The effect of image potential on electron transmission and electric current in the direct tunneling regime of ultra-thin MOS structures

The direct tunneling current through ultra-thin gate dielectrics is modeled by calculating the transmission coefficient of an idealized potential barrier that is modified by the image force. A numerical solution to the Schrödinger equation shows that the barrier lowering induced by image-potential affects the tunneling current largely. An analytical expression for the current is obtained within the Wentel–Kramers–Brillouin approximation. The effects of image force on the direct tunneling current are found to increase with the applied voltage across oxide (V_ox) and to decrease with the oxide thickness (T_ox).