Direct tunneling current model for MOS devices with ultra-thin gate oxide including quantization effect and polysilicon depletion effect

An efficient direct tunneling current model is presented for the ultra thin gate dielectric MOS structure. The tunneling current is modeled by including the inversion layer quantization effect with a finite potential barrier height as the boundary condition and the modified WKB method for calculating the transmission probability. The model is in good agreement with the full quantum calculation and the experiments. The results indicate that the finite boundary condition has to be considered for the ultra thin gate dielectric and the gate dielectric materials with lower barrier height. This model is accuracy and computational efficient and suitable to be used in characterized the sub-100 nm MOSFET with gate oxide below 2.0 nm.