To account for interface conditions, grid points located at the boundary of the
segments (see Fig. 4.4-a) are assigned three values, one for each segment
(see Fig. 4.4-b) and a third value assigned directly to the
interface, which can be used to formulate more complicated interface conditions such as,
for example, interface charges.
4.1.3 Interface Conditions
As discussed in Section 4.1, charges on the CNT are approximated as
sheet charges at the CNT-insulator interface.
The boundary flux due to interface charges is simply added
to the segment fluxes given by (4.5)
is the interface charge density at
some point along the insulator-CNT interface given by (4.2).
This method satisfies the condition of
the discontinuity of the electric displacement in the presence of interface
For the CNT the free-space relative permittivity,
, is assumed .
M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors
Interface points as given in a) are
split into three different points having the same geometrical
coordinates b) .