NANOSCALE DEVICES: APPLICATIONS AND MODELING - Bio-Inspired and Nanoscale Integrated Computing - page 59

device itself is small (nanoscale), the contacts are usually very large (microscale)
and could be treated as semi-infinite systems for the purposes of the analysis. The
use of Green's functions greatly simplifies the problem in such cases. In particular,
problems involving electronic transport usually have contacts playing a crucial
role and thus the so called nonequilibrium Green's function (NEGF) formalism is
commonly used. Moreover, Green's functions provide a way of dealing with inter-
particle interactions in electronic transport modeling. For a study of Green's
functions with application to transport problems in nanostructures the reader is
referred to [91-93].
2.5.4.4. System-Level Modeling. Although most of the research in the
field of nanodevices is currently focused on the device itself, it is noteworthy that
valuable efforts are being made on system-level issues, such as designing circuits
based on these novel nanodevices and analyzing such systems. Researchers have
worked on circuit design paradigms for future computers based on QD-type
devices such as quantum dot cellular automata (QCA) [94]. Although this research
is very new, even compared to the field of nanodevices itself, there are already
examples of computer-aided design (CAD) tools that have been developed for
circuit design applications. An example is the software called QCADesigner [95].
2.6. CONCLUSIONS
There are various methods that could be used for the analysis of a given device
depending on the aspects being studied. For instance, classical molecular
dynamics usually gives an accurate enough result for the mechanical structure
of the system, but does not provide much in the way of electronic structure. DFT
gives very accurate results for electronic structure and can be used to relax the
mechanical structure of the system, although it is extremely expensive computa-
tionally. To illustrate how these various methods could be used in practice, let us
consider the example of a carbon nanotube with a length of 10 nm connected
between two metal electrodes to form a quantum dot. One way to approach the
problem of electronic transport in this device is the following: the coordinates of
the carbon atoms as well as those of the metal atoms in the contact electrodes are
generated based on the lattice structures of the nanotube and the electrode.
However, we know that once a short section (10 nm) of the nanotube is cut and
put in contact with the electrodes, the atoms, especially at the edges, rearrange
themselves slightly. A molecular dynamics simulation is run to determine the
exact location of all the atoms in the metal-nanotube-metal structure. Then both
DFT and TB are used to determine the electronic structure (orbitals or band
structure), while using the NEGF approach to study the transport characteristics.
If the current as a function of applied voltage is to be found, it would mean a
series of electronic structure calculations with different system Hamiltonians
(each reflecting a single bias point). This is very time consuming with DFT. So,
one could use TB for this, and at the same time use DFT for some of the bias