2.7 Transport Properties

Considering an electric current in a square wire with a width $W$ and a length $L$, the resistance is given by OHM's law

$$R \ = \ \rho\ \frac{L}{W^2}$$ (2.20)

where $\rho$ is the resistivity. In a macroscopic conductor, the resistivity $\rho$ is a physical property which does not generally depend on either the length of the wire $L$ or the voltage applied to the sample but only on the material. However, when the size of the wire becomes small compared with the characteristic lengths for the motion of electrons, then $\rho$ depends on the length $L$ through quantum effects. In the quantum regime, electrons act like waves that show interference effects. Such devices are usually referred to as mesoscopic systems^2.3. In the following subsections the characteristics of ballistic and diffusive transport regimes are reviewed. These regimes pertain to transport in CNTs under appropriate conditions.
M. Pourfath: Numerical Study of Quantum Transport in Carbon Nanotube-Based Transistors