Modeling of charge quantization and wave function penetration effects in ultra thin body double gate MOSFETS

Abstract

Modeling of charge quantization and effects of wave function penetration into gate oxide on the properties of ultra thin body double gate (OG) MOSFET in deep submicron regime are studied. Self-eonsistent modeling of double gate MOS inversion layer has been performed, taking into account the effects of wave function penetration on the solutions of both Schrodinger and Poisson equations. A solver, based on Finite Element Method, has been applied for the solution of both Schrodinger and Poisson equations that is much faster and efficient than conventional Schrodinger-Poisson solver. The developed numerical solver has been applied to fully depleted OG MOSFET (both n-MOS & p-MOS) for analyzing electrostatics ofthe device such as, inversion layer charge, average penetration depth, surface potential and gate capacitance, and hence wave function penetration effects have been revealed by comparing the results with those of without penetration. Finally, the results have been compared with established numerical solver. The solver has the capability of analyzing both symmetric and asymmetric DGMOS structures. Average penetration depth for half of the silicon film and gate capacitance has been calculated. Wave function penetration effects with the variation of substrate doping, silicon film thickness and dielectric thickness has been illustrated. It has been shown that the concept of volume inversion is not accurate for thicker semiconductor region, Average penetration depth is overestimated and capacitance is underestimated if the penetration effect is not in consideration. Also it has been shown that the penetration effect is not same for different oxide thickness, semiconductor thickness and doping density and the reasons are discussed in details.