Validity and applicability of triangular potential well approximation in modeling of MOS structure inversion and accumulation layer

Two methods are presented to calculate the carrier distribution in MOS inversion and accumulation layer by self-consistent solution of Schrodinger and Poisson equations. One is the fully numerical solution of Schrodinger equation by finite difference method and the other is the analytical solution of Schrodinger equation under triangular potential well approximation. The effective electric field used in the analytical solution is properly determined. Results show that both carrier sheet density and surface potential in inversion layer and accumulation layer can be determined by analytical solution under triangular potential well approximation with sufficiently high accuracy. However, the carrier distribution profile and centroid of mobile charge layer, as well as the behavior at the flat-band region, have a large deviation from the numerical results.