Calculation of the inversion channel resistance for n-MOSFETs using a classical and semi-quantum-mechanical model

Two models are presented to calculate the inversion channel carrier distribution of an n-type MOSFET. The classical approach solves Poisson's equation and applies Fermi-Dirac statistics in conjunction with Gauss's law to determine the carrier distribution. The semi-quantum-mechanical model solves Schrodinger's equation decoupled from Poisson's equation and the Fermi-Dirac statistics by assuming a constant electrostatic field and quantized energy levels. The results of both models are used to determine the channel resistance taking transversal field initiated mobility reductions into account. A comparison is made to a practical device and the results discussed.