Modeling and simulation of tunneling through ultra-thin gate dielectrics

Direct and Fowler-Nordheim tunneling through ultra-thin gate dielectrics is modeled based on an approach for the transmission coefficient (TC) of a potential barrier that is modified by the image force. Under the constraint of equal actions the true barrier is mapped to a trapezoidal pseudobarrier resulting in a TC very close to the numerical solution of the Schrödinger equation for all insulator thicknesses and for all energies of the tunneling electron. The barrier height of the pseudopotential is used as a free parameter and becomes a function of energy in balancing the actions. This function can be approximated by a parabolic relation which makes the TC of arbitrary barriers fully analytical with little loss of accuracy. The model was implemented into a multidimensional device simulator and applied to the self-consistent simulation of gate currents in metal-oxide-semiconductor (MOS) capacitors with gate oxides in the thickness range 15 Å–42 Å. Excellent agreement with experimental data was obtained using a thickness-independent tunnel mass $mox=0.42 m0$⁠. Thanks to the CPU-time efficiency of the method the simulation of a complete MOS-field-effect-transistor with dominating gate current becomes possible and shows the potential for further applications.