The carrier concentration is related to the diagonal elements of the GREEN's
function. The calculation of the current requires only the nearest
off-diagonal elements of the GREEN's function. Furthermore, the HAMILTONian
matrix is tridiagonal. Considering these factors one can employ an efficient
method, such as the recursive GREEN's method, to calculate only the required
elements of the GREEN's functions.
The recursive method has been proposed in [116,8]. A brief
description of the method is presented in Appendix H. The operations
required to solve for all elements of
with a size of
scales as . However, the required operations for the recursive
method scales linearly with .
M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors