Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 39

I (nA)

1

-2 2

V (V)

-1

Fig. 1.37 The Zenner behavior of DNA between two electrodes

This is the typical semiconductor behavior of DNA, with a bandgap of about 1 eV
at room temperature. It was shown that the overlapping of the orbitals in the base-
pair stack coupled to the backbone is enough to explain the opening of the bandgap
in short DNA base sequences at room temperatures ( Cuniberti et al. 2002 ). Using
a Hamiltonian approach, it was evidenced that backbone coupling of overlapping
orbitals controls the energy gap opening in electron transmission along a DNA
oligomer consisting of 30 G-C base pairs.
In this case, the transmission is written as

4ı 2 sin 2
Œsin.N C 1/ ı 2 sin.N 1/ 2

T D

C 4ı 2 sin 2 N ;

(1.33)

where ˆ D cos is the backbone coupling parameter and N is the number of
resonances at the molecular orbitals, which are broadened by the spectral density
parameter ı. The gap opening is easily understandable by the dispersion equation of
the infinite G-C lattice: ˆ.E/ D cosq,whereq is the adimensional longitudinal
momentum of the lattice. The lack of electronic states between LUMO and HOMO
determines the bandgap opening.
The charge propagates along the orbitals by nearest-neighbor hopping with
probabilities t a and/or is hybridized at the two edges of the structure with probabili-
ties t b˙ . Based on this conduction mechanism model, a model of charge propagation
in C-G periodic base pairs forming a short DNA molecule is depicted in Fig. 1.38 .
The localized charges at the central and edge states are denoted by b and c ˙ ,
respectively, with an additional label indicating the specific base pair.
Using the above model and assuming that t bC D t b D t b , the gap in
transmission, which corresponds to a gap in the current according to the Landauer
formula, is given by

T g D 2.t a C t b / 1=2 2t a (1.34)