Biomedical Engineering Reference
In-Depth Information
Fig. 1.33
The dispersion
relation in graphene
E
electrons
k
y
k
x
0
E
F
Dirac
point
holes
In graphene, the linearity of the dispersion relation means that the effective mass of
electrons and holes is zero, and the charge carriers propagate balistically with the
velocity
v
F
D
10
6
ms
1
Š
c=300.
The gapless nature of graphene is in fact a disadvantage in many devices, so that
different methods have been sought to open bandgaps in this material. A possibility
is to confine the charge carriers by etching the graphene sheet contacted with
electrodes. The resulting narrow strips, with typical length of 1-2m, are called
graphene nanoribbons (GNR). The width W of such a strip controls the width of the
energy gap, which opens at the Dirac point, according to the relation (
Han et al 2007
)
E
g
D
˛=.W
W
/;
(1.32)
where ˛
D
0:2 eV
nm and W
D
16 nm are experimentally determined fitting
parameters. Thus, band engineering becomes possible by tailoring the dimensions
of the graphene nanoribbons. For example, the bandgap ranges from 100 to 3 meV
if the width of the nanoribbon varies in the 20-90-nm interval.
The physics and applications of graphene are reviewed in many recent papers
such as (
Dragoman and Dragoman 2009b
)and
We i a n d L i u
(
2010
). Graphene has
also important applications in the area of bionanoelectronics, biomolecule sensing,
DNA sequencing, and drug delivery. More details are found throughout this topic,
especially in the chapter dedicated to sensing of biomolecules, such as DNA.
1.3
Conduction Properties of Biological Materials
The conduction of biological materials relevant for nanoscale electronics is related
to the charged ions, which can be small molecules (
Š
0:2 nm), protein composites
(
Š
10 nm), or giant polymers (DNA is often few centimeters long and contains
millions of negative-charged groups in its backbone) (
Waigh 2007
). The charged
ions are surrounded by water molecules. Examples of charged ions are the COO
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