Two-dimensional numerical simulation of MOS transistors

Abstract

A two dimensional numerical analysis program, called SOMOS(two-dimensional numerical simulation of MOS transistors), has been developed for the simulation of the MOSFET with both small and large values of channel length at various bias conditions. The finite difference approximation of the fundamental equations are formulated using Newton``s method for Poisson``s equation and the divergence theorem for the continuity equation. For the solution of the linearized equations SOR(Successive Over Relaxation) method and Gummel``s algorithm have been employed. The total simulation time for one operating point is within 30 sec. to 4 min. on a VAX 11/780 computer depending on bias values. The nonuniform mesh is generated and refined, if necessary, automatically and accounts for bias values and the potential distribution. Some D.C physical quantities such as potential, mobility and carrier distributions were displayed by the surface plotting program.