G. Treatment of Contacts

In order to solve the transport equations, boundary conditions have to be specified. An important point is the treatment of contacts, which act as a source or drain for the carriers [97,181,116,284,8,285]. Here, the method described in [285] is followed.

One can partition the layered structure into left contact with index $L$, device with index $D$, and right contact with index $R$ (Fig. G.1). The device corresponds to the region where one solves the transport equations and the contacts are the highly conducting regions connected to the device.

While the device region consists of only $N$ layers, the matrices corresponding to the GREEN's functions (4.11) and (4.12) are infinite dimensional due to the semi-infinite contacts. It is shown next, that the influence of the semi-infinite contacts can be folded into the device region, where the semi-infinite contacts only affect layers $1$ and $N$ of the device region.

As shown next, the influence of the semi-infinite contacts can be folded into the device region by adding a self-energy to the device region. This can be viewed as an additional self-energy, due to the transitions between the device and the contacts.

Figure G.1: Partitioning of the simulation domain into device region and left and right contacts.

M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors