5.5.1 Electron-Phonon Coupling Strength

Fig. 5.20-a shows the ballisticity as a function of the electron-phonon coupling strength. The ballisticity is defined as $I_\mathrm{Sc}/I_\mathrm{Bl}$, the ratio of the on-current in the presence of electron-phonon interaction to the current in the ballistic case [276]. With increasing electron-phonon coupling strength the self-energy increases.

The left part of Fig. 5.20-b illustrates an electron losing its kinetic energy by emitting a phonon. The electron will be scattered either forward or backward. In the case of backward scattering the electron faces a thick barrier near the source contact and will be reflected with high probability, such that its momentum will again be directed towards the drain contact.

Elastic scattering conserves the energy of carriers, but the current decreases due to elastic back-scattering of carriers. Fig. 5.21-a shows that for elastic scattering the source and drain current spectra are symmetric. As the electron-phonon coupling strength increases, resonances in the current spectrum are washed out and the total current decreases due to elastic back-scattering. In the case of inelastic scattering, carriers acquiring enough kinetic energy can emit a phonon and scatter into lower energy states. Therefore, as shown in Fig. 5.21-b, the source and drain current spectra are not symmetric.

Figure 5.20: a) Ballisticity versus electron-phonon coupling strength for a CNT of 50 nm length. Results for both elastic and inelastic scattering with different phonon energies are shown. The operating point is $V_\textrm {G}$= $V_\textrm {D}$=1 V. b) Sketch of phonon emission and absorption processes in the channel.

Figure 5.21: The spectra of the source and drain currents. a) The effect of elastic phonon scattering with different coupling strengths is shown. As the coupling strength increases resonances in the current spectrum wash out and the total current decreases due to elastic back-scattering. b) The effect of inelastic phonon scattering with different coupling strengths is shown. The phonon energy is $\hbar \omega$=100 meV. Carriers acquiring enough kinetic energy can emit phonons and scatter into lower energy states. Since the energy of electrons is not conserved in this process, the source and drain current spectrum are not symmetric. As the coupling strength increases more electrons are scattered into lower energy states.

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