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 inve rsion and accumulation layer by self-consistent solution of Schrodinger and Poisson equations, One is the fully numerical solution of Schrodinger equa tion by finite difference method and the other is the analytical solution o f Schrodinger equation under triangular potential well approximation. The e ffective electric field used in the analytical solution is properly determi ned, Results show that both carrier sheet density and surface potential in inversion layer and accumulation layer can be determined by analytical solu tion under triangular potential well approximation with sufficiently high a ccuracy. However, the carrier distribution profile and centroid of mobile c harge layer as well as the behavior at the nat-band region, have a large de viation from the numerical results.