A quantitative physical model for the band-to-band tunneling-induced substrate hot electron injection in MOS devices

A quantitative physical model for band-to-band tunneling-induced substrate hot electron (BBISHE) injection in heavily doped n-channel MOSFETs is presented. In BBISHE injection, the injected substrate hot electrons across the gate oxide are generated by impact ionization by the energetic holes which are left behind by the tunneling electrons and become energetic when traveling across the surface high-field region in silicon. The finite available distance for the holes to gain energy for impact ionization is taken into account. A previously published theory of substrate hot electron injection is generalized to account for the spatially distributed nature of the injected electrons. This model is shown to be able to reproduce the I-V characteristics of the BBISHE injection for devices with different oxide thicknesses and substrate dopant concentration biased in inversion or deep depletion. Moreover, it is shown that the effective SiO₂ barrier height for over-the-barrier substrate hot electron injection is more accurately modeled