Biomedical Engineering Reference
In-Depth Information
I
(nA)
10
-2
2
V
(V)
-10
Fig. 1.42
The I
V characteristic for a single DNA molecule having as contacts nanoparticles
and a STM tip
is the number of electrons on the molecular level with energy E,andf
0
D
f.E
0
;E
F
/ is the Fermi-Dirac distribution function at equilibrium, when the molec-
ular level has energy E
0
. In the presence of an applied potential, E
D
E
0
C
U
bi
.
Equations (
1.38
)and(
1.39
) were solved, the theoretical I
V characteristics
were found to be in good agreement with experimental data when
1
D
0:1 eV,
2
D
0:4 eV, U
D
0:1 V, and the LUMO and HOMO levels of the DNA are of about
7.99 and
5.29 eV, respectively. The electrochemical potentials were written as
1
D
E
F
eV
(1.40a)
2
D
E
F
C
.1
/
eV
;
(1.40b)
where
Š
0:43 describes the electrostatic potential distribution between the
(DNA-nanoparticle)-substrate junction and the tip-(DNA-nanoparticle) junction.
Under these conditions, a typical I
V characteristic is displayed in Fig.
1.42
.
Strong nonlinear current-voltage behavior was found in circular DNA bundle
samples immersed in an aqueous solution, due to charge hopping through the DNA
network (
Romano et al. 2007
). Inside DNA molecules, the tunneling mechanism
describes the transport of carriers through the bases. The water solution containing
the circular DNA bundle was deposited over the 1-mm gap between vacuum-
evaporated gold electrodes deposited on a nylon substrate containing pores of
450 nm diameter (see Fig.
1.43
). In a hopping model for charge transport, the
charges hop from one localized site to the adjacent one due to the energy provided
by the applied bias and thermal vibrations. The thermally activated current is in this
case
I
Š
sinh.erV=2k
B
T/exp.
E
a
=k
B
T/; (1.41)
where E
a
is the thermal activation energy and r
D
a=d, with a the hopping distance
and d the gap between electrodes. By fitting the current-voltage data with the above
formula, the experimental and theoretical curves are found to be similar for E
a
D
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