Direct tunneling hole currents through ultrathin gate oxides in metal-oxide-semiconductor devices

We present a physical model to calculate the direct tunneling hole current through ultrathin gate oxides from the inversion layer of metal–oxide–semiconductor field-effect transistors. A parametric self-consistency method utilizing the triangular well approximation is used for the electrostatics of the inversion layer. For hole quantization in the inversion layer, an improved one-band effective mass approximation, which is a good approximation to the rigorous six-band effective mass theory, is used to account for the band-mixing effect. The tunneling probability is calculated by a modified Wentzel–Kramers–Brilliouin (WKB) approximation, which takes the reflections near the Si/SiO2 interfaces into account. It is found that the parabolic dispersion in the SiO2 band gap used in the WKB approximation is only applicable for hole tunneling in oxides thinner than about 2 nm and for low gate voltage. A more reasonable Freeman–Dahlke hole dispersion form with significantly improved fitting to all experimental data for different oxide thickness and gate voltage range is adopted and discussed.