Theoretical investigation of the phonon-assisted tunneling in TFET with an indirect band gap semiconductor

There are intense recent interests in quantum tunneling transistor as a way to go beyond the metal-oxide-semiconductor transistors. Phonon-assisted tunneling (PAT) plays the dominating role in tunneling field effect transistors with an indirect band gap semiconductor. In this work, we provide a convenient expression based on Fermi gold rule to study the electron tunneling assisted by phonon from the valence band top to the conduction band bottom. Through the comparison with different phonon modes, the transverse acoustic phonon mode provides the largest contribution to PAT. The results of the transfer matrix model predict slightly higher tunneling current compared to the Wentzel-Kramers-Brillouin approximation which ignores the effect of the reflection wave. However, the current density calculated by using our method shows that there is about an order of the magnitude lager than Kane's model. Additionally, the temperature enhances the phonon-assisted Zener tunneling current densities. Our results shed some light on understanding the PAT in indirect band gap semiconductors.