In this paper, we discuss the electron transmittance and tunneling current in high-k-based-MOS capacitors with trapping charge by including the off-diagonal effective-mass tensor elements and the effect of coupling between transverse and longitudinal energies represented by an electron velocity in the gate. The HfSiOxN/SiO2 dual ultrathin layer is used as the gate oxide in an n+ poly- Si/oxide/Si capacitor to replace SiO2. The main problem of using HfSiOxN is the charge trapping formed at the HfSiOxN/SiO2 interface that can influence the performance of the device. Therefore, it is important to develop a model taking into account the presence of electron traps at the HfSiOxN/SiO2 interface in the electron transmittance and tunneling current. The transmittance and tunneling current in n+ poly- Si/HfSiOxN/trap/SiO2/Si(100) capacitors are calculated by using Airy wavefunctions and a transfer matrix method (TMM) as analytical and numerical approaches, respectively. The transmittance and tunneling current obtained from the Airy wavefunction are compared to those computed by the TMM. The effects of the electron velocity on the transmittance and tunneling current are also discussed.

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