., Applications of Graphene: An Overview., Springer
Science, 2014.
[4] C. N. R. Rao, Ajay K. Sood, Graphene: Synthesis, Properties, and
Phenomena,John Wiley, 2013.
[5] Boya Dai, Lei Fu, Lei Liao, Nan Liu, Kai Yan, Yongsheng Chen, Zhong-
fan Liu., High-quality single-layer graphene via reparative reduction of
graphene oxide., Nano Research, 2011: 434-439.
[6] Raza, Hassan, Graphene nanoelectronics: Metrology, synthesis, properties
and applications, Springer Science & Business Media, 2012.9
[7] Graphite: A Multifunctional Additive for Paint and Coat-
ings.,Magazine, Paintings and Coatings Industry, October 1, 2003.
http://www.pcimag.com/articles/83004-graphite-a-multifunctional-
additive-for-paint-and-coatings (accessed April 1, 2015).
[8] P. R. Wallace, The Band Theory of Graphene, National Research Council
of Canada, vol 71, 1947.
[9] M. M-Kruczyski, PhD Thesis, Theory of Bilayer Graphene Spectroscopy,
UK, April 2012.

[10] Sam Vaziri, Msc Thesis, Fabrication and Characterization of Graphene
FET, KTH, June, 2011.
[11] E. L. Wolf, Applications of Graphene, SPRINGER BRIEFS IN MATE-
RIALS, Springer, ISBN 978-3-319-03945-9, 2014.
[12] Reddy, Dharmendar, et al., Graphene ﬁeld-effect transistors, Journal of
Physics D: Applied Physics 44.31 (2011): 313001, 2011.
[13] Chung, H. C., et al., Exploration of edge-dependent optical selection
rules for graphene nanoribbons, Optics express 19.23: 23350-23363,
2011.
[14] Neto, AH Castro, et al., The electronic properties of graphene, Reviews
of modern physics 81.1: 109, 2009.
[15] Lemme, Max C. Current status of graphene transistors, Solid State
Phenomena. Vol. 156. 2010.
[16] Tahy, Kristf, et al., Graphene transistors, INTECH Open Access Pub-
lisher, 2011.
[17] Tahy, Kristf., 2D Graphene and Graphene Nanoribbon Field Effect
Transistors, Diss. University of Notre Dame, 2012.
[18] Basu, D., et al., Effect of edge roughness on electronic transport
in graphene nanoribbon channel metal-oxide-semiconductor ﬁeld-effect
transistors, Applied Physics Letters 92.4, (2008).
[19] Davies, John H., The physics of low-dimensional semiconductors: an
introduction, Cambridge university press, 1997.
[20] Schwierz, Frank., Graphene transistors, Nature nanotechnology 5.7,
487-496, 2010.
[21] Zhang, Y., et al, Direct observation of a widely tunable bandgap in
bilayer graphene, Nature Letters, Vol 495, 11 June 2009.
[22] Xia, F., et al, Graphene Field-Effect Transistors with High On/Off
Current Ratio and Large Transport Band Gap at Room Temperature,
Nano Letters, Vol 495, 11 June 2009.
[23] ITRS, Science and technology roadmap for graphene, related two-
dimensional crystals, and hybrid systems, Royal Society of Chemistry,
Nanoscale, 2015, 7, 4598.

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