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. © 2002 American Institute of Physics.