A simple model for quantisation effects in heavily-doped silicon MOSFETs at inversion conditions

Abstract

\u3cp\u3eThe transistor parameters of state-of-the-art MOSFETs are affected by quantisation effects of the carrier motion in the inversion channel. To account for these effects in classical device stimulators, we show that a better modeling of the silicon bandgap at inversion conditions is ifE\u3csub\u3eg\u3c/sub\u3e\u3csup\u3eQM\u3c/sup\u3e = E\u3csub\u3eg\u3c/sub\u3e\u3csup\u3eCONV\u3c/sup\u3e + 13 9Δε{lunate} in which Δε{lunate} is the position of the first energy level with respect to the bottom of the conduction band. The improved modeling of the bandgap leads to a new model for the intrinsic carrier concentration n\u3csub\u3ei\u3c/sub\u3e. The model for n\u3csub\u3ei\u3c/sub\u3e has been tested against measurements and against self-consistent QM calculations. Excellent agreement is obtained.\u3c/p\u3