Modeling and simulation of tunneling through ultra-thin gate dielectrics

Abstract

Direct and Fowler-Nordheim tunneling through ultra-thin gate dielectrics is modeled based on an approach for the transmission coefficient ͑TC͒ 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 ͑MOS͒ 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 m ox ϭ0.42 m 0. 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.

Energy transfer in Er-dopedSiO2sensitized with Si nanocrystals

“…The wave function and flux continuities were used as the boundary conditions. 24,25 When calculating wave functions outside the NC, isotropic effective masses being equal to m 0 and 5m 0 were used for electron and hole states correspondingly. Spinorbit splitting was neglected in both Si and SiO 2 .…”

Determination of electron and hole effective masses in thermal oxide utilizing an n-channel silicon MOSFET

“…Therefore, the author predicts that the carrier effective masses will remain the same for all the thicknesses of the oxide or insulating materials. A recent report has modelled the direct and FN-tunneling of electrons utilizing a thickness independent tunnel mass of 0.42m [18]. Another report presents the electron effective mass in a thin tunnel oxide of 3.5nm as 0.42m [19], which is the same as that in thick oxides [2,3].…”

Kinetic Monte Carlo of transport processes in Al/AlOx/Au-layers: Impact of defects

“…Moreover, also the image potential for tunneling electrons can be omitted in the first approximation, as was discussed by Weinberg 29,30 and Schenk. 31 They came to the conclusion that it is negligible to include it for electrons tunneling through a barrier which is several 0.1 eV high. The short explanation is that the image potential induced by electrons must be weighted by the probability T(E) that a tunneling electron is present in the barrier.…”