Quantum mechanical analysis of the electrostatics in silicon nanowires and carbon nanotubes FETs

In this work we investigate the electrostatics of of the top-gate carbon-nanotube FET (CNT-FET) and the silicon-based π-gate FET at the ITRS 22 nm node. In order to do so, we solve the coupled Schroedinger and Poisson equations within the cross section of each device, and compare the channel-charge and capacitance curves as functions of the gate voltage. This study shows that, for a fixed cross-sectional area, the quantitative differences between the two devices are small both in terms of charge and capacitance. The use of a classical model for the π-gate FET shows instead that the resulting discrepancies with respect to the quantum-mechanical (QM) model are very relevant using both the Boltzmann and Fermi statistics. Thus, accounting for quantum-mechanical effects is essential for a realistic prediction of the device on-current and transconductance at the feature sizes considered here. The effect of high-κ dielectrics is also addressed. As opposed to planar-gate devices, the electrostatic performance of Si-based π-gate FETs and CNT-FETs is not adversely affected by the use of different insulating materials with the same equivalent oxide thickness. As a consequence, not only do high-κ dielectrics relieve the gate-leakage problem; they also improve the device performance in terms of the gate-control effectiveness over the channel.