Mathematical analysis of 1-D Poisson´s equation in the long channel SOI MOSFET

In the present work we have modeled a single gate SOI MOSFET using high K insulating layer of HfO₂ having dielectric constant of 26 and energy gap of 5.65 eV. The gradual channel approximation (GCA) has been considered in the channel region and solved the 1-D Poisson´s equation and four different potential profiles are obtained in the channel region depending on the gate biases. Insulating layer of HfO₂ shows several beneficial advantages over usually used SiO₂ material- (i) lowering the leakage current, (ii) lowering the threshold voltage and (iii) ideal sub threshold slope of 60 mV/decade.