IOP PUBLISHING NANOTECHNOLOGY
Nanotechnology 20 (2009) 275203 (4pp) doi:10.1088/0957-4484/20/27/275203
Finite size effects on the gate leakage
current in graphene nanoribbon
field-effect transistors
Ling-Feng Mao
School of Electronics and Information Engineering, Soochow University,
178 Gan-jiang East Road, Suzhou 215021, People’s Republic of China
E-mail: mail
lingfeng@yahoo.com.cn
Received 19 March 2009, in final form 3 May 2009
Published 16 June 2009
Online at stacks.iop.org/Nano/20/275203
Abstract
The finite size effects in nanoribbon graphene field-effect transistors (FETs) make the energy
distribution of the channel electrons very different from that when neglecting finite size effects.
Such an effect is especially obvious when the width of the graphene ribbon is a few nanometers.
Thus, it results in more high-energy electrons in a nanoribbon graphene FET than in a
two-dimensional graphene FET for the same device structure and parameters. Furthermore,
such an energy distribution of channel electrons results in a change in the gate leakage current
of a nanoribbon graphene FET. The numerical calculations demonstrate that the tunneling
current rapidly increases with decreasing width of the graphene ribbon. This implies that a
workable graphene FET after considering gate oxide reliability should have a channel width
larger than 100 nm.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
The fundamental limitations of silicon-based microelectronics
have inspired searches for new processes, methods, and
materials. Both academics and industry have been searching
for new materials with properties being better controlled
by the electric field to replace silicon. The most notable
candidates for such materials are organic conductors [1]and
carbon nanotubes [2]. Carbon nanotubes have been widely
investigated as novel electronic devices because of their unique
electrical, thermal, and mechanical properties. Most of the
properties of carbon nanotubes are shared with edge terminated
graphene nanoribbons.
Graphene, which is a hexagonal lattice of a single layer of
carbon atoms, has a 2D (two-dimensional) crystal structure.
Graphene has recently emerged as both a unique system
for fundamental studies of condensed matter and quantum
physics [3] and a fascinating building block for future devices
in a postsilicon era [4–8]. The unique properties of graphene
come from its energy band structure characterized by the zero
gap width and a linear energy–momentum relation [8]. Recent
breakthroughs in fabrication and characterization of graphene
have stirred up a major interest in potential applications of
graphene in electronic systems. Several groups have succeeded
in controlling both carrier types and density in graphene
using a single back gate [9–11]. A major difference between
carbon nanotubes and graphene nanoribbons is the presence of
dangling bonds at the edges of graphene nanoribbons.
To explore graphene for such a gate-controlled electronic
device, the gate leakage current is an important factor for the
quality of the device reliability. In this paper, the graphene
ribbon width effect on the energy distribution of channel
electrons and average channel electron energy will be firstly
discussed. And thus its impacts on the gate leakage current
in the graphene ribbon FETs will be calculated via numerical
solutions to the Schr¨odinger equation using a transfer-matrix
method.
2. Theory
The electron states can be severely distorted by the boundaries
along the
y direction in a graphene ribbon with a finite size.
For such a graphene ribbon of width
W, the boundaries impose
a constraint on the transverse motion so that wavevector
k
y
is quantized: k
y
= nπ/W (n =±1, ±2,...), where n is
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