G.1 Matrix Truncation
By defining
|
(G.1) |
the equation (4.11) (
) can be written
as,
|
(G.2) |
where
|
(G.3) |
corresponds to the left semi-infinite contact,
|
(G.4) |
corresponds to the right semi-infinite contact, and
|
(G.5) |
corresponds to the device region.
The coupling between the left and right contacts and device are respectively
given by
|
(G.6) |
and
|
(G.7) |
It should be noted that
,
, and
and
(
, and
) are sparse matrices. Their only
non-zero entry represents the coupling of the left (right) contact and device.
From (G.2), one obtains
|
(G.8) |
|
(G.9) |
|
(G.10) |
Substituting (G.8) and (G.9) in (G.10), one obtains a matrix
equation with a dimension corresponding to the total number of grid points in device
layers,
|
(G.11) |
The second and third terms of (G.11) are self-energies due to coupling of
the device region to left and right contacts, respectively.
The GREEN's functions of the isolated semi-infinite contacts are defined as
|
(G.12) |
The surface GREEN's function of the left and right contacts are the
GREEN's function elements corresponding to the first edge layer of the respective contact
|
(G.13) |
M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors