5.5.3 Diffusive Limit

All the above discussed results were calculated for a device with a CNT length of $\mathrm{50~nm}$. In the case of ballistic transport the current is independent of the device length, but in the presence of scattering it decreases as the device length increases. Fig. 5.25-a shows the ballisticity as a function of the CNT length in the presence of elastic and inelastic electron-phonon interaction. An artificially large value for the electron-phonon coupling strength and a small value for the phonon energy is chosen to simulate the diffusive limit (see Fig. 5.25-b). In this case, the current is expected to be inversely proportional to the device length according to OHM's law.

Figure 5.25: a) Ballisticity versus CNT length. The electron-phonon coupling strength for both elastic and inelastic scattering is D=$10^{-1}$ eV$^2$, and $\hbar \omega$=25 meV for inelastic scattering. These scattering parameters simulate the diffusive regime. In this case the ballisticity is inversely proportional to the device length [277]. b) Ballisticity as a function of the electron-phonon coupling strength and phonon energy for inelastic scattering. The scale of the ballisticity is shown in the color bar. The regions of ballistic and diffusive transport are shown. As the strength of the electron-phonon interaction increases transport of carriers deviates from the ballistic limit and becomes more diffusive.

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