Modeling the Channel Charge and Potential in Quasi-Ballistic Nanoscale Double-Gate MOSFETs

In this paper, we present an analytical semiempirical model of the profile of the channel charge and potential in quasi-ballistic double-gate (DG) MOSFETs. The charge model is based on the premise of separating the charge density in the quasi-ballistic channel into two hypothetical components: 1) exclusively ballistic (collision-free) and 2) collision-dominated components, which are governed by the same electrostatics. These components are related to each other through a ballisticity parameter whose values lie between 0 and 1. Varying the value of this parameter allows us to model the charge profile continuously between diffusive and purely ballistic devices. Using the proposed charge model and the DG MOSFET electrostatics, an analytical expression for the channel potential is derived which, like the charge model, is continuous between the diffusive and ballistic regimes.