Phonon scattering in carbon nanotube field-effect transistors (CNTFETs) is treated using the nonequilibrium Green's function formalism with the self-consistent Born approximation. The treatment simultaneously captures the essential physics of phonon scattering and important quantum effects. For a one-dimensional channel, it is computationally as efficient as and physically more rigorous than the so-called "Buettiker probe" approach [Phys. Rev. Lett. 57, 1761 (1986)], which has been widely used in mesoscopic physics. The non-self-consistent simulation results confirm that the short mean-free-path optical phonon (OP) scattering, though expected to dominate even in a short channel CNTFET, essentially has no direct effect on the dc on current under modest gate biases. The self-consistent simulation results indicate that OP scattering, however, can have an indirect effect on the on current through self-consistent electrostatics. Using a high-κ gate insulator suppresses the indirect effect and leads to a dc on current closer to the ballistic limit. The indirect effect in a CNT Schottky barrier FET can be more important than that in a metal-oxide semiconductor FET.
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