A QUANTITATIVE PHYSICAL MODEL FOR THE BAND-TO-BAND TUNNELING-INDUCED SUBSTRATE HOT-ELECTRON INJECTION IN MOS DEVICES

A quantitative physical model for the band-to-band tunneling-induced substrate hot electron (BBISHE) injection in heavily doped n-channel MOSFET's is presented and successfully demonstrated. In the BBISHE injection, the injected substrate hot electrons across the gate oxide are generated via impact ionization by the energetic holes which are left behind by the band-to-band tunneling electrons and become energetic when traveling across the surface high field (approximately 1 MV/cm) region in silicon. The finite available distance for the holes to gain energy for impact ionization is taken into account by a first-order energy gain/relaxation kinetics. A previously published theory of substrate hot electron injection is generalized to account for the spatially distributed nature of the injected electrons. With only one adjustable parameter, 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 considering image force barrier lowering only. These results not only support the validity of the BBISHE injection model, but also show that it is an indispensable tool for the design of the nonvolatile memory devices that utilize the BBISHE injection as the programming mechanism.