HighIon/Ioffcurrent ratio graphene field effect transistor: the role of line defect

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# High I on/ I off current ratio graphene field effect transistor: the role of line defect

Mohammad Hadi Tajarrod and Hassan Rasooli Saghai *§

Full Research Paper [Open Access](http://www.beilstein-journals.org/bjnano/about/openAccess.htm)

Address:

Department of Electrical Engineering, Tabriz Branch, Islamic Azad

University, Tabriz, Iran

Email:
Hassan Rasooli Saghai * [- h_rasooli@iaut.ac.ir](mailto:h_rasooli@iaut.ac.ir)

- Corresponding author

§ Tel/Fax: +98 411 3328560

Keywords:

field effect transistor; graphene; line defect

_Beilstein J. Nanotechnol._ 2015, _6,_ 2062–2068.

[doi:10.3762/bjnano.6.210](http://dx.doi.org/10.3762%2Fbjnano.6.210)

Received: 19 March 2015

Accepted: 05 October 2015

Published: 23 October 2015

Associate Editor: J. Lau

License and terms: see end of document.

## Abstract

The present paper casts light upon the performance of an armchair graphene nanoribbon (AGNR) field effect transistor in the presence of one-dimensional topological defects. The defects containing 5–8–5 sp 2 -hybridized carbon rings were placed in a perfect

graphene sheet. The atomic scale behavior of the transistor was investigated in the non-equilibrium Green's function (NEGF) and

tight-binding Hamiltonian frameworks. AGNRFET basic terms such as the on/off current, transconductance and subthreshold

swing were investigated along with the extended line defect (ELD). The results indicated that the presence of ELDs had a signifi
cant effect on the parameters of the GNRFET. Compared to conventional transistors, the increase of the _I_ on/ _I_ off ratio in graphene
transistors with ELDs enhances their applicability in digital devices.

## Introduction

Graphene, a two-dimensional allotrope of carbon with the thick
ness of one atom, has attracted the attention of researchers

because of its unique electronic transport properties. The prop
erties of graphene such ultra-thin body properties for optimum

electrostatic scaling and excellent thermal conductivity has

made it a potential alternative to silicon and facilitated the

manufacture of devices [1,2]. Furthermore, the high carrier

mobility and velocity of graphene is utilized in ballistic and

high switching speeds devices [3,4]. However, the very large

off-current of graphene at room temperature, which is asso
ciated with the small band gap, renders it incapable of being

integrated as a building block for pure carbon-based transistor

devices [5,6]. The electronic properties of graphene are the

result of its particular structure. In order to modify the transport

behavior, the physical structure of graphene needs to be

changed. Consequently, topological defects such as vacancies,

impurities, adatoms and Stone–Wales defects are the best candi
dates for changing the hexagon structure of graphene with

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acceptable C–C distances and angles for sp 2 hybridization [7].

These defects play a remarkable role in graphene and nano
structured devices. One controlled defect in graphene are grain

boundaries. The electrical and thermal conductivity decrease

with grain boundaries in materials [8,9]. By studying the grain

boundaries in graphite, extended line defects become visible in

the STM analysis [10]. The first experimental report of the

extended line defect (ELD), which was studied through alter
nating Stone–Thrower–Wales defects, was presented by Lahiri

et al. [11]. Applying defects and divacancies in a pristine sheet

creates a 5–8–5 line defect. They found that one-dimensionally

extended defects could be used as metallic wire. Following this

study, a valley filter, based on line defects scattering in

graphene, was introduced by Gunlycke et al. [12]. Later, by

applying the tight-binding calculation, Bahamon et al. demon
strated metallic characteristics and Fabry–Pérot oscillation

phenomena in graphene [13]. Afterwards, some works

addressed the effect of the extended line defect along the edges.

For example, G. P. Tang et al. showed that spin polarization and

carrier transport in zigzag graphene nanoribbons (ZGNR) were

mainly dependent on the position of the line defect [14]. In ad
dition, Hu et al. investigated the electrical and magnetic prop
erties of zigzag edge graphene under external strain. They found

that the local magnetic moments on the line defect were ampli
fied by strain, coupling this with the edge magnetic moments

caused a modification of the spin polarization on one edge [15].

Some studies investigating the effect of line defects on zigzag

nanoribbon could have been motivated by the fact that the line

defect develops along the edge of zigzag nanoribbons. There are

also studies on the line defects in armchair nanoribbons [16,17].

The research into divacancies and ELD in armchair nanorib
bons shows that the presence of divacancy defects has

significant impacts on the band structure and electronic trans
port properties of AGNR. However, no study has yet been

conducted on the effect of the extended line defect on field

effect transistors. In the present study, first, the device perfor
mance of an AGNR field effect transistor with ELD was

investigated by employing self-consistent NEGF formalism and

tight-binding Hamiltonian calculation. Then various parameters

of the transistor, e.g., on/off current, transconductance and

subthreshold swing, were calculated, and the influence of the

line defect in different channel sizes was compared to the ideal

AGNRFET.

## Model

Figure 1a illustrates the schematic diagram of GNRFET

channel, which contains a 5–8–5 extended line defect in the

center of the armchair graphene nanoribbon. The C–C bond

lengths in the line defect are between 1.43–1.83 Å, that indicating sp 2 hybridization [18]. The tight-binding model with the

first nearest-neighbor approximation was used to model the

_Beilstein J. Nanotechnol._ 2015, _6,_ 2062–2068.

electrical structure of the transistor channel, which conformed

to the first-principles calculations used to describe the elec
tronic band structure of ELD-AGNRs [19,20]. The Hamil
tonian computation in this system was separated into AGNR

(HA), line defect (HD) and coupling between AGNR and the
defect (HC). The relevant formulas are as follows [21]:

(1)

(2)

(3)

where and are the on-site energies in the AGNR and the

line defect, respectively; t0 (tD) is the hopping energy of the
AGNR (line defect); tc denotes the coupling between AGNR
and line defect; H.c. stands for the Hermitian conjugate; indices

ia and md are the site coordinates in the AGNR and line defect
respectively; <ia,ja>(<md,nd>) represent the pair of nearest
neighbors. Thus, the whole Hamiltonian system is defined as a

three-part summation (H = HA + HD + HC). Non-equilibrium
Green's functions method was employed to simulate the device

performance in the atomic scale simulation. In the general

context of nano-transistor modeling, the retarded Green's func
tion of the channel in between the right and left contacts, which

can be evaluated as follows [22]:

(4)

where HT is the tight-binding Hamiltonian matrix of the GNR
channel, which can be evaluated using a tight-binding model as

explained before; and are the self-energies describing

the coupling between the device and source and drain region,

respectively; U is the self-consistent potential matrix deter
mined by the solution of a 3D Poisson equation; and η is an

infinitesimally small quantity. Accordingly, the transmission

probability of carriers through the device can be written as:

(5)

where is the coupling between source

(drain) contact and the device region; represents

the retarded (advanced) Green's function for the device
region, which follows the relationship of G a = [G r ] †,

with gs/d being the surface-state Green’s functions of the source and drain contacts. Here, gs/d are solved

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by sticking out a semi-infinite one dimensional double-atom

chain from semi-infinite AGNR in the Green’s function space

[23]. The Green’s function coefficients extracted by deriva
tion,,

and,

are the on-site energy, the coupling between the two atoms in

each primitive cell, and the coupling between the neighboring

two primitive cells of the chain, respectively. For AGNR with

even width (M), N = M/2 and [Ξ] = 2δjl – δ11 + δj,l+1 + δj,l−1.
Otherwise, N = (M – 1)/2 and [Ξ] = δjl + δj,l+1 + δj,l−1. To transform the double-atom chain into its molecular orbit representa
tion, diagonalization of the matrix [Ξ] is performed, allowing

the surface-states Green’s function of the semi-infinite AGNR

to be found. The current can be calculated by using the

Landauer formula [24]:

(6)

Here, fR and fL are the Fermi functions of the right and the left
contact, respectively.

## Results and Discussion

In this section, the carrier transport and electrical properties of

ELD-GNRFET are reported. Figure 1a is the schematic diagram

of the transistor. The transistor device contains a top gate struc

_Beilstein J. Nanotechnol._ 2015, _6,_ 2062–2068.

ture of Al2O3 (εr = 9.8) gate oxide embedded along the gate and
a channel with 2 nm width. The armchair nanoribbon channel

used with the extended line defect was placed in the center. The

drain and source contacts were doped with concentrations of
1 × 10 9 m −1 . Room temperature (300 K) operation was assumed

in all simulations and the bias voltage was set to _V_ d = 0.7 V.
Depending on the edge geometry, ELDs take different configu
rations. The same configuration of line defects was assumed in

all simulations [25] (see in Figure 1b).

Figure 1b shows transport pathways in an ideal GNR

nanoribbon and in one with an ELD. The addition of the line

defect reduces the paths of conducting channels, making larger

effective transport gaps. However, with the reduction of paths,

the mobility and carrier density at higher energies is extremely

reduced. Figure 1c shows the band structure of ideal and defect

AGNR. Compared to the ideal AGNR, the band gap of ELD
AGNR is increased up to 0.91 eV (assuming the line defect in

the configuration), owing to the reduction of conducting chan
nels in ELD-AGNR.

The transmission probability in Figure 2a clearly shows local
ized energy states in these two devices. To describe the channel
performance, a probability of transmission below 10 −2, which

has no experimentally significance, is regarded as the reference

for the transmission of the defined bulk transport gap [26,27].

The result indicates that the transmission spectrum is influ

Figure 1: (a) Schematic sketch of a simulated GNRFET with an extended line defect in the center of the channel, N-type contacts, Al2O3 gate dielectric and SiO2 substrate. (b) Transmission pathway along 1.8 × 20 nm armchair graphene nanoribbon. The arrows show the magnitude of carrier transport. (c) Band structure of 1.8 × 20 nm AGNR (top image) and ELD-AGNR (bottom image).

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_Beilstein J. Nanotechnol._ 2015, _6,_ 2062–2068.

Figure 2: (a) Comparison between average transmission probabilities as a function of the energy in 1.8 × 20 nm armchair graphene nanoribbons.
Inset shows transmission probabilities compared to the minimum effective band structure transmission (dashed green). (b) _I_ d vs _V_ g characteristics
(logarithmic scale) for ELD-GNRFET (dashed red) and GNRFET (dashed blue) containing a 1.8 × 20 nm armchair graphene nanoribbon channel. The
inset shows linearly scaled transfer characteristics. ( _I_ on extracted from _I_ ds at _V_ gs = _V_ off + _V_ DD ( _V_ DD = 0.7 V), where _V_ off = _V_ gs at _I_ ds = _I_ off). Symbols
show the exact value, and dashed lines are fitted to data points.

enced by adding a line defect. The reduction of the transmis
sion that follows the widening of the effective band gap

(Figure 1c) is considerable. Figure 2b shows the transfer charac
teristics of the transistors. As shown in the figure, compared to

the ideal GNRFET, ELD-GNRFET has a lower current value in

various gate voltages. Thanks to a significant increase of the

effective band gap, off-current decrease is much more signifi
cant than the on-current reduction in ELD-GNRFET. The

results indicate that on/off ratio improved 30% in the defected

transistor. The simulating of the average of transconductance

and the subthreshold swing describe the switching-on and the

immunity of the short channel effects in the switching-off

performance. In this study, the transconductance decreased

from _g_ m = 94 μS in the ideal transistor to _g_ m = 55.7 μS for the
defected transistor. The subthreshold swing, which is defined as

∆ _V_ G/∆log(∆ _I_ D) at the subthreshold region in GNRFET,
was _S_ = 166.9 mV/dec, whereas in ELD-GNRFET, reduction

in the tunneling current made a higher subthreshold swing

( _S_ = 209.7 mV/dec) [28].

Length effect

On-current and off-current values for channel lengths from 10

to 60 nm are shown in Figure 3a and Figure 3b. Because of the

decrease of the tunneling current in longer channels, the off
current decreases when the channel length is increased. Due to

the increase of the band gap in the defected channels, the off
current in ELD-GNRFETs (about 70%) was smaller than that in

ideal transistors. The transmission reduction in ELD-GNRFET

caused an on-current decrease by 47%. Nevertheless, as seen in

Figure 3c, the on/off current increased by a factor of 1.30 (30%

improvement).

Due to ballistic transport, the transconductance remains

constant when the channel length is reduced. Although in the

defect channel transconductance is reduced because of a smaller

transition probability. Figure 4a shows that by introducing an

ELD in the transistors, the transconductance decreases in

various channels. In Figure 4b, the subthreshold swings as a

function of the device length are compared in the defect and the

ideal transistor. Stronger electrostatic control of the gate at

larger lengths leads to a decrease of the subthreshold swing in

both devices. However, in the short-channel devices a decrease

of the tunneling current in ELD-GNRFETs result in a smaller

subthreshold swing.

Width effect

Studies on the width of graphene show that GNR nanoribbon

band gap decreases for larger nanoribbons. Additionally, the

localization of carriers in GNR nanoribbon with the line defect

contributes to the increase of the band gap. Figure 5a and

Figure 5b show on-current and off current versus channel width

(0.80–2.77 nm). The increase of the channel led to the increase

of the on-current, and the increase of the off-current caused the

band gap at large widths to decrease even more. The proportion

of the conducting channels in defect vs ideal graphene nanorib
bons increased by increasing the width of the nanoribbon, and,

accordingly, the slope of on-current became gentler in the

defected device (Figure 5c).

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_Beilstein J. Nanotechnol._ 2015, _6,_ 2062–2068.

Figure 3: Channel length dependence of (a) on-current (b) off current (c) on/off current. The lines are a guide to the eye. The dashed blue line is for
ELD-GNRFET and the dashed red line is for GNRFET.

Figure 4: Comparison between average of (a) transconductance and (b) subthreshold swing of ELD-GNRFET and GNRFET as a function of the
channel length. The lines are a guide to the eye.

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_Beilstein J. Nanotechnol._ 2015, _6,_ 2062–2068.

Figure 5: Channel width dependence of (a) on-current (b) off current (c) on/off current. The lines are a guide to the eye. The dashed blue line is for
ELD-GNRFET and the dashed red line is for GNRFET.

Because of the reduction of the tunneling current, the off
current in ELD-GNRFET transistors decreases by factor of

ca. 2.5 compared to GNRFET transistors. Overall, the on/off

current ratio increased in various widths with the line defect

attendance. The overall increase in terms of transconductance

and subthreshold swing in Figure 6 related to the increase in

Figure 6: Comparison between average of (a) transconductance and (b) subthreshold swing of ELD-GNRFET and GNRFET as a function of the
channel width. Symbols show the exact value, and dashed lines are fitted to data points.

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conducting channel and decrease in the band gap, respectively.

Despite this, in the defected device, the decreased transmission

probability caused light growth in the transconductance, while

less tunneling current increase the subthreshold swing.

## Conclusion

In this study a comprehensive numerical analysis was

conducted about graphene nanoribbon field effect transistors

with extended line defects (ELD-GNRFET) based on the NEGF

formalism. According to the simulation results, applying a

perpendicular line defect in an AGNR channel led to the

decrease of the transport paths, causing a larger band gap in the

device. The transistor behavior examined in different geome
tries showed that on/off current and transconductance decreased

and subthreshold swing increased by adding line defect.

However, the _I_ on/ _I_ off ratio recognized as a considerable problem
in graphene transistors, increased in these structures.

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