A physical model for hole direct tunneling current in p+ poly-gate pMOSFETs with ultrathin gate oxides

A model of the hole direct tunneling gate current accounting for heavy and light hole´s subbands in the quantized inversion layer is built explicitly. This model comprises four key physical parameters: inversion layer charge density, hole impact frequency on SiO₂-Si interface, WKB transmission probability, and reflection correction factor. With the effective hole mass m_oxh =0.51 M_o for the parabolic dispersion relationship in the oxide, experimental reproduction without any parameter adjustment is consistently achieved in p⁺ poly-gate pMOSFETs with 1.23, 1.85, and 2.16 nm gate oxide thicknesses. The proposed model can thereby serve as a promising characterization means of direct tunnel oxides. In particular, it is calculated that the secondary subbands and beyond, although occupying few holes, indeed contribute substantially to the direct tunneling conduction due to effective lower barrier heights, and are prevailing over the first subbands for reducing the oxide field down below 1 MV/cm