An Analytic Model to Account for Quantum–Mechanical Effects of MOSFETs Using a Parabolic Potential Well Approximation

An analytic model to account for the quantum–mechanical effects (QMEs) of the MOSFETs using a parabolic potential well approximation is presented in this paper. Based on the solution of the coupled SchrÖdinger and Poisson equations following the Wentzel–Kramer–Brillouin method, a transcendental equation of the subband energy level has been rigorously derived to obtain an approximate analytic solution for the subband energy levels and the inversion charge centroid. Calculated results from the obtained analytical solution are compared with the previous approximate solutions reported in the literature and the numerically simulated data. A good agreement between the analytical and numerical is obtained, proving the validity of the analytic modeling of QMEs.