A unified charge model comprising both 2D quantum mechanical effects in channels and in poly-silicon gates of MOSFETs

In this paper, an approach to modeling the tunneling current along the channel, i.e. the 2D quantum mechanical (QM) effects, on the charge distribution in the carrier confinement direction is developed using the concept of “locality” and the analytical solution to the 2D Poisson equation. Then, another approach, which is the gate-capacitance-shift (GCS) approach, is described. This approach is developed for the physical effects in decanano-scaled MOSFETs that have gate-bias-dependent nature, e.g. QM effects in polysilicon gates (poly-gates). Based on this approach, the QM effects in poly-gates are considered based on the density gradient (DG) formulation. Based on the above two corrections, a unified analytical charge model is established, which yields satisfactory results compared with numerical results under different device parameters. It is further embedded into a compact ballistic model for sub-100-nm MOSFETs. It is concluded that the 2D-QM effects on the threshold voltage are non-negligible through comparison to the experimental data of a 45 nm MOSFET from TSMC [TSMC 45 nm MOSFET, internal documentation].