Analytical Description of Inversion-Layer Quantum Effects Using the Density Gradient Model and Singular Perturbation Theory

Analytical formulae for electrostatic potential and electron density profiles in the n-type planar metal oxide semiconductor field-effect-transistor inversion layer are presented. Equations based on the density gradient model are analytically solved using singular perturbation theory. The formulae give good agreement with exact numerical solutions over a broad range of voltages and device structures.