Analytical charge model for MOSFETs with 2-D quantum mechanical effects

In sub-50-nanometer (nm) MOSFETs, the Quantum Mechanical (QM) effects, particularly along the channel, have a significant influence on device characteristics. Based on the WKB theory, the QM effects in the transport direction of a MOSFET are taken into account to revise the energy levels in the carrier confinement direction. This semi-analytical scheme introduces a threshold voltage shift, which is then used to establish a fully analytical 2-D QM charge model with the usage of parabolic approximation to subband edge profiles and numerical fitting. The relation of 2-D QM corrections to channel lengths and other material parameters is ascertained. Comparing to numerical 2-D QM simulation, the correction must not be ignored in sub-50 nm MOSFETs and the fully-analytical charge model renders satisfactory results.