Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 42

Fig. 1.40 The dsDNA
terminated with nanoparticles
as electrodes

STM tip

gold nanoparticles

dsDNA

Au
grain

Au film

Fig. 1.41 The energy
diagram of the single DNA
molecule connected to a
nanoparticle STM electrodes

LUMO

E F

HOMO

m 1

m 2

- +

The Landauer model is again used to explain the conduction mechanisms
encountered in the above nanostructure. Considering that the dc voltage V is applied
between the STM tip and the gold substrate, the electrochemical potential of the tip,
2 , differs by the quantity eV from the electrochemical potential of the substrate 1 :
it is higher or smaller than 1 if a negative or a positive voltage V , respectively, is
applied. The energy level diagram is presented in Fig. 1.41 when a positive voltage
is applied on the tip. Thus, the current is given by

2e
„

1 2
1 C 2 Œf.E; 1 / f.E; 2 /;

I D (1.38)

where 1;2 are the widths of the broadened molecular energy levels in the presence
of metallic contacts, E is the energy level of the molecule, and f.E; 1;2 / are
the Fermi functions of the contacts. Charging effects are expressed by a built-in
electric potential U bi D U.N 2f 0 /,whereU is the potential per electron in the
nonequilibrium state,

N D 2 1 f.E; 1 / C 2 f.E; 2 /
1 C 2

(1.39)