3.4 Surface Potential Calculation

The surface potential calculations take quantum-mechanical (QM) effects into account. These QM effects become relevant for smaller fin thicknesses and are seen both in terms of higher band-gap due to size confinement (higher threshold voltage) as well as in terms of charge confinement (different charge distribution from the conventional semi-classical case, where the Poisson equation solution is sufficient to determine the charge distribution). Surface potentials at the source and drain ends are derived from Poisson’s equation with a perturbation method [4] and computed using the Householder’s cubic iteration method [5] [6]. Perturbation allows accurate modeling of finite body doping.

References

[4] M. V. Dunga, Ph.D. Dissertation: Nanoscale CMOS Modeling. UC Berkeley, 2007.

[5] A. S. Householder, The Numerical Treatment of a Single Nonlinear Equation. McGraw-Hill, New York, 1970.

[6] X. Gourdon and P. Sebah, Newton's method and high order iterations.