Physics-based compact model of nanoscale MOSFETs - Part II: Effects of degeneracy on transport

In this paper, we extend our derivation of an analytical model for nanoscale MOSFETs, focusing on the effects of Fermi-Dirac statistics on vertical electrostatics and on carrier transport. We derive a relation between mobility and mean-free path valid under degenerate statistics, and investigate the cases of rectangular and triangular quantum confinement under Fermi-Dirac statistics in the transition from DD to B transport. We derive a simple, physics-based and continuous analytical model that describes double-gate MOSFETs, fully depleted silicon-on-insulator MOSFETs, and bulk MOSFETs in the electric quantum limit in the whole range of transport regimes comprised between DD (device length much larger than mean-free path) and B (device length much mailer than mean-free path).