Understanding the effects of wave function penetration on theinversion layer capacitance of NMOSFETs

A comprehensive analysis of the effects of wave function penetration on the capacitance of NMOS capacitors has been performed for the first time, using a self-consistent Schrodinger-Poisson solver. The study reveals that accounting for wave function penetration into the gate dielectric causes carrier profile to be shifted closer to the gate dielectric reducing the electrical oxide thickness. This shift increases with increasing gate voltage. For example, in one simulation, the peak is shifted by about 0.2 nm at a surface field of 1.96 MV/cm and 0.33 nm at a surface field of 3.7 MV/cm. This shifting results in all increased capacitance. The increase in capacitance observed in the inversion region is relatively insignificant when a poly gate electrode with a doping of less than 1×10²⁰ cm^-3 is used due to the poly-depletion effect. A physical picture of the effect of physical thickness on the tunneling current is also presented